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№84, 2024
Slovak international scientific journal
VOL.1
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Slovak international scientific journal
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CONTENT
BIOCHEMISTRY AND GENETICS OF ANIMALS
Adesehinwa O.A., Boladuro B.A.,
Makanjuola B.A.M., Sorunke A.O.,
Bolaji A.A., Agbede J.O., Adesehinwa A.O.K.
GROWTH, HEALTH STATUS AND COST BENEFIT
ANALYSIS OF WEANER PIGS FED DIET SUPPLEMENTED
WITH MALTODEXTRIN................................................. 4
COMPUTER SCIENCES
Episkoposian S., Grigoryan S.
STEP-BY-STEP GREEDY ALGORITHMS WITH RESPECT
TO WALSH SYSTEM ................................................... 11
Manafov E., Sardarova I.
SMART HOME TECHNOLOGY AND TRENDS IN LIVING
SPACE TRANSFORMATIONS ...................................... 15
Gurbanova N., Hajiyev Z., Abdullayeva G.
MOBILE MEDICAL APPLICATIONS IN DIGITALIZATION
OF HEALTHCARE ........................................................ 18
Al-Ammori Ali, Ishchenko R.,
Klochan A., Shkurko O., Povoroznik D.
ANALYSIS AND ASSESSMENT OF INFORMATION
THREATS IN THE TRANSPORT SECTOR ...................... 21
CONSTRUCTION AND ARCHITECTURE
Ignatenko O.
IMPROVEMENT OF TECHNOLOGICAL SOLUTIONS FOR
ERECTION OF LARGE-SPAN COATINGS WITH LIFTING
MODULES .................................................................. 28
Salimova A.
REFLECTION OF ANCIENT CULTS IN AZERBAIJANI ART
................................................................................... 35
ECONOMY
Ayyubov M.
ECONOMETRIC MODEL OF THE CYCLICAL
FUNCTIONING OF THE NATIONAL ECONOMY IN THE
LONG-TERM PERSPEKTIVE (ON THE EXAMPLE OF THE
NATIONAL ECONOMY OF AZERBAIJAN) .................... 41
HISTORY
Ismayilowa A., Abbasova S.
GENOCIDE CARRIED OUT IN WESTERN AZERBAIJAN IN
1918-1920 ................................................................. 47
MATHEMATICS
Antonov A.
IT FOLLOWS FROM THE SPECIAL THEORY OF
RELATIVITY THAT INVISIBLE AFTERLIFE WORLD IS IN
FACT PHYSICALLY REAL ............................................. 52
Ramani J.V., Kumar Dinesh
A FINITE DIFFERENCE METHOD FOR THE SOLUTION
OF THIRD ORDER BOUNDARY VALUE PROBLEMS IN
ORDINARY DIFFERENTIAL EQUATIONS ...................... 59
NORMAL AND PATHOLOGICAL PHYSIOLOGY
Bukach O., Ariichuk D.,
Babchenko V., Soha N., Stefurak M.
A CLINICAL CASE IN THE PRACTICE OF A
RHEUMATOLOGIST: SYSTEMIC LUPUS ERYTHOMUS
WITH INFLAMMATION OF ORGANS AND SYSTEMS .. 63
PEDAGOGY
Abbasova S.
SETTING THE PROBLEM IN TEXTBOOKS AND
METHODICAL MATERIALS FOR TEACHERS ................ 66
Kostadinov O.
MODEL OF PASSIVE AND ACTIVE FOREIGN LANGUAGE
VOCABULARY DYNAMICS .......................................... 69
PHYSICS
Khalilov S.
INFLUENCE OF HEAT TREATMENT ON THERMAL AND
ELECTRICAL PROPERTIES OF POLYMER
SEMICONDUCTOR POLYHYDROCHYNONE ................ 74
Robert Lloyd Jackson II
THE GENERATING FUNCTION TECHNIQUE
AMELIORATES EFFECTIVE AND STRING FIELD
THEORIES AND FORESHADOWS THEIR LINKAGE TO
QUANTUM INFORMATION THEORY .......................... 77
ZOOLOGY
Bely D., Niyazaliev K.,
Nurbaev K., Kopkova A., Sayakova Z.
SPECIES COMPOSITION AND NUMBER OF RODENT
CARRIERS OF THE PLAGUE PATHOGEN IN THE
(MOYINKUM DESERT PLAGUE FOCUS IN 2021 ......... 89
4 Slovak international scientific journal # 84, (2024)
BIOCHEMISTRY AND GENETICS OF ANIMALS
GROWTH, HEALTH STATUS AND COST BENEFIT ANALYSIS OF WEANER PIGS FED DIET
SUPPLEMENTED WITH MALTODEXTRIN
Adesehinwa O.A.,
Department of Animal Production and Health, Federal University of Technology, Akure
Boladuro B.A.,
Makanjuola B.A.M.,
Sorunke A.O.,
Bolaji A.A.,
Institute of Agricultural Research and Training, Obafemi Awolowo University, Ibadan
Agbede J.O.,
Department of Animal Production and Health, Federal University of Technology, Akure
Adesehinwa A.O.K.
Institute of Agricultural Research and Training, Obafemi Awolowo University, Ibadan
DOI: 10.5281/zenodo.11624284
Abstract
This study evaluated the influence of maltodextrin in the diet of weaned pigs on growth, backfat thickness,
haematology, serum biochemical and cost benefit indices. A total of 54 weaned pigs which are largewhite × land-
race crosses with average weight of 9.35±2.36 kg were used for this study. They were randomly allotted to three
dietary treatments (T1 - basal diet, T2 - 500g/tonne maltodextrin inclusion, T3 - 1kg/tonne maltodextrin inclusion)
with three replicates each and six animals per replicate in a completely randomized design. The body weight gains
of the pigs were not significantly (P>0.05) affected by the dietary treatments. They were 23.65, 25.92 and 24.63
kg in T1, T2 and T3 respectively. At the 6th week of the study, the FCR was significant (P<0.05) and were 3.62,
4.26 and 3.81 in T1, T2 and T3 respectively. However, the FCR at the 13th week was not significant (P>0.05)
among the treatments. The high density lipoprotein cholesterol were significantly higher in T2 (56.33 mg/dL) and
T3 (52.00 mg/dL) than in T1 (46.00 mg/dL). The back fat thickness and all the haematological indices measured
were not significantly (P>0.05) influenced by the dietary treatment. The feed cost per weight gain improved with
inclusion of maltodextrin from ₦1,213.03 in T1 to ₦1,153.77 in T2 and ₦1,120.75 in T3. The supplementation of
maltodextrin in the diet of weaned pigs did not negatively influence the growth and the health status of the animals.
Keywords: Health Status, Maltodextrin, Postweaning performance, Feed utilization, Blood profile.
Introduction
Weaning is one of the most critical stages in pig’s
life because of the need to adjust to dietary and envi-
ronmental changes. These changes could have adverse
effect on the intestinal and immune systems resulting in
impaired health and growth particularly during the first
few weeks post-weaning. At weaning, the sows' milk is
replaced by a dry and less digestible starch-based diet
(Williams, 2003), resulting in significantly reduced en-
ergy intake for epithelial structure maintenance (Pluske
et al., 1996), reduced transmucosal resistance (Spreeu-
wenberg et al., 2001, Boudry et al., 2004), and in-
creased secretory activity in the small intestine (Boudry
et al., 2004). With the underdeveloped innate and adap-
tive immune systems of the weaned pigs, damage to the
epithelial layers also reduces the ability of nutrients to
be digested and absorbed into the blood stream which
increases the substrates available for pathogen prolifer-
ation (Pluske et al., 2002). These biological changes
have short and long-term effects on subsequent perfor-
mance of pig in terms of growth and well being. As a
result of this, it is important that swine producers use
appropriate health, nutrition, and management strate-
gies to minimize the adverse effects of weaning stress
so as to improve productivity.
A nutritional strategy to promote an early feed
consumption after weaning is the use of highly palata-
ble and digestible ingredients in the post-weaning diet,
such as milk-derived products, or highly digestible ce-
real or animal origin protein sources (Solà-Oriol et al.,
2009). Apart from the main ingredients, non-nutritive
feed additives, such as zinc oxide, acidifier, flavour and
antibiotics are often incorporated to stimulate gut
health and digestive capacity (Heo et al., 2013). Hence,
the need for an alternative non-conventional feed addi-
tive. Due to the adaptive nature of piglet’s digestive
system to milk components, post weaning diets have
been formulated with lactose-rich ingredient that stim-
ulate the intake of feed, help diet transitions (Berrocoso
et al., 2012), and increase nutrient digestibility
(O’Doherty et al., 2005), thereby mitigating the de-
crease in post weaning performance. Studies by Mahan
and Newton (1993) and Oliver et al. (2002) have shown
that it is possible to use hydrolyzed corn starch (Malto-
dextrin) as replacement for lactose in diets of infants
without adversely affecting performance.
Notably, one of the main sources of energy for an
infant's development and growth comes from carbohy-
drates. Maltodextrins (MDs) are a class of carbohy-
drates (CHOs) industrially produced by enzymatic or
acid hydrolysis of the starch, followed by purification
and spray drying (Takeiti et al., 2010). It has an energy
value of approximately 4 kcal/g (Katouzian et al.,
2015). Studies have shown that maltose and maltodex-
trin are digested by a set of enzymes called maltases.
These enzymes are responsible for about 70 and 20%
of the hydrolysis of those carbohydrates, respectively.
Slovak international scientific journal # 84, (2024) 5
Maltodextrin has the ability to lower the pH of the con-
tents of the rectal cavity and has been implicated in
lowering the total coliform and E. coli populations in
the caecum thus, having a prebiotic effect (Pivetta et
al., 2014). Also, it has been reported to be effective in
partially or totally (Augusto et al., 2011; Pivetta et al.,
2014) substituting lactose in the feed of weaned piglets.
Lactase activity has been reported to be lower than
maltase activity in weaner pigs (Kidder, 1980), hence,
maltodextrin supplementation in the diet of weaner pigs
might induce the synthesis of maltase through the mod-
ulation of enzyme activity exerted by the substrate with
improved performance. This study assessed the influ-
ence of supplementing the diet of weaned pigs with var-
ying level of maltodextrin on the performance, back fat
thickness, cost benefit and health status of the animals
in a tropical environment.
Materials and methods
This study was carried out at AK Research Farms,
Eleyele, Ibadan, Oyo State, Nigeria with daily temper-
ature ranging between 25 - 350C and annual rainfall of
1800mm (Victory et al, 2022). The study lasted 91
days. Fifty-four weaned piglets (large white x landrace
crosses) with mean weight of 9.35±2.36kg (±SE) were
used for the experiment. They were administered 0.2 -
0.3 mg/kg of ivermectin injection sub-cutaneously
against internal and external parasites before the com-
mencement of the experiment.
The animals were housed in open sided cross ven-
tilated pens with concrete floor under good manage-
ment practices. The pens were equipped with concrete
water trough and Big Dutchman’s semi-automatic
feeder. Water and Feed were supplied ad libitum
throughout the experimental period. Daily routine prac-
tices carried out included feeding, watering, waste dis-
posal, washing of pens and general observation of the
animal’s welfare.
The pigs were randomly allotted into 3 dietary
treatments labeled T1, T2 and T3 in a completely ran-
domized design (CRD). Each treatment was replicated
3 times with 6 animals per replicate. The diet of T1
(control/basal diet) was formulated to meet the nutri-
ents requirements as recommended by the National Re-
search Council (2012) for weaned pigs raised in tropi-
cal environment (Table 1). Pigs in T2 were fed basal
diet with 500g/tonne maltodextrin while T3 contained
the basal diet with an inclusion rate of 1kg/tonne malto-
dextrin.
The feed intake was estimated daily by subtracting
the weight of the left over feed from that of the feed
given. The body weight of the pigs were determined
weekly using a walk-through digital measuring scale.
The weight gain was calculated as the difference be-
tween the initial weight and the final weight. The feed
conversion ratio (FCR) was determined as the ratio of
feed intake to weight gain. Table 1
Percentage Composition of Basal Diet
Ingredients
Quantity %
Maize
40.00
Groundnut cake
25.00
Wheat offal
10.00
Corn bran
16.00
Fish meal
2.50
Limestone
2.00
Bone meal
2.00
Lysine
0.40
Methionine
0.325
Salt
0.40
Starter Premix
0.25
Toxin binder
0.05
Multi enzyme
0.05
Lavaricide
0.025
Palm oil
1.00
Total
100
Calculated Composition
Metabolizable energy (Kcal/kg)
2650
Crude fiber (%)
5.73
Crude protein (%)
19.67
The proximate composition of the samples of the
three diet were determined using the recommended
procedures described by Association of Official Ana-
lytical Chemists (AOAC, 2010). The backfat thickness
were measured across the treatment at the 12th week of
the study using the ultrasonic probe technique de-
scribed by Fortin et al. (1980) and modified by Jiang et
al. (2014). The ultrasonic probe technique works on the
principle of reflection of sound wave. The calibration
of the instrument was based on the assumption that the
ultrasonic sound waves travels through fatty tissue at a
velocity of 1480 m/s. The backfat thickness was taken
off the midline over the last rib using ultrasound gel on
the probe. This was done using the Dramiski ultrasound
scanner.
At the end of the feeding trial, pigs were randomly
selected from each treatment and sampled for blood
through the jugular vein into clinical sample bottles for
analysis using hypodermic syringe and needle. The
blood sampled for serum biochemistry analysis were
collected into sterile plain sample bottles without anti-
coagulant while those for haematological analysis were
6 Slovak international scientific journal # 84, (2024)
sampled into bottles with anti-coagulant (EDTA) to
prevent the blood from clotting. The sampling was
done in the morning before feeding. About 5mls of
blood samples were collected from each animal and
were stored in iced flask till it was delivered to the la-
boratory some minutes after collection. The blood sam-
pled for haematology were analysed for packed cell
volume (PCV), haemoglobin concentration, erythro-
cyte count, leucocyte count, platelets, lymphocytes,
neutrophils, monocytes, eosinophils, mean corpuscular
haemoglobin concentration (MCHC), mean corpuscu-
lar haemoglobin (MCH) and mean cell volume (MCV).
For serum biochemical analysis, the sampled blood
were centrifuged for 20 - 30 min at 4000 rpm to sepa-
rate the serum from the cells. The serum was analysed
for total protein, albumin, aspartate aminotransferase
(AST), alanine amino transferase (ALT), blood urea ni-
trogen, creatinine, glucose, total cholesterol, high den-
sity lipoprotein cholesterol and triglyceride. The glob-
ulin, albumin-globulin ratio (A:G) and low density
lipo-protein cholesterol were estimated.
Data were subjected to analysis of variance
(ANOVA) procedures using the General Linear Model
procedures of SAS (2002). The means among variables
that were significant were separated using the Duncan’s
Multiple Range (DMR) Test. Table 2
Proximate Composition of Experimental Diet
SAMPLE
T1
T2
T3
Crude Protein (%)
19.43
19.625
19.835
Ether Extract (%)
3.79
3.865
3.825
Crude Fibre (%)
3.595
3.555
3.52
Ash (%)
5.59
5.46
5.345
Moisture (%)
11.355
11.19
11.135
Gross Energy (Kcal/g)
4.0215
4.031
4.0395
Nitrogen free extract (%)
67.595
67.495
67.475
Results and Discussion
The performance of weaned pig fed different lev-
els of maltodextrin till week 6 is as highlighted in Table
3. At week 6 no significant difference was observed in
the body weight, feed intake and weight gain among the
treatments. The weight gain were 8.68, 7.24 and 7.75
kg in T1, T2 and T3 respectively at week 6. However,
the feed conversion ratio (FCR) significantly differs
among the treatments. The group fed with diet contain-
ing 500g/tonne maltodextrin (T2) had the significantly
(P<0.05) highest FCR (4.26) but was not significantly
(P>0.05) different from group fed with 1kg/tonne
maltodextrin, T3 (3.81). The FCR of T2 however, differ
significantly (P<0.05) from that of T1 fed the control
diet (3.62). The FCR of T1 and T3 were however not
significantly (P>0.05) different. At the 13th week of the
study, the result obtained is as indicated in Table 4
showed that the feeding of varying levels of maltodex-
trin to weaned pigs in this study did not significantly
(P>0.05) influence all the growth indices measured.
The final weights were 33.15, 35.20 and 33.89 kg in T1,
T2 and T3 respectively. The average daily feed intake
ranged from 1.11 kg in the group fed control diet (T1)
and 1.21 kg in T2 fed 0.05 % maltodextrin inclusion in
the diet. Pigs in T2 had the highest (4.23) feed conver-
sion ratio (FCR), while the lowest was (4.11) recorded
in the group fed 0.1% maltodextrin inclusion (T3). This
corroborates the findings of Hauptli et al. (2016) who
reported no significant effect of feeding weaner pigs
with maltodextrin. Pivetta et al. (2014) also reported
that the inclusion of maltodextrin on the diet of weaned
pigs did not compromise the performance of the pigs
but depressed feed intake. The significant difference
seen between the FCR of T1 and T2 at week 6 may sug-
gest that feeding maltodextrin may only be useful for a
short period postweaning. The reports of O’Doherty et
al. (2010) and Kim et al., (2010) suggest that maltodex-
trin improve the performance of weaned pigs from first
week of inclusion and was identified to have similar ef-
fects with lactose. However, there may be need to as-
certain the effect of feeding maltodextrin for longer pe-
riods on the performance of the pigs. The thickness of
back fat in weaner pig is related to growth and repro-
ductive indices (Roongsitthichai and Tummaruk,
2014). The backfat thickness of pigs fed varying levels
of maltodextrin the diet is as shown in Figure 1. The
backfat thickness of the weaner pigs were not signifi-
cantly influence by the inclusion of maltodextrin in the
diet. They were 8.50, 10.25 and 9.75 mm in T1, T2 and
T3 respectively.
Table 3
Performance of Weaned Piglets Fed Different Levels of Maltodextrin at Week 6
PARAMETERS
T1
T2
T3
SEM
Initial Weight (kg)
9.50
9.28
9.26
0.91
Final Weight (kg)
18.17
16.52
17.0
1.76
Weight Gain (kg)
8.68
7.24
7.75
0.91
Average Daily Gain (g)
206.60
172.36
184.47
21.6
Feed Intake (kg)
30.83
30.88
29.15
2.94
Average Daily
Feed Intake (g)
734.10
735.23
721.16
69.97
Feed conversion Ratio
3.62b
4.26a
3.81ab
0.10
a, b Means with different superscript across the row are significantly different at α=0.05
T1 - Control (Without maltodextrin)
T2 - 500g/tonne maltodextrin inclusion
T3 - 1kg/tonne maltodextrin inclusion
Slovak international scientific journal # 84, (2024) 7
Table 4
Performance of Weaned Piglets Fed Different Levels of Maltodextrin at Week 13
PARAMETERS
T1
T2
T3
SEM
Initial Weight (kg)
9.50
9.28
9.26
0.91
Final Weight (kg)
33.15
35.20
33.89
2.07
Weight Gain (kg)
23.65
25.30
24.63
1.29
Average Daily Gain (g)
0.26
0.28
0.27
0.02
Feed Intake (kg)
101.20
109.73
102.46
7.63
Average Daily Feed Intake (Kg)
1.11
1.21
1.13
0.08
Feed conversion Ratio
4.20
4.23
4.11
0.17
T1 - Control (Without maltodextrin)
T2 - 500g/tonne maltodextrin inclusion
T3 - 1kg/tonne maltodextrin inclusion
Fig 1: Back fat thickness (mm) of weaner pigs fed varying levels of maltodextrin in the diet.
Haematological and serum biochemical assays
play crucial roles in assessing the physiological and
health status of animals (Adenkola et al., 2009; Etim,
2014; Koomkrong et al., 2017). The haematology indi-
ces of weaner pigs fed varying levels of maltodextrin is
as presented in Table 5. No significant (P>0.05) effect
of the dietary treatments were seen on the haematolog-
ical indices measured in this study. Similarly, Pivetta et
al. (2014) that fed maltodextrin at inclusion rate above
those in this study reported no significant interaction
between diet with maltodextrin and that of fructooligo-
saccharides for all the haematological parameters
measured. Although not significantly (P>0.05) notable,
maltodextrin had lowering effect on the levels of hae-
matological parameters measured in this study. The
packed cell volume (PCV) was 38.00 % in the animals
on the control diet (T1), 33.00 % in animals fed
0.5kg/tonne maltodextrin in the diet (T2) while those
fed 1kg/tonne maltodextrin in the diet (T3) had 35.33
%. Haemoglobin ranged from 10.67 to 12.40 g/dL in
T2 and T1 respectively. The erythrocyte count also re-
ferred to as red blood cell (RBC) were 6.05, 5.23 and
5.80 µL in T1, T2 and T3 respectively. The eosinophils
were 4.67, 3.33 and 2.33 % in T1, T2 and T3 respec-
tively. Mean corpuscular haemoglobin concentration
(MCHC) reduced fom 32.64 g/dL in T1 to 32.32 g/dL
in T2 and 31.90 g/dL in T3. Similarly, Mean haemoglo-
bin concentration (MCH) reduced from 20.83 pg in T1
to 20.39 pg in T2 and 19.47 pg in T3. The reducing ef-
fect of maltodextrin on the haematological indices es-
pecially the packed cell volume, haemoglobin and red
blood cells calls for a monitoring in the use of malto-
dextrin as a reduction below certain levels will suggest
anaemia in the piglets. The values obtained for all the
haematological indices in this study fall within the nor-
mal physiological range of a weaner pig (Merck Man-
ual, 2012).
0
2
4
6
8
10
12
T1 T2 T3
Back fat thickness (mm)
T1- Control (without maltodextrin)
T2 - 500g/tonne maltodextrin inclusion
T3 - 1kg/tonne maltodextrin inclusion
8 Slovak international scientific journal # 84, (2024)
Table 5
Haematological parameters of weaner pigs fed varying levels of maltodextrin
Parameters
T1
T2
T3
SEM
Packed cell volume (%)
38.00
33.00
35.33
35.44
Haemoglobin (g/dL)
12.40
10.67
11.27
11.44
Erythrocytes Count (µL)
6.05
5.23
5.80
5.69
Total Leucocytes (µL)
4400.00
4433.33
4300.00
4377.78
Platelets (µL)
169666.67
116333.33
103333.33
129777.78
Lymphocytes (%)
49.33
48.33
49.33
49.00
Neutrophils (%)
46.33
45.00
45.33
45.56
Monocytes (%)
3.00
3.33
2.33
2.89
Eosinophil (%)
4.67
3.33
4.33
4.11
MCHC (g/dL)
32.64
32.32
31.90
32.29
MCH (pg)
20.83
20.39
19.47
20.23
Mean cell volume (fL)
63.82
61.02
62.65
62.65
T1 - Control (Without maltodextrin)
T2 - 500g/tonne maltodextrin inclusion
T3 - 1kg/tonne maltodextrin inclusion
MCHC - Mean corpuscular haemoglobin concentration
MCH - Mean corpuscular haemoglobin
The serum biochemicals are important biomakers
which could be suggestive of the impact of external fac-
tors such as plane of nutrition on the functionality of
tissues, organs and body systems as a whole (Adenkola
et al., 2009; Koomkrong et al., 2017). The serum bio-
chemical indices of piglets fed diet containing different
inclusion levels of maltodextrin is highlighted in Table
6. The varying inclusion levels of maltodextrin in the
diets presented to weaner pigs in this study did not sig-
nificantly influence the serum biochemical indices as-
sayed in this study except the High density lipoprotein
(HDL) cholesterol. HDL was significantly (P<0.05)
highest (56.33mg/dL) in T2 fed diet containing
500g/tonne maltodextrin and different from 46.00 and
52.00 mg/dL recorded in T1and T3 respectively. The
level of HDL in the serum increased with inclusion of
maltodextrin in this study. The maltodextrin had a hy-
polipidemic effect (Hassan et al., 2014) on the pigs.
This corroborate the report of Inglett and Grisamore
(1991) who stated that the inclusion of maltodextrin in
the diet has the potential to reduce bad fat (LDL) and
increase good fat (HDL). This is made possible by the
action of the beta-glucan component of maltodextrin
which lowers total blood cholesterol by improving the
HDL and lowering the LDL cholesterol (Inglett and
Grisamore, 1991). This is beneficial to the health of the
pig. The total protein were 7.00, 7.20 and 7.40 g/dl in
T1, T2 and T3 respectively. The Alanine aminotrans-
ferase increased from 38.97 IU/l in T1 to 39.67 IU/l in
T2 and 40.50 IU/l in T3. The creatine was 0.77mg/dL
in T1 and 0.80 mg/dL in both T2 and T3.
Feed cost takes a very huge proportion of the var-
iable cost of production in most livestock enterprises,
that is why farmers are always on the look out for
cheaper and effective alternatives. Maltodextrin has
been identified as cheaper alternative to other expen-
sive carbohydrate sources especially in the diet of
weaner pigs (Machado and Carvalho, 2015). The cost-
benefit analysis of maltodextrin supplementation in the
diet of weaner pigs is as presented in Table 7. The result
showed no significant effect (P>0.05) of maltodextrin
supplementation on overall cost of feeding. The aver-
age cost of feed consumed per day were ₦270.63,
₦293.72 and 274.51 in T1, T2 and T3 respectively. The
feed cost per weight gain decreased across the treat-
ments with increasing level of maltodextrin in the diet.
Feed cost per weight gain were ₦1,213.03 in diet fed
0 % maltodextrin (T1), ₦1,153.77 in T2 fed 0.05 %
maltodextrin and ₦1,120.75 in T3 fed 0.1 % maltodex-
trin. The cost per weight gain which was estimated to
be higher for the control diet (T1) than in the diets sup-
plemented with maltodextrin (T2 and T3) implies that
the cost of including maltodextrin in the diet of pigs is
beneficial considering that less is spent on feeding to
produce a kg of live weight. This is an indication that
the inclusion of maltodextrin diet is beneficial cost and
health wise.
Slovak international scientific journal # 84, (2024) 9
Table 6
Serum Biochemical Parameters of Weaners Fed Varying Levels of Maltodextrin
Parameters
T1
T2
T3
SEM
Total protein (g/dL)
7.00
7.20
7.40
0.11
Albumin (g/dL)
2.90
3.07
3.25
0.06
Globulin (g/dL)
4.10
4.13
4.15
0.06
RATIO
0.71
0.74
0.78
0.01
AST (IU/l)
44.00
47.00
47.00
2.58
ALT (IU/l)
38.67
39.67
40.50
1.95
Blood urea nitrogen (mg/dL)
8.43
8.83
8.80
0.12
Creatinine (mg/dL)
0.77
0.80
0.80
0.01
Glucose (mg/dL)
78.33
82.00
84.50
1.52
Total cholesterol (mg/dL)
91.00
93.67
96.50
1.78
High density lipoprotein (mg/dl)
46.00c
56.33a
52.00b
1.14
Triglyceride (mg/dL)
79.00
84.00
81.50
0.87
Low density lipopretein (mg/dL)
29.20
20.53
28.20
1.57
a, b c Means with different superscript across the row are significantly different at α=0.05
T1 - Control (without maltodextrin)
T2 - 500g/tonne maltodextrin inclusion
T3 - 1kg/tonne maltodextrin inclusion
AST - Aspartate transaminase
ALT - Alanine aminotransferase
Table 7
Cost-Benefit Analysis of Maltodextrin Supplementation in Diet of Weaner Pigs
Parameters
T1
T2
T3
SEM
Cost of feed per kg (₦/Kg)
243.36
243.58
243.8
0.06
Total cost of feeding (₦)
24626.95
24626.96
24980.82
1857.51
Average Daily Feed Intake (Kg)
1.11
1.21
1.13
0.08
Average cost of feed/day (₦)
270.63
293.72
274.51
20.41
Feed conversion Ratio
4.20
4.23
4.11
0.17
Feed Cost/Weight Gain (₦/Kg)
1021.30
1029.53
1001.75
40.82
T1 - Control (Without maltodextrin)
T2 - 500g/tonne maltodextrin inclusion
T3 - 1kg/tonne maltodextrin inclusion
Dollar to Naira- $1 = ₦403
Conclusion
The inclusion of maltodextrin in the diet of
weaned pigs did not negatively influence the growth,
back fat thickness and health status of the pigs. Malto-
dextrin had a hypolipidism effect on the pigs by in-
creasing the high dendity lipoprotein (HDL) and reduc-
ing the low density (LDL). Its inclusion also improved
the cost per weight of the gain of the pigs. Thus, malto-
dextrin can be added up to 0.1% in the diet of pigs in
the tropics.
Acknowledgement: The authors appreciate the
management and staff of AK Research Farm, Eleyele,
Ibadan, Nigeria for their assistance and contributions to
this research work.
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Slovak international scientific journal # 84, (2024) 11
COMPUTER SCIENCES
STEP-BY-STEP GREEDY ALGORITHMS WITH RESPECT TO WALSH SYSTEM
Episkoposian S.,
Faculty of Applied Mathematics and Physics,
National Polytechnic University of Armenia
Grigoryan S.
Faculty of Applied Mathematics and Physics,
National Polytechnic University of Armenia
DOI: 10.5281/zenodo.11624303
Abstract
This paper proposes a modified step-by-step "greedy" algorithm for approximating functions with respect to
Walsh system. This algorithm works iteratively, adding the next largest coefficient at each step and evaluating the
approximation error. The paper describes the algorithm, its Python implementation, and examples of its application
to test functions.
Keywords: greedy algorithm, Walsh system, Walsh-Fourier coefficients.
1. Introduction
The expansion of functions in systems of basis
functions is a fundamental problem in various areas of
mathematics and its applications. One widely used ba-
sis is the Walsh-Fourier system, based on Rademacher
functions and their products. Efficient function expan-
sions in the Walsh basis have important applications in
signal processing, data compression, approximation
theory, and other fields.
The classic method for constructing function ap-
proximations is the Fourier series truncation method,
where the first N terms of the expansion are kept. How-
ever, this approach is not always optimal, as achieving
good approximation accuracy may require a significant
number of expansion terms. An alternative approach is
the so-called "greedy" algorithms, which select the ex-
pansion terms not in the order of their appearance, but
in the order of decreasing their weights (coefficients).
This method often provides faster convergence for the
same number of series terms.
This paper proposes a modified step-by-step
"greedy" algorithm for approximating functions in the
Walsh-Fourier system [1,2]. The classical "greedy" al-
gorithm selects a fixed number n of the largest absolute
Walsh-Fourier coefficients to approximate the func-
tion. However, this approach is not always optimal in
terms of accuracy for a given number of series terms.
The proposed algorithm works iteratively, adding the
next largest coefficient at each step and evaluating the
approximation error. The process stops once the error
becomes less than a specified threshold ε. This allows
achieving the required accuracy with a minimal number
of series terms. The paper describes the algorithm, its
Python implementation, and examples of its application
to test functions. The results demonstrate that the mod-
ified "greedy" algorithm can provide more efficient ap-
proximations compared to the classical method and
partial Fourier approximation when reaching the re-
quired level of accuracy.
2. Step-by-step "greedy" algorithm with re-
spect to Walsh system
To define the Walsh function, it is necessary to de-
fine the Rademacher function [1].
Definition 1. The Rademacher system is defined
as
,
...,
i.e. to find the Rademacher function, the inter-
val is split of equal subintervals, on each of
which the function takes +1 and -1 values succes-
sively.
The Walsh system is defined as all possible finite
products of Rademacher functions. More precisely, we
define the Walsh system by Paley numbering as follows
[2,3]:
Definition 2. . Let n be any natural
number, represented as
,
. The n-th Walsh function will be defined as
follows:
.
The function is given. Let us denote its Fou-
rier-Walsh -th partial sum as follows:
where
are the Fourier-
Walsh coefficients of the function .
The greedy algorithms ([4]) with respect to Walsh
system defined the following way.
Let's arrange the coefficients in descend-
ing order of their absolute values, as follows:
and consider the greedy approximant of the func-
tion . Let's designate it as follows:
It's known that the greedy algorithm, for example,
for the Walsh system, is not always optimal ([5.6]).
In particular, we have shown that for example
,
,
12 Slovak international scientific journal # 84, (2024)
and
.
Thus, we find that .
Now let's modify the algorithm by implementing
a "greedy" approach with sequential steps. Our objec-
tive is to develop a "greedy" algorithm with incremen-
tal steps of arbitrary precision.
First, we fix an arbitrary number . If
, then the process halts, and the
value of should be decreased.
We select from the sequence the
term for which
,
and we estimate
.
We verify the following condition:
(1)
If the condition (1) is satisfied, then we compute
the difference
,
and the process halts.
If condition (1) is not met, then we define
.
Now we select and create the
difference .
Let's reevaluate:
(2)
Again, if condition (2) is fulfilled, the process
halts, and we calculate:
And if condition (2) does not occur, then we con-
tinue the process for the function:
We continue this process until it stops at any step,
meaning we will have
,
and then calculate the difference
.
And if the process continues until reaching , then
we conclude that the outcome of the "greedy" algorithm
with successive steps is equivalent to the outcome of
the complete "greedy" algorithm.
The algorithm was implemented using a Python
program. It takes inputs such as M (for the partial Fou-
rier-Walsh sum calculation), n (for the complete
"greedy" algorithm calculation), (precision level),
and (the function under consideration) data.
3. Code in Python
from scipy.linalg import hadamard
import sympy as sp
# Symbolic variable
x = sp.symbols('x')
M=int(input("Enter M number: "))
n = int(input("Enter n number for Greedy: "))
E=float(input("Enter epsilion: "))
# User input for the expression
user_input = input("Enter a mathematical expres-
sion in terms of 'x': ")
# Parse the user input into a SymPy expression
expr = sp.sympify(user_input) #function
def generate_x_values(M):
return [k/M for k in range(M+1)]
x_values = generate_x_values(M)
#define Walsh
c_index=M # initial index
N = 1
N_check = 0
binary_length = 0
d_bool = False
while N_check < M:
N = N * 2
binary_length += 1
if M > 0 and (M & (M - 1)) == 0:
d_bool = True
M += 1
if M == 1:
d_bool = False
N_check = N
step_size = 1 / N
step_sizes = [i * step_size for i in range(N + 1)]
hadamard_matrix = [hm for hm in hadamard(N)]
def index_convert(N, l):
walsh_index = []
for i in range(N):
decimal_number = i
desired_length = l
binary_number = format(decimal_number,
f"0{desired_length}b")
reversed_code = binary_number[::-1]
walsh_index.append(int(reversed_code, 2))
return walsh_index
walsh_index = index_convert(N, binary_length)
walsh_function = [hadamard_matrix[i] for i in
walsh_index]
M=c_index
def calculate_coefficients(integrated_expr,
step_sizes, walsh_function, c_index):
differences = []
for interval_start, interval_end in
zip(step_sizes[:-1], step_sizes[1:]):
integrated_value_start = inte-
grated_expr.subs(x, interval_start)
integrated_value_end = inte-
grated_expr.subs(x, interval_end)
Slovak international scientific journal # 84, (2024) 13
difference = float(integrated_value_end - in-
tegrated_value_start)
differences.append(difference)
coefficients = []
for c in range(c_index + 1):
c_list = [diff * walsh for diff, walsh in
zip(differences, walsh_function[c])]
coefficient = sum(c_list)
coefficients.append(coefficient)
return coefficients
integrated_expr = sp.integrate(expr, x)
coefficients = calculate_coefficients(inte-
grated_expr, step_sizes, walsh_function, c_index)
sorted_c=sorted(coefficients,key=lambda x:
abs(x), reverse=True)#decreasing order
def get_f_for_x(x_values, step_sizes, w):
w_x = []
for i, x in enumerate(x_values):
for j in range(len(step_sizes) - 1):
if step_sizes[j] <= x < step_sizes[j + 1]:
w_x.append(w[j])
break
else:
w_x.append(w[-1])
return w_x
f_x=[]
for j in range(M+1):
expr_value = expr.subs(x, x_values[j])
f_x.append(expr_value)
def calculate_cw(coefficients, walsh_function, M,
N): c_w = []
for j in range(M+1):
c_w_values = []
for i in range(N):
c_w_values.append(coefficients[j] *
walsh_function[j][i])
c_w.append(c_w_values)
return c_w
c_w = calculate_cw(coefficients, walsh_function,
M, N)
sorted_cw=calculate_cw(sorted_c,walsh_func-
tion,M,N)
c_w = []
walsh_values_in_x = []
sorted_c_w_in_x=[]
for i in range(M+1):
w_x = get_f_for_x(x_values, step_sizes,
walsh_function[i]) #Values of w_i(x)
cw_x=get_f_for_x(x_val-
ues,step_sizes,sorted_cw[i])
walsh_values_in_x.append(w_x)
sorted_c_w_in_x.append(cw_x)
transposed_sorted_cw_x = [[row[i] for row in
sorted_c_w_in_x] for i in
range(len(sorted_c_w_in_x[0]))] # cw(0),
cw(0),...cw(1), cw(1)
sigma = []
s=[] #for fourier M
for row in transposed_sorted_cw_x:
row_sum = sum(row[:n+1])
sum_fourier=sum(row[:M+1])
sigma.append(row_sum)
s.append(sum_fourier)
#greedy normal
a=[]
for i in range (M+1):
fs=abs(f_x[i]-sigma[i])
a.append(fs)
B=sum(a)/len(a)
#Fourier
fourier=[]
for i in range (M+1):
four=abs(f_x[i]-s[i])
fourier.append(four)
A=sum(fourier)/len(fourier)
#greedy step by step
b=[]
b_without_abs=[]
f_k=[]
greedy_step=0
t=False
while t==False:
while t==False:
for i in range(n+1):
for j in range(M+1):
b_i_without_abs=f_x[j]-
sorted_c_w_in_x[i][j]
b_i=abs(f_x[j]-sorted_c_w_in_x[i][j])
b.append(b_i)
b_without_abs.append(b_i_without_abs)
greedy_step+=1
GS=sum(b)/len(b)
if b_i<E:
t=True
break
else:
f_x=b_without_abs
b=[]
b_without_abs=[]
t=False
break
print("Greedy Normal Form=",B)
print("Greedy step by step=",GS)
print("Fourier approximation=",A)
print("steps=",greedy_step)
The results of the algorithm are then presented in
the following format:
14 Slovak international scientific journal # 84, (2024)
Example 1․
Greedy Normal Form= 0.0702512254901961
Greedy step by step= 0.0638235294117647
Fourier approximation= 0.0702512254901961
step=3, where 'step' indicates in which steps the
algorithm performed the approximation with the accu-
racy .
Example 2․
Greedy Normal Form= 0.0451854271375904
Greedy step by step= 0.0451854271375904
Fourier approximation= 0.0453110690028777
In this example, the values of Greedy Normal
Form and Greedy step by step are identical, which
means that the "greedy" algorithm with successive
steps continued the calculations until completion,
reaching n, and as a result matched the outcome of the
full "greedy" algorithm.
Conclusion
In this paper, we proposed a modified step-by-step
"greedy" algorithm for approximating functions in the
Walsh basis with arbitrary precision. The classical
"greedy" algorithm fixes the number of expansion
terms, which is not always optimal in terms of approx-
imation accuracy. The proposed algorithm works itera-
tively, adding terms until the required accuracy is
achieved. The Python implementation and examples
demonstrate that this approach can provide more effi-
cient approximations compared to classical methods
when reaching a given accuracy level. Future work will
investigate the convergence and error estimates for the
modified algorithm.
References
1. Rademacher H., Einige Sätze über Reihen von
allgemeinen Orthogonalfunktionen, Math. Ann., 1922,
v. 87, no. 1–2, p. 112 – 138.
2. Walsh J., A Closed Set of Normal Orthogonal
Functions, Amer. J. Math.,1923., v. 45. p. 5 – 24.
3. Paley R., A Remarkable Series of Orthogonal
Functions, Proc. Lond. Math. Soc. 1932, v. 34, p. 241
– 279.
4. Temlyakov, V.N., Greedy approximations,
Cambridge University Press, 2011
5. Episkoposian S.A., On the divergence of
Greedy algorithms with respect to Walsh subsystems in
1
L
, Nonlinear Analysis: Theory, Methods & Applica-
tions, v. 66, n. 8, 2007, p. 1782-1787.
Slovak international scientific journal # 84, (2024) 15
SMART HOME TECHNOLOGY AND TRENDS IN LIVING SPACE TRANSFORMATIONS
Manafov E.,
Doctoral student
Sardarova I.
Academic supervisor, PhD, Assoc. Prof.
Department of Electronics and automation,
Azerbaijan State Oil and Industry University
Baku, Azerbaijan
DOI: 10.5281/zenodo.11624311
Abstract
The improvement of management systems has opened the gate for complex automation of processes. Now-
days, technologies are developing. Similar results are also used in the smart control systems applied in houses and
other buildings. In recent years, innovations in the technologies, the development process in automation systems
allow to use devices faster and more productive and flexible.
Modernization of management systems in our time has led to complex mechanization and automation of
production processes. By applying new and modern progressive methods, the intensification of production is en-
sured, thus, the quality indicator of the produced product is improved. Such achievements are also used in intelli-
gent management systems applied in buildings. Today, technology is constantly developing. Of course, the devel-
opment of technologies plays a big role in people's lives. We are living in such a time that before, "This cannot be
realized, it is impossible to do." Projects using sentences like these are very easy to implement nowadays. Innova-
tions that have happened in the field of technology in recent years, of course, have an impact on us. The develop-
ment process in mechatronic systems makes it possible to use devices with faster and larger capacities. Technolo-
gies are evolving today. The results of technological development are also used in smart control systems applied
in homes and other buildings. In recent years, innovations in technologies, the development process in automation
systems allow using devices faster, more productively and flexibly.
The level of development in smart homes did not happen by itself. All innovations first take place within
society and are shaped by the influence of trends within society. Also, with the use of special technologies to
increase the value of smart homes, it is also aimed at improving the smart home environment.
A smart home is a home equipped with technological solutions designed to provide services that meet people's
needs. The purpose of this article is to systematically evaluate the latest smart home literature and review research
and developments in the living space and smart technologies transformationsş In addition to providing a overview
of the development and performance of current smart home systems and this paper provides detailed information
on the latest equipment and systems.
Keywords: smart systems, sensors, electronic systems, automation, smart transformation.
The Smart Home - technology of the century. It
integrates many new technologies through home net-
works to improve the quality of human life. Smart
home commerce has attracted the attention of research-
ers for over a decade. Smart home technology is a com-
bination of networks and services. In recent years, the
term "smart" has become synonymous with any tech-
nology that has some level of artificial intelligence. The
ability to collect information from the environment and
react accordingly is a critical feature of smart technol-
ogies. Smart technology has become the main driver of
innovative ideas such as the smart home system. With
the development of smart products and services, the
world has witnessed an increase in device interaction
and data sharing, which has influenced the rapid devel-
opment of smart home technologies worldwide. Due to
the advantages provided by smart technologies and the
possible large global market, interest in smart home
technologies among researchers has increased dramati-
cally.
In the field of home automation and control, the
smart home has become a very promising sector. The
term "smart home" is not limited to human residences.
Rather, it has broader technological implications, in-
cluding smart housing and living.
A smart home is a home equipped with technolog-
ical solutions designed to provide services that meet
people's needs. The purpose of this article is to system-
atically evaluate the latest smart home literature and re-
view research and developments in the sensors types
and security systems field. In addition to providing a
overview of the development and performance of cur-
rent smart home systems and this paper provides de-
tailed information on the latest equipment and systems.
Details of the by smart home management system com-
ponents provided and its advantages pointed in the ar-
ticle.
Smart technologies are currently developing rap-
idly. We understand a certain concept of a computer
network that connects various devices into a network;
these devices interact and are able to exchange infor-
mation offline without human intervention or with min-
imal participation. Now Smart technologies used in the
industrial sector, the so-called B2B (business to busi-
ness) technologies, and in the B2C (business to con-
sumer) consumer sector. One of the striking examples
of the use of technology in the space of everyday prac-
tices can be the concept of a “smart home” - a house
within which the technology of interconnected “smart”
things is used, which are part of the internal and exter-
16 Slovak international scientific journal # 84, (2024)
nal home spaces. Such a “smart home” is a self-regu-
lating system containing a number of subsystems: mi-
croclimate subsystems, subsystems for lighting and
regulation of the operation of electronic devices; within
the framework of a “smart home” a “smart refrigerator”
can operate, equipped with devices with artificial intel-
ligence, which can analyze the consumption of certain
products, their stock and consumption dynamics. You
can also include a security system here. It must be said
that the concept of a “smart home” presupposes, on the
one hand, devices that can operate autonomously in a
systemic unity, on the other hand, a “house”, which is,
as a rule, a separate building, they are conveniently and
rationally designed, taking into account the possibility
of using smart technologies.The purpose of this work is
to highlight and consider some trends in the transfor-
mation of living space within the framework of smart
home technology.
After analyzing some changings home space in re-
lation to smart home technology, some trends are visi-
ble as follows:
The first trend is the increasing functionality of the
home and home spaces. Configuration of living space
reflects social realities is an opportunity for customized
home design, taking into account both design and aes-
thetic imperatives, which can be unique, and functional
and technological solutions. Of course, it is worth say-
ing that we are talking about the premium segment of
houses and corresponding solutions which are not
available to all segments of the population, even if we
take into account residents of large cities. Researchers
note that only laying the necessary cables and sensors
is comparable in the cost of purchasing a good class car.
The popularity of individual design solutions, loft de-
sign (mainly in urban environments), regarding interior
design of space is increasing. Some producing compa-
nies even say that such design correlates with the life-
style of single people and married couples without chil-
dren, as opposed to traditional design and architectural
solutions of the industrial era, designed for the tradi-
tional family. As a rule, loft design involves technolog-
ical equipment. It is logical to assume that smart home
technologies will focus on this kind of solutions, alt-
hough a traditional house, without large internal
“empty spaces,” is also relevant for the implementation
of the smart home technologies. The individualized de-
sign of a modern home, which applies to both the pre-
mium segment and more budget options, represents the
trend of customizing a home, and many areas of life of
a modern person. By customization we mean a certain
trend which appeared as part of marketing strategies, it
is associated with the development of personalized
products and services aimed at specific customers.
Customization may imply the opportunity for the
consumers themselves to participate in the creation of a
product in terms of developing its features, design in a
broad sense, or personalized service. It is clear that so-
lutions in the field of the Internet of Things, such as
“multi-home” technologies, require customization,
since it is impossible to unify the needs and features of
a home (especially when it comes to the premium seg-
ment and a separate house). In addition, customization
will also concern the ability to create interior elements,
furniture and, probably, integrate them with devices
within the “smart home” system (sensors, drives and
other elements can already be purchased). Moreover, it
is even possible to print building elements for a house
and create the house itself using a 3D printer (here, of
course, questions arise about the reliability of parts and
their technical characteristics, compliance with build-
ing codes and regulations). It is possible that such a
practice, focused on functionality and decentralized
customized production, will seriously change the con-
tours of the socio-economic system, and the very atti-
tude towards consumption throughout society.
So, highlighted aspects of increasing the im-
portance of the functional component of the space of
the house, customization and the possibility of autono-
mous creation of elements of the home space.
As for the trend towards autonomy, it also applies
to the devices themselves within the framework of the
“smart home” concept. For example, there are already
sensor networks that implement “smart dust” technol-
ogy. “Smart dust” is a collection of miniature sensors
with computing and wireless communication capabili-
ties, in addition, these elements have memory for data
storage and special sensitive elements for environmen-
tal analysis. These elements are comparable in size to
sand grains. Each element, or “mote” (speck of dust),
can have its own sensors, power supply, communica-
tion and computing node. Such motes can group to-
gether and create flexible and mobile networks, con-
suming a small amount of energy. “Smart dust” can be
used in climate control systems and multimedia envi-
ronments in the “smart home” space.
Conclusion
So, trends are identified in autonomization and in-
creased functionality in various aspects of smart home
technology. These trends echo the general vector of de-
velopment of the technical and information universe in
which modern people live. As information technologies
develop, these trends will intensify—customization of
various spheres and practices, strengthening of their
functional potential, at the same time as “smarter”, au-
tonomization at various levels. All this will concern the
development of the home environment of the “smart
home”, which can turn into something different com-
pared to the current home space (if we understand the
home space as a set of everyday practices). It is possible
that the very principle of autonomy and autonomization
of the elements of the house in its correlation with the
expansion of the “computational potential” of things
and objects will give rise to some new contours of hu-
man living space.
References
1. Arduino Smart Home Automation by Alan
Trevennor was published in 2013. It was officially pub-
lished by Apress and has the ISBN: 1430257709.
2. The Smart Smart Home Handbook: Control
Your Home with Your Voice by Adam Juniper (2018)
It was officially published by Ilex Press and has the
ISBN: 1781575800.
3. Smart home Complete Self-Assessment Guide
by Gerardus Blokdyk was published in 20180105. It
Slovak international scientific journal # 84, (2024) 17
was officially published by Emereo and has the ISBN:
1489195637.
4. Harper, R. (2003). Inside the Smart Home.
London: Springer.
5. Burkhard, S., & Bouée, C.-E. (2013). Home
Automation Solutions
6. Stefen Robs, Programmable Logic Controller
(PLC) Tutorial, Siemens Simatic S7-200, 2007
7. Madhuchhanda Mitra, Industrial Automation
an Introduction, 2005
8. Con Veb. Principles and Applications, 1988
9. Stefen Tub, (PLC) Tutorial: Circuits and Pro-
grams, 2005
10. Harry Enderson, PLC Programming Using
RSLogix 500: Basic Concepts of Ladder Logic, 2015
11. Khaled Kamel, Industrial Controllers, 2013
18 Slovak international scientific journal # 84, (2024)
МОБИЛЬНЫЕ МЕДИЦИНСКИЕ ПРИЛОЖЕНИЯ В ЦИФРОВИЗАЦИИ ЗДРАВООХРАНЕНИЯ
Курбанова Н.Г.
Кандидат технических наук,
доцент кафедры медицинской и биологической физики
Азербайджанский Медицинский Университет
Гаджиев З.А.
Кандидат технических наук,
ассистент кафедры медицинской и биологической физики
Азербайджанский Медицинский Университет
Абдуллаева Г.А.
Кандидат технических наук,
ассистент кафедры медицинской и биологической физики
Азербайджанский Медицинский Университет
MOBILE MEDICAL APPLICATIONS IN DIGITALIZATION OF HEALTHCARE
Gurbanova N.,
Ph.D, assistant of professor, department “Medical and biological physics”,
Azerbaijan Medical University
Hajiyev Z.,
Ph.D, assistant, department “Medical and biological physics”,
Azerbaijan Medical University
Abdullayeva G.
Ph.D, assistant, department “Medical and biological physics”,
Azerbaijan Medical University
DOI: 10.5281/zenodo.11624332
Аннотация
В современном мире многие люди активно пользуются мобильными приложениями. За последние
годы разработки в сфере здравоохранения внесли большой вклад в рост мобильных приложений. Многие
из которых работают в режиме оффлайна и позволяют пользователям отслеживать свое здоровье, физиче-
скую активность, сон, пульс, артериальное давление, уровень сахара в крови и другие параметры. Цифро-
визация здравоохранения требует от медицинских мобильных приложений стать частью единой медицин-
ской экосистемы.
Abstract
In the modern world, many people actively use mobile applications. Developments in the healthcare sector
have contributed greatly to the growth of mobile apps in recent years. Many of which work offline and allow users
to track their health, physical activity, sleep, pulse, blood pressure, blood sugar and other parameters. Digitalization
of healthcare requires medical mobile applications to become part of a unified healthcare ecosystem.
Ключевые слова: мобильные медицинские приложения, электронный рецепт, цифровизация здраво-
охранения, медицинская экосистема.
Keywords: mobile medical applications, electronic prescription, digitalization of healthcare, healthcare eco-
system.
Цифровизация сферы здравоохранения жиз-
ненная необходимость современности, которая
направлена на повышение эффективности и дей-
ственности оказания медицинской помощи за счет
применения инновационных подходов. Целью циф-
рового здравоохранения является объединение ме-
дицинских данных в рамках единого цифровой
платформы, анализ которых позволит обеспечить
высокий уровень качества медицинских услуг и за-
боту о здоровье населения. Анализ медицинских
данных граждан, накапливаемых в течение всего
жизненного цикла, позволяет лучше понять при-
чину заболевания, поставить точный диагноз и
обеспечить наиболее правильное лечение. Напри-
мер, в сфере радиологии данные и алгоритмы ис-
кусственного интеллекта являются незаменимым
инструментом диагностирования заболеваний на
самой ранней стадии. Анализ больших данных поз-
воляет выстраивать модели оптимизации процес-
сов, предотвращения распространения пандемий и
улучшения качества здоровья и продолжительно-
сти жизни [4, 5].
В стратегии цифрового здравоохранения ос-
новной задачей является формирование единой
экосистемы медицинских данных, объединяющей
все медицинские учреждения страны и обеспечение
беспрерывного доступа к этим данным со стороны
медицинского персонала. Что позволит им в приня-
тии решений в процессе диагностирования заболе-
ваний и назначении наиболее эффективных мето-
дов лечения. Основным источником данных будет
реестр под названием «Медицинский цифровой
двойник гражданина», в котором будет отражена
вся информация о здоровье - медицинские истории,
Slovak international scientific journal # 84, (2024) 19
диагнозы, методы лечения, результаты анализов и
радиологии, назначения рецептов, анамнестическая
история о генетической предрасположенности к за-
болеваниям с момента идентификации факта бере-
менности во время обращения матери в медицин-
ское учреждение до момента трансплантологии ор-
ганов, в случае если гражданин дал согласие стать
донором после смерти. Накапливаемые медицин-
ские данные станут основой для макроанализа со-
стояния здоровья населения в масштабах всей
страны, понимания востребованности и удовлетво-
ренности качеством медицинских услуг, планиро-
вания развития необходимой инфраструктуры,
применения эффективных экономических моделей,
включая страхование, развития кадрового потенци-
ала и соответственно гибкого планирования разви-
тия отрасли и реализации приоритетных для госу-
дарства задач в здравоохранении [3].
На сегодняшний день в Единой информацион-
ной системе Министерства здравоохранения Азер-
байджана функционирует 20 электронных систем,
включающих более 70 программных модулей, не-
которые из них также функционируют в качестве
мобильного приложения.
В современном мире мобильные медицинские
приложения становятся все более популярными,
меняющим парадигмы здравоохранения. С разви-
тием мобильных технологий и доступности смарт-
фонов, мобильные медицинские приложения пред-
лагают широкий спектр возможностей для улучше-
ния здоровья, диагностики, мониторинга и
управления медицинскими состояниями.
Центром Общественного Здравоохранения и
Реформ Министерства здравоохранения Азербай-
джана разработаны некоторые мобильные прило-
жения [1]:
1. Приложение "Здоровое питание" поможет
составить правильный рацион питания и рассчи-
тать калории. Приложение также работает в ре-
жиме OFFLINE и не требует подключения к Интер-
нету. Оно состоит из 5 основных функций: 1) Каль-
кулятор калорий,
2) Калькулятор массы тела, 3) Калькулятор по-
лезности пищи, 4) Ежедневный калькулятор кало-
рии и 5) Статьи с информацией о полезном питании
2. Основной целью создания мобильного при-
ложения “Сахарный диабет” является информи-
рование населения о профилактике, лечении и кон-
троле уровня сахара при диабете. Программу могут
использовать как больные сахарным диабетом, так
и люди, уделяющие внимание питанию и углевод-
ному обмену. Мобильное приложение предостав-
ляет отделение памяти для своевременного приема
лекарств, калькулятор единиц хлеба и полезную ин-
формацию о диабете (типы, диабет, осложнения,
использование инсулина и т. д.).
3. С помощью мобильного приложения "За-
щити свое сердце" вы можете постоянно контро-
лировать здоровье своего сердца, можете ознако-
миться с основными факторами риска сердечно-со-
судистых заболеваний, с методами борьбы со
стрессом и другими полезными материалами. Раз-
делы «Назначение времени приема лекарств», «Из-
мерение артериального давления и пульса» в при-
ложении напоминают о своевременном приеме
назначенных лекарств. Вы можете мгновенно запи-
сывать информацию о вашем здоровье (артериаль-
ное давление и пульс) и отправлять в виде таблицы
на адрес электронной почты своего врача с помо-
щью мобильного устройства в течение дня или не-
дели.
4. Мобильное приложение “Паллиативная
помощь” . Паллиативная помощь – это междисци-
плинарная медицинская специальность, направлен-
ная на уменьшение страданий и поддержание мак-
симально возможного качества жизни пациентов в
критическом состоянии и их семей. Основная цель
мобильного приложения предоставить пациентам,
членам их семей, а также медицинскому персоналу
подробную информацию о паллиативной помощи,
помочь найти ответы на вопросы, которые могут
возникнуть.
Помимо характеристик паллиативной помощи,
в мобильном приложении описаны меры, направ-
ленные на уменьшение симптомов, оказание психо-
логической и социальной поддержки, снижение
страха или тревоги потери близкого человека в се-
мье. Также в него включен национальный и между-
народный опыт паллиативной помощи, организа-
ции, занимающиеся паллиативной помощью в
Азербайджане, и новости об их деятельности.
5. Мобильное приложение «Бурла Хатун».
Каждая беременная женщина хочет знать и следить
за тем, как растет ее будущий ребенок в утробе ма-
тери и за его здоровьем. Мобильное приложение
«Бурла Хатун» обеспечивает быстрый и удобный
доступ к информации о вашей беременности, раз-
витии ребенка и важным рекомендациям для бере-
менных, а также простым языком объясняет самые
важные моменты по уходу за новорожденными и
младенцами после рождения.
6. Приложение “Первая помощь” помогает
реагировать на повседневные чрезвычайные ситуа-
ции и дает советы, что делать в случае неотложной
медицинской помощи. Приложение предоставляет
доступ к тематическим видеороликам и простым
пошаговым инструкциям по выполнению мер пер-
вой помощи или помощи в мерах, принимаемых
при необходимости или по указанию служб скорой
медицинской помощи или других экстренных
служб.
7. Приложение “ВидеоДоктор”, это телеме-
дицинские услуги, предоставляемые лицензиро-
ванными врачами, работающими в группе незави-
симых специализированных практик, известных
под общим названием VideoDoktor Professionals.
Эти специалисты оказывают услуги через телеме-
дицинскую платформу «ВидеоДоктор» ежедневно
и в любом месте. Очные видео сеансы могут прово-
диться по запросу или в заранее оговоренное время,
днем и ночью, включая праздничные дни. Получите
качественную медицинскую помощь в безопасно-
сти вашего дома.
20 Slovak international scientific journal # 84, (2024)
8. Приложение “Электронный рецепт” явля-
ется мобильным применением системы «Электрон-
ный рецепт», который является единым реестром
регистрации и управления рецептами по медицин-
ским препаратам, выписанным гражданам в госу-
дарственных и частных медицинских учреждениях
Азербайджана. Воспользоваться системой «Элек-
тронный рецепт» могут все граждане, получающие
услуги по обязательному медицинскому страхова-
нию, граждане, относящиеся к льготной категории,
а также граждане, получающие услуги по частному
медицинскому страхованию, а также незастрахо-
ванные граждане [2].
Мобильные приложения здравоохранения от-
ражают уровень цифровизации этой отрасли. По из-
менению уровня мобильных приложений можно
сделать вывод об сегодняшних успехах в цифрови-
зации здравоохранения в республике. Как видно, из
описанных выше приложений первые из них предо-
ставляли информацию даже в режиме оффлайна.
Обмен информацией можно было выполнить в виде
отправления СМС сообщений, или специализиро-
ванных видео-чатов. А приложение “Электрон-
ный рецепт” является уже мобильным примене-
нием системы «Электронный рецепт» анонсиро-
ванном в 2023 году, в котором, пользователь
должен иметь уже идентификационный код, т.е. ре-
гистрацию в государственном реестре. Что явля-
ется новым этапом цифровизации здравоохранения
с использованием централизованной государствен-
ный базы. Предлагается формировать единое ин-
формационное пространство при помощи системы
электронного рецепта, которая будет охватывать
поликлиники, стационары и сети аптек страны. В
будущем интеграция системы с реестром контроля
за движением лекарственных средств, позволит
усилить контроль за операциями реализации меди-
каментов, включая предотвращение распростране-
ния незарегистрированных препаратов. Также че-
рез это мобильное приложение можно будет
удобно вести поиск аптеки для приобретения нуж-
ного препарата или заказывать его заранее. Счи-
таем, что мобильное приложение электронного ре-
цепта особенно будет необходимым для пациентов
с хроническими заболеваниями. Им больше не при-
дется отсиживать очередь к врачу для выписки не-
обходимого препарата. Когда система полностью
заработает, то продлевать рецепт они смогут уда-
ленно по согласованию с доктором. А приходить к
врачу на прием необходимо будет уже только на
обязательные осмотры.
Список литературы
1. https://isim.az/ru/pages/46
2. https://reseptim.az
3. Зуенкова Ю.А. Опыт и перспективы при-
менения цифровых двойников в общественном
здравоохранении // Менеджер здравоохранения,
2022, № 6, c. 69-77
4. Кудратиллаев М.Б. Мобильные медицин-
ские приложения: значение в жизни человека и их
особенности, обзор существующих приложении //
"Science and Education" Scientific Journal, May 2023,
Volume 4 Issue 5, p.803-811
5. Kernebeck S., Busse T., Böttcher M. et al. Im-
pact of mobile health and medical applications on clin-
ical practice in gastroenterology // World J Gastroen-
terol., 2020, 26 (29), p. 4182–4197
Slovak international scientific journal # 84, (2024) 21
АНАЛІЗ ТА ОЦІНКА ІНФОРМАЦІЙНИХ ЗАГРОЗ ТРАНСПОРТНОГО СЕКТОРУ
Аль-Амморі Алі
д.т.н., професор,
завідувач кафедри інформаційно-аналітичної діяльності та інформаційної безпеки,
Національний транспортний університет, Київ, Україна
Іщенко Р.М.
к.ф.-м.н., доцент, доцент кафедри інформаційно-аналітичної діяльності та інформаційної безпеки,
Національний транспортний університет, Київ, Україна
Клочан А.Є.
PhD, асистент кафедри інформаційно-аналітичної діяльності та інформаційної безпеки,
Національний транспортний університет, Київ, Україна
Шкурко О.П.
к.соц.ком., доцент кафедри інформаційно-аналітичної діяльності та інформаційної безпеки,
Національний транспортний університет, Київ, Україна
Поворознік Д.Є.
студент кафедри інформаційно-аналітичної діяльності та інформаційної безпеки,
Національний транспортний університет, Київ, Україна
ANALYSIS AND ASSESSMENT OF INFORMATION THREATS IN THE TRANSPORT SECTOR
Al-Ammori Ali,
Doctor of Technical Sciences, Full Professor, head of the Department of Information Analysis and Infor-
mation Security,
National Transport University, Kyiv, Ukraine
Ishchenko R.,
Candidate of Physical and Mathematical Sciences (Ph.D), Docent, Associate Professor of the Department
of Information Analysis and Information Security,
National Transport University, Kyiv, Ukraine
Klochan A.,
PhD, Assistant Lecturer of the Department of Information Analysis and Information Security,
National Transport University, Kyiv, Ukraine
Shkurko O.,
Candidate of Sciences in Social Communications (PhD), Associate Professor of the Department of Infor-
mation Analysis and Information Security,
National Transport University, Kyiv, Ukraine
Povoroznik D.
student of the Department of Information Analysis and Information Security,
National Transport University, Kyiv, Ukraine
DOI: 10.5281/zenodo.11624349
Анотація
Останніми роками транспортний сектор України зазнав цифрової трансформації, що значно вплинуло
як на ефективність його роботи, так і на комфорт пасажирів. Однак, зростаюча залежність від інформа-
ційно-комунікаційних технологій призвела до того, що зазначена галузь стала достатньо вразливою через
вплив різноманітних кіберзагроз, які можуть завдати суттєвої шкоди підприємству транспортної галузі.
Відповідно, визначення та аналіз існуючих інформаційних загроз, що виникають під час роботи транспо-
ртних підприємств та оперативне реагування на них з метою запобігання катастроф є актуальною науково-
технічною задачею.
Abstract
In recent years, the transport sector of Ukraine has undergone a digital transformation, which significantly
affected both the efficiency of its work and the comfort of passengers. However, the growing dependence on
information and communication technologies has led to the fact that the mentioned industry has become quite
vulnerable due to the impact of various cyber threats that can cause significant damage to the transport industry
enterprise. Accordingly, the identification and analysis of existing information threats arising during the operation
of transport enterprises and prompt response to them in order to prevent disasters is an urgent scientific and tech-
nical task.
Ключові слова: транспортний сектор, інформаційна безпека, інформаційна технологія, інформаційні
загрози, DDoS-атаки, кібератака.
Keywords: transport sector, information security, information technology, information threats, DDoS at-
tacks, cyber attack.
22 Slovak international scientific journal # 84, (2024)
Вступ. Інформаційна безпека відіграє важливу
роль у забезпеченні ефективного функціонування
підприємств транспортного сектору [1]. В науково-
технічній літературі існує достатньо робіт, присвя-
чених аналізу інформаційних загроз, що можуть ви-
никати в різних галузях транспортного комплексу
країни. Зокрема, в роботі [4] розглянуто сукупність
методів і практик захисту від атак зловмисників для
забезпечення безперебійної роботи комп’ютерів,
електронних систем, мереж та даних на автомобіль-
ному транспорті. В роботі [2] проаналізовано існу-
ючі проблеми інформаційної безпеки авіаційного
транспорту. Автором роботи [3] запропоновано ро-
зглядати інформаційну безпеку як елемент підви-
щення ефективності комплексного контролю на
підприємствах водного транспорту. У роботі [5] до-
сліджено питання організації, впровадження та за-
безпечення інформаційної безпеки на водному тра-
нспорті, зокрема, на морських суднах. Деякі про-
блеми впровадження стандартів кібербезпеки на
морському транспорті розглянуто авторами роботи
[6]. Однак, для ефективного забезпечення інфор-
маційної безпеки підприємств транспортного сек-
тору необхідно провести комплексний аналіз інфо-
рмаційних загроз, які завдають найбільшої шкоди
зазначеній галузі. Останнє дозволить визначити
вразливі місця, розробити план реагування, впрова-
дити усі необхідні заходи безпеки та підготувати
персонал для успішного розпізнавання та реагу-
вання на кібератаки.
Таким чином, метою даної роботи є прове-
дення комплексного аналізу інформаційних загроз,
що виникають під час функціонування підприємств
транспортного сектору.
Основна частина. Визначимо, яка частка кібе-
ратак припадає на транспортний сектор. Для цього
використаємо річний звіт компанії Microsoft за
2022 рік [9]. На діаграмі (рис. 1) продемонстровано
сектори економіки, що найчастіше піддавались на-
падам кіберзлочинців.
Рисунок 1 – Галузі, що зазнали кібератак в усьому світі на 2022 рік
В цьому ж звіті була подана інформація про галузі в Україні, що найбільше підпали під удар після
вторгнення. Результати дослідження зображені на наступній діаграмі (рис. 2).
Slovak international scientific journal # 84, (2024) 23
Рисунок 2 – Галузі в Україні, що зазнали кібератак на 2022 рік
Проаналізувавши діаграми, можна помітити,
що сектори економіки в світі, що найчастіше підда-
ються кібератакам, значною мірою відрізняються
від тих, що зазнали кібератак в Україні. Також це
помітно й для транспортної інфраструктури, де кі-
бератаки на Україну становлять 7% (на відміну від
тих, що стосуються світу – 2%). Велику роль в цих
змінах відіграє вторгнення ворога в нашу країну.
Цілеспрямовані обстріли транспорту станов-
лять загрозу для сфери, що має вирішальне зна-
чення для громадян України, які намагаються ви-
жити в умовах війни. Згідно з опитуванням, прове-
деним за підтримки ЮНІСЕФ у травні 2022 року,
респонденти в постраждалих від конфлікту міських
районах були найбільше занепокоєні проблемами
транспорту і палива, перебоями в постачанні, без-
пекою та обмеженим доступом до продуктів харчу-
вання, медичних і фінансових послуг.
Для визначення безпосерніх загроз, що мають
найбільший прояв у транспортному секторі, скори-
стаємось ще одним звітом. Європейське агентство з
мережевої та інформаційної безпеки (ENISA) впе-
рше провело аналіз по ландшафту кіберзагроз у
транспортному секторі ЄС [8]. Звіт має на меті на-
дати нове розуміння реальності транспортного сек-
тору шляхом картографування та вивчення кіберін-
цидентів з січня 2021 року по жовтень 2022 року.
Він визначає основні загрози, суб'єкти та тенденції
на основі аналізу кібератак, спрямованих на авіа-
ційний, морський, залізничний та автомобільний
транспорт за майже 2 роки.
Розглянемо статистику інцидентів на різні тра-
нспортні сектори. За звітний період проаналізовано
27 інцидентів, спрямованих на авіаційний транс-
порт (28%), 18 інцидентів, спрямованих на морсь-
кий транспорт (18%), 21 інцидент, спрямований на
залізничний транспорт (21%) і 24 інциденти, спря-
мовані на автомобільний транспорт (25%). Також
було включено 8 інцидентів (8%), які стосувалися
транспортного сектору в цілому, або інциденти,
спрямовані проти транспортних міністерств.
Рисунок 3 – Загрози транспортним секторам за звітній період
24 Slovak international scientific journal # 84, (2024)
Протягом звітного періоду спостерігалися на-
ступні види загроз (рис. 4) для транспортної галузі.
В даному випадку, інцидент можна віднести до кі-
лькох категорій загроз, який означає, що загальний
відсоток загроз, показаних на рис. 4, перевищує
100%. Наприклад, вектор атаки для початкового до-
ступу може включати фішингову кампанію, яка по-
тім супроводжується компрометацією за допомо-
гою програми-вимагача. Подібним чином, інциде-
нти, які включали атаку на постачальника, класифі-
кувалися як атаки на ланцюг постачання, так і як
тип атаки, використаний для компрометації.
Рисунок 4 – Основні загрози транспортному сектору (січень 2021 – жовтень 2022)
Розглянемо основні загрози транспортному
сектору.
Програми-вимагачі. Програмне забезпе-
чення-вимагач визначається як тип атаки, під час
якого зловмисники захоплюють контроль над акти-
вами та вимагають викуп в обмін на повернення до-
ступності активу. Інциденти з програмами-вимага-
чами представлені окремо від шкідливих програм,
оскільки вони становлять значну частину виявле-
них інцидентів (38%) протягом звітного періоду, з
кількома резонансними інцидентами, які отримали
широкий розголос.
Загрози, що пов’язані з даними. Джерела да-
них стають об'єктами атак з метою несанкціонова-
ного доступу та розголошення, а також маніпулю-
вання даними для втручання в поведінку систем. Ці
загрози є основою для багатьох інших загроз, які та-
кож розглядаються. Наприклад, програми-вима-
гачі, або DDoS-атаки, мають на меті відмовити в до-
ступі до даних і, можливо, вимагати плату за відно-
влення цього доступу. З технічної точки зору,
загрози для даних в основному можна класифіку-
вати як витоки та порушення даних. Порушення да-
них – це навмисна атака, здійснена кіберзлочинцем
з метою отримання несанкціонованого доступу та
витоку чутливих, конфіденційних або захищених
даних. Витік даних – це подія, яка може призвести
до ненавмисного витоку чутливих, конфіденційних
або захищених даних через, наприклад, неправи-
льні конфігурації, вразливості або людські поми-
лки. У звітному періоді близько 30% спостережува-
них інцидентів були формою загрози для даних тра-
нспортних організацій.
Шкідливе програмне забезпечення. Шкід-
ливе програмне забезпечення – це загальний тер-
мін, який використовується для опису будь-якого
програмного забезпечення або мікропрограми, при-
значеної для виконання несанкціонованих проце-
сів, що негативно впливають на конфіденційність,
цілісність або доступність системи. Традиційно
прикладами шкідливого коду є віруси, хробаки,
троянські програми, шпигунські програми, рекла-
мні програми та інші кодові об'єкти, які вражають
комп'ютер. Протягом звітного періоду 17% інциде-
нтів, спрямованих на транспортний сектор, були
пов'язані зі зловмисним програмним забезпечен-
ням. Відмова в обслуговуванні. Доступність є об'-
єктом безлічі загроз і атак, серед яких виділяється
DDoS-атака. DDoS-атаки націлені на доступність
систем і даних і, хоча не є новою загрозою, відігра-
ють значну роль у ландшафті загроз кібербезпеки
транспортного сектору. Атаки відбуваються, коли
користувачі системи або сервісу не можуть отри-
мати доступ до відповідних даних, послуг або ін-
ших ресурсів. Це може бути досягнуто шляхом ви-
снаження сервісу та його ресурсів або переванта-
ження компонентів мережевої інфраструктури.
Протягом звітного періоду геополітичні події та ак-
тивність хактивістів збільшили кількість DDoS-
атак на транспортні організації, досягнувши 16%
від загальної кількості інцидентів.
Використання вразливостей. Експлуатація
вразливостей – це використання відомих вразливо-
стей або вразливостей нульового дня.
Slovak international scientific journal # 84, (2024) 25
Соціальна інженерія. Соціальна інженерія
охоплює широкий спектр діяльності, яка намага-
ється використати людську помилку або поведінку
людини з метою отримання доступу до інформації
або послуг. Вона використовує різні форми маніпу-
ляцій, щоб змусити жертв припуститися помилки
або передати конфіденційну чи секретну інформа-
цію. У сфері кібербезпеки соціальна інженерія за-
манює користувачів відкривати документи, файли
або електронні листи, відвідувати веб-сайти або на-
давати неавторизованим особам доступ до систем
або послуг. Ця канва загроз складається переважно
з таких векторів: фішинг, спам-фішинг, «китобій»,
«смішинг», «вішинг», компрометація ділової елек-
тронної пошти, шахрайство, видавання себе за іншу
особу та підробка документів. У цьому звітному пе-
ріоді спостерігались переважно фішингові атаки,
спрямовані на користувачів транспорту (10%), а та-
кож інциденти, пов'язані з шахрайством, видаван-
ням себе за іншу особу та підробкою документів
(6%).
Атаки на постачальників і ланцюги поста-
вок. Атака на ланцюг постачання спрямована на ві-
дносини між організаціями та їхніми постачальни-
ками. У цьому звіті використовується визначення,
наведене в ландшафті загроз ENISA для ланцюга
поставок, де атака вважається такою, що містить
компонент ланцюга постачання, якщо вона склада-
ється з комбінації принаймні двох атак. Щоб атаку
можна було класифікувати як атаку на ланцюг пос-
тавок, цілями мають бути як постачальник, так і
клієнт. Схоже, що зловмисники продовжують кори-
стуватись цим джерелом, щоб проводити свої опе-
рації та закріплюватися в організаціях, намагаю-
чись отримати вигоду від широкого впливу та поте-
нційної бази жертв таких атак. У звіті
спостерігались як атаки на ланцюг постачання, як
визначено вище, так і атаки на постачальників, які
призвели до збоїв або збитків суб’єктам у транспо-
ртному секторі (10% від загальної кількості інциде-
нтів). Цей вплив не обов’язково був наслідком вто-
ринної атаки.
Порушення/вторгнення. Порушення/вторг-
нення – це інциденти, коли атака на систему була
підтверджена або оприлюднена, і зловмисники
отримали доступ до системи, але деталі того, як ві-
дбулося порушення або вторгнення, не були розк-
риті.
Інші загрози включають поодинокі випадки
збору облікових даних і підробку геолокації в мор-
ському секторі.
Нарешті, є невеликий відсоток інцидентів,
коли навіть якщо відбулася кібератака, недостатньо
інформації, щоб дозволити класифікувати інци-
дент. Загалом це становить 7% інцидентів (невідо-
мих).
Дані про інциденти, зібрані до жовтня 2022
року, свідчать про збільшення кількості повідом-
лень про атаки з використанням програм-вимагачів
протягом 2022 року (рис. 5). Кількість повідомлень
про ці атаки у транспортному секторі майже подво-
їлася, збільшившись до 25% у 2022 році з 13% у
2021 році. На відміну від програм-вимагачів, у 2022
році спостерігалось зниження кількості інцидентів,
пов'язаних зі шкідливим програмним забезпечен-
ням, порівняно з 2021 роком (з 11% до 6%) [7].
Загрози, пов'язані з даними (зломи, витоки),
зменшилися порівняно з програмами-вимагачами,
але залишаються значними. Атаки, що спостеріга-
лися у 2021 та 2022 роках, були спрямовані на облі-
кові дані, персональні дані співробітників та паса-
жирів, корпоративні дані та інтелектуальну влас-
ність.
У 2022 році спостерігалось збільшення кілько-
сті DDoS-атак, що здебільшого пов'язано з нещода-
вньою активністю хактивістів. Частота цих атак зо-
середжена на конкретних регіонах і залежить від
поточної геополітичної напруженості.
26 Slovak international scientific journal # 84, (2024)
Рисунок 5 – Порівняння частоти загроз для транспортного сектору
Далі розглянемо мотиви, якими керуються зло-
вмисники при здійснені кібератак на транспортні
підприємства (рис. 6). Можливими мотивами є на-
ступні:
- шпигунство, коли метою атаки є збір інфо-
рмації (інтелектуальної власності або інформації
державного значення);
- фінансова вигода, коли за атакою є чітка
грошова вимога, наприклад, вимагання, продаж ви-
крадених даних тощо;
- ідеологічні, коли атака пов'язана з хактиві-
стською діяльністю і є чіткі декларації про мету
атаки з боку суб'єкта;
- порушення роботи, коли атака спрямована
на порушення роботи сервісів, на відміну від випа-
дків, коли це є побічним ефектом атаки.
Рисунок 6 – Мотиви атак на транспортні підприємства
Slovak international scientific journal # 84, (2024) 27
Більше половини інцидентів, зафіксованих у
звітному періоді, були пов'язані з кіберзлочинцями
(55%). Це також пов'язано з мотивацією цих атак,
яка переважно полягає у фінансовій вигоді (38%).
Транспортний сектор вважається прибутковим
бізнесом для кіберзлочинців, оскільки дані клієнтів
розглядаються як товар, а при атаках на транспор-
тні ланцюги поставок – як дуже цінна інформація,
що становить комерційну таємницю. Чверть атак
пов'язана з хактивістськими групами (23%), моти-
вація яких зазвичай пов'язана з геополітичною си-
туацією і спрямована на порушення роботи (20%)
або з ідеологічними мотивами (6%).
Висновки. Таким чином, транспортний сектор
є життєво важливим для економіки та суспільства в
цілому. Кібератака може порушити нормальне фу-
нкціонування міста, регіону чи цілої країни, одно-
часно завдаючи шкоди багатьом галузям промисло-
вості.
Транспортний комплекс входить до списку се-
кторів, що найчастіше піддаються кібератакам зло-
чинців. В Україні відсоток кібератак на транспор-
тну інфраструктуру ще більший, ніж у світі (2% у
світі, 7% в Україні). Зростання загрози значною мі-
рою пов’язано з подіями останніх років.
Аналіз загроз інформаційної безпеки з січня
2021 року по жовтень 2022 року показав, що найча-
стіше транспортний сектор зіштовхується з наступ-
ними видами загроз: програми-вимагачі; загрози,
пов’язані з даними; шкідливе програмне забезпе-
чення; відмова в обслуговуванні; атаки на ланцюги
поставок; порушення/вторгнення; шахрайство; ви-
користання вразливостей. При цьому основними
мотивами порушників є шпигунство, фінансова ви-
года, ідеологічні мотиви та порушення роботи сер-
вісів.
Список літератури
1. Аль-Амморі А.Н., Дехтяр М.М., Іщенко
Р.М., Клочан А.Є. Методи та засоби захисту інфор-
мації. Системи управління, навігації та зв’язку. Збі-
рник наукових праць. 2024. № 1. С. 38-44.
2. Бугайко Д., Харазішвілі Ю., Ляшенко В.,
Квілінський О. Системний підхід до визначення рі-
вня розвитку авіаційного транспорту: індикатори,
рівень, загрози. Журнал європейської економіки.
2021. Том 20, № 1(76). С. 152-190.
3. Євтушевська О.А. Інформаційна безпека як
елемент підвищення ефективності комплексного
контролю підприємств водного транспорту. Зовні-
шня торгівля: економіка, фінанси, право. Науковий
журнал. Серія: Економічні науки. 2015. № 5-6 (82-
83). С. 157-162.
4. Колодяжний В.М., Левтеров А.І., Малащук
Є.В. Кібербезпека автомобілів: історія цифровізації
автомобілів, поточний стан проблеми, цілі сталого
розвитку та стандарти. Вісник ХНАДУ. 2022. Ви-
пуск 96. С. 59-65.
5. Мельник О.М., Волошин А.О., Онищенко
О.А., Щербина О.В., Васалатій Н.В., Нікітюк П.В.
Організація забезпечення інформаційної безпеки
морського судна. Збірник наукових праць Україн-
ського державного університету залізничного тран-
спорту. 2022. Випуск 201. С. 69-78.
6. Трофименко А.О., Майданевич С.Б., Вой-
ченко Т.О., Дорофєєва З.Я. Деякі проблеми питання
впровадження стандартів кібербезпеки на морсь-
кому транспорті. Водний транспорт. 2023. № 1 (37).
С. 179-188.
7. Cyberthreats in the transportation industry
[Електронний ресурс] – Режим доступу до ресурсу:
https://www.ptsecurity.com/ww-en/analytics/cyber-
threats-in-the-transport-sector-2023/.
8. ENISA Transport Threat Landscape [Елект-
ронний ресурс] – Режим доступу до ресурсу:
https://www.enisa.europa.eu/publications/enisa-
transport-threat-landscape.
9. Microsoft Digital Defense Report 2022 [Еле-
ктронний ресурс] – Режим доступу до ресурсу:
https://www.microsoft.com/en-
us/security/business/microsoft-digital-defense-report
2022#tabx9128d5321b074ae784b8e940d6d5fd4eі.
28 Slovak international scientific journal # 84, (2024)
CONSTRUCTION AND ARCHITECTURE
ВДОСКОНАЛЕННЯ ТЕХНОЛОГІЧНИХ РІШЕНЬ ЗВЕДЕННЯ ВЕЛИКОПРОГОНОВИХ
ПОКРИТТІВ ПІДЙОМНИМИ МОДУЛЯМИ
Ігнатенко О.О.
Кандидат технічних наук, докторант каф. Будівельних технологій
Київського національного університету будівництва і архітектури,
Україна
https://orcid.org/0009-0009-7691-884X
IMPROVEMENT OF TECHNOLOGICAL SOLUTIONS FOR ERECTION OF LARGE-SPAN
COATINGS WITH LIFTING MODULES
Ignatenko O.
Candidate of Technical Sciences, doctoral student of the Department of
Construction Technologies of Kyiv National University of Construction and
Architecture, Ukraine
https://orcid.org/0009-0009-7691-884X
DOI: 10.5281/zenodo.11624363
Анотація
В статті описане нове технологічне рішення по зведенню великопрогонових покриттів підйомними
модулями. Опорні ригелі покриття в процесі укрупнення на фундаментах розміщуються в просторі між
спареними колонами несучого каркасу. Переміщення ригелів покриттів на проектну висоту виконують зі
спиранням на стволи підйомних модулів, які підрощуються в міжколонному просторі. Нове рішення доз-
воляє суттєво скоротити об’єми висотних монтажних робіт та загальні строки підйомних робіт.
Abstract
The article describes a new technological solution for erection of large-span coatings by lifting modules.
Support crossbars of coating in process of enlargement on foundations are placed in space between paired columns
of bearing frame. Movement of cross-bars of coatings to design height is performed with resting on trunks of
lifting modules, which are grown in inter-column space. The new solution allows to significantly reduce the vol-
ume of high-altitude installation work and the overall time of lifting work.
Ключові слова: зведення великопрогонових покриттів, підйомні модулів
Keywords: erection of large-span coatings, lifting modules
Актуальність проблеми
Сучасні технології зведення великопрогоно-
вих покриттів промислових та цивільних об’єктів
передбачають попереднє укрупнення блоків пок-
риттів на низьких риштуваннях методами вільного
підйому з використанням самохідних стрілових
кранів [1,c.80 – 62] та наступне примусове перемі-
щення покриттів на проектну висоту методами під-
тягування або виштовхування [2, c.12-14]. Переваги
відомих рішень примусового підйому покриттів ак-
цептуються при розробці нових технологій підйому
з використанням підйомних модулів. Зменшення
об’ємів монтажних висотних робіт та скорочення
загальних строків підйомних робіт з використан-
ням підйомних модулів, є актуальним направлен-
ням вдосконалення технологічних рішень зведення
великопрогонових покриттів.
Аналіз публікацій
Результати вивчення організаційно-технологі-
чних варіантів зведення великопрогонових залізо-
бетонних та металевих покриттів відображені в на-
укових працях українських та закордонних вчених.
Серед українських вчених найбільший вклад в роз-
робку технологій по зведенню конструктивно-тех-
нологічних блоків покриттів з використанням під-
йомних модулів зробили Колесник Л. А. [3], Наза-
ренко В.Ф. [4], Ніжніковський Г.С. [1], Осипов O.Ф.
[2], Ситнік Н.П.[4], Собко Ю.Т. [5], Тонкачеєв Г.М.
[2], , Федоренко П.П.[6], Черненко В.К. [2], Шкро-
мада А.А.[6] . Серед закордонних вчених великий
внесок в розробку науково-теоретичних рішень по
зведенню великопрогонових покриттів промисло-
вих та громадянських об’єктів зробили Fliger K. [7],
Rоwinski L. [7], Kühn E. [8], Rühle H. [8], Orlik G.
[9], Ziólko J. [9].
Мета роботи
На закладі аналізу переваг і недоліків відомих
варіантів зведення великопрогонових покриттів ме-
тодами підтягування або виштовхування, необхі-
дно розробити рішення з використанням механізо-
ваного технологічного обладнання, представленого
підйомними модулями. Згідно з розробленою тех-
нологією, підрощувальні стволи підйомних моду-
лів виштовхують опорні ригелі конструкцій пок-
риттів в просторі між спареними колонами несу-
чого каркасу. Підрощування секцій стволів
підйомних модулів виконують гідравлічні домк-
рати, розташовані на фундаментах між спареними
колонами. Навантаження від ригелів покриття, що
піднімається, почергово сприймають підйомні пло-
Slovak international scientific journal # 84, (2024) 29
щадки , з’єднанні зі штоками гідравлічних домкра-
тів підйомних модулів та ригелі фіксаторів під-
йому, змонтовані на зовнішніх сторонах спарених
колон. Використання розроблених підйомних мо-
дулів дозволяє оптимізувати монтажні процеси по
зведенню покриттів за рахунок суттєвого змен-
шення кількості монтажних операцій та скорочення
тривалості підйому покриттів на проектну висоту.
Виклад основного матеріалу досліджень
Підйом великопрогонового металевого конс-
труктивно-технологічного блоку покриття методом
підтягування був використаний при зведенні пок-
риття цехів авіаційного заводу. Покриття склада-
лось з блоків розмірами 96 х 48м та 96 х 54м і масою
1100 – 1200 т [ 6, c.74 - 76]. Процес підйому пок-
риття методом підтягування та вузол фіксації ри-
геля піднімаємого покриття показані на Рис.1.
Рис.1 Підйом великопрогонового покриття методом підтягування: а – покриття в процесі підйому,
б – вузол фіксації опорного ригеля піднімаємого покриття, 1- блок покриття, 2- стійка ферми пок-
риття, 3 – верхній пояс ферми покриття, 4 – опорний ригель покриття, 5 – колона несучого каркасу,
6 – підйомник ПШ-330, 7 – опора підйомника, 8 – проміжний підйомний упор, 9 – тягова стрічка,
10 – перехідна ланка тягової стрічки, 11 – стропувальна траверса.
Підйом покриття на висоту 34м тривав 10 змін.
Гідропідйомники ПШ-330 були розташовані на
оголовках проектних колон і виконували циклічне
підтягування блоків покриттів за допомогою шар-
нірно-ланцюгової тягової стрічки. Гідропідйомник
тягнучого типу ПШ – 330 складався з двох гідрав-
лічних домкратів ГД – 170 (вантажопідйомність по
170 тон кожний, довжина робочого ходу штоку до-
мкрата 1120мм), двох страхувальних гвинтів, під-
домкратної і наддмократної балок, цільнозвареної
челночної стрічки (довжина 12м), яка з’єднана ни-
жнім кінцем з тяговою стрічкою (в перерізі
600х40мм). Тягова стрічка складалась з шарнірно
з’єднаних ланок довжиною 6м. Тягова стрічка була
шарнірно прикріплена до балки піднімаємого пок-
риття. В якості опорних конструкцій для гідропід-
йомника використовувались колони несучого кар-
касу з проміжними столиками для тимчасового
спирання блоку покриття в процесі переміщення на
проектну висоту. Підйом двох покрівельних блоків
(загальна площа 40000 м2 на висоту 34 м був вико-
наний за 10 змін. [4]. Процес підйому кожного
блоку складався з шістьох повторних циклів. До ко-
жного циклу входили два послідовних етапи – під-
йом блоку покриття на 6м та проміжне спирання
покриття на опорні столики колон. В кожному ци-
клі підйому покриття шість разів підтягувалось до
гори на висоту 1м, яка була відповідна ходу штоків
домкратів та кроку отворів в тяговій стрічці. Під час
підйому покриття в колонах за допомогою ручної
лебідки в міжколонному просторі демонтувались
елементи решітки на ділянці висотою 6м з подаль-
шим монтажем решіток після підйому ригеля пок-
риття. До недоліків справжнього методу монтажу
можна віднести складний монтаж і демонтаж під-
йомного обладнання на значній висоті з утворен-
ням висотних опорних площадок для підйомників
(додатковий розхід опорних металоконструкцій
склав 160т), складне і небезпечне обслуговування
підйомника на висоті 34 м, необхідність утворення
великої кількості проміжних висотних площадок
для демонтажу ланцюгів тягової стрічки по мірі пі-
дйому покриття. До переваг аналізуємого рішення
можна віднести утворення жорсткого поперечного
каркасу з несучих колон та міжколонних балок, ко-
нтроль вертикальності підйомного процесу пок-
риття, який забезпечувався переміщенням опорних
ригелів блоку покриття між спареними несучими
колонами.
Характерним прикладом використання методу
виштовхування зі спиранням ригелів покриття, що
піднімається, на оголовки підрощувальних стволів
підйомників, є зведення покриття цеху авіазаводу
розмірами 144 х 275м. Покриття площею 39600 м2 і
масою 1100т піднімалось на висоту 24 м за 12 змін.
В підрощуванні стволів підйомників були задіяні
гідропідйомники ПГ-300 [5]. Варіант підйому пок-
риття методом виштовхування зі спиранням на ого-
ловки підрощувальних стволів підйомників показа-
ний на Рис.2.
30 Slovak international scientific journal # 84, (2024)
Рис.2 Підйом покриття методом виштовхування зі спиранням ригелів покриття на оголовки підрощува-
льних стволів підйомників: (а) – великопрольотне покриття в процесі підйому, (б) – підйомний модуль
ПГ–300, 1 – покриття, 2 – сегменти ствола підйомника, 3 – підрощенний ствол підйомника,
4 – цілісна проектна колона, 5 – гідравлічні домкрати.
В процесі вертикального переміщення несучі
ригелі покриття спирались на оголовки підрощува-
льних стовпів підйомників. Суцільні проектні ко-
лони буди прикріплені до нижньої поверхні несу-
чих ригелів покриття в період укрупнення велико-
прольотного блоку покриття на низьких
риштуваннях (висота 2,0 м). По мірі підрощування
стовпів підйомників, проектні колони змінювали
положення з нахиленого до вертикального. На заве-
ршальній фазі підрощування стволів підйомників
проектні колони закріплювались в вертикальному
положенні в фундаментних стаканах. На наступ-
ному етапі монтажних робіт на оголовки проектних
колон передавалось навантаження від опорних ри-
гелів покриття. Після цього стволи підйомників де-
монтувались. Враховуючи те, що в процесі підйому
покриття методом підрощування проектні колони
не були задіяні, можна класифікувати підрощу-
ванні стволи підйомників як «підрощувальні мон-
тажні колони». Для остаточної посадки блоків пок-
риття на проектній висоті багаторазово виконувати
цикли «підйом-опускання» в висотних межах 200 –
300 мм з постійним регулюванням місць стику-
вання ригелів окремих блоків покриття. До недолі-
ків технології, що розглядається, можна віднести
складність посадки блоків покриття на оголовки
проектних колон та значна працеємність монтаж-
них процесів на висоті 24м, пов’язаних зі стиков-
кою між собою ригелів піднятих блоків покриття.
До переваг розглянутого варіанту підйому пок-
риття можна віднести відсутність проміжних висо-
тних монтажних площадок в процесі вертикального
переміщення ригелів покриття. Весь процес пі-
дойму покриття був сконцентрований на фундаме-
нтах. В роботах на висоті 24м монтажники були за-
діяні тільки на завершальній фазі при фіксації ого-
ловків проектних колон на нижніх гранях ригелів
покриття та остаточному скріпленні між собою ок-
ремих сегментів покрівельної конструкції.
З урахуванням переваг варіанту підйому пок-
риття методом підтягування, коли проектні спарені
колони, які разом з міжколонними балками та зв’яз-
ками створювали поперечний каркас жорсткості та
виконували функцію направляючих для перемі-
щення в міжколонному просторі спарених колон
опорних ригелів конструкції покриття та методу
виштовхування, коли до переліку верхолазних ро-
біт відносились тільки монтажні роботи по остато-
чній фіксації опорних ригелів покриття на оголов-
ках колон несучого каркасу та концентрація всіх
процесі підрощування колон в зоні фундаментів,
була розроблена нова технологія зведення великоп-
рогонових покриттів з використанням підйомних
модулів.
Згідно з розробленою технологією, перемі-
щення опорних ригелів покриття з рівня укруп-
нення на риштуваннях (висота до 2м) до рівня про-
ектної висоти виконувалось в просторі між спаре-
ними колонами несучого каркасу зі спиранням но
оголовки підрощувальних стволів підйомних моду-
лів. Фази циклу підрощування секцій стволів підйо-
много модуля показані на Рис.3.
Slovak international scientific journal # 84, (2024) 31
Рис.3 Фази циклу підйому покриття зі спиранням на підрощуванні стволи підйомних модулів:
а – сприйняття навантаження від покриття підрощувальним стволом підйомного модуля,
б – виштовхування покриття стволом підйомного модуля, в – передача навантаження від покриття на
фіксатори підйому, 1 – колона каркасу, 2 – напрямний профіль, 3 – ригель покриття, 4 – опорна рама
покриття, 5 – верхня секція ствола підйомника, 6 – консольний виступ секції ствола підйомника,
7 – опорна рама , 8 – ригель фіксатора підйому, 9 – риштування.
Послідовність зведення блоку покриття зі спиранням несучих ригелів покриття на підрощувальні
стволи підйомних модулів показана на Рис. 4.
32 Slovak international scientific journal # 84, (2024)
Рис.4 Послідовність зведення блоку покриття зі спиранням несучих ригелів покриття на підрощувальні
стволи підйомних модулів: а, б – передпідйомний етап, в, г, д – підйомний етап, е – післяпідйомний етап,
1 – колона каркасу, 2 – напрямний профіль, 3 – гідропідйомник, 4 – опорна площадка модуля,
5 – верхня секція ствола підйомника, 6 – ригель покриття, 7 – опорна рама , 8 – ригель фіксатора під-
йому, 9 – риштування.
Процес зведення великопрогонових покриття
зі спиранням на оголовки підрощувальних стволів
підйомних модулів складався з трьох етапів. - Пе-
редпідйомний етап. З використанням самохідних
стрілових кранів встановлюють на фундаменти спа-
рені колони несучого каркасу, на внутрішніх пове-
рхнях колон закріплюють вертикальні напрямні
профілі, в міжколонному просторі на фундаментах
розміщують гідропідйомники та опорні площадки
підйомного модуля, на опорні площадки подають
оголовки підрощувального ствола підйомного мо-
дуля. На торцьових поверхнях колон на висотній
відмітці, нижчий ніж висотна відмітка верхньої по-
верхні оголовків стволів підйомників, закріплюють
ригелі фіксатору підйому. На низьких риштування
(висота до 2м) виконують монтаж конструкцій
блоку покриття. Несучі ригелі покриття, при цьому,
монтують в міжколонному просторі над верхніми
секціями ствола підйомника. Між верхніми секці-
ями стволів підйомників та несучими ригелями по-
криття розміщують опорні рами. Виконують весь
комплекс робіт по монтажу технологічного облад-
нання в покрівельному просторі, по утворенню всіх
паро-, тепло, гідро та зовнішніх фінішних покріве-
льних прошарків., Зібраний на фундаментах вели-
копрогоновий блок покриття 100% готовності може
бути переміщений на проектну висоту.
- Підйомний етап. Подають робочу рідину в
корпуси гідропідйомників підйомного модуля.
Штоки гідропідйомників переміщують верхню сек-
цію ствола підйомного модуля , опорну раму та не-
сучий ригель покриття до рівня вищого, ніж рівень
закріплення ригелів фіксатору підйому. В нижній
Slovak international scientific journal # 84, (2024) 33
частині двох бокових поверхонь оголовка підрощу-
вального ствола підйомного модуля і у всіх подаль-
ших секціях підрощувального ствола підйомника
передбачені опорні консольні виступи. Ригелі фік-
сатору підйому розміщенні на горизонтальних опо-
рних площадках з можливістю переміщення в гори-
зонтальні площині. Горизонтальне переміщення
ригелів фіксатору підйому забезпечують гідроцилі-
ндри, закріплені в торцях площадок. При виштов-
хуванні оголовків ствола підйомника, ригелі фікса-
тору підйому знаходяться в початковому поло-
женні, при якому опорні консольні виступи
оголовків стволів підйомників безперешкодно під-
німаються вище рівня розміщення ригелів фікса-
тору підойма. Після підйому консольних виступів
оголовків ствола підйомника вище рівня ригелів фі-
ксатору підйому, виконують горизонтальне перемі-
щення ригелів фіксатору підйому до моменту, поки
ригелі фіксатору підйому не опиняться під консо-
льними виступами оголовків ствола підйомника.
Наступний крок – опускання оголовків ствола
підйомника до моменту спирання консольних ви-
ступів оголовків стовла підйомника на ригелі фік-
сатору підйому. Після передачі навантаження від
піднімаємого покриття на ригелі фіксатору під-
йому, опорні площадки підйомного модуля перемі-
щують в початкове положення.
На опорні площадки підйомного модуля пода-
ють другу секцію підрощувального ствола. Перемі-
щення другої секції ствола підйомного модуля опо-
рною площадкою підйомника між вертикальними
напрямними профілями виконують до моменту до-
тику верхньою поверхнею другої секції ствола під-
йомника нижньої поверхні оголовка ствола підйом-
ника. При подальшому вертикальному переміщенні
опорних площадок підйомника, навантаження від
піднімаємого покриття передається на підрощува-
льний ствол підйомного модуля. Звільнені від нава-
нтаження, ригелі фіксатору підйому можуть бути
переміщенні в початкове положення. Таким чином
забезпечується безперешкодний підйом консоль-
них виступів другої секції підрощувального ствола
підйомника вище рівня розташування ригелів фік-
сатору підйому. Надалі, після горизонтального пе-
реміщення ригелів фіксатору підйому під консольні
виступи другої секції ствола підйомника, викону-
ють опускання консольних виступів другої секції
ствола підйомників на ригелі фіксатору підйому.
Звільнена від навантаження, опорна площадка під-
йомного модуля може бути перемішена в початкове
положення для підрощування наступних секцій
ствола підйомника.
Процес почергової передачі навантаження від
піднімаємого покриття на підрощувальний ствол
підйомника та ригелі фіксатору підйому продовжу-
ють до моменту досягнення покриттям проектної
висоти. На завершальній фазі підйому остаточне
висотне положення опорних рам покриттів для за-
кріплення на оголовках колон забезпечується, дис-
танційно керованим, мінімальним «підніманням-
опусканням» оголовка підрощенного ствола підйо-
много модуля . - Післяпідйомний етап. Після закрі-
плення опорних рам покриття на оголовках колон
виконують демонтаж секцій ствола підйомного мо-
дуля. В процесі опускання секцій ствола підйом-
ного модуля навантаження від демонтуємих секцій
почергово сприймають ригелі фіксатору підйому та
опорні площадки підйомних модулів.
При використанні пропонуємого підйомного
модуля процеси підрощування секцій стволів під-
йомників сконцентровані на рівні фундаментів, на-
вантаження від ригелів покриття, що піднімається,
передається на фундаментну плиту через гідропід-
йомники або через колони, на яких в нижньому ви-
сотному рівні закріплені горизонтальні площадки
ригелів фіксаторів підйому. Всі процеси по підро-
щуванню секцій стволів підйомників виконуються
в автоматичному режимі. Керування процесами пі-
дйому виконують оператори, командний пункт
яких розташований за межами зони монтажних ро-
біт.
Висновки
- на закладі аналізу відомих варіантів підйому
великопрогонових покриттів методами виштовху-
вання та підтягування був визначений напрямок
вдосконалення організаційно-технологічних і конс-
труктивно-технічних рішень, а саме, утворення не-
сучого каркасу в одному монтажно-технологічному
етапі з укрупненням покриттів в конструктивно-те-
хнологічний блок на низьких риштуваннях (висота
до 2м), забезпечення вертикальності підйому пок-
риття за рахунок переміщення опорних покрівель-
них ригелів між спареними несучими колонами зі
спиранням на оголовки підрощувальних стволів пі-
дйомних модулів, вертикальність переміщення під-
рощувальних секцій стволів підйомників забезпе-
чується напрямними вертикальними профілями, за-
кріпленими на внутрішніх поверхнях спарених
колон;
- зменшення процесів, в яких задіяні монтаж-
ники під час підйому конструктивно-технологіч-
ного блоку покриття, до операцій по фіксації опор-
них ригелів покриття на оголовках проектних ко-
лон на завершальній фазі підйому;
Список літератури
1. Нижниковский Г.С, Гуревич Э.И., Ланда
С.Л. и др. Крупноблочный монтаж промышленных
зданий и сооружений: Киев, Будівельник, 1979,
256с.
2.Черненко В.К., Осипов О.Ф., Тонкачеєв Г.М.,
Назаренко І.І. Технологія монтажу будівельних
конструкцій. За редакцією Черненко В.К., Київ,
Будівельник, 2011, 374 с.
3. Колесник Л. А., Шнайдер А. И., Черненко
B.К. и др. Крупноблочный монтаж строительных
конструкций: Киев, Будівельник, 1990, 320 с.
4. Назаренко В.Ф., Сытник Н.П., Николаев
В.В., Гидроподъемные установки на монтаже боль-
шепролетных конструкций: Киев, Монтажные и
специальные работы в строительстве. Научно-прак-
тический журнал. 1986, №5, С.15-20.
5. Черненко В.К., Собко Ю.Т. Дослідження ос-
новних технологічних показників, що впливають на
34 Slovak international scientific journal # 84, (2024)
безкранові методи піднімання структурних покрит-
тів: Київ, Нові технології в будівництві. Науково-
технічний журнал. 2016, №36, С.50 – 55.
6. Федоренко П.П., Шкромада А.А. Индустри-
альные методы строительства промышленных
предприятий: Киев, Будівельник, 1988, 200 с.
7. Fligier, K., Rowinski, L. (1977). Montaz zin-
tegrowanych konstrukcji budowlanych. Warszawa:
Pansnwowe wydawnictwo naukowe, 128.
8. Rühle, H., Kühn, E., Weissbach, K. (1978).
Priestorové strešné konštrukcie. Bratislava: Vyda-
vateľstvo ALFA, 328.
9. Ziólko, J., Orlik, G. (1980). Montaž konstrukcjí
stalowych. Warszawa: Arcady
Slovak international scientific journal # 84, (2024) 35
AZƏRBAYCAN İNCƏSƏNƏTİNDƏ QƏDİM AYİNLƏRİN ƏKSİ
Səlimova A.T.
fəlsəfə doktoru , dosent AzMİU (Azərbaycan)
REFLECTION OF ANCIENT CULTS IN AZERBAIJANI ART
Salimova A.
PhD, Dosent, AzUAC (Azerbaijan)
DOI: 10.5281/zenodo.11624380
Xülasə
Əcdadlarımızın təfəkküründə bizdən gizlənən arxetipin məntiqi ən bariz şəkildə dekorativ-tətbiqi sənətdə və
memarlıqda özünü göstərirdi. Cənnət və Yer rəmzləri mədəniyyət aləminə üzvi şəkildə toxunmuşdur - insan səmaya
baxmaqla məkanı və vaxtı ölçməyi öyrənmişdir. Əvvəlcə həndəsi simvolizmdə ifadə olunan mənəvi prosesin mahiy-
yəti və məqsədi simvolik və tətbiqi funksiyaları yerinə yetirən çoxsaylı variasiyalara səbəb olmuşdur.
Abstract
The concealed logic of archetypal thought among our ancestors is most vividly manifested in decorative arts
and architecture. Symbols of the Sky and Earth are organically woven into the cultural world—by observing the
sky, humanity learned to measure space and time. The essence and purpose of the spiritual process, initially ex-
pressed through geometric symbolism, gave rise to numerous variations that serve both symbolic and practical
functions.
Açar sözlər: Azərbaycan, Göy Tanrı, "babil" işarəsi, kult, kainatın üç hissəli şəkli.
Keywords: Azerbaijan, Gok Tanry, "Babylon" symbol, cult, tripartite cosmology.
Bu günə qədər gəlib çatmış ayin və mərasimlər
bəşər mədəniyyətinin nadir təbəqəsini təmsil edir. Son
onilliklərdə əcdadlarımızın müqəddəs həyatı mövzusu
xüsusi aktuallıq qazanmışdır. Bu, əsasən yeni arxeoloji
materialların və tədqiqatların ortaya çıxması ilə
bağlıdır. Göy Tanrıya inam göylə yerin birliyi haqqında
qədim fikirlərdən qaynaqlanır. Qədim insanın dünya
mənzərəsi kainatla sıx qarşılıqlı əlaqədən for-
malaşmışdır. Belə ki, onu əhatə edən mikrokosmosda
makrokosmik münasibətləri təqlid edən strukturları ye-
nidən yaratması təəccüblü deyil. İncəsənət əvvəlcə
sinestetik xüsusiyyətlərə malik idi - onun növlərinin hər
biri sinesteziya ilə xarakterizə olunur. Sinesteziya
sayəsində incəsənətdə vahid bədii məkan anlayışının
universallığını və qarşılıqlı təsir göstərən sənətlərin
problemini izah etmək mümkündür.
Hər bir fərdi sənət forması özünəməxsus xüsusiy-
yətlərə malik olan öz sinestetik bütövlüyünü for-
malaşdırır. Belə simvolik elementlərə "Babil" işarəsi -
bir-birinin içərisində çəkilmiş bir neçə düzbucaqlı təs-
viri daxildir. Kiçik Asiyada neolit dövründə belə bir
simvol Yerin əlaməti idi: "onun mərkəzini təcəssüm
etdirən müqəddəs bir dağın timsalında" [12, s. 131].
“Babil” təsviri Azərbaycan, Türkiyə, İran, Şimali
Qafqaz, Dağıstan, Bolqarıstan ərazisində tapılıb. O,
ziqqurat və ya piramida planına bənzəyir [12, s. 131].
Mifoloji olaraq Kainat üç mərtəbə ilə təmsil olunurdu -
Cənnət, Yer, Cəhənnəm, bir-birilərinə mərkəzi ox ilə
bağlıdırlar. Üç kosmik sferanın vəhdətini və əlaqəsini
ifadə edən simvolizm çox mürəkkəb və ziddiyyətlidir
ki, bu da onun min illər ərzində dəyişdirilməsi və za-
man keçdikcə sonrakı kosmik simvolizmlərə
çevrilməsi ilə izah olunur. H.Heyrman hesab edir ki,
sinesteziya sənətin bütün növlərində özünü biruzə
verir, çünki sinesteziya “mənanın psixoloji vahidi” va-
sitəsilə sənəti birləşdirən vasitədir. Sinesteziya ümumi
cəhətlərə və analogiyalara, eləcə də metaforalara işarə
edə bilər [34]. K.Yunqun fikrincə, ilkin mifoloji
obrazlar - arxetiplər düşünülmədən yaradılırdı, mənaca
bənzər idi, bir-biri ilə əlaqəsi olmayan mifologiyalarda
rast gəlinirdi, bu da, onların bir-birindən köçürülməsi
izahını inkar edir. [20, s.110]. Qeyd etmək lazımdır ki,
Almaniyada “Babil” dedikdə Ağ dəniz bölgəsinin
labirintləri daş halqalı kurqanlar nəzərdə tutulur. [12,
s.131]. Azərbaycan, Dağıstan və Şərqi Avropadakı
“Babillər”in təsvirlərini müqayisə edən Ariel Qolanın
fikrincə, Qobustan variantı ən qədimdir. [12, s.131].
Bundan əlavə, Qala (Abşeron) kəndində mərkəzi altı
çəkilmiş üç kvadratın təsviri aşkar edilmişdir (daş
üzərindəYekəxana kəndində, Göyçay rayonu) və s.
Həmçinin Muğla (Türkiyə) ərazisində qayalarda,
Batmandan (Türkiyə) qəbir daşlarında, Çara Təpə
(İran) qayalarında da rast gəlinir.
Gəmiqaya (Naxçıvan, Azərbaycan) petroqlifləri
arasında araba, yaşayış tikililəri, Babillərin təsvirləri
kimi şərh edilə bilən düzbucaqlı təsvirlər vardır. Ən
maraqlısı Gəmiqaya 498 daşı üzərində üç həkk
olunmuş düzbucaqlının təsviridir (ümumiyyətlə,
burada xronoloji diapazon eramızdan əvvəl IV
minilliyin sonu - I minilliyin əvvəlləri daxil olmaqla -
Tunc və Erkən Dəmir dövrlərini əhatə edir). Oxşar
təsvirlər Çatal Höyükda var və yaşayış binalarin
planina bənzəyir [26, s.35].
36 Slovak international scientific journal # 84, (2024)
1. 2. 3. 4.
1-4. Çatal Höyük
Bəzi tədqiqatçılar “Babillər” təsvirlərinin
labirintlərlə əlaqəli olduğunu düşünürlər [7, s. 21-23].
Tamamilə mümkündür ki, “Babil” semantik cəhətdən
Azərbaycanın və Dağıstanın maddi mədəniyyət
abidələrində təsvirinə tez-tez rast gəlinən labirintlə
bağlıdır. Həm "labirint", həm də "Babil" simvolunun
"yeraltı dünya tanrısı" qala evinin təsviri olduğuna dair
bir fikir var. [12, s. 132]. Başqa bir versiyaya görə,
Babillər – qədim memarların binaları işarələmək üçün
istifadə etdikləri cizgilərdir. Beləliklə, Rıbakovun
fikrincə, “Babillər”in həndəsi quruluşu qızıl bölgünün
ahəngdar hissələrini ehtiva edir və yəqin ki, tikinti işləri
zamanı mütənasiblik aləti kimi istifadə edilmişdir. Eyni
fikrə Bolqarıstan memarlığının tədqiqatçıları G.M.
Davletşin və F.Ş. Xuzin də gəlmişlər [13, 26, s. 34].
1. 2. 3. 4.
Petroqliflər. 1. Qobustan. Böyükdaş. Daş-23 (İ.Cəfərzadə, 1973-cü il); 2. Abşeron, Qala kəndi;
3. daş, Yekyaxana kəndi, Göyçay rayonu; 4. Xəlil Baba məqbərəsi, Siyəzən rayonu [26, s. 34]
1. 2. 3. 4.
1-3. Boşqablar, Hacılar kəndi.e.ə. 6000-ci il, Anadolu Sivilizasiyası Muzeyi, Ankara (Türkiyə);
4. Xanlar, Azərbaycan, Tunc dövrü
Dunay Bolqarıstanında məşhur zadəgan Mostiçin
(X əsrin ortaları) qəbir daşında və Pliskada qədim
daşlardan birində “Babil” kvadratı (7-ci əsrin sonu-IX
əsrlər) təsvir edilmişdir [13]. Dağıstanda "babillər"
qayalarda və yaşayış binalarında olur, hətta cüzi
dəyişikliklə onlar oyunlar üçün istifadə olunur; [5].
Şolde-Teyada (Tıva, Rusiya) yerin səthində cığırlarla
hissələrə bölünmüş şaquli yerləşdirilmiş kiçik
daşlardan ibarət müntəzəm düzbucaqlı aşkar
edilmişdir. Onun şimal-şərqdəki xəttinin ucu dairə-
"ruhlar evi" kimi təsvir edilir [18, s. 46; 19, 77-109; 14
, s. 32]. Muğur-Sarqol və Aldı-Mozaqada (Tuva,
Rusiya) daxili xətlərlə bir neçə hissəyə bölünmüş
düzbucaqlılar şəklində çoxsaylı həndəsi fiqurlar
məlumdur [19, s. 77-109] . Bu təsvirləri nəzərdən
keçirən M.Kilunovskaya onları ev kimi təsəvvür edir:
“yaşayış yeri” və ya “ruhların məskənləri”: Orta
Asiyada Son Tunc dövründə geniş yayılmış daş tikililər
kontekstində olan “Yaşayış yerləri”-içərisi xətlərlə və
ya, nöqtələrlə doldurulmuş düzbucaqlı həndəsi
fiqurlardır. [18, s. 46]. Eramızdan əvvəl 6-cı
minillikdən 1-ci minilliyə qədər inkişaf edən əkinçilik
və heyvandarlıq dövrünün qədim yaşayış
məskənlərinin memarlığına xüsusi diqqət yetirmək
istərdim. Azərbaycan ərazisində tapılan bu dövrə xas
(Kül-təpə, e.ə. V-IV min, Naxçıvan; Şomu-təpə, e.ə. VI
- V min, Qazax vilayəti) [8, s.14] təsvirlər Qobustan və
Gəmiqaya petroqliflərindəki təsvirlərə bənzəyir.
D.A.Axundov Qobustan qayalarındakı təsvirlərin
qədim kəndlərin (Şomu-təpə, Toyrə-təpə) plan həllərilə
oxşarlığını da vurğulayıb. [8, s. 15-30] .
1. 2. 3. 4.
1,2. Qobustan, petroglif; 3,4. Qobustan qayalarında yaşayış binalarının görüntüləri
(D.A. Axundovun rekonstruksiyası [9])
Slovak international scientific journal # 84, (2024) 37
1. 2. 3. 4.
1. Muğla. Türk gaya resimleri 2. Alıçlı. Batman Kozluk mahalı; 3-4.
Qəbir daşı. Meşkin. Ərdəbil (İran Azərbaycanı)
Qeyd etmək lazımdır ki, “Babillər”in təsvirləri
əsasən ziqquratın planı ilə eynidir. Mesopotamiyada
ziqqurat dünyanın mərkəzində dayanan müqəddəs
dağın reproduksiyası idi, yəni “yerin göbəyi”. Ziqqurat
göylə yer arasında əlaqə idi [24]. Ziqquratlar İraqda
(Borsippa, Babil, Dur-Şarrukində - e.ə. I minillik) və
İranda (Çoqa-Zənbil, 2-ci minillik) qorunub
saxlanılmışdır. Maraqlı təsvirləri Təpə-Sialkdan (e.ə.
3000-ci il; Kaşan, İran) tapılmış polixrom keramika
üzərində də görmək olar. Fars mifologiyasında Varanın
səhabələrinin məskəni kvadrat formasındadır; bu təsvir
əsasən zahirində xaos və ölümlə dolu olan bir dünya ilə
ziddiyyət təşkil edən daxili kvadrat ideyasını əks
etdirir. Bu kompozisiyaya ən çox Şirvan-Quba
məktəbinin xalçalarında rast gəlinir.
1. 2. 3.
Dashly-3. e.ə. XVII əsr. Əfqanıstan [36]
Daşlı-3 xüsusi diqqətə layiqdir. e.ə e. Arxeoloqlar
arasında onun məqsədi ilə bağlı fikir birliyi yoxdur.
Daşlı-3 yaşayış məskəni bir neçə əsrlər boyu mövcud
olub, 600 nəfərə qədər yerləşə bilən 130 x 150 m ərazini
tutub. Maraqlı faktlar, məsələn: dairəvi plan, dolama
dəhliz, binanın xarici perimetri boyunca doqquz
“qüllə”-nin təşkili, adətən məbədlərə xas olan bir kult
fokusunun olması.
Bəzi təsvirlərin simvolu digər bir semantik par-
aleli xatırladır - mandala simvollarını. Burada
Azərbaycan xalça sənətinin ornament xüsusiyyətlərini
nəzərə alaraq, əsas semantik elementi - “gölləri” qeyd
etmək olar ki, bu da, Orta Asiya və Türkiyə xalçalarına
aiddir. Türk xalçalarının göllərində dərin kosmik mən-
alar var. Azərbaycan incəsənəti abidələrinin həndəsi
bəzəyində də göllər şərh edilmişdir. Qeyd edək ki,
Quba (Azərbaycan) toxucuları medalyonları – orta
ölçülü gölləri “çarhovuz” (hovuz), onun üzərində yer-
ləşən elementləri “ordək” adlandırırlar. [17]. Bu
təəccüblü deyil, çünki mifoloji Göy Tanrısının iradəsi
ilə “insan oğullarının” məskunlaşdığı yerin -Orta
Tenqri dünyasının əsas tanrısı “Müqəddəs Torpaq-Su”
hesab olunurdu. [10]. Həmçinin Azərbaycanda tunc
dövründən qalmış məşhur zərgərlik məmulatları - Ayın
təsviri ilə bağlı iç-içə üç dairəvi elementi olan həmayil-
boyunbağı və ya, çevrələr - mərkəzi aydın şəkildə
görünərək üç dairə ilə əhatə olunmuş təsvirlər də
maraqlıdır. Oxşar bəzəklər Sarmato-Alanda da geniş
yayılmışdır. Qədim iranlılar arasında yeri üç dəfə
genişləndirən günəş qəhrəmanı Yimanın əfsanəsinə
uyğun olaraq müqəddəs məkanı təşkil etmək üçün üç
konsentrik dairədən istifadə edilirdi.
1. 2. 3. 4. 5.
1,2,3. Dekorativ boyunbağılar [30]. Nərgizava (Azərbaycan); 4-5.
Qəbir daşı, Kəngəmiran kəndi, Azərbaycan (Lerik rayonu)
Bənzər bir kompozisiyanı Arkaimin memarlığında
(Orta Tunc III-II min e.ə.) görürük. [6]. Göbəkli - Təpə
də (Türkiyə) demək olar ki, eyni plana malikdir. Oxşar
ənənə Kiçik Asiya mənşəli Etrusk məbədində də var -
müqəddəs məkanın bütün hissələrinin ibadətgahın
üfüqi müstəviyə proyeksiyası kimi qəbul edilən və
Kainatın şaquli oxu ilə birləşdirilmiş üç dairəvi pillədən
- göy, yer və yeraltı dünyadan ibarət ideal məbəd. [11,
s. 58]. Oxşar kompozisiya quruluşu tarixi İslam
şəhərlərinin təməlində dayanır, harada ki, inkişaf
müqəddəs mərkəzdən periferiyaya – ibadətgah mərkəzi
olan qala, yaxud içəri şəhərdən xaricə doğru gedirdi.
Belə bir kompozisiyanın kökləri həm də mənəvi
dünyanın üçlüyünü əks etdirən Göy Tanrı anlayışının
ifadəsi sayıla bilər. Tenqrizm eyni zamanda Kainatın üç
zonasına vurğu ilə xarakterizə olunur: səmavi, yerüstü
və yeraltı [31]. Səmavi dünya “üç, doqquz və ya, daha
çox üfüqi pillələrdən ibarət idi, onların hər biri bir
tanrının məskəni idi; sonuncu pillə Səmanın Böyük
Ruhuna - Göy Tanrısına aid idi" [31]. Səmada atlara
minən insanlara qarşı yüngül və xeyirxah tanrılar və
ruhlar var idi, buna görə də atlar onlara qurban verilirdi.
[31]. Heyvandarlıqla bağlı iş, təbiətin ilahiləşdirilmiş
qüvvələrinə sitayiş və əcdadların ayinlərilə əlaqəsi olan
təbii ritmlərdən asılı (vaxt, fəsillərin ardıcıl dəyişməsi
və səma cisimlərinin hərəkəti) bütün rituallar,
mərasimlər, bayramlar birbaşa və ya, dolayı yolla
həyatın uzadılmasına yönəldilmişdi [31].
38 Slovak international scientific journal # 84, (2024)
1. 2. 3.
1,2. Yallı. Qobustan petroqlifi (Apşeron, Azərbaycan); 3. Zərövşən. Tacikistan. Tunc dövrü
Bir çox qədim xalqlar arxaik "dairəvi rəqsləri" -
qoruyub saxlayıblar: deyə bilərik ki, onlar meditasi-
yanın xüsusi formalarına əsaslanır. Bütün dünyada
ibtidai ritualların əsasında səmavi simvolizm və səmavi
gücə inam dayanır: odun, qurbangah və ya büt ətrafında
dairəvi rəqslər və yurdların, çadırların dairəvi forma-
ları; fırlanan şamanlar; meqalitik işarə və strukturların
dairəvi quruluşu. Şübhəsiz ki, “dairəvi rəqslər” ilə göy
cisimlərinin Günəş ətrafında hərəkəti ilə səma tanrısına
– “Göy Tanrı”ya pərəstiş arasında əlaqə var. Bu cür
“sirlər” ali dini biliklərin mövcudluğunu, eləcə də vəcd
halında yenilənməni – bir tərəfdən paklaşmanı, kəffarə
qurbanlarını nəzərdə tuturdu; yürüşlər, mahnılar,
rəqslər və ekstazın müxtəlif təzahürləri isə simvolizm
və alleqoriya elementləri ilə sirlərin əsas məzmununu
təşkil edirdi. Qədim Yunanıstanın bir çox müəmmaları
hələ də öz sirlərini qoruyub saxlayır. Qədim yunanlar
yay gündönümündə bir sıra rəqqasların ilan kimi
qıvrıldığı "od" rəqsi ifa edirdilər. [12, s. 31].
Qurbangahın ətrafında dairəvi ritual hərəkətlər də
zərdüştilərin ənənəvi rituallarına daxil idi [4, s. 56-57].
Svan mədəniyyətində üç pilləli dairəvi rəqs var: “on iki
rəqs edən adamdan ibarət dairədən formalaşıb, hər biri
iştirakçını qabaqda kəmərdən tutur; dairəvi rəqsin
ikinci pilləsi birincinin çiyinlərinə, üçüncü pilləsi
ikincinin çiyinlərinə söykənir. [29, s. 101]. Bir çox
xalqların mədəniyyətində qorunub saxlanılan arxaik
dairəvi rəqslər indi də şənliklər zamanı keçirilir. Xüsusi
qrupa türk xalqlarının kollektiv rəqsləri daxil
edilməlidir - bunlara Orta Asiya, Sibir və Anadolu
xalqları daxildir. Bu gün də geniş yayılan Azərbaycan
milli rəqsi “Yallı”nın tarixi çoxəsrlik tarixə malikdir.
Qobustanda mezolit dövrünə (e.ə. 8-ci minillik) aid
olan, rəqs edən insanları təsvir edən petroqliflər buna
sübutdur. Gəmiqayanın (Kəlbəcər rayonu, Azərbaycan)
görüntüləri arasında kollektiv rəqs səhnələri də qeydə
alınıb [3, s. 175]. Maraqlıdır ki, Naxçıvandan
götürülmüş tunc dövrü keramika məmulatlarında da
rəqs edən insanları təsvir edən kompozisiyalara rast
gəlinir. [3, s. 35]. A.Ələkbərova “yallı”nı ritual hesab
edir, rəqsin bütün hərəkət və ritmləri öz orijinal
formasında qorunub saxlanılıb, burada əsas qüvvə
ritmdədir. [2, s. 10-11]. Bir qayda olaraq, Azərbaycan
rəqsi üç hissədən ibarətdir: birinci hissə dairəvi hərəkət,
ikinci hissə yerində lirik dönmə (süzmə) və üçüncü
hissədə yenidən dairəvi hərəkət, lakin daha sürətli və
daha çox təntənəli şəkildə.
Dairəvi ritual rəqslər səs ritmi ilə müşayiət olunur
- bura əl çalmaq, ayaqları ştamplamaq, insan səsi,
həmçinin müxtəlif zərb alətlərindən istifadə daxildir.
Musiqi müşayiəti çox ritmikdir, getdikcə daha sürətli
olur. Yallı rəqsi sürətli temp və ritmlə səciyyələnir:
yavaş ritmlə başlayır və temp tədricən artır.
Qobustanlılar ayinlərin rəqsi zamanı Qobustan
ərazisində Cingirdağ dağının ətəyində və Böyükdaş
dağında yerləşən “qavaldaş” daşından istifadə edirdilər.
Xalq arasında Cingir-baba adlanan Cingirdağ dağı 19-
cu əsrin əvvəllərinə qədər ziyarətgah idi. Alimlərin
fikrincə, qavaldaş insanlara yuxarı paleolitdən
məlumdur. Qaval daşı nəhəng əhəng daşıdır - onu
ritmik vurmaqla aydın motivli mahnılar çalmaq olur.
Zərbənin vurulduğu sahədən asılı olaraq üç rezonansda
müxtəlif yüksəklikli səs yaranır [1, s. 33].
Dairəvi rəqslər dünya dinləri yaranandan sonra da
öz simvolikasını saxlamışdır. Belə ki, sufilərin ritual
rəqsi ulduzların hərəkətini təkrarlayır, Kainatın
simvolik quruluşuna əsaslanır və “Allahı dərk etmək
yolunu” təmsil edir. [4, s. 56-57]. Sufi dərvişlərinin
rəqsi öz oxu ətrafında fırlananların özlərini Allaha
yaxınlaşdırdıqları düşüncədir. Yenə də rəqs nağara,
fleyta və qavalın müşayiəti ilə təmsil olunur. Onu da
qeyd etmək lazımdır ki, bu mənəvi təcrübənin bütün
bədənin sağalmasına müsbət təsiri vardır. Ritual dairəvi
rəqsləri öyrənərkən, rəqs hərəkətinin gedişatına diqqət
yetirə bilərsiniz - burada konsentrik və spiralvari
elementlərdən istifadə edilir. Bu, həm bir nöqtə
(rəqqas), həm də vahid mərkəz ətrafında hərəkətin
sintezində özünü göstərir. Prosesin qurulması prinsipi
cisimlərin dairəvi hərəkətilə təcəssüm olunan atəşə
qarşı ayinlərlə bağlı arxetipik obrazları özündə əks
etdirən dinamikadadır - əsas parametrlərə görə onlar
“təsəvvüf” və “şiə”liyin yeddi pilləli” ucaltma ritualları
ilə üst-üstə düşür [29, s. 78] .
1. 2.
Qafqaz Albaniyasının mərkəzi günbəzli kilsələri. Kilisadağ ( II - III əsrlər, Kabala rayonu)
və Mamrux məbədləri ( III - IV əsrlər, Kutkaşenski rayonu)
Kainatın mənzərəsini çoxmərhələli quruluş
şəklində nəzərə alan əcdadlarımız öz dini-memorial
strukturlarını pilləli formalarda yaratmışlar. Şərq
memarlığını təhlil etdikdə, bu ideyaya mütənasib
kromlexləri, Sasani İranının dörd sütunlu od
məbədlərini, son antik Şərq və erkən xristian
Slovak international scientific journal # 84, (2024) 39
memarlığının memorial sallaxlarını, eləcə də Şimali və
Cənubi Azərbaycanın müqəddəs atəşə ehtiram edilən
çoxsaylı mərkəzi ibadətgahlarını qeyd etmək olar.
Onların tərkibi çoxpilləli qüllə quruluşuna malikdir,
çox vaxt günbəzlə vurğulanıb. Kainat sisteminin məkan
qavrayışı məbəd məkanlarının şaquli inkişafına və
üfüqi dərinliyinə təsir etdi. Qafqaz Albaniyasındakı
(Azərbaycan) mərkəzi günbəzli, pilləli Xristian
kilsələrini təhlil edərkən – burada aşağı səthinin dairəvi
yerləşmiş oyuqlardan, yuxarı səthinin isə binanın
mərkəzinə doğru yüksələn və zirvəsində günbəz
qoyulmuşdur konstruksiyasına rast gəlirik [27, s. 12-
14]. Onları şaquli bölgü kompozisiyalarındakı zamanın
müntəzəm cəhətini əks etdirən vahid mərkəzə doğru
yönəlmiş “zaman və məkan quruluşu ideyası” əsasında
bərpa etmək olar.
Bu cür mərkəzlilik, konsentriklik və ritmiklik
sistemi ən qədim arxaik musiqi forması sayılan –
muğamatda (dəstgah) da özünü göstərir. Azərbaycan
muğamı öz quruluşunda özünəməxsus dramaturgiyaya
malik bütöv bir kompozisiyadır - giriş, işlənmiş süjet
xətti, kulminasiya nöqtəsi və yekun [29, s. 13].
Muğamın quruluşu ilkin səs tonlarınadönüş edərək,
getdikcə səs axınının yuxarıya doğru dairəvi hərəkətini
xatırladır [29, s. 42]. Tədqiqatçıların fikrincə:
“Muğam-dəstgah kompozisiyasında konstantlıq “yeddi
pillə”nin ritmik formuluna və modallıq prinsipinə
çevrilən daxili prosesin dinamikası ilə ifadə olunur”
[29, s. 52]. Azərbaycan muğamı türk taksimləri, İran
dəstgahları, uyğur muğamları, özbək-tacik
şaşmaqamları, ərəb maqomları, hind raqaları və s. kimi
şərq musiqi ənənələri ilə ümumi kompozisiya
xüsusiyyətlərinə malikdir. Kosmik ayin hərəkətləri
təkamül nəticəsində muğamı ritmik piramidal
konsepsiyaya çatdırmışdır. Məhz mənəvi yüksəlişin
ritmik təşkilatında - ucalığa doğru gedişatında ritual
təcrübə, ayin formaları, miflərin, əfsanələrin, bir sözlə,
nəsillərdən miras qalan bütün mənəvi sərvətlərin zaman
keçdikcə muğam-dəsgahında saflaşaraq təməlli
formaya çevrilməsi məsələsi durur [29, s. 74].
Azərbaycan xalq musiqisinin əsasını təşkil edən ladlar
beş növ tetrakordun birləşməsindən formalaşmışdır.
[32, s. 15-17]. Fərhadova S.M. hesab edir ki, “Muğam,
ilk növbədə, mənəvi prosesdir, xalqın təfəkkürünü
formalaşdırıb, dinamikasını qoruyan aparıcı bir
qüvvədir” [29, s. 16]; musiqi vasitəsilə düşüncə
prosesinin universallığının və konseptuallığının
təzahürüdür [29, s. 17]. R.Zöhrabovun fikrincə:
Azərbaycan “muğamları maddi-mənəvi
mədəniyyətimizin ən qiymətli abidəsidir” [16, s. 69].
Kompozisiyanın mərkəzdən çiçəklənməsinin
universal prinsipini muğamın bütün səviyyələrində tək
seqmentdən - ritm-intonasiyasından tutmuş bütövlükdə
formaya qədər izləmək olar [29, s. 52]. Dairə içində
dairə, kvadrat içində kvadrat, açılan spiral kimi həndəsi
şəkildə ifadə edilən mənəvi prosesin simvolik obrazları
xalqımızın mədəniyyətində özünü göstərən vahid
semantik nüvənin böyüməsi konsepsiyasını ehtiva edir
və gördüyümüz kimi, mədəniyyətimiz dünya nizamının
kosmik qavrayışı olan “dairələr nəzəriyyəsi”nə
əsaslanır. Ritmik dairələr nəzəriyyəsi orta əsrlər musiqi
elminin əsasını təşkil edir. Nəzəriyyəçi və bəstəkar
Səfiəddin Urməvi (təxminən 1217-1294) “Kitab-ül-
ədvar” əsərində də musiqinin ilk növbədə ritmik
şəkildə təşkil olunmuş kosmik proses olduğunu qeyd
etmişdir: “Uca Allah göyləri yaradaraq, fırlanmalarını
əmr etdi. Səslər onların fırlanmasından yaranır və bu
səslərə “mənəvi melodiyalar” deyilir [29 , s. 63].
1. 2. 3. 4. 5. 6. 7.
1.2. Şəbəkə və ornament, Şəki Xan sarayı, Azərbaycan . 3.4. Urmiya, Güney Azərbaycan, 5, 6 .
Şirvan xalçası, Azərbaycan; 7. Quba Xalçası (Azərbaycan)
Qobustanda təsvir olunan "Babil" işarəsi ən qədim
hesab olunur. Qədim yaşayış məskənlərinin (Kül-tepe,
Şomu-tepe, Azərbaycan) memarlığı Qobustan
(Azərbaycan) və Gəmiqaya (Azərbaycan)
petroqliflərindəki təsvirlərə bənzəyir [26, s. 36]. Tunc
dövrünün mənəvi aləminin üçqatlığını əks etdirən maraqlı
zərgərlik əşyaları var. "Babil" simvolu, konsentrik dairələr
kult memarlığında və şəhərsalmada, həmçinin qəbir daşları
və ornament şəklində tapılır. Əvvəlcə həndəsi simvolizmdə
ifadə olunan ruhani prosesin mahiyyəti və məqsədi (bir
cadugərın və ya şamanın şəxsində enerji mərkəzi ilə ritual
dairəvi rəqsi, eləcə də bir şamanın qavalı kimi) yalnız
simvolik deyil, həm də tətbiq olunan funksiyaları yerinə
yetirən çoxsaylı dəyişikliklərə səbəb oldu [26, s. 36]
“Babil” simvolu və konsentrik dairələrə dini
memarlıqda və şəhərsalmada, qəbir daşları üzərində və
ornamental sənətdə rast gəlinir. Bu simvollar müxtəlif
ərazilərdə eyni dövrdə yaranmış və nəsillərin
yaddaşında müxtəlif assosiasiyalar şəklində - dekorativ
ornamentlər (xalçalar, rəngli vitrajlar – şüşə şəbəkə, daş
şəbəkə), oyunlar və s. kimi qorunub saxlanılmışdır.
Aparılan təhlil tam əminliklə təsdiq etməyə imkan verir
ki, Azərbaycan ta qədimdən dünya kosmoloji
təfəkkürünün formalaşma prosesinin vahid bir hissəsi
olub. Burada Göy Tanrıya inam ən mərkəzi yeri
tuturdu. İşarə komplekslərinin simvolikasının bərpası
və dünyanın realizasiya edilmiş müxtəlif modelləri
arasındakı semantik əlaqə əcdadlarımızın dini,
kosmoqonik ənənələrinin əsaslarını üzə çıxarır. İbtidai
sənətkarlıqda sinesteziya daha çox ibtidai cəmiyyətdə
təbiətinə görə vəhdət təşkil edən dini səviyyədə
ideyaların əlaqəsidir. İbtidai dövrün simvolik
kosmoloji konsepsiyalarının spesifik kateqoriyaları
məkan, zaman və hərəkətin vəhdəti haqqında ümumi
fəlsəfi fikirləri əks etdirir. Biz dünya nizamının yenidən
qurulması prosesində bütün sənət növlərinin icmasının
40 Slovak international scientific journal # 84, (2024)
sinesteziyasını görürük. Rəsmlərin təhlili göstərir ki,
maddi mədəniyyət abidələrinin dekorativ-tətbiqi bəzəyi
Azərbaycan xalqının bütün həyatına sirayət etmiş,
şifahi xalq yaradıcılığında, adət-ənənələrdə, dekorativ-
tətbiqi sənətdə öz əksini tapmış ibtidai ayin və
əfsanələrlə bağlı dəyişməz obrazlar çevrəsini ehtiva
edir. References
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Slovak international scientific journal # 84, (2024) 41
ECONOMY
ECONOMETRIC MODEL OF THE CYCLICAL FUNCTIONING OF THE NATIONAL ECONOMY
IN THE LONG-TERM PERSPEKTIVE
(ON THE EXAMPLE OF THE NATIONAL ECONOMY OF AZERBAIJAN)
Ayyubov M.
Leading research fellow, Institute of Economics
Ministry of Science and Education of the Republic of Azerbaijan
https://orcid.org/0000-0002-2255-1706
DOI: 10.5281/zenodo.11624382
Abstract
The article discusses the methodological foundations for the development of a “conjunctural-structural”
macro-econometric model of the cyclical functioning of the country’s national economy. It argued that, along with
various processes that are cyclical in the country’s economy, the country’s economy as a whole at the macro level
operates in a cyclical mode. One cycle of functioning consists of the stages of development and decline in the rate
of development, crisis, decline and stabilization. At the stage of development of the country's economy, an intra-
system economic threat to the state structure does not arise. Intra-system economic threats to the state structure
manifest themselves at the stages of declining growth rates of economic development and crisis. Therefore, it is
necessary to have tools with the help of which one could determine the time of formation of stages of declining
growth rates and the manifestation of crisis situation in the country’s economy. We believe that by developing a
“conjunctural-structural” macro-econometric model of the cyclical functioning of the country’s national economy,
it is possible to determine the possible time of onset of economic threats to the state structure and prepare a program
for eliminating threats beforehand.
Keywords: cyclical economic process; econometric model; cyclical functioning of the country's national
economy; “conjunctural-structural” macro econometric model; economic threats to the state structure.
Methodology. The research methodology is a sys-
tems approach, the basic principles of the general the-
ory of dynamic systems. To compile a “conjunctural-
structural” equation for a macro-econometric model of
the cyclical functioning of the country’s national econ-
omy, the author of the article has developed a method-
ology based on statistical-economic, calculation-con-
structive, econometric methods of cognition.
Based on the research methodology developed by
the author of the article, an algorithm for performing
calculations to compile a “conjunctural-structural”
equation of a macro-econometric model of the cyclical
functioning of the country’s national economy con-
structed.
Introduction. Since the mid-19th century, many
scientific works published explaining the essence and
content of cyclical processes of various durations in the
country's economy. The American economist, repre-
sentative of the neoclassical economic school E.H.
Hansen in the 30s of the last century systematized ideas
about the economic cycles occurring in the national
economy of the country [1]. In modern macroeconomic
theory, related to investments directed into the national
economy of the country, the following cycles are dis-
tinguished:
1. The role of growth and decline in investment
volume.
2. Analysis of the dynamics of factors determining
the volume of investment: graph of the limits of invest-
ment efficiency suitable for interest rates.
3. Dynamics of technical, natural resource, territo-
rial factors, as well as population growth factors that
determine the volume of investments and their impact
on the cyclical nature of the functioning of the coun-
try’s economy.
4. Chain characteristics of investments related to
the development of innovations, scientific, and techno-
logical progress (Schumpeter);
5. Long-term production of elements of fixed as-
sets, the impact of the durability of fixed capital on eco-
nomic systems.
6. Initial impulses that create economic processes
caused by economic growth, which have an oscillatory,
cyclical nature.
Also, in economic theory, there are several types
of macroeconomic cycles, differing in the duration of
the periods. Modern concepts of macroeconomic cycles
of various durations can grouped as follows.
1. Short-term cycles with a period of 3-5 years. 3-
5-year short-term cycles include: the life cycle of man-
ufactured products (service life of product types)
Schumpeter, associated with innovation; K. Kitchen’s
cycles associated with world gold reserves and vital
material reserves; cycles of K. Marx and E. Hansen of
uneven reproduction of working capital in the country's
economy.
2. Medium-term 8-12 year cycles associated with
fixed production assets. These types of cycles include
the cycles of K. Marx on the massive renewal of fixed
assets of production, as well as the cycles of K. Juglar
on the influence of monetary factors associated with the
activities of banks on the period of change in fixed cap-
ital. 3. Long-term 15-25-year cycles of the American
economist, Nobel Prize winner S. Kuznets, related to
the demographic situation in the country, migration,
construction, including the renewal of infrastructure fa-
cilities.
42 Slovak international scientific journal # 84, (2024)
4. Long-term (more than 40 years) oscillatory cy-
cles of N. Kondratiev, associated with the economic sit-
uation, that is, with the situation and with the state of
social reproduction. N. Kondratiev, based on statistical
data from European countries (period 1800-1920), hav-
ing studied the functioning of national economies, con-
cluded that national economies in the long term (40-60
years), depending on the situation, have an oscillatory
nature.
Discussion. Conjuncture factors include factors
that influence the elements of the reproduction process,
consisting of the stages of production, exchange, in-
come distribution and consumption.
According to N. Kondratiev and followers of Kon-
dratiev’s theory, due to the fact that the functioning of
national economies, as well as large regional economic
systems over a long period (40-60 years) is of an oscil-
latory nature. These vibrations have a “long-wave”
characteristic [203]. However, neither Kondratiev nor
his followers proposed an econometric model assessing
the “long-wave” oscillatory activity of the national
economy.
In studies of the functioning of the national econ-
omy of different countries, the American economist
R.G. Hawtry [400] concluded that macroeconomic
fluctuations in the functioning of the national economy
do not depend on technological progress, capital accu-
mulation or population growth. Macroeconomic fluctu-
ations are a secondary indicator of development, and
they are just fluctuations. In reality, the country's econ-
omy has the character of development, and indicators
characterizing fluctuations are secondary indicators
and are not important.
We believe that, along with cycles of economic
processes of different nature and duration, in the longer
term (more than 30 years) the country’s national econ-
omy operates in a cyclical mode.
In the mid-20th century, US economists A. Burns
and W. K. Mitchell [398] proposed a concept that ex-
plains the essence of the cyclical functioning of the
country’s economy over 25-30 years.
According to the authors, business activity in the
national economy of the country, that is, the production
of material products and the provision of services,
flows along a straight line, characterized by long-term
development along the Y curve, which rises and falls
around the trend Ỹ (diagram). However, the authors be-
lieved that in the long term, the development of the
country’s economy has a direct trend of constant
growth Ỹ, and the factors shaping the production of ma-
terial products and the provision of services Y have vir-
tually no effect on the direct trend Ỹ.
In our opinion, the American economists A. Burns
and W. K. Mitchell, in their studies of the cyclical na-
ture of the functioning of the country's economy in the
long term, came to the wrong conclusion.
So firstly, in classical and neoclassical economic
theories it believed to be that the functioning of national
economic systems has a cyclical nature, consisting of
stages: development → slowdown development → cri-
sis → decline → stabilization (Diagram.1).
Secondly, the indicator of production and provi-
sion of services Y, expressing the result of the function-
ing of the national economy, depends on changes in
fixed capital, working capital, labor, money supply, as
well as from the multiplier effect of investments and the
effect of acceleration of production volumes, provision
of services.
Thirdly, in the long term, the dependence of the
trend parameter of the country's economic development
ỹ on the actual parameter of production of goods and
provision of services y, is measured by a linear function
As can be seen from the function, provided that
parameters a0 and a1 remain constant, large values of
the parameter y correspond to large values of the pa-
rameter ỹ, and small values of the parameter y corre-
spond to small values of the parameter ỹ.
Slovak international scientific journal # 84, (2024) 43
Conclusions. We believe that, along with cyclical
economic processes that differ in essence and duration,
in the longer term (more than 30 years) the country's
national economy operates in a cyclical mode. (Dia-
gram 1).
In contrast to the opinion of the American econo-
mist R.G. Hawtry, we believe that the country's econ-
omy has the character of development at a certain stage.
The indicators characterizing fluctuations are the pri-
mary indicators that form the growth rate of develop-
ment.
In addition, in contrast to the opinion of American
economists A. Burns and W. K. Mitchell, we believe
that in the long term, the development of the country’s
economy has a direct trend of constant growth Ỹ, and
the factors that shape the production of products and the
provision of services Y shape the development trend.
We believe that in the long term, the development
of the country's economy has a constantly increasing Ỹ
-direct trend. However, the factors that shape the Y row
have a direct impact on the trend line Ỹ (diagram 1).
Methodology for developing an econometric
model of the cyclical functioning of the national
economy in the long-term (more than 30 years) pe-
riod.
The parameter ỹS, characterizing the periodic pro-
cess, can be expressed as the algebraic sum of the re-
duced parameter ỹ of the empirical series y for time t:
(1)
And the parameter of the empirical series y, ex-
panded into a trigonometric Fourier series f(x):
(2)
That is:
(3)
Or,
(4)
In this case, the parameters ỹS of the cyclic process are expressed by the trigonometric Fourier function with
a period of 2π. Dividing the parameter of an empirical series of a cyclic process into trigonometric Fourier series
is considered a Problem of harmonic analysis [264, pp. 165-169; 129, pp. 418-419; 344, p. 427-463].
We believe that the function expressing the dynamics of the indicator of total output ỹS for the period T
(4)
is a “conjunctural-structural” function, expressing
a change in the structure of gross output, depending on
the conjuncture of the functioning of the national eco-
nomy in the long term.
According to the method we proposed, when ex-
pressing the parameters of the ỹS of a periodic process
using the trigonometric Fourier function, harmonic se-
ries are calculated that approximate a given empirical
series, and a function with a correlation coefficient of
the highest harmonic order is selected.
When expressing the parameters of a periodic se-
ries using the trigonometric Fourier function, the para-
meters of the Fourier series are determined using the
following system of equations:
(5)
In the system of equations (5): y is an indicator of
the dynamics of the empirical series, ỹ is an indicator
of the dynamics of the aligned empirical series; n is the
number of years of the empirical series; t – expression
of time sequence (T) in radians:
t = (0.2π/n,2 2π/n,3 2π/n,…,(n-1) 2π/n, 2π);
k - the number of harmonics that bring the Fourier
series closer to the empirical series.
Algorithm for compiling a macroeconometric
model of the cyclical functioning of the country’s
national economy
We believe that the macroeconomic model of the
cyclical functioning of the national economy in the
long-term (more than 30 years) period must be com-
piled according to the equations we proposed (1), (2),
(3), (4), (5).
The macroeconomic “conjunctural-structural”
model of the cyclical functioning of the national econ-
omy in the long term (more than 30 years) is compiled
in the following sequence.
1. At the first stage, the dynamics of the empirical
indicator of total output over the past (more than 30
years) period in the country’s national economy is ex-
amined. If the graph of the dynamics of the empirical
indicator of total output y for the period under study
shows signs of cyclicality, begin the study.
2. Dynamics of the aggregate output volume pa-
rameter y levels off in a straight line
(1)
44 Slovak international scientific journal # 84, (2024)
3. The indicator ∑ u is calculated as the sum of the
differences between the empirical series of total
production output y and the calculated indicator ỹ:
(5)
4. The expression of moments of the time period
T, in t radians, for the purpose of decomposing the
empirical series of the total volume of output of goods
and services Y into the trigonometric Fourier series is
calculated by the formula
(6)
In formula (6): n is an indicator of the number of
moments in the time period T, measured in years. In
calculations when expressing the time period T in terms
of t radians, the initial year of the time period T is
assumed to be zero. For example, if the time period T
covers 30 years, then the expression for n moments of
period T in t radians is calculated as:
(7)
5. The harmony of the first row ỸSI at values k =
1 is calculated in the following sequence.
5.1. The trigonometric functions cos t and sin t are
calculated in radians;
5.2. Parameters ∑(u·cos t) and ∑(u·sin t) are
calculated;
5.3. The parameters a0, a1, b1 of the trigonometric
Fourier series are calculated using the formulas:
(8)
5.4. Based on the calculated parameters a0, a1, b1,
the Fourier trigonometric series f(x) is calculated:
(9)
Thus, with the cyclical functioning of the national
economy of the country, the calculation equation of the
“conjuncture-structural” model - the dynamics of gross
output in the long term in the first harmony is expressed
by the function:
(10)
The correlation coefficient calculated between the
empirical series of gross output Y and the series of dy-
namics of gross output ỸSI in the first harmony.
If the calculated value of the correlation coeffi-
cient RI is between the values of 0.950 ≤ r ≤ 1.000, then
it considered there is a high relationship between the
calculated first harmonic series ỸSI and the empirical
series of total output Y the relationship is high.
5.5. The equation of the “conjunctural-structural”
model is calculated:
1) Second harmony ỸSII, with values:
(11)
(12)
2) Third harmony ỸSIII, with values:
(13)
(12)
And so on.
Calculations continue until the maximum value r
MAX obtained.
Thus, we believe that, based on the methodology
we propose, it is possible to form a “conjunctural-struc-
tural” econometric model of the cyclical functioning of
the country’s national economy in the distant future. By
calculating the normative forecasts for the indicator of
total output in the national economy, as well as socio-
economic indicators arising from the indicator of total
output, it is possible to assess the possible state of the
country’s national economy in the distant future.
Compilation of an econometric model of the cy-
clical functioning of the national economy of Azer-
baijan in 1965-2000.
The national economy of the Republic of Azerbai-
jan until 1992 of the 20th century functioned as part of
the national economic system of the USSR. As result of
the collapse of the national economic system of the
USSR state, in the 90s of the last century, the national
economy of the Republic of Azerbaijan transformed
from a structure based on a social formation into a new
structure of a market economy.
During the study, we believed that the essence of
the theoretical provisions of the mechanism of produc-
tion and provision of services in the period 1965-1992
and in the period 1992-2000 in the national economy of
Azerbaijan has not changed.
Based on information from the State Committee
for Statistics of Azerbaijan, we have compiled statisti-
cal data on the indicator of the total output of products
and services in Azerbaijan for the period 1965-2020.
Research has shown that the period of one full cycle
of functioning of the national economy of Azerbaijan is
35-36 years. It was determined that the national economy
of Azerbaijan: in the period 1965-1984 functioned at the
stage of development; in the period 1984-1990 at the stage
slowdown and crisis; in the period 1990-1995 during the
recession; and in the period 1995-2000 at the stage of sta-
bilization.
The compilation of the “conjunctural-structural”
econometric model was carried out in the following se-
quence.
1. Dynamics of Y volumes of gross output of the na-
tional economy of Azerbaijan during the study period
1965-2000, in 2000 prices, aligned by linear function
Ῡ = 0,0036·T + 0,5048.
In the resulting linear function: T – time points for
1965-2000; 0.0036 – average annual increase in the dy-
namics of total output of products and services in 2000
prices; the value 0.5048 represents the initial value of the
aligned time series of total output at 2000 prices.
2. The indicator (∑ u) calculated.
3. Moments of the time period T are expressed in
t radians:
Slovak international scientific journal # 84, (2024) 45
4. Calculated by:
5. Calculated by:
6. The functions ỸSI, ỸSII, ỸSIII of the harmonic series k = (1,2,3) of gross output are compiled.
Calculations showed that in the period 1965-2000 the “conjunctural-structural” equation of the full cycle
functioning of the national economy of Azerbaijan in third harmony (k=3), at r = 0.977 is expressed as:
Thus, based on our research, we came to the con-
clusion that:
1) the national economy of Azerbaijan operates in
a cyclical mode in the long-term period;
2) the period of one complete cycle is 35-36 years.
3) it was determined that in the twentieth century,
in the period 1894-2000, the national economy of Azer-
baijan functioned in three complete cycles;
4) from the beginning of the new 21st century,
from 2001, the national economy of Azerbaijan began
to function in a new 35-36 flight cycle;
Based on statistical data from the State Statistics
Committee of the Republic, it was established that the
economy of Azerbaijan from 2001 to 2014 functioned
at the stage of development. And starting from 2015,
the pace of economic development began to decline.
So, it was established that, if the average annual rate of
total output of products and provision of services at the
development stage was 20.5%, after 2014, the average
annual growth rate of total output of products and pro-
vision of services tended to decrease and amounted to
(-0.1)%.
We believe that using our proposed methodology
for compiling a “conjunctural-structural” macro-econ-
ometric model of the cyclical functioning of the coun-
try’s national economy, it is possible to draw conclu-
sions about the history of the functioning of the coun-
try’s economy in the distant past, and based on the
forecasts compiled, conclusions can be drawn about the
state of the country’s national economy in the long-
term future period.
References
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Slovak international scientific journal # 84, (2024) 47
HISTORY
GENOCIDE CARRIED OUT IN WESTERN AZERBAIJAN IN 1918-1920
Ismayilowa A.
Phd Student of Baku State University, lecturer of Baku Eurasian University
Abbasova S.
Phd Student of Baku State University, lecturer of Azerbaijan University Languages
https://orcid.org/0000-0003-4507-994X
DOI: 10.5281/zenodo.11624403
Abstract
Four times in the 20th century (1905-1906, 1918-1920, 1948-1953, 1988-1991) Azerbaijanis were deported
from the territory of present-day Armenia - their historical-ethnic land - with massacres. Armenians fighting for
"Turkless Armenia" and their ideologues, as well as their patrons from near and far abroad, completed the ethnic
cleansing operation in the 90s of the 20th century. The last settlement of Azerbaijanis in Armenia - the village of
Nuvedi was subjected to genocide by the Armenians and the indigenous inhabitants of the village - Azerbaijanis -
were deported from their historical and ethnic lands. Thus, not a single Azerbaijani remained in Western Azerbai-
jan, which is now called Armenia. This article talks about the genocides carried out by Armenians against the
Azerbaijani people in Western Azerbaijan in 1918-1920. Valuable documents proving these genocides are today
in the documents of the Extraordinary Investigation Commission preserved in the National Archives of the Re-
public of Azerbaijan, the "General Staff Military History and Strategic Studies Archive", the "Başbakanlık Otto-
man Archive" of the Republic of Turkey and the "Political Archive of the German Ministry of Foreign Affairs" in
Berlin, Germany "(Politischen Archiv den Auswätrigen) are preserved in the funds of the First World War and the
War of Independence. The actual materials in those archival documents prove that from 1917 to 1920, Armenians
mercilessly killed tens of thousands of peaceful, unarmed Turkish-Muslim population in Zangazur district of Azer-
baijan due to their ethnicity. Historical facts are shown in the article referring to these sources.
Keywords: Western Azerbaijan, Yerevan, Zangazur, genocide, Turkish-Muslim, Armenians.
This work was supported by the Azerbaijan Science Foundation – Grant № AEF-GAT-7-2023-2(44)-10/10/5-
M-10
Introduction
At the beginning of the 20th century, Armenians
purposefully implemented the policy of genocide in the
territory of Azerbaijan. Taking advantage of the politi-
cal situation after the February revolution and the Oc-
tober coup in 1917, the Armenians colluded with the
Bolsheviks and committed genocide against the Turk-
ish-Muslim population. The main goal was to weaken
the social base of "Musavat", which won the elections
to the Baku Soviet. The Armenian-Bolshevik forces led
by S. Shaumyan started from Baku and from March 31
continued in Shamakhi, Lankaran, Zangezur, Iravan, as
well as in Urmiya, Khoy and Maku. This is not the first
murder committed by Armenians against the local pop-
ulation. Armenians tried to implement their plans by
abusing the disruption of historical and political stabil-
ity. Thus, trying to benefit from the revolution that took
place in Tsarist Russia in 1905-1907, Armenians com-
mitted genocide against the Turkish-Muslim popula-
tion. Unthinkable crimes were committed against the
peaceful, innocent population during these events,
which are recorded in history as the Armenian-Muslim
conflict. There is enough information about this in his-
torical sources. In the works "Bloody Years" by
Mammad Said Ordubadi and "Armenian-Muslim con-
flict in 1905-1906" by Mir Mohsen Nawab, important
facts related to the atrocities committed against Azer-
baijanis in 1905-1906 were found. In the 1905-1906
editions of the "Kaspi" newspaper printed in Baku in
Russian, as well as in the book "Armenian-Turkish
clashes in the Caucasus (1905-1906)" by A. Don, pub-
lished in Armenian in 1907, with the events that took
place during that period related information can be
found [1, 36]. However, Azerbaijanis did not learn
from this, even after these events, they wrote works
promoting humanism and coexistence. However, such
works by Armenians do not exist.
At that time, they covered up this genocide, which
was organized by the Dashnak military forces, in a dif-
ferent way. Thus, the Armenian Bolsheviks, led by Ste-
pan Shaumyan, tried to paint it as a civil war and
thereby cover up the real historical truth. The ugly,
criminal acts of Armenians who committed genocide in
Azerbaijan are known from archival materials and wit-
ness statements. However, despite this, after the estab-
lishment of the Soviet government in Azerbaijan, this
issue was not objectively investigated in a scientific di-
rection, and in historiography, the genocide committed
against the Azerbaijani people was characterized as
"civil war", "Musavat massacre", and "March Upris-
ing". However, after the fall of the USSR, the oppor-
tunity to objectively investigate the historical truths
was obtained. It was possible to express and analyze
historical documents and sources as they are. This is a
direct blow to the plans of the Armenians and their pa-
trons, who are trying to falsify and hide their actions.
Genocide in Zangezur
In 1918-1920, Zangezur district was one of the ter-
ritories of Azerbaijan that suffered the genocide of Ar-
menians. Armenian gangs led by Andranik and Nijde
attacked the territories of Azerbaijan, threatened the
48 Slovak international scientific journal # 84, (2024)
population, and called for submission to the Armenian
government. Those who did not submit to the Arme-
nian government had to leave the city or become vic-
tims of Andranik's brutal crimes. It should be noted that
in the 19th century, as a result of the Russo-Qajar and
Russo-Turkish wars, Armenians from both Ottoman
and Qajar empires and other regions of Tsarist Russia
were moved to this area with the agreements concluded
between the parties. As a result of the resettlement, the
Armenians who settled in the historical lands of Azer-
baijan carried out a policy of ethnic cleansing against
the local population. It is no coincidence that the Arme-
nian population living here played an active role in the
genocide carried out in the 20th century. When Andran-
ik's and others' gangs attacked, the Armenians living in
these areas also supported the implementation of the
genocide, since they were resettled here in the 19th cen-
tury, they knew the region better, which allowed them
to help the attacking gangs and strike from within
against the Azerbaijanis who were trying to defend
themselves.
On July 15, 1918, the government of the Azerbai-
jan Democratic Republic established an Extraordinary
Commission of Inquiry to investigate the genocide
against Azerbaijanis in 1918 [13, 27]. The massacres
that took place through this institution were investi-
gated, witness statements and information obtained
from those involved in the investigation once again
confirm that the Armenian-Bolshevik forces committed
genocide on purpose. Two of the 36 volumes of inves-
tigative materials examined by this institution refer to
the events that took place in Zangezur. It is known from
the documents of the Extraordinary Investigation Com-
mission that 115 villages of Zangezur district were de-
stroyed by Armenians. The names of those villages are
mentioned in these documents. [6 p. 127]. 3257 men,
2276 women, 2196 children were killed from 115 vil-
lages. In addition, it should be noted that 10,068 Azer-
baijanis were killed by Armenians and maimed as a re-
sult of serious injuries before the report of the Extraor-
dinary Investigation Commission was prepared. The
chaotic and unstable situation during the events of the
genocide did not allow identifying all of the victims of
Armenian atrocities [3, 166].
The events that took place in Zangezur accident
are proof of Armenian atrocities. Armenians killed the
population mercilessly. This can be seen from the facts
and examples known from the investigation. Children's
corpses found on the streets of Sheki village, divided
into two parts, nursing babies who were bayoneted in
Irmishli village, families burned alive along with their
houses, people whose hands, feet, and various organs
were cut off and put in a terrible condition show the
scale and horror of the murders committed by Armeni-
ans [9, 47]. With this, they tried to create fear among
the population and drive the survivors out of their
places once and for all with such "examples". Armeni-
ans did not ignore the religion and customs of the pop-
ulation and did not hesitate to damage the holy places.
Thus, in the village of Vagudu of Zangezur district,
more than 400 people, who assumed that the Armeni-
ans would not touch the mosque, hid there and tried to
protect themselves in the mosque. However, the Arme-
nians threw a bomb into the mosque, set it on fire and
burned it together with the people inside it [6, 128]. It
should be noted that the damage done to holy places
and historical monuments does not end there. The gen-
ocides committed by Armenians against the people of
Azerbaijan and the policy of ethnic cleansing do not
consist only of the events that took place in 1918-20.
From the end of the 20th century, starting from the 80s,
they began to occupy the territories of Azerbaijan. As a
result, they have damaged the monuments and material-
cultural examples here. It is enough to show that ani-
mals were kept in mosques.
The attacks, which started in 1918, intensified in
November 1919. Armenians organized more extensive
attacks and carried out heavy operations in the villages
of Zangezur such as Okchu, Atgiz, and Shabadan.
Since 1920, it was the Republic of Ararat that organized
the intensification of these massacres [4]. The main
purpose of this was to cleanse Zangezur of Azerbaijanis
and completely armenize it, and after capturing Zange-
zur, it was permanently captured by the main states that
participated in the Paris peace conference and legiti-
mized it. It is no coincidence that the official armed
forces of Ararat state participated in the process of eth-
nic cleansing.
From January 1920, letters were sent to the Parlia-
ment of Azerbaijan and political circles about the dete-
rioration of the situation in Zangezur, mass massacres
committed by Armenians, and they asked for help to
prevent Armenian atrocities. Among such telegrams
addressed to the government of Azerbaijan, it is possi-
ble to mention the ones sent by Jalil Sultanov, a mem-
ber of the Azerbaijani parliament who visited
Zanegzur, and Huseyn Akhundzade, a teacher from
Jabrayl. From the telegrams sent on January 21 and 23,
1920, it is once again clear that the Armenians were
mercilessly oppressing the Azerbaijani people and try-
ing to seize these territories by committing genocide
against the population. As stated in the telegram sent by
Jalil Sultanov on January 23, 1920, the goal of the Ar-
menians was to completely capture the territories of
Karabakh, Nakhchivan, Iravan, and Zangezur, to re-
move the local population from here and to armenize
them: completely destroyed. The number of regular Ar-
menian army that participated in the battle reaches ten
thousand. According to the information we received, an
attack on Jabrayil district will be launched tomorrow
from the Zangezur side. The goal of the Armenians is
to completely cut off the connection with Nakhchivan,
thus solving the issue of both Karabakh and Na-
khchivan once and for all. The time has come to put an
end to the protests on paper, to reveal to the world the
treacherous Armenians who led to the destruction of the
over two hundred thousand Zangezur Muslim popula-
tion. Please take immediate action so that at least
Shusha and Gabriel can be saved. Every minute is pre-
cious. Being late is equal to crime and treason in front
of the people and the country" [6, 130].
It should be noted that what was written in the
book "Garagin Nizhde i eqo ucheniya («Гарагин
Нижде и его учения») published in Armenia in 2004
about the genocide in Zangezur is proof of the actions
Slovak international scientific journal # 84, (2024) 49
committed by Armenians. It is written here that more
Azerbaijanis were killed, and that 200 villages inhab-
ited by Turks and Tatars were "returned" to Armenians.
This should be considered as an acknowledgment of the
actions committed by Armenians [16, 8]
Genocide in Irevan
With the collapse of empires at the end of the First
World War, peoples had the opportunity to determine
their own destiny. As a result, with the collapse of Tsar-
ist Russia, the peoples of the Caucasus managed to de-
clare their independence. The Republic of Azerbaijan,
Armenia (Ararat) and Georgia were formed in the
South Caucasus. There were problems in determining
the borders of the states. Thus, Armenians trying to re-
alize the dream of "Great Armenia" wanted to set the
borders according to the borders of this desired "state".
According to the unfounded claims of Armenians, the
Armenian state should have included the territories of
the Ottoman Empire, Azerbaijan and Georgia. They
tried to realize these plans in the following years [10,
49]. Territorial disputes with Azerbaijan and Georgia
are also the result of this policy of the Armenians, who
are trying to appropriate the ancient and eternal lands
of the peoples in order to build the "Great Armenia",
which never existed and is only a dream. In order to
realize their plans, the Armenians, who tried to seize
foreign lands, and for this purpose, tried to expel the
local, aboriginal population from their homeland by
committing murders and exiles, although they could not
build the "Great Armenia" of their dreams, they man-
aged to create the currently existing Republic of Arme-
nia. On May 29, 1918, in order to end the massacres
committed by the Armenians against Azerbaijan, the
groundless territorial claims, the government of Azer-
baijan was forced to give its historical lands, Iravan, to
the Armenians as the capital. The main condition for
the concession of Yerevan to the Armenians was that
the Armenians renounced their claims to other territo-
ries. One of the factors that created conditions for this
was the transfer of Gyumri (Alexandropol) territories,
which the Armenians envisioned as the capital, to the
control of the Ottomans [8, 136]. According to the in-
formation stored in the Russian archives, it is clear that
the Provisional government, which was established af-
ter the February revolution of 1917, also used Armeni-
ans for its own purposes. For this purpose, he adopted
the concept of "Turkey Armenia" [15, 356-357]. To
weaken and defeat the Ottomans, the Russian, British
and other forces used the Armenians living here, giving
them promises and making concessions to create a
state. The goal was to strengthen in these areas and to
use the Armenians as a political tool for this. The fact
that both the newly formed government, the successor
of Tsarist Russia, and Soviet Russia drew Armenians to
their side served this purpose. They tried to create a
state for them by applying the concept of "Turkey-Ar-
menia". However, as is known from history, the plan to
create a state for Armenians was transferred to the Cau-
casus because the Ottoman state later liberated those
territories. With this, the Armenian state was estab-
lished in the historical lands of Azerbaijan in the terri-
tory of the South Caucasus - in the lands of Western
Azerbaijan [12, 249]
Iravan was one of the territories of Azerbaijan
where Armenians committed genocide. Back in No-
vember 1917, after the October coup in Russia, Arme-
nians who seized the weapons of the Russian troops re-
treating from Eastern Anatolia and the Caucasus front
committed genocides against Turks and Azerbaijanis.
Thus, on December 5, 1917, an agreement was signed
in Erzincan between the South Caucasian Commissar-
iat and the Ottoman government. After that, the Arme-
nians, who took advantage of the retreat of the Russian
troops from Eastern Anatolia, seized the weapons and
started slaughtering the Turkish-Muslim population
[14, 21]. In this regard, information is also provided in
the documents kept in the political archive of the Ger-
man Ministry of Foreign Affairs. At that time, the Ger-
man representative in the South Caucasus, Bernstroff,
sent to the German Ministry of Foreign Affairs on Feb-
ruary 27, 1918, it was written: "Atrocities committed
by Armenian volunteer groups in Erzincan should be
considered very important. The population in the vil-
lages was completely destroyed" [11, 41].
From the beginning of 1918, Armenian armed
groups started to commit mass massacres against Azer-
baijanis in Iravan province. Until March 1918, Arme-
nian armed groups destroyed 198 villages, including 32
villages in Iravan District, 84 in Echmiadzin District, 7
in Yeni-Beyazid District, and 75 in Surmali District of
Iravan Governorate. In those districts, approximately
135,000 Azerbaijanis were subjected to genocide [6,
133].
Until September 1919, except for some village of
Zangibasar, all the villages of Iravan district and also of
Vedibasar were destroyed, their inhabitants were mer-
cilessly killed, and the survivors were removed from
their native lands. In 1920, the "Azerbaijan" newspaper
published information about this in April: "There are no
more Muslims left in Goycha district. Currently, 84
Muslim villages have been destroyed in Yeni Beyazid
district, 22 of them were destroyed in April alone. Tash-
kent, Goshabulaq, Sariyagub, Bash Shorja, Ashagi
Shorja, Sogangulu-Agali, Agkilsa, Zod, Gulu, Agali, B.
Garagoyunlu, K. Garagoyunlu, Zarzibil, Adli, Inakdag,
Garaiman, Kaseman, Bashkend, Bala Marza, Shish-
gaya, Bash The population of Haji and Garibgaya vil-
lages with more than 15,000 houses fled, leaving be-
hind all their property and the state. All this wealth is
now left to Armenians, the looted property is worth sev-
eral millions or even billions" [6, 135]. The information
published in this newspaper is once again a proof that
Armenians have taken possession of someone else's
land by force and committed genocide, displacing the
local population. Also, if you pay attention to the ety-
mology of the listed village names, it shows that each
of them belongs to Azerbaijan. However, later Armeni-
ans changed the names of the native lands of Azerbai-
jan in order to Armenianize them by implementing a
genocidal policy against toponyms. With this, they are
trying to deny that these territories historically belong
to Azerbaijan and falsify history. However, the names
50 Slovak international scientific journal # 84, (2024)
mentioned in sources and historical documents and
their origin also expose Armenian lies.
There is also information about the subsequent re-
settlement of Armenians to these areas in English doc-
uments kept in the archives of Great Britain. Of these,
the memorandum prepared by the political intelligence
department of the British Foreign Ministry on October
28, 1918 states: "When solving the Armenian question,
it should be taken into account that its center of gravity
is not in the Caucasus, but in the south of Asia Minor.
Armenians came to the Caucasus from Turkey mainly
as refugees during the last decades during the Russian
rule. The Russian government used them here to incite
disputes between Georgians and Tatars" [2, 110]. Im-
portant facts related to the genocides committed by Ar-
menians in Azerbaijan were also reflected in the docu-
ments of the British government stored in the British
archives. Among them, the letters sent by the high com-
missioner for the South Caucasus appointed by the Brit-
ish government, General O. Wardrop, to his govern-
ment, the information contained in his correspondence
can be cited as an example. In his report sent to London
on October 2, 1919, he informed: "Recently, the Arme-
nians destroyed 60 Muslim villages in Yeni Beyazid,
Alexandropol and Iravan regions" [5, 30].
In the letters sent by O. Wardrop in December
1919, it was mentioned that the Armenians killed the
civilian population - the Muslim population, including
women and children, in the mosque, and the Muslims
of Zangezur are in a state of panic. It should be noted
that in addition to O. Wardrop's information, the Azer-
baijani government also sent a letter to the British
Prime Minister Lord Curzon, informed about the geno-
cide committed by the Armenians in Zangezur, and the
British government officially recognized these territo-
ries as Azerbaijani territory. [5, 31].
It is known from the British documents that the
British government tried to use the Armenians against
the Ottomans, and even for this purpose Andranik was
provided with weapons and financial support for the re-
sistance against the Turks. Genocides committed by
Armenians in Azerbaijan were evaluated as damage to
British plans. In this regard, it is stated in official doc-
uments and correspondence that if the Armenians do
not stop the massacres, the aid to them will be stopped.
O. Wardrop wrote about this in document No. 52 sent
on January 28, 1920: "The main purpose of my visit to
Yerevan was to put pressure on the Armenian Prime
Minister to withdraw the regular troops from Zangezur
and punish the culprits. I have already sent a telegram
to his relatives that if the Armenian government does
not stop the aggression, I will advise His Majesty's gov-
ernment not to help them" [5, 34] Each of these facts
confirms that Armenians committed genocide against
the people of Azerbaijan. In matters related to the gen-
ocide, it is once again proven that the events were com-
mitted by the political line of the Armenians and the
state of Ararat.
The genocides carried out by Armenians in the ter-
ritory of Iravan governorate in 1918-1920 were also re-
flected in the Ottoman archival documents. In these
documents, it was also mentioned that he asked for help
from the Ottoman 15th regular army command to de-
fend against Armenian oppression and atrocities com-
mitted by Armenians against the population. Among
the documents of this period, there are also maps de-
scribing the territories where the Armenians committed
genocide, which are historical sources of great im-
portance in terms of specifying the territory covered by
the massacres. One such map was drawn on July 3,
1919. The map called "Description of the places where
Armenians committed atrocities against the population
of Goyja" shows the areas where the Armenians com-
mitted genocide - Agbulag, Shoreyel, Gamarli and
other areas. Another map drawn up in the same month
shows regions affected by genocide such as Iravan, Big
Vedi, Karalar, Shirazli, Khalisa, Sadarak, Alisar [11,
43]. In Ottoman archival documents from 1920, it is
possible to find information about atrocities committed
by Armenians, killing the population in an inhuman
manner. An example of this is the documents where 50
children and teenagers were chopped with axes by Ar-
menians in 1920 in Gizilkilsa village of Yerevan, their
eyes were removed with red skewers, and people were
burned in cauldrons and destroyed by torture. The doc-
uments belonging to the Ottoman archives once again
prove that in 1918-1920, Armenians committed geno-
cide against Azerbaijanis, invaded Azerbaijani territo-
ries by committing brutal murders, and as a result of all
this, created a state for themselves in the historical
lands of Azerbaijan.
The result
The territory of Western Azerbaijan, which is now
the territory of the state called Armenia, is the historical
land of Azerbaijan. There are historical sources, topo-
nyms, and monuments that prove this place belongs to
Turkish culture. However, Armenians living with the
dreams of "Great Armenia" displaced the aboriginal
population of this place from their native lands through
genocide and deportation. When we look at history, we
see that the current historical and political conditions
are effective for Armenians in this regard. During Tsar-
ist Russia and later during the USSR, Armenians used
the opportunity for their own plans. The genocides car-
ried out by the Armenians in 1918-1920 were a contin-
uation of the massacres committed in 1905-1906 and
the same policy they pursued. However, the policy of
genocide and ethnic cleansing against Azerbaijan and
Azerbaijanis did not end there. V. I. In December 1920,
Zangezur was given to Armenia unconditionally as a
result of the new colonial policy implemented in this
region by the dictates of the Armenian and Georgian
Bolsheviks, who had great influence in the ruling cir-
cles of Soviet Russia headed by Lenin. Armenians, who
felt that this issue was completely resolved for their
own benefit, did not object to the return of the Azerbai-
jani population expelled from Zangezur to their homes
in order to create temporary calm, but in the following
years, they again displaced the Azerbaijanis from their
native places. Azerbaijanis were deported from the Ar-
menian SSR from 1948-53 by the hands of the Soviet
regime. Armenians were settled in their houses, native
and historical territories. The Armenians used all the
means and every opportunity to expel the Azerbaijanis
Slovak international scientific journal # 84, (2024) 51
from this area. Starting from the late 1980s, they man-
aged to completely expel Azerbaijanis from Western
Azerbaijan using the current political situation in the
USSR. These facts once again prove that the actions of
Armenians are against humanity and international law
norms. The rights of the displaced Azerbaijani popula-
tion must be restored. This is the historical and legal
right of the expelled population.
References
1. Arzumanlı V., Həbiboğlu V., Muxtarov K..
1918-ci il qırğınları. Tarixi araşdırmalar Bakı,
“Öyrətmən”. 1995. 90 səh.
2. Azerbaijan Democratic Republic: Great Brit-
ain's Archive documents, Baku, 2008, 576 p.
3. Bayranov İ. M. Qərbi Azərbaycan: Tarixi
həqiqətlər вə ya Ermənistanın etnik təmizləmə siyasəti,
Bakı: 2011,288səh.
4. Əmrahov M. Ermənilərin Cənubi Qafqaza
köçürülərək Qərbi Azərbaycan torpaqlarına ərazi
iddiaları üçün zəmin yaradılması. “Qərbi
Azərbaycanın tarixi və mədəniyyəti” konfransının
materialları, Bakı, 2023 //
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Ermnilrin_Cnubi_Qafqaza_kocurulrk_Qrbi_Azrbayca
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5. Gözəlova N. Azərbaycanın türk-müsəlman
əhlaisinin soyqırımı: Britaniya kitabxanasının arxiv
sənədlərində (1918-1920). Bakı, 2017, 76 s.
6. İsgəndərli A. C. Azərbaycan həqiqətləri:
1917-1920. Bakı, “Elm və təhsil”, 2012, 228 s.
7. İsmayılov K. Zəngəzur bölgəsində
azərbaycanlıların soyqırımı. “Azərbaycan”.-2015.-3
aprel.-N 68.-S.7.
8. Qasımlı M. “Erməni məsələsi”ndən “erməni
soyqırımı”na: gerçək tarix axtarışında (1724-1920) /
M.Qasımlı. – Bakı: “Mütərcim”, 2014.
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52 Slovak international scientific journal # 84, (2024)
MATHEMATICS
IT FOLLOWS FROM THE SPECIAL THEORY OF RELATIVITY THAT INVISIBLE AFTERLIFE
WORLD IS IN FACT PHYSICALLY REAL
1
Antonov A.
PhD, HonDSc, H.Prof.Sci
Independent researcher, Kiev, Ukraine
DOI: 10.5281/zenodo.11624422
Abstract
The article proves that the generally accepted version of special theory relativity (SRT), which states that
imaginary numbers are physically unreal, is incorrect. Experimental evidence is given of the general scientific
principle of the physical reality of imaginary numbers, with the use of which a corrected version of the SRT was
created. She argues that in addition to our visible universe, there are many other mutually invisible universes in
nature. And they form the actually physically existing afterlife invisible world, predicted by all religions.
Keywords: imaginary numbers, special theory of relativity, invisible universes, invisible afterlife world.
1. Introduction
Imaginary numbers, discovered about 500 years
ago by Scipione Del Ferro, Niccolò Fontana Tartaglia,
Gerolamo Cardano, Lodovico Ferrari and Raphael
Bombelli [1], are known to everyone and are currently
used in all exact sciences. They are even studied in
school mathematics courses. But unlike other numbers
that are understandable to everyone - integers and frac-
tions, positive and negative, scalar and vector, etc. -
their physical essence has not yet been explained. In-
deed, what 2 kg., 3 m., 4 sec. is clear to everyone, but
what is 2i kg., 3i m., 4i sec., where
1−=i
, no one
can explain. Nevertheless, no one cared about this, just
as, for example, now no one can explain. Nevertheless,
no one cared about this, just as, for example, now no
one cares that the phenomenon of ball lightning is not
explained.
But at the beginning of the 20th century Joseph
Larmor [2], Nobel Prize winner Hendrik Anton Lorenz
[3], Jules Henri Poincaré [4], Nobel Prize winner Albert
Einstein [5] and other outstanding scientists created the
special theory of relativity, which rightly accepted to be
considered an outstanding scientific achievement of
physics of the 20th century, because it proposed the
principle of relativity. And which is therefore now stud-
ied in all physics textbooks used in the educational pro-
cess even at the most prestigious universities. However,
in this theory, calculations using relativistic formulas,
which were the final result of all reasoning, in some
1
This is reprint of the article “Antonov A. A. From the physical reality of imaginary numbers it follows that the invisible
afterlife world predicted by all religions actually exits. Norwegian Journal of development of the International Science. 130.
36-41.
https://doi.org/10.5281/zenodo.10975059”.
cases led to a result measured by imaginary numbers.
And this result already needed to be explained. After
all, no one would need a theory that even its creators
could not explain. But the authors of SRT did not know
how to do this. And the fate of the service station hung
in the balance. But it was saved by the fact that an ad-
ditional postulate was introduced into the SRT, called
the principle of not exceeding the speed of light, from
which it followed that quantities measured by imagi-
nary numbers do not exist in nature. And therefore,
there is no need to explain them.
This is the form in which SRT is still taught.
2. The physical reality of imaginary numbers.
But besides STR there are other sciences. Includ-
ing the theory of electrical circuits, which is used in ra-
dio engineering, electrical engineering and computer
science. Fundamental to this theory is Ohm’s law [6],
[7], discovered in 1826 for DC electrical circuits, which
is now studied even in school physics textbooks. And
in 1893, Charles Proteus Steinmetz proposed its inter-
pretation of Ohm’s law for alternating current electrical
circuits [8], which is now used daily by millions of en-
gineers around the world in their work. In this theory of
electrical circuits, the imaginary resistances of capaci-
tors and inductors, which can be measured by instru-
ments, were recognized as actually physically existing.
And if these imaginary resistances were recognized as
physically unreal, as follows from SRT, then neither ra-
dio engineering, nor electrical engineering, nor com-
puters, nor radio measuring instruments should exist.
Slovak international scientific journal # 84, (2024) 53
Fig. 1. In any radio-technical laboratory there are devices called frequency response meters, which prove the
physical reality of imaginary and complex numbers by their mere existence
But they do exist. And thereby they prove the
physical reality of imaginary numbers [9]-[33]. Conse-
quently, by the existence of radio- and electrical engi-
neering, the generally accepted version of SRT was re-
futed even before its creation. Other proofs of the phys-
ical reality of imaginary numbers have been published
in [34]-[46]. Therefore, the logical conclusion is that
the version of SRT currently presented in all physics
textbooks is incorrect [47]-[66]
3. Physical reality of invisible parallel universes
In the existing generally recognized version of
SRT from its relativistic formulas and the principle of
non-exceeding the speed of light also follows that in
nature there is only our visible universe in which eve-
rything is measured only by real numbers. However, in
the corrected version of SRT [67]-[74], from its relativ-
istic formulas it follows that in our Multiverse [75]-
[85], in addition to our visible universe, there are also
about twenty other mutually invisible parallel universes
And one can be convinced of their existence [86]-
[91]. as a result of astronomical observations of the
starry sky in portals [92]-[94], since the constellations
in them will differ - and the further into the portal one
penetrates, the greater the differences will be - from the
constellations observed at the same time in the same re-
gion outside the portals. And since there are a lot of
anomalous zones [95]-[98] on Earth, such anomalous
zones. Like, for example, the main astronomical obser-
vatory of the National Academy of Sciences of
Ukraine, located in Goloseyevsky forest 12 km from
the center of Kyiv. Therefore, in order to verify the ex-
istence of neighboring invisible universes adjacent to
our visible universe, it is enough to compare on a com-
puter the observations of this observatory with the ob-
servations of neighboring observatories located outside
the anomalous zones.
Fig. 2. Scheme of an astronomical experiment to detect invisible universes
4. Why, despite all the refutations of the gener-
ally accepted version of SRT, set out in all physics
textbooks, it continues to be taught.
But this simple and low-cost experiment, which in
the most indisputable way will allow us to answer the
question of whether there are invisible universes neigh-
boring our visible universe, no one has done or is going
to do. Obviously, because physicists do not need such
an answer, since it will refute the version of SRT stud-
ied in textbooks.
The corrected version of SRT states that imaginary
numbers are physically real and invisible universes ex-
ist. Therefore, having become convinced of the exist-
ence of invisible universes, we will have to admit that
the corrected version of SRT is correct and once again
be convinced that imaginary numbers actually physi-
cally exist. And then it will inevitably be necessary to
explain their physical meaning of imaginary numbers.
And it is obvious - in addition to our visible world, there
is an invisible world.
5. The existence of a physically real invisible
world
However, the usefulness for science of the above
experimental evidence of the physical reality of imagi-
nary numbers goes beyond problems of correcting the
54 Slovak international scientific journal # 84, (2024)
version of SRT given in physics textbooks. From ex-
perimentally proven principle of the physical reality of
imaginary numbers, one will inevitably have to con-
clude that the results of all studies described by imagi-
nary numbers in all other exact sciences also are phys-
ically real.
Then many difficult questions will arise. For ex-
ample, what exists in the looking glass when we see
ourselves in the mirror? And therefore, in the end, we
will have to admit that in addition to our visible world,
there is also a huge (most likely even much larger than
our visible world) invisible world [99]-[107]. Indeed,
in addition to the room in which we are now and which
we see, there are a large number of other invisible to us
rooms in other apartments, houses, cities and countries.
The same situation is in space – in addition to our visi-
ble universe, in other dimensions there are about twenty
other parallel universes of the hidden Multiverse that
are invisible to us. And outside of our hidden Multi-
verse in the Hyperverse, there are many other Multi-
verses.
And the existence of such a world invisible to us,
in which Gods and the souls of the dead live, was long
predicted by all world religions. Consequently, what
these religions say about the world order, about the af-
terlife, is true. And therefore, all of us, the inhabitants
of planet Earth, will now have to believe in this.
6. Conclusion
The author hopes that the information presented in
the article will be an incentive to unite the efforts of
science and religions in their activities for the benefit of
people.
Acknowledgments
The author is cordially grateful for the understand-
ing, comments and help of his wife Olga Ilyinichna An-
tonova.
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18. Antonov A.A. (2022). The version of STR set
out in physics textbooks is incorrect because it states
that Ohm's law as interpreted by Steinmetz does not re-
ally exist, and therefore radio engineering does not ex-
ist either. Sciences of Europe (Praha, Czech Republic).
87(1). 54-57. DOI: 10.24412/3162-2364-2022-1-54-57
19. Antonov A.A. (2022). Why the physics text-
books teach an incorrect version of the special theory
of relativity which denies the existence of radio- and
electrical engineering. III international scientific con-
ference “Challenges and problems of modern science”.
London. Great Britain. 78-86. DOI:
https://doi/org/10.528/zenodo.7486814
Slovak international scientific journal # 84, (2024) 55
20. Antonov A. A. (2023). Why is the incorrect
version of the special theory of relativity being studied
in physics textbooks, refuted the existence of radio- and
electrical engineering even before its creation? The sci-
entific heritage. (Budapest, Hungary). 105. 83-89. DOI:
10.5281/zenodo.7560145
21. Antonov A.A. (2023). Why is an incorrect ver-
sion of the special theory of relativity that denies the
possibility of the existence radio and electrical engi-
neering being studied in physics textbooks? German In-
ternational Journal of Modern Science. 48. 23-29. DOI:
https://doi.org/10.5281/zenodo.7541137
22. Antonov A.A. (2023). Who needs the incorrect
version of special relativity taught in physics textbooks
despite all its experimental refutations? Annali d’Italia.
39, 64-70. DOI: 10.5281/zenodo.7568916
23. Antonov A.A. (2023). Why is incorrect ver-
sion of the special theory of relativity that denies the
possibility of the existence of radio and electrical engi-
neering being studied in textbooks of physics? Norwe-
gian Journal of development of the International Sci-
ence. 100. 27-33. https://doi.org/10.5281/ze-
nodo.7528512
24. Antonov A.A. (2023). Why is incorrect ver-
sion of the special theory of relativity, refuted by the
existence of radio and electrical engineering, is still
studies in all university physics textbooks? Danish Sci-
entific Journal. 69. 66-72. https://doi.org/10.5281/ze-
nodo.7692053
25. Antonov A.A. (2023). Why is incorrect ver-
sion of the special relativity still being studied in phys-
ics textbooks, which denies Ohm’s law for alternating
current used worldwide by millions of radio- and elec-
trical engineers? International independent scientific
journal. 46. 38-44. https://doi.org/10.5281/ze-
nodo.7525751.
26. Antonov A.A. (2023). Why is the generally ac-
cepted version of STR, which denies the possibility of
the existence of radio engineering and electrical engi-
neering, tsunamis and bell ringing, the physical phe-
nomenon of resonance and Ohm’s physical law for al-
ternating current, music created by the piano and even
swing swings on the playground, nevertheless is still
considered correct and studied in physics textbooks?
Sciences of Europe (Praha, Czech Republic). 112. 44-
50. DOI: 10.5281/zenodo.7708515
27. Antonov A.A. (2023). Why is the incorrect
version of the special theory of relativity still being
studied in physics textbooks, despite all its experi-
mental refutations. European Journal of Applied Sci-
ences. Services for Science and Education. UK. 11(2).
61-71. DOI: https://doi.org/10.14738/aivp.112.14128
28. Antonov A.A. (2023). Why the incorrect ver-
sion of the special theory of relativity, which denies the
possibility of the existence of radio engineering and
electrical engineering, has not yet been refuted. Journal
of science. Lyon. 40. 19-25. https://doi.org/10.5281/ze-
nodo.7704392
29. Antonov A. A. (2008). Physical Reality of
Resonance on Complex Frequencies. European Journal
of Scientific Research. 21(4). 627-641. http://www.eu-
rojournals.com/ejsr.htm
30. Antonov A. A. (2009). Resonance on Real and
Complex Frequencies. European Journal of Scientific
Research. 28(2). 193-204. http://www.eurojoun-
als.com/ejsr.htm
31. Antonov A. A. (2010). New Interpretation of
Resonance. International Journal of Pure and Applied
Sciences and Technology. 1(2). 1-12.
http://doi.org/10.17686/sced_rusnauka_ 2010-888
32. Antonov A. A. (2010). Oscillation processes
as a tool of physics cognition. American Journal of Sci-
entific and Industrial Research. 1(2). 342-349.
doi:10.5251/ajsir.2010.1.2.342.349
33. Antonov A. A. (2010). Solution of algebraic
quadratic equations taking into account transitional
processes in oscillation systems. General Mathematics
Notes. 1(9). 11-16.
http://doi.org/10.17686/sced_rusnauka_2010-887
34. Antonov A. A. (2013). Physical Reality of
Complex Numbers. International Journal of Manage-
ment, IT and Engineering. 3(4). 219-230
http://doi.org/10.17686/sced_rusnauka_2013-898
35. Antonov A. A. (2014). Correction of the spe-
cial theory of relativity: physical reality and nature of
imaginary and complex numbers. American Journal of
Scientific and Indus-trial Research. 5(2). 40-52.
doi:10.5251/ajsir.2014.5.2.40.52
36. Antonov A. A. (2015). Physical reality of com-
plex numbers is proved by research of resonance. Gen-
eral Mathematics Notes. 31(2). 34-53.
http;//www.emis.de/jour-
nals/GMN/yahoo_site_admin/asets/docs/4_GMN9212
-V31N2.129701.pdf
37. Antonov A.A. (2015). Principle of physical re-
ality of imaginary and complex numbers in modern
cosmology: the nature of dark matter and dark energy.
Journal of the Russian physico-chemical society. 87(1).
328-355. (In Russian).
http://doi.org/10.17686/sced_rusnauka_2015-1119
38. Antonov A. A. (2016). Physical Reality and
Nature of Imaginary, Complex and Hypercomplex
Numbers. General Mathematics Notes. 35(2). 40-63.
http://www.geman.in/yahoo_site_admin/as-
sets/docs/4_GMN-10932-V35N2.31895146. pdf
39. Antonov A. A. (2015). Ohm’s law explains as-
trophysical phenomenon of dark matter and dark en-
ergy. Global Journal of Physics. 2(2). 145-149.
http://gpcpublishing.com/index.php?jour-
nal=gjp&page=arti-
cle&op=view&path%5B%5D=294&path%5B%5D=p
df_14
40. Antonov A. A. (2015). Adjustment of the spe-
cial theory of relativity according to the Ohm’s law.
American Journal of Electrical and Electronics Engi-
neering. 3(5). 124-129. doi: 10.12691/ajeee-3-5-3
41. Antonov A. A. (2016). Ohm's Law is the gen-
eral law of exact sciences. PONTE. 72(7) 131-142. doi:
10.21506/j.ponte.2016.7/9
42. Antonov A. A. (2016). Ohm’s Law explains
phenomenon of dark matter and dark energy. Interna-
tional Review of Physics. 10(2). 31-35.
https://www.praiseworthyprize.org/jsm/in-
dex.php?journal=irephy&page=arti-
cle&op=view&path%5B%5D=18615
56 Slovak international scientific journal # 84, (2024)
43. Antonov A. A. (2016). Ohm’s law refutes cur-
rent version of the special theory of relativity. Journal
of Modern Physics. 7. 2299-2313.
http://dx.doi.org/10.4236/jmp.2016.716198
44. Antonov A.A. (2021). The special theory of
relativity stated in physics textbooks is incorrect. 77th
International Scientific Conference of the Eurasian Sci-
entific Association "Theoretical and practical issues of
modern science". Moscow. ESA. 11-15
45. Antonov A. A. (2021). Version of the special
theory of relativity that is studied in all physics text-
books is incorrect. Österreichisches Multiscience Jour-
nal (Insbruck, Austria). 43(1). 17-22. http://osterr-sci-
ence.com
46. Antonov A. A. (2021). Generally accepted ver-
sion of the special theory of relativity contained in
physics textbooks is incorrect. The scientific heritage.
(Budapest, Hungary). 73(2). 39-43. DOI:
19.24412/9215-0365-2021-73-2-39-43
47. Antonov A. A. (2021). Special theory of rela-
tivity, which is studied in physics text-books, is incor-
rect. German International Journal of Modern Science.
16, 49-53. DOI: 10.24412/2701-8369-2021-16-49-53
48. Antonov A. A. (2021). Special theory of rela-
tivity, which is studied in all physics textbooks, is in-
correct. Danish Scientific Journal. 51(1). 31-35.
http://www.danish-journal.com
49. Antonov A. A. (2021). Special theory of rela-
tivity taught in all physics textbooks is incorrect. An-
nali d’Italia. 22(1). 39-44. https://www.anditalia.com/
50. Antonov A. A. (2021). Special theory of rela-
tivity presented in physics textbooks is wrong. Norwe-
gian Journal of development of the International Sci-
ence 68(1). 3-7. DOI: 10.24412/3453-9875-2021-68-3-
7. 51. Antonov A. A. (2021). In all physics textbooks
an erroneous version of special theory of relativity is
given. International independent scientific journal.
31.34-39. http://www.iis-journal.com
52. Antonov A. A. (2021). Special theory of rela-
tivity taught in physics textbooks is wrong. Journal of
science. Lyon. 23. 47-52. https://www.joslyon.com/
53. Antonov A. A. (2021). All physics textbooks
study incorrect special theory of relativity. Sciences of
Europe. (Praha, Czech Republic) 79(1). 30-35. DOI:
10/24412/3162-2364-2021-79-30-35
54. Antonov A. A. (2021). Experimental proofs of
infidelity of the version of the special theory of relativ-
ity studied in physics textbooks and the truth of its al-
ternative version. 80th International Scientific Confer-
ence of the Eurasian Scientific Association "Develop-
ment of science and education in the conditions of
global instability". Moscow. ESA. 8-17. https://esa-
conference.ru/sborniki/?y=2021
55. Antonov A. A. (2021). The fallacy of the STR
version studied in physics text- books proved experi-
mentally. Österreichisches Multiscience Journal (Inns-
bruck, Austria). 45(1). 17-26. http://osterr-science.com
56. Antonov A. A. (2021). Experimental evi-
dences for the fallacy of the STR version in the physics
textbooks. European Journal of Applied Sciences. Ser-
vices for Science and Education. UK. 9(6). 349-364.
DOI:10.14738/aivp.96.11304.
57. Antonov A. A. (2021). If the STR version in
physics textbooks were true, we would never have
heard the music of the piano and the bell ringing, there
would be no television, no cellular telephony, no radar
or GPS navigation, we would not even be aware of the
existence of resonance and Ohm’s law as interpreted by
Steinmetz, and our children could not swing on the
swings. The scientific heritage (Budapest, Hungary).
78(2). 41-50. DOI: 10.24412/9215-0365-2021-78-2-
41-50
58. Antonov A. A. (2021). Experimental refuta-
tions of the STR version contained in physics textbooks
and confirmations of the truth of its alternative version.
German International Journal of Modern Science. 22.
52-61. DOI: 10.24412/2701-8369-2021-22-52-61
59. Antonov A. A. (2021). The STR version in
physics textbooks must be corrected, be-cause if it were
true, there would be no tsunamis or indian summer in
nature, we would be never have heard piano music, en-
gineers would be not have been able to create televi-
sion, cell phones, GPS trackers, and even children
would not be able to swing on swings. Danish Scientific
Journal. 54(1). 29-38. http://www.danish-journal.com
60. Antonov A. A. (2021). Experimental evidence
of the incorrectness of the STR version studied in phys-
ics textbooks. Annali d’Italia. 25(1). 32-41.
https://www.anditalia.com/
61. Antonov A. A. (2021). The incorrectness of
the STR version presented in physics textbooks proven
experimentally. Norwegian Journal of development of
the International Science. 74(1). 3-7. DOI:
10.24412/2453-9875-2021-74-53-62.
62. Antonov A. A. (2021). Experimental refuta-
tions of the generally accepted version of the SRT stud-
ied in physics textbooks. International independent sci-
entific journal. 34(1). 23-32. http://www.iis-jour-
nal.com
63. Antonov A. A. (2021). Experimental refuta-
tions of the SRT version in the physics textbooks. Jour-
nal of science. Lyon. 26(1). 29-37.
https://www.joslyon.com/
64. Antonov A. A. (2021). Experimental evi-
dences for the fallacy of the STR version in physics
textbooks. Sciences of Europe (Praha, Czech Repub-
lic). 82(2). 19-28. DOI: 10.24412/3162-2364-2021-82-
2-19-28
65. Antonov A.A. (2023). The Corrected Version
of the Special Theory of Relativity. European Journal
of Applied Sciences. Services for Science and Educa-
tion. UK. 11(5). 68-83. DOI:10.14738/aivp.115.15474
66. Antonov A. A. (2023). Corrected special the-
ory of relativity. Journal of science. Lyon. 48. 27-36.
https://doi.org/10.5281/zenodo.10277156
67. Antonov A. A. (2023). Corrected special the-
ory of relativity. Annali d’Italia. 49, 25-35. DOI:
10.5281/zenodo.10214679
68. Antonov A. A. (2023). The Corrected Version
of the Special Theory of Relativity. The scientific her-
itage. (Budapest, Hungary). 123. 72-81,
69. Antonov A. A. (2023). The Corrected Version
of the Special Theory of Relativity. Norwegian Journal
of development of the International Science. 118. 40-
49. https://doi.org/10.5281/zenodo.10009500
Slovak international scientific journal # 84, (2024) 57
70. Antonov A. A. (2023). Alternative Version of
the Special Theory of Relativity. Sciences of Europe.
(Praha, Czech Republic). 128. 62-71.
71. Antonov A. A. (2023). Special Theory of Rel-
ativity. German International Journal of Modern Sci-
ence. 67. 64-73. DOI: 10.5281/ zenodo.10966458
72. Antonov A. A. (2023). Corrected Version of
the Special Theory of Relativity. Danish Scientific
Journal. 77. 88-97. https://doi.org/10.5281/ze-
nodo.10054677
73. Antonov A. A. (2011), Structure of the Multi-
verse. British Journal of Science. 2(2). 51-60.
http://doi.org/10.17686/sced_rusnauka_2011892
74. Antonov A. A. (2012). Multiverse. Time Trav-
els. International Journal of Pure and Applied Sciences
and Technology. 12(2). 43-56.
http://doi.org/10.17686/sced_rusnauka_2012-896
75. Antonov A. A. (2012). Discovery of the real
multiverse. Encyclopedia of Russian thought, Reports
to the Russian Physical Society. 16(3). 3-20. (In Rus-
sian). http://doi.org/10.17686/sced_rusnauka_2012-
1115
76. Antonov A. A. (2013). Cognition of the multi-
verse as a factor in accelerating the development of hu-
man civilization. Journal of Russian physical thought.
1-12, 6-77. (In Russian).
http://doi.org/10.17686/sced_rusnauka_2011-1117
77. Antonov A. A. (2015). Hidden Multiverse. In-
ternational Journal of Advanced Research in Physical
Science. 2(1). 25-32.
http://doi.org/10.17686/sced_rusnauka_2015-903.
78. Antonov A.A. (2015). The astrophysical phe-
nomenon of dark matter and dark energy proves the ex-
istence of the hidden Multiverse. American Journal of
Modern Physics. 4(4). 180-188. DOI:
10.11648/j.jamp.20150404.14
79. Antonov A. A. (2015). Hidden Multiverse: ex-
planation of dark matter and dark energy phenomena.
International Journal of Physics. 3(2). 84-87.
doi:10.12691/ijp-3-2-6
80. Antonov A. A. (2015). Principles and structure
of the real Multiverse: explanation of dark matter and
dark energy phenomena. American Journal of Modern
Physics. 4(1). 1-9. doi: 10.11648/j.ajmp.20150401.11
81. Antonov A. A. (2016). Hypothesis of the Hid-
den Multiverse: Explains Dark Matter and Dark En-
ergy. Journal of Modern Physics. 7(10), 1228- 1246.
doi: 10.4236/jmp.2016.710111
82. Antonov A. A. (2015). Quaternion structure of
the hidden Multiverse: explanation of dark matter and
dark energy. Global Journal of Science. Frontier Re-
search A: Physics and Space Science. 15(8). 8-15.
https://globaljournals.org/GJSFR_Volume15/2-
Quaternion-Structure-of-the-Hidden.pdf
83. Antonov A. A. (2016). Verifiable Multiverse.
Global Journal of Science Frontier Research: A Physics
and Space Science. 16(4) 4-12. doi: 10.17406/GJSFR
84. Antonov A. A. (2020). How to See Invisible
Universes. Journal of Modern Physics. 11(05), 593-
607. DOI: 10.4236/jmp.2020.115039
85. Antonov A. A. (2020). Can invisible universes
be seen? International independent scientific journal.
21(2). 51-60. http://www.iis-journal.com
86. Antonov A. A. (2020), How to discover invis-
ible universes. Norwegian Journal of development of
the International Science. 42(1). 36-48.
http://www.njd-iscience.com
87. Antonov A. A. (2020). Universes Being Invis-
ible on Earth outside the Portals Are Visible in Portals.
Natural Science. 12(8). 569-587.
https://doi.org/10.4236/ns.2020.128044
88. Antonov A. A. (2020). Invisible universes can
be seen in anomalous zones. Danish Scientific Journal.
43(1). 9-24. http://www.danish-journal.com
89. Antonov A. A. (2021). Invisible universes can
be seen in anomalous zones. International independent
scientific journal. 23(1). 28-44.
90. Antonov А. А. (2012), Earth, portals, parallel
universes. American Journal of Scientific and Indus-
trial Research. 3(6). 464-473.
doi:10.5251/ajsir.2012.3.6.464.473
91. Antonov A. A. (13 January 2016). How Portals
of the Invisible Multiverse Operate. Science PG Fron-
tiers. http://www.sciencepublishing-
group.com/news/sciencepgfrontiersinfo?artic leid=7
92. Antonov, A. A. (2016). Star gates of the hid-
den multiverse. Philosophy and cosmology. 6. 11-27.
(In Russian). http://ispcjournal.org/journals/2016-
16/Antonov16.pdf
93. Chernobrov, V. (2000). Encyclopedia of mys-
terious places of the Earth. Veche Publishing House.
Moscow. (In Russian).
94. Chernobrov, V. (2004). Encyclopedia of mys-
terious places of Russia. Veche Publishing House.
Moscow. (In Russian).
95. Chernobrov, V. (2007). Encyclopedia of mys-
terious places of the Earth and space. Veche Publishing
House. Moscow. (In Russian).
96. Chernobrov, V. (2009). Encyclopedia of mys-
terious places of Moscow and Moscow region. Helios
ARV Publishing House. Moscow. (In Russian).
97. Antonov A. A. (2017). The physical reality
and essence of imaginary numbers. Norwegian Journal
of development of the International Science. 6. 50-63.
http://www.njd-iscience.com
98. Antonov A. A. (2018). Physical Reality and
Essence of Imaginary Numbers in Astrophysics: Dark
Matter, Dark Energy, Dark Space. Natural Science.
10(1). 11-30. doi:10.4236/ns.2018.101002
99. Antonov A. A. (2023). Proving physical real-
ity and explaining the physical essence of imaginary
numbers. Norwegian Journal of development of the In-
ternational Science. 123. 26-36.
https://doi.org/10.5281/zenodo.10451085
100. Antonov A. A. (2024). Physical reality of im-
aginary numbers and their physical essence. Danish
Scientific Journal. 80. 25-35/
https://doi.org/10.5281/zenodo.10594282
101. Antonov A. A. (2024). Proof of physical re-
ality of imaginary numbers and explanation of their
physical essence. German International Journal of
Modern Science. 72. 17-27.
102. Antonov A. A. (2024). Physical reality of im-
aginary numbers and their physical essence. Sciences
of Europe. (Praha, Czech Republic). 133(1). 79-90.
DOI: 10.5281/zenodo.10575590
58 Slovak international scientific journal # 84, (2024)
103. Antonov A. A. (2024). Physical reality of im-
aginary numbers and their physical essence. The scien-
tific heritage. (Budapest, Hungary). 129. 43-53. DOI:
10.5281/zenodo.10558263
104. Antonov A. A. (2024). Proving Physical Re-
ality and Explaining Physical Essence of Imaginary
Numbers. Journal of science. Lyon. 50. 25-35.
https://doi.org/10.5281/zenodo.10609816
105. Antonov A. A. (2024). Physical reality of
complex numbers and their physical essence. Interna-
tional independent scientific journal. 58. 3-13.
https://doi.org/10.5281/zenodo.10491923
106. Antonov A. A. (2024). Proof of physical re-
ality of imaginary numbers and explanation of their
physical essence. Annali d’Italia. 51, 25-35. DOI:
10.5281/zenodo.10573831
Slovak international scientific journal # 84, (2024) 59
A FINITE DIFFERENCE METHOD FOR THE SOLUTION OF THIRD ORDER BOUNDARY VALUE
PROBLEMS IN ORDINARY DIFFERENTIAL EQUATIONS
Ramani J.V.,
Department of Mathematics, Dyal Singh College (University of Delhi),
Lodhi Road, New Delhi, India
Kumar Dinesh
Department of Mathematics, Dyal Singh College (University of Delhi),
Lodhi Road, New Delhi, India
DOI: 10.5281/zenodo.11624443
Abstract
In this paper, we propose an efficient finite difference method to solve third order boundary value problems.
Analysis proves that the proposed method have at least quadratic convergence. Numerical results confirm the
accuracy and efficiency of the proposed method.
Keywords: Boundary Value Problems, Finite Difference, Taylor series, Row Sum Norm, Maximum Error.
1. Introduction
Third-order differential equations arise in many
modelling problems like aeroelasticity, beam deflection
theory, electromagnetic waves, theory of thin film flow.
In this paper, we study an effective numerical
technique based on finite differences to solve third or-
der boundary value problems(BVPs) of the following
type: (1.1)
subject to the boundary conditions
(1.2)
where the , and are arbitrary constants.
The discussion on the existence, uniqueness and
convergence of the solution of problem 1.1 can be
found in the literature [1], [12], [3], [6]. We wont men-
tion the conditions on the existence and uniqueness of
the solution to problem 1.1.
We assume the existence and uniqueness of the so-
lution to problem 1.1. We also assume that problem 1.1
is well posed.
This article is arranged in the following order. In
section 2, we propose the finite difference method. In
section 3, we discuss the convergence of the proposed
method. In section 4, we illustrate the method with ex-
amples and finally in section 5 we present the perfor-
mance of our proposed method.
2. The Difference method
To find an approximation to the solution of the
problem 1.1, we discretize the domain into
equal subintervals each of size
:
(2.1)
where the nodes are given by .
We want to determine the numerical approximation of the true solution of the problem 1.1 at the nodal
point
Let and denote the numerical approximations of and at which
allows us to write the boundary value problem 1.1 at node as written as
(2.2)
subject to the boundary conditions
.
We define the nodes as
and denote the solution of the problem 2.2 at
by
Using the method of undetermined coefficients and Taylor’s series expansion [7, 8, 9], we get the following
scheme:
(2.3)
where
60 Slovak international scientific journal # 84, (2024)
is the truncation error.
After neglecting the truncation errors at the nodes
, in 2.3, we obtain a system of
equations in the unknowns
, which may be linear or non-linear according as is linear or non-linear.
Using the values
, we compute the values , according to the second-order approximation
(2.4)
3. Convergence Analysis
Let
, denote the true solution of the problem 1.1 at the
and let be the
column vector
(3.1)
Also let, be the column vector consisting of the approximations
at the nodes
,
(3.2)
and the errors at the nodes
be denoted by
(3.3)
and the error vector in column form be denoted by
(3.4)
Then, we have the following equations (3.5)
(3.6)
where the matrix and column vectors and are given by
(3.7)
(3.8)
(3.9)
and the ’s and ’s are given by
(3.10)
and
(3.11)
The matrix is nonsingular [4, 5] and its inverse is given by
Slovak international scientific journal # 84, (2024) 61
(3.12)
and
(3.13)
Here denotes the maximum row sum norm of .
Now,
(3.14)
From equations 3.5 and 3.6, we have (3.15)
which gives (3.16)
Therefore, (3.17)
where is the maximum norm of .
If we let,
(3.18)
Then (3.19)
Hence
(3.20)
which shows that the our proposed scheme 2.3, 2.4 has second order convergence.
4. Numerical Examples
The following problems illustrate the performance of our method. We compute the maximum absolute error
MAE in the true solution, namely:
All the computations were performed on Ubuntu 20.04.4 LTS GNU linux operating system with IDLE 3.8.10
running Python version 3.8.10 on Intel® Corei5-9400 CPU @ 2.90GHz × 6 PC.
Example 4.1. Consider the linear model problem in [10] given by:
(4.1)
with the boundary conditions (4.2)
with the exact solution (4.3)
The MAE computed by method 2.3 for different values of N are given below
N
MAE
128
8.150736478892279e-05
256
2.0557217413813555e-05
512
5.161967603378552e-06
1024
1.2933322996243161e-06
2048
3.2368860043946283e-07
4096
8.096661511538226e-08
Example 4.2. Consider the linear model problem in [11] given by:
, (4.4)
with the boundary conditions (4.5)
with the exact solution (4.6)
62 Slovak international scientific journal # 84, (2024)
The MAE computed by method 2.3 for different values of N are given below:
N
MAE
128
3.0204368352604316e-05
256
7.55068418839544e-06
512
1.8876175097159997e-06
1024
4.71897596415749e-07
2048
1.1797358473453201e-07
4096
2.9493265135682734e-08
Example 4.3. Consider the nonlinear model problem in [12] given by:
, (4.7)
with the boundary conditions
(4.8)
with the exact solution (4.9)
The MAE computed by method 2.3 for different values of N are given below:
N
MAE
128
2.2417700782846953e-05
256
5.662842074857788e-06
512
1.4230859950213962e-06
1024
3.5669952002108547e-07
2048
8.92905674886816e-08
4096
2.2330040715915107e-08
5. Conclusion
In this paper we have proposed a numerical
method to solve third order boundary value problems
having quadratic convergence. We have estimated the
error involved. We have also given several numerical
examples which confirms our claim.
References
1. Ravi P. Agarwal, Boundary value problems for
higher order differential equations, World-Scientific,
Singapore, (1986).
2. Gregus M., Third order linear differential equa-
tions, Series: Mathematics and its Applications,
Springer Netherlands, Vol. 22, (1987).
3. Gupta C. P. and Lakshmikantham V., Existence
and uniqueness theorems for a third-order threepoint
boundary value problem, Nonlinear Analysis: Theory,
Methods and Applications, Vol. 16, No. 11, pp.949–
957, (1991).
4. M. K. Jain, Numerical Solution of Differential
Equations, New Age International, (2018).
5. Horn, R. A. and Johnson C. R., Matrix Analysis,
Cambridge University Press, New York, NY 10011,
USA, (1990).
6. Murty, K.N. and Rao, Y.S., A theory for exist-
ence and uniqueness of solutions to three-point bound-
ary value problems, Journal of Mathematical Analysis
and Applications, Vol. 167, No. 1, 43–48, (1992).
7. P. K. Pandey, The numerical solution of third
order differential equation containing the first deriva-
tive, Neural Parallel and Scientific Comp., Vol. 13,
297–304, (2005).
8. P. K. Pandey, An efficient numerical method for
the solution of third order boundary value problem in
ordinary differential equations, Int. J. Computing Sci-
ence and Mathematics, Vol.9, No. 2, 171-180, (2018).
9. P. K. Pandey, The Numerical Solution of Three
Point Third Order Boundary Value Problems in Odes,
Journal of Science and Arts, Year 20, No. 3(52), 529-
536, (2020).
10. Calgar, H. N., Calgar, S. H. and Twizell, E. H.,
The Numerical Solution of Third-Order Boundary-
Value Problems with Fourth-Degree B-Spline Func-
tions, Intern. J. Computer Math., Vol. 71, 373-381
(1999).
11. El-Danaf, T. S., Quartic Nonpolynomial
Spline Solutions for Third Order Two-Point Boundary
Value Problem, World Academy of Science, Engineer-
ing and Technology, International Journal of Mathe-
matical, Computational, Physical, Electrical and Com-
puter Engineering 2(9), 637-640 (2008).
12. Ghazala, A., Muhammad, T., Shahid, S. S. and
Hamood, U. R., Solution of a Linear Third order Multi-
Point Boundary Value Problem using RKM, British
Journal of Mathematics and Computer Science 3(2):
180-194 (2013).
Slovak international scientific journal # 84, (2024) 63
NORMAL AND PATHOLOGICAL PHYSIOLOGY
A CLINICAL CASE IN THE PRACTICE OF A RHEUMATOLOGIST: SYSTEMIC LUPUS
ERYTHOMUS WITH INFLAMMATION OF ORGANS AND SYSTEMS
Bukach O.,
assistant of the department of internal medicine
Ariichuk D.,
Babchenko V.,
Soha N.,
Stefurak M.
Bukovyna State Medical University
DOI: 10.5281/zenodo.11624463
Abstract
Systemic lupus erythematosus (SLE) is one of the most serious systemic connective tissue diseases that de-
velops more often in young women and girls, although it can occur at any age. Patients with SLE still have a high
risk of death (3 times higher than in the general population). Early diagnosis, intensification of basic therapy and
minimization of the dose of glucocorticoids (GC), assessment of cardiovascular risk and treatment of cardiovas-
cular diseases are considered to be the basis for improving the prognosis in SLE.
Keywords: systemic lupus erythematosus, facial erythema, polyarthritis, pneumosclerosis, myocardiofibro-
sis.
Introduction
Rheumatology is one of the most diagnostically
complex medical disciplines, which is at the intersec-
tion of many specialties. A rheumatologist needs a high
level of professional skills, because he often has to di-
agnose conditions that can hide under the mask of rheu-
matological symptoms. One of the most difficult
groups of rheumatological diseases to differentiate is
systemic lupus erythematosus.
Systemic lupus erythematosus (SLE) is a systemic
autoimmune polyetiological disease characterized by
hyperproduction of autoantibodies to various compo-
nents of the cell nucleus with the development of im-
munoinflammatory damage to tissues and internal or-
gans [1, 7]. In all age groups, the incidence is higher
among women, especially those of reproductive age,
when the ratio of the incidence of women to men is 8:1–
15:1, while this pattern is least pronounced in prepuber-
tal age — 4:3 [2, 11] According to over the past 60
years, the 5-year survival of patients with SLE has in-
creased from 50 to 91–97% [16, 18]. Such an improve-
ment is primarily associated with timely diagnosis, and
therefore early initiation of therapy, and management
of patients based on the principle of "treatment until the
goal is achieved" — stable clinical and laboratory re-
mission [12].
SLE is accompanied by multiple organ damage
and the development of various complications, includ-
ing both typical and rare ones. In particular, one of the
main reasons for the unfavorable prognosis of the dis-
ease is kidney damage [5]. Despite progress in the di-
agnosis and treatment of this pathology, kidney damage
remains the leading cause of death in patients with SLE.
Many such patients develop chronic kidney disease
(CKD), as well as complications, concomitant diseases
and conditions that are a consequence of immunosup-
pressive therapy: infections, osteoporosis, damage to
the cardiovascular and reproductive systems, etc. [3, 4].
Regarding methods of treatment of lupus nephritis in
SLE, many studies are being conducted, new promising
drugs are appearing [9, 15]. CKD is also associated
with the development of vitamin D deficiency, sys-
temic osteoporosis, and secondary hyperparathyroid-
ism [6].
According to the literature, there are 5 main types
of soft tissue calcification: dystrophic, metastatic, idio-
pathic, iatrogenic, and calciphylaxis [10, 17]. Most of-
ten, in systemic connective tissue diseases, a dystrophic
process is noted, which consists in secondary tissue
damage and the formation of calcifications [8]. It is
generally accepted that soft tissue calcifications are de-
tected in dermatomyositis, systemic scleroderma,
CREST syndrome, overlap syndrome, but they are rare
in SLE [13, 14].
We bring to your attention a clinical case of the
development of myocardial cardiomyopathy, pneu-
mosclerosis, polyarthritis and dyscirculatory encepha-
lopathy in a patient with SLE.
Purpose: to describe a clinical case of the devel-
opment of damage to all organs and systems in a patient
with SLE and to prescribe combined treatment depend-
ing on the damage to the relevant body systems.
Materials and methods
Patient V., 50 years old, complains of difficulty in
self-care, pain and stiffness in the joints of the hands
and feet, periodic aching pain in the area of the heart,
palpitations, rapid fatigue, coldness of the hands, suffo-
cation during physical exertion.
She considers herself a patient for 11 years. He is
periodically treated as an inpatient. Systematically
takes GC (diprospan, medrol). In connection with dete-
rioration of well-being and strengthening of the above-
mentioned symptoms, she was sent for inpatient treat-
ment in the rheumatology department of the OKL.
Objectively upon admission: the general condi-
tion of the patient is of moderate severity. Normos-
thenic. Swelling of the feet. Body temperature is
37.1oC. Pulse 82 per minute, satisfactory properties.
Blood pressure 140/90 mm Hg. The rhythm of cardiac
activity is correct, the ratio of tones is preserved. In the
64 Slovak international scientific journal # 84, (2024)
lungs, percussion is clear pulmonary sound, ausculta-
tion – vesicular breathing, basally weakened. Respira-
tory rate - 22 per minute. The tongue is wet, covered
with a white coating. The abdomen is soft, sensitive in
the epigastric region, in the left hypochondrium, the
edge of the liver is sensitive to palpation. Symptom
Pasternacki is negative on both sides. Limitation of
movements in the radiocarpal joints: right - dorsiflex-
ion 00, palmar flexion - 250, left - dorsiflexion 00, pal-
mar - 250. Left shoulder joint: flexion 900, abduction
900. Knee joints: right flexion 400, extension 1800, left
flexion 450, extension 1750. Ankle-foot joints: right
dorsiflexion - 300, plantar flexion - 100, left dorsiflexion
300, plantar 100. Contractures of both radiocarpal joints.
Contracture of the left shoulder joint. Extensor contrac-
ture of the right knee joint with impaired function. Flex-
ion-extension contracture of the left knee joint without
impaired locomotor function. Contractures of both an-
kle-foot joints with impaired function. Pain along the
paravertebral points of the thoracic spine.
Conducted examination:
PRS from 06.22.23 - negative. Blood group B(III),
Rh-positive
General blood test from June 21, 2023 - erythro-
cytes- 3.4x1012/l, Hb - 106 g/l, k.p. - 0.9, platelets–
216x109, leukocytes– 5.1x109/l, eosinophils – 2%, rod
nuclear – 2%, segment nuclear– 70%, lymphocytes –
25%, monocytes – 1%; erythrocyte sedimentation rate
–34 mm/h.
Biochemical analysis of blood from July 1, 2023.
protein 76.0 g/l, urea – 6.8 mmol/l, total bilirubin – 11.0
µm/l, blood glucose – 3.6 mmol/l.
Biochemical analysis of blood from July 9, 2023.
protein 77.0 g/l, urea – 6.7 mmol/l, total bilirubin – 18.0
µmol/l, blood glucose – 5.1 mmol/l, AsAT – 0.2
µmol/l, AlAT – 0.41 µmol/l, thymol test – 1.0 units,
urea – 6.6 mmol/l l, cholesterol - 4.2 mm/l.
Blood glucose as of March 7, 2023 - 6.4 mmol/l.
Rheumatic tests from June 23, 2023 - ASLO - 200;
CRP - 42 mg/ml, sialic test - 328 units, sulfur mucoid -
280 units.
General urine tests from 01.07.23 - 100 ml, light
yellow, transparent, specific weight- 1012, weakly
acidic, single transitional epithelium, single leukocytes,
single bacteria, protein, glucose - not found.
Daily glucosuria 06/21/23 1.00 l
Fecal analysis from June 21, 2023 – no helminth
eggs were found.
Fluorography of the chest organs from June 29,
2023 – lungs and heart within normal limits.
Electrocardiography from July 1, 2023 – sinus
rhythm, regular, heart rate 87 beats per minute.
Changes in the myocardium of the back wall of the left
ventricle, hypertrophy of the myocardium of the left
ventricle.
Ultrasound diagnostics of the abdominal cavity
from June 24, 2023 - vertical size of the right lobe of
the liver - 152 mm, increased echogenicity. The
gallbladder is oval in shape, contains echogenic bile,
the walls are compacted. Pancreas of increased echo-
genicity. Spleen 110x41mm, homogeneous. The right
kidney is moderately lowered, N sizes. In both kidneys,
the calyces are compacted, casts of salts, the paren-
chyma is preserved. Signs of chronic cholecysto-pan-
creatitis.
Ultrasound diagnostics of the thyroid gland (thy-
roid gland) - both lobes of the thyroid gland are of nor-
mal size, the tissue of the thyroid gland is homogene-
ously heterogeneous, more on the right. Signs of diffuse
goiter.
Consultation of a gynecologist on November 6,
2023, she is healthy.
Consultation of an endocrinologist - Diffuse non-
toxic goiter II st. Autoimmune thyroiditis.
The diagnosis was made: Systemic lupus erythe-
matosus, chronic course, activity of the 1 degree, with
lesions of the skin (erythema of the face, décolletage,
reticular liver), heart (myocarditic myocardiofibrosis,
arrhythmic variant of Heart failure IIA, functional class
II), lungs (pneumosclerosis Pulmonary failure I) , joints
(Polyarthritis Ro II stage, Joint functional insufficiency
II stage, contractures of carpal, knee, ankle-foot joints),
nervous system (dyscirculatory encephalopathy), RES
(lymphoadenopathy).
And the treatment carried out: diet No. 10, medrol,
dexamethasone, panangin, renalgan, corvitin, tivortin,
reosorbilact, metamax, thiotriazoline, neocardil,
aspecard, megafen, calcium-D3 nicomed. Passed health
school No. 6.
On July 6, 2023, she was discharged home to con-
tinue outpatient treatment.
RECOMMENDED in the future for the patient:
1. "D" registration with a rheumatologist, endocri-
nologist, gastroenterologist at the place of residence.
2. Methylprednisolone 20 mg (according to the
scheme).
3. Plaquenil 1 tablet at night- 6 months
4. Calcium - D3 Nikomed 1 tablet x 2 r per day -
during the period of taking GC.
5. Pantaprozole 40 mg 1 tablet x 1 per day - during
the period of GC reception.
6. Curantyl 1 tablet x 2 times (2 weeks).
7. Panangin 1 tablet x 3 times a day – the entire
period of taking GCS
8. Sedative therapy (barboval, motherwort, seda-
tive herbal preparation).
9. Observe the regime of work and rest.
CONCLUSION
A large number of pathological conditions unre-
lated to rheumatology can be hidden under the mask of
rheumatological symptoms. Systemic lupus erythema-
tosus, which is characterized by polymorphism of man-
ifestations, requires special attention. The presence of
comorbid pathology in patients with systemic lupus er-
ythematosus creates problems for verifying the diagno-
sis of this disease and conducting high-quality multi-
symptom treatment.
References
1. Achebe I., Mbachi C., Asotibe J.C. Paintsil I.
(2020) Dystrophic Calcinosis Cutis in Systemic Lupus
Erythematosus. Cureus. 2020;12(6):e8727.
doi.org/10.7759/cureus.8727.
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2. Almaani S., Meara A., Rovin B.H. Update on
Lupus Nephritis. Clinical journal of the American So-
ciety of Nephrology: CJASN. 2017;12(5):825–835.
doi.org/10.2215/CJN.05780616.
3. Anders H.J., Saxena R., Zhao M.H. et al. Lupus
nephritis. Nature reviews. Disease primers.
2020;6(1):7. doi.org/10.1038/s41572–019–0141–9.
4. Andrews J., Psaltis P.J., Bayturan O. et al. War-
farin use is associated with progressive coronary arte-
rial calcification: insights from serial intravascular ul-
trasound. JACC: Cardiovascular Imag-
ing.2018;11(9):1315–1323.
5. Aringer M., Costenbader K., Daikh D. et al. Eu-
ropean League Against Rheumatism/American College
of Rheumatology classification criteria for systemic lu-
pus erythematosusAnnals of the Rheumatic Diseases.
2019;78:1151–1159.
6. Chandran M., Wong J. (2019) Secondary and
Tertiary Hyperparathyroidism in Chronic Kidney Dis-
ease: An Endocrine and Renal Perspective. Indian jour-
nal of endocrinology and metabolism. 2019;23(4):391–
399. doi.org/10.4103/ijem.IJEM_292_19.
7. Dima A., Balanescu P., Baicus C. (2014) Phar-
macological treatment in calcinosis cutis associated
with connective-tissue diseases. Romanian journal of
internal medicine = Revue roumaine de medecine in-
terne. 2014;52(2):55–67.
8. Freire V., Moser T.P., Lepage-Saucier M. Radi-
ological identification and analysis of soft tissue mus-
culoskeletal calcifications. Insights into imaging. 2018;
9(4): 477–492. doi.org/10.1007/s13244-018-0619-0.
9. Imran T.F., Yick F., Verma S. et al. Lupus ne-
phritis: an update. Clinical and experimental nephrol-
ogy. 2016;20(1):1–13. doi.org/10.1007/s10157-015-
1179-y.
10. Jimenez-Gallo D., Ossorio-Garcia L., Linares-
Barrios M. Calcinosis cutis and calciphylaxis. Actas
Dermosifiliogr. 2015;106(10):785–794.
11. Le C., Bedocs P.M. Updated. Treasure Island,
FL: StatPearls Publishing. Calcinosis Cutis.2020.
12. Lederhandler M., Valins W., Zoghbi Z.,
Grossman M.E. Leg ulcers in systemic lupus erythema-
tosus associated with underlying dystrophic calcinosis
and bone infarcts in the absence of antiphospholipid an-
tibodies. JAAD case reports. 2016;2(2):164–167.
doi.org/10.1016/j.jdcr.2016.02.009.
13. Lopez A.T., Grossman M.E. Facial calcinosis
cutis in a patient with systemic lupus erythematosus: A
case report of tissue injury owing to photosensitivity as
the cause of dystrophic calcification. JAAD case re-
ports. 2017;3(5):460–
463.doi.org/10.1016/j.jdcr.2017.06.018.
14. Muñoz C., Isenberg D.A. Review of major en-
docrine abnormalities in patients with systemic lupus
erythematosus. Clinical and experimental rheumatol-
ogy. 2019;37(5):791–796.
15. Rattazzi M., Faggin E., Bertacco E. et al. War-
farin, but not rivaroxaban, promotes the calcification of
the aortic valve in ApoE-/- mice. Cardiovascular thera-
peutics. 2018;36(4):e12438. doi.org/10.1111/1755–
5922.12438.
16. Soudet S., Delaporte E., Hatron P.Y. Diffuse
calcinosis cutis in systemic lupus erythematosus: an ex-
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doi.org/10.1177/0961203316630819.
17. Traineau H., Aggarwal R., Monfort J.B. et al.
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18. Zaremba Ye.Kh, Virna M.M, Shykh L.B, Bu-
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66 Slovak international scientific journal # 84, (2024)
PEDAGOGY
SETTING THE PROBLEM IN TEXTBOOKS AND METHODICAL MATERIALS FOR TEACHERS
Abbasova S.
Candidate of pedagogical sciences, docent
DOI: 10.5281/zenodo.11624493
Abstract
The situation of teaching includes the existence of a problem (contradiction) and the way to solve it. That is,
the teacher should put a problem in front of the children, deeply understand the nature of the question, and also
imagine how the children can answer. He should always be ready to help students not get confused in the formu-
lation of problems and discussions. Creating a learning situation is a process of conducting problem-based learn-
ing. Keywords: Active training, cognitive activity, methodological tools, types of work, reproductive.
The teaching situation ensures creative assimila-
tion of knowledge by students through dialogue with
the teacher. This method allows to develop cognition
and communication skills, provides effective develop-
ment of high-quality knowledge, intelligence and crea-
tive abilities, education of an active personality.
By creating a learning situation, the teaching
method is aimed at:
1) identification of the problem (difficulties);
2) choosing a solution to the problem;
3) ability to work with information;
4) listening and understanding other people;
5) ability to work in a group.
Teacher's duty:
- creating learning situations (determining the ped-
agogical task (developing writing skills);
- choose the teaching material;
- to determine the way of organizing the learning
situation (how to start, what to do for everyone);
- predict possible actions of children;
- turning training tasks into learning situations (not
only with the learning task, but also its "regulation" -
putting this task in conditions that encourage children
to be active, create motivation for learning).
Types of learning situations:
1. Selection. A number of ready-made solutions
are provided, including incorrect ones. You need to
choose the right one.
2. Uncertainty. Uncertain decisions due to lack of
information.
3. Surprise. It causes surprising unusualness, par-
adoxically.
4. Conflict. A situation that thinks otherwise.
5. Incompatibility. It does not "fit" existing prac-
tices and ideas. [3, p.13-14]
The requirements for carrying out the study are:
- that students have basic knowledge and skills in
subjects (have program material);
- ability to work independently;
- the value of the expected training results;
- the ability to change the way of thinking.
In the lesson of learning new material, two con-
nections should be worked out: the formulation of an
educational problem and the search for its solution. The
formation of the educational problem and the search for
a solution are carried out by students during a specially
structured dialogue.
Dialogue is at the heart of any learning situation,
and dialogue is essential to resolving this situation.
Methods of creating a learning situation with prob-
lem formulation and solving occur in three stages of
lessons:
1) updating knowledge.
2) statement of the problem.
3) "discovery" of new knowledge by children.
"Discovery" of new knowledge by children is
based on some mental operations, so tasks that teach
this mental operation should be included in the stage of
updating knowledge. Thought must be put into "form".
Therefore, in the actualization of knowledge, it is nec-
essary to include tasks of this type: find the excess, di-
vide into groups, compare and show the difference,
tasks for the development of variant thinking, attention,
memory, etc. In the final task, "complexity" is planned.
Completion of the stage of updating knowledge is as-
sociated with the identification of "difficulties" in the
activity. [2, p.101]
To create a learning situation means to present stu-
dents with a sense of surprise or any contradiction that
arises in relation to difficulties. For example: it is
enough to look at the methods of creating educational
situations in the lessons of the special course "Preven-
tion of spelling errors".
Methodical material for Azerbaijani language les-
sons is prepared according to demand. At the heart of
the outline plans is a modern approach to learning.
Various innovative techniques, methods and
forms were used during the development of lessons.
The realities of modern life require students to develop
a creative approach to learning, so it is rational to apply
group work to lessons in order to understand the im-
portance of teamwork, develop research skills, deepen,
systematize and summarize the material.
Lessons in groups assume the presence of children
with a high, sufficient, medium and low level of
knowledge in each group. Groups can be permanent or
changing (depending on their deep goals and tasks, the
degree of complexity, the level of mastery of the mate-
rial, the wishes of the students). Improving speech cul-
ture is one of the main goals of learning at this stage, so
it is appropriate to include elements of literature in
Azerbaijani language classes. It also helps students to
have a coherent understanding of the texts.
Slovak international scientific journal # 84, (2024) 67
In the methodical materials presented for class V,
a sufficient amount of different materials have been se-
lected for all these types of work, so that each teacher
can choose the necessary option, focusing on his class.
[7, p.13] The presented textbook set consists of two
books: a textbook and a teacher. funds for (MMV). Ac-
cording to this set, it is planned to teach the Azerbaijani
language in 6 sections. In the 5th grade, the subject of
the Azerbaijani language is taught for 5 hours a week
for 34 weeks (170 hours).
A small summative assessment (KSQ) is carried
out no earlier than 4 weeks and no later than 6 weeks,
and each educational stage covering this period corre-
sponds to a certain section (topic) reflected in the text-
book. A major summative assessment (BSQ) is con-
ducted at the end of each semester. The number of
hours allocated for each section includes 1 hour for
KSQ. Hours intended for BSQ are not reflected in the
schedule. The reading and listening materials, as well
as the speaking and writing activities presented in each
unit, are related to the topic of that unit.
Materials related to language rules are divided into
sections as follows: Section I – the sound and letter
composition of the word (phonetics); Section II – se-
mantic features of the word (lexicon); Section III –
word composition and formation methods (word crea-
tion); Section IV – words denoting name, sign, action
(morphology); Section V – spelling of compound
words. Section VI - types of sentences according to pur-
pose and intonation, punctuation in dialogue. At the end
of each section, the textbook provides materials for re-
peated lessons on the language rules taught in the cor-
responding section. [8, p. 4]
Tasks of various levels of complexity combine
knowledge of theoretical material in practice, allowing
not only to perform training exercises of a reproductive
nature, but also to use the creative component that con-
tributes to the further development of the individual,
the manifestation of activity, and also increases interest
in the subject.
The manual will help novice teachers to acquire
the first methodical skills, and will give experienced
teachers the opportunity to diversify the methodical
techniques used in the lesson. Plans are designed taking
into account the age characteristics of students and con-
tain not only educational material, but also game tasks
that develop the creative activity of schoolchildren,
take them to the interesting country of the Azerbaijani
language and help them to remember easily. The pro-
posed coursework will provide practical help in choos-
ing the types of training and control work that are fully
presented and meet the requirements of the National
Curriculum for the Azerbaijani language for grades V-
XI. Methodical resources are designed for creative use
by diversifying the methods of presenting the material.
Training can be effective if there is a qualitative change
in training methods, and attention is paid to the active
inclusion of thinking in the process of cognition and
knowledge acquisition. The concept of "active learning
method" characterizes learning based on active cogni-
tive activity in the process of cooperation with other
participants of the educational process. Often, the con-
cept of "interactive teaching methods" is used as a syn-
onym of this concept.
Active learning is a set of ways of organizing and
managing teaching and cognitive activity, which are
characterized by the following: creation of a cognitive
problem situation by the teacher; stimulating the active
research position of students in the process of solving
the problem situation; creating conditions for independ-
ent discovery, assimilation and assimilation of new
knowledge for students. The essence of this approach
to teaching is that training is not based on enriching stu-
dents' memory with new knowledge, but on the system-
atic development of thinking and skills for self-assimi-
lation and assimilation of knowledge. [2, p. 114]
The main condition for learning in this case is the
need for the child to consciously isolate the educational
task as a cognitive task: what to learn, why to learn,
how to learn and what results it will lead to. The teach-
er's position is that of a "facilitator". The main function
that determines the role of the teacher in active learning
as a guide on the way to knowledge is called facilitation
(creating favorable conditions). It is a new type of
teacher leadership, based on the joint activity of stu-
dents and teachers, aimed at achieving a common edu-
cational goal. At the same time, the teacher does not
rule the classroom as an undisputed authority and does
not stand outside of it.
He cooperates with him in a systematic and pur-
poseful way: he organizes problematic situations, helps
students formulate research problems, provides me-
thodical assistance in solving them, directs and shows
the way to acquire knowledge. The task of the teacher-
facilitator is to teach learning, that is, to help the child:
master the main components of the learning activity; to
master in practice the set of mental methods and meth-
ods necessary for the acquisition and application of
knowledge. This curriculum has an action quality and
is designed to help each student become a competent,
independent researcher, independently acquire the nec-
essary knowledge, and become a lifelong learner.
However, in order to implement such a training
scheme, the teacher should not only understand the role
of a guide in the path of acquiring knowledge, but also
know its specific functions and be able to apply them in
practice. For this, first of all, it is necessary to under-
stand the facilitation process itself: facilitation as a pro-
cess is the process of organizing the discussion, activat-
ing the students by effectively using guiding, guiding
questions, leading to the discovery of new knowledge;
the main feature of facilitation is that new knowledge
is acquired not by the teacher, but by the students; the
position of the facilitator, whose main function is to en-
courage thinking and guide it in the right direction. The
main goal of the facilitation approach is to fully satisfy
cognitive and creative needs and create opportunities
for students' self-realization.
Since active learning methods are based on con-
ducting research for the purpose of discovering new
knowledge, active teaching itself is based on the laws
of conducting research.
.
68 Slovak international scientific journal # 84, (2024)
References
1. Abdullayev N.A. Spelling and orthography
training issues. Baku, 1983, 90 p.
2. Abdullayev A.S., Karimov Y.Sh. Methodology
of mother tongue teaching in primary classes. Baku,
Maarif, 1968, 316 p.
3. Abdullayev A.S. Methodology of teaching
Azerbaijani language in secondary school. Baku, Maa-
rif, 1978, 279 p.
4. Spelling dictionary of the Azerbaijani language,
Baku, Lider publishing house, 2004, 723 p.
5. Explanatory dictionary of the Azerbaijani lan-
guage. Baku, East-West Publishing House, Volume IV,
2011, 709 p.
6. Efendizade A. Scientific basis of correct writing
training. Baku, 1975, 173 p.
Slovak international scientific journal # 84, (2024) 69
MODEL OF PASSIVE AND ACTIVE FOREIGN LANGUAGE VOCABULARY DYNAMICS
Kostadinov O.
Ph.D., Guest Lecturer
Nikola Vaptsarov Naval Academy
Varna, Bulgaria
ORCID ID: 0000-0002-9183-5243
DOI: 10.5281/zenodo.11624502
Abstract
Learning a foreign language requires the perception and assimilation of foreign language knowledge to mem-
orize and use it later. The process of remembering is accompanied by forgetting. Memorizing foreign words hap-
pens gradually and in stages, which is why foreign language vocabulary is divided into two categories: passive
and active vocabulary. For these reasons, we have different degrees of mastery of foreign words. These features
of the process of acquiring foreign language knowledge make it dynamic. Between passive and active vocabulary,
there is constant movement of vocabulary in both directions. Repetition of foreign words from the passive vocab-
ulary leads to their passage into the active vocabulary and vice versa – when a given foreign word is not actively
used, it returns to the passive vocabulary. The dynamics of learning the foreign language determines the result.
Knowledge of this dynamic is important for the correct construction of teaching methods and conducting the pro-
cess of learning a foreign language.
Keywords: Passive Vocabulary; Memorization; Repetition; Language Dynamics; Contextual Memory; For-
eign Language Acquisition.
1. Dynamics of Passive and Active Vocabu-
lary in Foreign Language Acquisition
It is natural for foreign language learners to under-
stand some words during conversation or reading, but
when it comes time to speak or write, these words dis-
appear. This phenomenon is known as passive and ac-
tive vocabulary and is crucial for foreign language
learning. Our ability to differentiate between these
types of vocabulary is very important for anyone trying
to acquire or improve their foreign language profi-
ciency.
Passive and active foreign language vocabulary, as
well as the dynamics between them, are essential ele-
ments of foreign language learning and acquisition.
There are two main factors that determine the outcome
of foreign language acquisition. On the one hand, these
are the motivation and attention of the learner, and on
the other hand, an important factor is the process of for-
getting. Learning the vocabulary and grammar of a for-
eign language is a prolonged process that goes through
several stages concerning each lexical or grammatical
unit. Each foreign word must first be perceived aurally
or read, after which its meaning must be understood.
Memorizing foreign words and their active use takes
time, during which the studied vocabulary is reviewed
repeatedly. The very act of memorizing vocabulary is
conditional and variable. In human memory, there are
two main sectors where foreign language information
is stored: short-term and long-term memory. Infor-
mation stored in short-term memory needs to be further
developed, and information stored in long-term
memory must be maintained to avoid being lost.
Knowing foreign vocabulary is a broader concept
that includes foreign words whose meanings can be un-
derstood only in context, but a word read or heard out-
side of context can also be understood. On the other
hand, there are foreign words that are only understood
but not actively used in speaking or writing. In this re-
gard, the main characteristic of foreign language acqui-
sition can be noted as its dynamic nature.
One of the key tasks in foreign language acquisi-
tion is converting passive vocabulary into active vocab-
ulary. This requires constant practice and use of new
words in various contexts. Regular review and practice
help reinforce vocabulary and prevent forgetting. Ad-
ditionally, using different learning methods such as lis-
tening, reading, writing, and speaking is essential for
effective foreign language acquisition.
In conclusion, the dynamics between passive and
active vocabulary are crucial for successful foreign lan-
guage acquisition. Understanding these processes and
using appropriate learning methods can significantly
improve language skills and facilitate the transition
from passive knowledge to active use of the foreign lan-
guage.
2. Analysis of Passive and Active Foreign Lan-
guage Vocabulary
2.1. Passive Vocabulary
Laufer, B., (1998). The passive vocabulary in-
cludes words that we recognize and understand when
we hear or read them but do not use actively. These can
be words encountered in books, movies, or conversa-
tions but not fully integrated into our own language use.
The passive vocabulary is divided into two categories.
In the first category are words that are understood only
in context, without being understood out of context.
This part of memory is called Contextual Passive
Memory. The second category includes words that are
understood out of context but not used actively, mean-
ing their level of familiarity is higher than words that
can only be understood in context. This part of memory
is called Non-contextual Passive Memory. [1]
The passive vocabulary is divided into two
categories:
70 Slovak international scientific journal # 84, (2024)
• Contextual Passive Memory:
− Words and expressions understood only
within a specific context.
− Maintained through passive repetition (listen-
ing and reading).
• Non-contextual Passive Memory:
− Words and expressions understood even out-
side a specific context.
− Maintained through active repetition (active
learning, translation).
• Characteristics of Passive Vocabulary:
− Recognition: Words are recognized when seen
or heard.
− Limited Use: Rarely used in active speech or
writing.
− Activation: May require effort to recall and
use effectively.
Primary Conclusion:
Passive memory is divided into two categories:
− Contextual Passive Memory: Words and ex-
pressions understood only in context, maintained
through passive repetition (listening and reading).
− Non-contextual Passive Memory: Words and
expressions understood outside context, maintained
through active repetition (active learning, translation).
2.2. Active Vocabulary
Laufer, B., (1998). The active vocabulary consists
of foreign language words that are frequently and con-
fidently used in daily communication. These are the
words that come naturally, without us having to think,
when we speak or write. The active vocabulary is a fun-
damental tool for any foreign language; it is always
available and ready for use without the need for a dic-
tionary or reference.
Active vocabulary is a measure of language profi-
ciency and overall fluency. It is dynamic and ever-
changing. Words and expressions that are not used fre-
quently decrease in their level of familiarity within the
foreign language vocabulary of the speaker, resulting in
their return to one of the previous levels of mastery
found in the passive vocabulary. This process of words
shifting between active and passive memory highlights
the importance of regular usage for maintaining lan-
guage skills. [1]
• Characteristics of Active Vocabulary:
− Frequent Use: Regularly employed in both
spoken and written communication.
− Confident and Accurate Use: Words are un-
derstood and used correctly, with a high level of confi-
dence.
− Quick and Automatic Recall: Words come to
mind effortlessly, without the need for pauses or deep
thinking.
− Spontaneity: Ability to use words naturally
and spontaneously in various contexts.
Primary Conclusion:
Laufer, B., (1998). Active memory is created after
the assimilation of words and expressions. These words
are easily accessible and can be used spontaneously and
effectively. The dynamic nature of active vocabulary
underscores the need for consistent practice and en-
gagement with the language to ensure that words re-
main readily available for use. Regular interaction with
the language, through speaking, writing, and other
forms of communication, is essential for maintaining
and expanding one's active vocabulary.
3. Analysis of Kostadinov’s Model of Passive
and Active Foreign Language Vocabulary Dynam-
ics Ognyan Kostadinov's model for the dynamics of
passive and active foreign language vocabulary is pre-
sented in a table that examines the different stages and
processes related to the acquisition and use of foreign
words (Table 1). Table 1
The analysis of this model can be described as fol-
lows:
• Reception of Foreign Words (INPUT Info):
− Listening and Reading are the primary meth-
ods for receiving new information. These activities
include:
• Understanding of meaning by:
− Interpretation: Understanding the meaning of
words in the context of the sentence.
− Comprehension: Fully grasping the meaning
of the text.
− Translation: Translating words or text into the
native language.
• Passive Memory:
− This stage includes **Memorization** and
**Contextual Passive Memory**. Words are memo-
rized in the context in which they are encountered, aid-
ing better retention.
• Active Memory:
− Non-Contextual Passive Memory**: Words
are memorized without connection to a specific con-
text.
− Repetition: Repeating words helps retain them
longer and transition them to active memory.
• Active Usage:
− Assimilation: Integrating new words into ac-
tive vocabulary through Practice and Activation, lead-
ing to dynamic use in speech and writing.
Slovak international scientific journal # 84, (2024) 71
− Dynamics: Transition of words between active
and passive memory depending on frequency of use.
• Speaking and Writing (OUTPUT Info):
− These activities represent the ultimate goals of
the model—the active use of foreign words in speech
and written texts.
This model emphasizes the importance of both
passive and active learning strategies, highlighting the
dynamic nature of vocabulary acquisition and reten-
tion. It illustrates the process from passive to active
memory through practical application and repetition,
underscoring the necessity of frequent use for maintain-
ing an active vocabulary.
• Key points of the model include:
− The importance of practice and repetition for
retention and activation of foreign words.
− The significance of context for effective mem-
orization and understanding.
− The process of fading, where infrequent use
leads to words transitioning from active to passive
memory.
4. Basic Stages of Foreign Word Acquisition
and Knowledge Transition from Passive to Active
Vocabulary
Via listening to, reading, and writing texts, as well
as via the use of visual dictionaries that offer each word
in textual form together with a picture, we can acquaint
with foreign vocabulary. The use of word cards and the
repetition of reading phrases from dictionaries are also
standard practices. It is also beneficial to make use of
all the available ways to learn foreign words, as this will
ensure effective and long-lasting memory. One of the
most important factors in keeping new language is con-
sistent exposure and practice. In addition, participating
in discussions and using language that is applicable to
real-world situations strengthens both memory and
comprehension.
4.1. Listening to Unfamiliar Words:
The first stage is to get comfortable with foreign
words by listening to them several times without being
aware of what they signify in one's home language. The
listener is supposed to adjust their ears to the sounds to
achieve the aim. Hearing a foreign word several times
helps in its memory, which in turn causes the listener to
view the word as being familiar each time they hear it.
The first step in being comfortable with a foreign term
is to get familiar with it. This stage assists the student
in becoming used to the phonetic structure of the new
language he or she is learning.
4.2. Using Expressions with Unfamiliar Words:
When there are phrases that include words that are
not easily understood in a foreign language, it is im-
portant to learn them in the appropriate manner. For
students who are learning a foreign language, it is of
utmost importance to comprehend the meaning of new
terms in the context in which they are used. However,
the degree of difficulty of these expressions must cor-
respond with the amount of knowledge that they pos-
sess; otherwise, relying on a dictionary, which may be
distracting, is not the most effective method. New
words are easier to recall when they are associated with
previously learned ideas, which is accomplished via
contextual learning.
4.3. Repetition of Foreign Words and Building
Passive Vocabulary:
Passive vocabulary consists of two distinct cate-
gories: contextual and non-contextual words. These
represent separate groups within the realm of passive
vocabulary. The transition of words from contextual to
non-contextual occurs through continuous exposure to
a variety of texts, whether through listening or reading.
This process exemplifies a dynamic interaction within
passive vocabulary, where the acquisition and assimi-
lation of words undergo transformative phases.
4.4. Utilizing Dictionaries and Digital Tools for
Vocabulary Enhancement:
In the later stages of learning, students should em-
ploy dictionaries to delve into unfamiliar words, com-
prehending their fundamental meanings and broader
applications. Additionally, numerous digital dictionar-
ies offer audio features, enabling users to listen to the
pronunciation of the word. Moreover, these dictionaries
often provide contextual sentence examples, signifi-
cantly aiding in grasping the accurate meaning of the
word and facilitating its retention. This phase repre-
sents the mastery stage in enhancing one's familiarity
with words. By utilizing sentence examples, learners
can better grasp the proper usage and nuances of the
word.
4.5. Mastering Memory: The Art of Effective
Retention and Repetition
Memorization is not a single act, and to memorize
information effectively, it is important to repeat what
we have learned a great number of times.
Marousis, A., (2023). According to Harman Eb-
binghaus's forgetting curve, the retention rate of infor-
mation decreases over time:
− After 1 hour about 50% of the information is
retained.
− After 1 day about 30% of the information is
retained.
− After 1 week about 10% of the information is
retained.[2]
Jaap, M., Murre, J., Dros, J. (2015). These values
are approximate and may vary depending on various
factors such as methods and individual differences. The
Ebbinghaus Forgetting Curve (fig. 1) shows how
quickly new information can be retained if it is not used
or practiced regularly.
72 Slovak international scientific journal # 84, (2024)
Figure 1
The repetitions should be planned out and spaced
out over a period of one month to assist the learner's
passive memory in absorbing the knowledge. To boost
retention, this strategy makes use of the spacing effect,
which involves extending the amount of time that
passes between review sessions. Reviewing the content
on a regular basis helps to reinforce the knowledge,
which in turn increases the probability that it will be
retained in long-term memory.
According to Harman Ebbinghaus, the forgetting
curve (fig. 2) with periodic negotiation of what has
been learned every 12 hours illustrates how regular rep-
etition of information significantly improves its reten-
tion in memory:
− 1 hour after learning about 50% of the infor-
mation is retained.
− 12 hours after the first repetition the retention
increases to 70%.
− 24 hours after learning (after the second repe-
tition) retention is around 60%.
− After each subsequent iteration, the retention
rate increases or stabilizes at high levels.
Figure 2
Regular repetition helps consolidate knowledge in
long-term memory and significantly minimizes the
pace at which information is forgotten. This may be ac-
complished using the most efficient means possible,
which include the comprehension of relevant educa-
tional information by reading and comprehension. One
example of this would be viewing films or television
shows that are captivating and that pique the learner's
interest and curiosity. It is possible that we may refer to
this task as the third stage of learning foreign words
since it is a job that will never be finished. Within the
context of building passive vocabulary in a foreign lan-
guage, this stage acts as a transitional stage leading to
the fourth step. [3]
4.6. Transition from Passive to Active Memory:
Passive memory is often where a foreign word is
stored after it has been mastered. When the words are
spoken or heard often, they have the potential to enter
active memory. As a rule, we need to take into consid-
eration the fact that passive foreign language study,
which includes listening to comprehension and reading
comprehension, often only results in the improvement
of passive memory. Only a small number of passive
words can make their way into active memory without
conscious effort. It is necessary to participate in active
use, such as speaking or writing, to develop one's active
vocabulary. This is because active usage helps to rein-
force the words that are learnt via practical application.
This is the fourth step of creating an active vocabulary
inside a foreign language, often known as the process
Slovak international scientific journal # 84, (2024) 73
of acquiring foreign words. Active use of the foreign
language, which involves conversation as well as ver-
bal and written translation from the native language
into the foreign language, is the most effective method
for accomplishing this goal.
4.7. Building Active Vocabulary:
Active foreign language vocabulary building is the
last stage of memorization. It necessitates the active use
of foreign words. This could be accomplished through
dialog, oral, or written translations from a native lan-
guage into a foreign language. The active foreign lan-
guage vocabulary is based on passive vocabulary. Only
after repeated use of passive words and their active use
in speaking and writing can we expect to enhance ac-
tive vocabulary. Practical usage solidifies the transition
of words from passive to active memory. The level of
fluency and proficiency in a foreign language measures
the permanent process of building an active vocabulary.
Active vocabulary building is the final stage of
memorization for acquiring foreign words. It requires
actively using these words in various contexts. Dia-
logue, oral practice, or written translations from one's
native language into the foreign language can achieve
this active utilization of foreign words. A language
builds its active vocabulary on its passive vocabulary.
Mastery of words, initially encountered passively, only
comes after repeated use in speaking and writing. Prac-
tical application further solidifies the transition of
words from passive to active memory, reinforcing lan-
guage acquisition. "The development of active vocabu-
lary is an ongoing process in foreign language acquisi-
tion, measured by one's fluency and proficiency in the
language.
4.8. Maintaining Vocabulary:
There is a possibility that some words may return
to their passive form if we do not make consistent use
of them in our active vocabulary. When it comes to
keeping an active vocabulary, regular practice and use
are very necessary. It is helpful to keep words active
and prevent them from reverting to passive memory by
reviewing them and utilizing them in a variety of set-
tings. Active and passive language usage on a regular
basis may assist in the maintenance of vocabulary in a
foreign language.
Conclusion:
The study outlines a model of passive and active
foreign language vocabulary dynamics, emphasizing
the importance of memorization and forgetting in lan-
guage learning. It differentiates between passive vocab-
ulary (words recognized and understood but not ac-
tively used) and active vocabulary (words frequently
and confidently used in daily communication). The dy-
namic nature of vocabulary acquisition involves a con-
tinuous movement of words between passive and active
states. Regular practice and repetition are crucial for
maintaining and expanding active vocabulary. Under-
standing these dynamics is essential for developing ef-
fective teaching methods and enhancing language
learning outcomes.
References
1. Laufer, B., (1998). The Development of Pas-
sive and Active Vocabulary in a Second Language:
Same or Different? Applied Linguistics, DOI:
10.1093/applin/19.2.255
2. Marousis, A., (2023). What is the Ebbinhaus
forgetting curve? Examples and strategies for overcom-
ing it. Talencards, Available on: https://www.talent-
cards.com/blog/ebbinghaus-forgetting-curve/
3. Jaap, M., Murre, J., Dros, J. (2015). Replica-
tion and Analysis of Ebbinghaus’ Forgetting Curve,
PLOS / one, DOI:10.1371/journal.pone.0120644
74 Slovak international scientific journal # 84, (2024)
PHYSICS
ВЛИЯНИЕ ТЕРМООБРАБОТКИ НА ТЕПЛОВЫЕ И ЭЛЕКТРИЧЕСКИЕ СВОЙСТВА
ПОЛИМЕРНОГО ПОЛУПРОВОДНИКА ПОЛИГИДРОХИНОНА
Халилов С.Х.
Кандидат физико-математических наук, доцент кафедры «Инженерная физика и электроника»
Азербайджанского Технического Университета
INFLUENCE OF HEAT TREATMENT ON THERMAL AND ELECTRICAL PROPERTIES OF
POLYMER SEMICONDUCTOR POLYHYDROCHYNONE
Khalilov S.
Candidate of Physical and Mathematical Science,
Associate Professor of the Department of Engineering Physics and Electronics,
Azerbaijan Technical University
DOI: 10.5281/zenodo.11624509
Аннотация
Исследование показало, что более высокая температура термообработки полимерного полипровод-
ника полигидрохинона, обеспечивает более плотную упаковку макромолекул, измена межмолекулярные
расстояния и условия контакта между молекулами. Это приводит к увеличению длины эффективного со-
пряжения, благодаря улучшению при процессе термообработки условий для осуществления компланар-
ности макромолекул.
Аbstract
The study showed that a higher heat treatment temperature provides a more dense packing of macromolecules,
changing the intermolecular distances and contact conditions between molecules. This leads to an increase in the
effective conjugation length, due to the improvement in the heat treatment process of conditions for the coplanarity
of macromolecules.
Ключевые слова: Электропроводность, теплопроводность, термообработка, компланарност.
Keywords: Electrical conductivity, thermal conductivity, heat treatment, coplanarity.
Еще 2018 году ученые из MIT и Аргоннской
национальной лаборатории предположили, что по-
тенциальными кандидатами на роль теплопроводя-
щих полимеров могут стать макромолекулы с со-
пряженными связями в главной цепи. Система со-
пряжения связей в полимерах возникает либо за
счет чередования двойных и одинарных связей,
либо за счет чередования соединенных одинар-
ными связями ароматических фрагментов, либо за
счет сочетания этих случаев. [1,2]
Существующие литературные данные [3,4,5]
показывают, что в полимерных полупроводниках
области полясопражения разделены менее структу-
рированными прослойками и эти прослойки можно
рассматривать как потенциальные барьеры для
дрейфа носителей тока, высота которых определяет
энергию активации проводимости постоянном
токе.
С целью выяснения связи между электропро-
водности с теплопроводностю, а также влияния
термообработки на высоту потенциального барь-
ера, который существует в объеме полимерного по-
лупроводника полигидрохинона, была исследована
температурная зависимость удельной электропро-
водности σ и коэффициента теплопроводности λ.
Измерение теплопроводности и электропро-
водности проводилась на прессованных образцах,
приготовленных в виде таблеток. Для уменьшения
доли общего теплового потока, идущего на излуче-
ние, применялись плоские образцы сечения 0,3
0,4 см2 и высотой 0,1 0,2 см. Принятые меры поз-
волили обеспечить измерение абсолютной вели-
чины λ в интервале
804200К с точностью не менее 5%. Темпе-
ратура размягчения полигидрохинона Т > 4300К.
Методика измерения описана в работе [6]. Исследо-
вание проводилось в вакууме 10-5 Торр (133,322 Па)
На рис. I и 2 представлены температурные за-
висимости удельной электропроводности σ и коэф-
фициенты теплопроводимост λ и полимер ного по-
лупроводника полигидрохинона. Результаты изме-
рения зависимости σ(Т) и λ (Т) воспроизводимы
для каждой температуры термообработки. Из рис.1
видно, что каждое повышение температуры термо-
обработки приводит к увеличению электропрово-
димости, следовательно уменьшается энергия акти-
вации (ΔE ), определяемой по наклону прямой σ (Т)
высокотемпературной области, которая характери-
зует потенциальной барьер в полигидрохиноне.
Slovak international scientific journal # 84, (2024) 75
Рис.1. Температурные зависимости удельной электропроводности при разных температурах термооб-
работки.
1. Т = 3730К 2. Т = 3830К 3. Т = 3930К 4. Т = 4130К
Повышение температуры термообработки незначительно увеличивает величину теплопроводности
(рис.2.)
Рис.2.
Температурные зависимости удельной теплопроводности при разных температурах термообработки.
1. Т = 3730К 2. Т = 3830К 3. Т = 3930К 4. Т = 4130К
76 Slovak international scientific journal # 84, (2024)
В таблице приведены значения σ, λ и ΔE при температуре 2930К для каждой температуры термообработки.
Температура термообработки
Т (К)
σ
Ом-I см- I
λ
Вт/Ом.град.
ΔE
eV.
373
1·10-14
3,1·10-3
1,3
383
1,2·10-13
4,0·10-3
1,1
396
9·10-13
4,8·10-3
0,96
413
8·10-12
5,8·10-3
0,82
Как видно, значение λ достаточно низко, по-
этому электронная теплопроводность рассчитанная
на соотношений Видемана-Франца, а также за счет
биполярной диффузии оказывается несуществен-
ным. Низкие значения коэффициента инфракрас-
ного поглощения, также позволяет предположить,
что измеренная на опыте λ является теплопровод-
ностью фонов во всем исследованном интервале
температуры.
Особенности λ могут быть связаны двумя об-
стоятельствами. Во-первых: тем, макромолекула
содержит большое число атомов порядка 1000 Во-
вторых: существенным является, по-видимому,
большое различие взаимодействия внутри молекул
и молекулярного взаимодействия. Внутримолеку-
лярные связи являются ковалентными. Межмоле-
кулярное взаимодействие существенно более сла-
бое. Взаимодействие между линейными цепями
этого полимера обусловлено межмолекулярной
связью радикалов ОН [6]. Непрерывный рост λ с по-
вышением температуры связано о характером фо-
нонного спектра. Фононный спектр делится на две
части: первая низкочастотная часть спектра, кото-
рая связана с колебаниями целой молекулы. Вторая
часть спектра – это внутримолекулярные колеба-
тельные и вращательные движение отдельных ато-
мов и групп атомов. Эти колебания возбуждаются
уже при Т ˂ 1000К и могут участвовать в переносе
тепла. Таким образом, более высокая температура
термообработки, видимо обеспечивает более плот-
ную упаковку макромолекул, измена межмолеку-
лярные расстояния и условия контакта между моле-
кулами. Это приводит к увеличению длины эффек-
тивного сопряжения, благодаря улучшению при
процессе термообработки условий для осуществле-
ния компланарности макромолекул.
Вышеуказанное предположение согласуется с
существующей теорией о структуре и свойствах по-
лимерных полупроводников [7].
Список литературы
1. Yanfei Xu, Xiaoxue Wang, Jiawei Zhou, Bai
Song, Zhang Jiang, Elizabeth M. Y. Lee, Samuel
Huberman, Karen K. Gleason, Gang Chen. Molecular
engineered conjugated polymer with high thermal con-
ductivity, Science Advances. 2018.
2. Гагарин В.Г., Пастушков П.П. Изменение во
времени теплопроводности газонаполненных поли-
мерных теплоизоляционных материалов, Строи-
тельные материалы. 2017. № 6. С. 28–31.
3. Бах Н.А., Ванников А.В., Гришина А.Д.,
Нижний С.В., Усп. Химии, 35, 1733, 1965.
4. Богуславский Л.Н., Стильбанс, Докл, АН
СССР, 147, 1114, 1968.
5. Халилов С.Х. Исследование центры захвата
в полигидрохиноне, IV Республиканская межвузов-
ская конференция по физике., стр.22., 1978, Баку.
6. Основы физики и химии полимеров. Изд.
Высшая школа, М., 1976
7. Органические полупроводники., Изд. Наука,
1968.
Slovak international scientific journal # 84, (2024) 77
THE GENERATING FUNCTION TECHNIQUE AMELIORATES EFFECTIVE AND STRING FIELD
THEORIES AND FORESHADOWS THEIR LINKAGE TO QUANTUM INFORMATION THEORY
Robert Lloyd Jackson II
M.D.
Stilwell, KS
DOI: 10.5281/zenodo.11624536
Abstract
Many scientists are trying to develop a theory of everything or a supposition to explain all aspects of the
physical universe. This paper explores a set of theories called effective and string field theory or EFT and SFT,
respectively. These suppositions can be utilized in both old and possibly new physics. Typically, EFT and SFT
have a mathematical method for solving problems called the perturbation theory (PT); the generating function
technique or GFT can substitute this means of problem-solving. The latter method is used to solve several examples
of physical problems, such as determining the cause of muon g-2 experimental deviations, the means for the cal-
culation of glueballs via meson decay, the ascertainment of tetraquark mass from their decay products, and the
analysis of binary black hole mergers. Ultimately, GFT, instead of traditional PT methods, is a potent tool for
improving our understanding of concepts in contemporary physics, such as in EFT and SFT. Also, GFT shows the
existence of a triality between EFT, SFT, and Quantum Information theory (QIT).
Keywords: generating function technique, effective, quantum, and string field theory.
1.) Introduction
An appropriate theory of everything or ToE should
adequately combine general relativity and quantum me-
chanics [2,57,61,62]. Physics significantly grew after
Sir Isaac Newton discovered gravity [1,38]. Then, Al-
bert Einstein radically updated humanity’s current un-
derstanding of gravity with his General Theory of Rel-
ativity [13,19,29,37,38,46,91]. General relativity her-
alded another revolution in physics [1]. Quantum
mechanics, the study of quanta or particles, underwent
a revolution a little after the world recognized general
relativity as being virtually true [18,25,59]. Even
though many physicists developed putative mathemat-
ical frameworks, there was no provable strong theory
combining general relativity and quantum mechanics to
date.
Two basic systems of ideas that attempted to ex-
plain aspects of the universe involved fields. EFT and
SFT implemented physical body (i.e., particle) and
string fields to describe the behavior of facets of classi-
cal and quantum physics [21,26,52]. Hypothetically,
both theories served as a basis for a new ToE.
Calculus was the field of mathematics heavily en-
trenched in physics; thus, methods for solving such
problems incorporating differential equations were es-
sential. Since the inception of calculus, individuals
have established various techniques (i.e., perturbation
theory or PT) for deriving the solutions to differential
equations [20]. The latest method for solving physics
problems, GFT, which this author discovered, involved
using several truncated Laurent series of formal power
series or generating functions to solve problems known
to old physics (i.e., Boussinesq equation, Navier-Stokes
problems, etc.) [3,63]. This novel method of accruing
solutions to differential equations has a broad reach and
is considered capable of solving a wide range of prob-
lems in mathematical physics [88].
This paper discusses EFT and SFT via PT as prac-
tical ToEs. This study is divided into several sections:
section 2 provides concepts in perturbation, effective,
and string field theories; the next section shows how
GFT serves as a template for solving problems linked
to EFT and SFT; Section 4 shows how EFT and SFT
via GFT can be used in deriving solutions to four issues
alluding to old and new physics; finally, the last section
gives a quick review of EFT and SFT that shows GFT
is a highly effective means for solving problems related
to the two suppositions. In addition, the GFT claims at
least two significant links are apparent between the two
field theories and QIT in the last section.
2.) Basics of EFT and SFT after the consideration
of PT, then GFT
2.1.) PT synopsis
In PT, an individual finds an approximate solution
to a more straightforward defined problem [64]. The
solution becomes more accurate as the approximate so-
lution gains terms with decreasing parameters [64,89].
Ultimately, the approximate solution asymptotically
approaches the exact solution as the number of terms
added to the perturbation series approaches infinity
[64]. In other words, the perturbation series becomes a
formal power series over time [64].
2.2.) EFT synopsis
EFT encompasses an extensive array of fields in
physics [21]. Therefore, EFT covers quantum, classi-
cal, and cosmological fields [21]. In this study, we will
focus on quantum field theory, or QFT, and the cosmo-
logical aspects of EFT.
QFT combines quantum mechanics, classical field
theory, and special relativity [4,24,28,47,60]. It is com-
monly applied to particle physics and, thus, essential in
forming models within subatomic and condensed mat-
ter physics [4,24,28,47,60,92]. Since its advent in the
1920s and rebirth in the 1970s, QFT has had a promi-
nent role in describing contemporary physics.
QFT was divided into at least three branches:
quantum electrodynamics (QED), quantum flavor-dy-
namics (QFD), and quantum chromodynamics (QCD).
QED was primarily developed by Dirac in 1927 and
was built upon canonical quantization [9,32,40,44].
Also, it dealt with the interaction of fermionic and elec-
tromagnetic fields. QFD studied electroweak nuclear
force, such as bosons Z0 and W+ activities, while QCD
involved nuclear solid interactions, generally mediated
78 Slovak international scientific journal # 84, (2024)
gluon fields [12,23,47]. It is expected to find situations
where certain branches, like QED and QCD, cross over
or encroach on each other.
PT can be used to solve many problems in QFT
[47,60,92]. The interaction between particle fields is
treated as small perturbations in a free field. Finally, the
integration of PT with QFT is called perturbative quan-
tum field theory or pQFT.
EFT can also be applied to cosmology [14,15,29].
Cosmology is the study of the universe and its evolu-
tion. This realm of study includes the observations of
large-scale structures (LSS) and the laws that dictate
their behavior [95]. PT plays an active role in solving
problems associated with cosmology: The combination
of PT and this area of study is called cosmological per-
turbation theory [14,15,29]. The practical field theory
of large-scale structures or EFToLSS is used to enhance
the derivation of solutions in this area of science via
novel PT methodologies [96].
2.3.) SFT synopsis
This supposition involves reformulating relativ-
istic strings to QFT [12,24,28,60,92]. Unlike QFT,
which treats an individual field of particles in excited
states or quanta, string theory converts point-like parti-
cles into one-dimensional entities, referred to as strings.
Thus, string field theory uses these one-dimensional
strings to define excited particle fields.
Second quantization dictates the type of SFT to be
considered, such as open and closed string fields [97].
In the standard model of particle physics, some open
string fields are represented by gauge (gluons, photons,
W and Z bosons) and quark or lepton fermions [90].
Fields that describe the scattering of open or closed
strings are called open or closed SFT, respectively.
However, if a field contains a combination of both open
and closed strings, it is referred to as an open-closed
SFT.
SFT possesses advantages over regular string the-
ory. For instance, it permits the calculation of “off-
shell” amplitudes and thus provides information about
string scattering [52]. In addition to giving an individ-
ual the means to calculate the masses of particle sys-
tems that obey classical equations of motion, it can be
used to determine particle systems that do the contrary.
This process is called “off the mass shell” or off-shell
of the mass hyperboloid via perturbation methods [52].
In other words, SFT can be used to define attributes of
particles that do not follow the equations of motion in
a classical sense (i.e., virtual particles, dark sector
quanta, etc.) due to its innate ability to depict particles
as string fields.
2.4.) Mathematical descriptions of effective and
string fields via GFT
In EFT, an elementary field is a formal power
series of a function . A physical body, such as a parti-
cle, can be designated as an exponential function , as-
suming the auxiliary/characteristic equation is of the
first order, takes the following form:
,
where is an arbitrary constant, and is the an-
satz transform variable. (Note: For GFT purposes, the
auxiliary function is generally designated by the Greek
letter . However, this study will designate the auxil-
iary function with the alphanumeric letter due to par-
ticle physicists' conventional use of for bosons.) The
ansatz transformed variable for a (3+1) system was
defined as .
On the other hand, the expression of a “brane,”
which can be designated by a sinusoidal wave function
, Assuming the auxiliary/characteristic equation is of
the second order and is expressed as
or
where is the imaginary ansatz transform varia-
ble, where , and is another arbitrary constant.
The physical body and wave function leads to
EFT and SFT, respectively.
Thus, the elementary physical body or string field
can be defined as
,
where is the k-th parameter/coefficient of the
formal power series . On the contrary, its conjugate
elementary qubit gate is the following expression:
.
The formal power series and are also elemen-
tary effective or string fields. It is important to state an
elementary string field is an object with an infinite
number of branes; one of the branes acts as the “string”
while the other branes serve as the “bulk” space or com-
pactified dimensions of the universe [82,87]. Finally, a
truncated Laurent series of the elementary effective or
string field or raised by some power forms a
transformed compound effective or string field if
is combinatorial or trigonometric:
or
,
where is the absolute integer value of the trun-
cated power and is the -th parameter/coefficient and
power. Regarding string field theory, is equal to the
supersymmetry level . Ultimately, the difference be-
tween PT and GFT is that one method builds upon an
approximate solution while the other narrows the gen-
eral solution to derive the exact solution. The former
method would require many steps to achieve its objec-
tive due to adding higher-order terms. At the same time,
the latter only needs a few steps, like solving the pa-
rameter/coefficient and arbitrary constants.
3.) GFT as a new mathematical basis for garner-
ing solutions in EFT or SFT
3.1.) GFT and general solutions to particles
GFT, with some modification, was a method im-
plemented to find the solution of [non]linear PDEs. Its
transformed general solution U comprised a Laurent se-
ries set of combinatorial or trigonometric-based gener-
ating functions [3]. One should consider the trans-
formed general solution U as a transformed effective or
string field. After one assessed the maximal and mini-
mal power , through which the Laurent series of vari-
ous types of elementary practical or string field or ,
their conjugate is eventually truncated, (s)he plugs in
the predefined function into the transformed general
solutions for effective or string fields , , , ,
, , , and
:
Slovak international scientific journal # 84, (2024) 79
and
where and are the transformed scalar
bosonic effective or string fields, and are trans-
formed vector bosonic effective or string fields,
and are the transformed tensor bosonic effective
or string fields, and
are the transformed fermi-
onic effective or string fields, and is a specific ansatz
transformed time variable or
.
The parameter/coefficient was defined as com-
binatorial numbers to the i-th power like
and .
The square root of the k-th Fibonacci number
at/about zero, or Sk(0), was
while the k-th Chebyshev T or U (not to be con-
fused with the transformed general solution of the ef-
fective or string field) number at/about zero, or Ck(0),
was
.
For this article, the parameter/coefficient was
either or for bosonic effective or string field
while the parameter/coefficient was either or
were used for the fermionic effective or string
fields, where and .
Ultimately, mesonic effective or string fields ex-
hibit as a hyperbolic secant function raised by some
power. In contrast, gauge bosonic and fermionic effec-
tive or string fields can be expressed as a logistic func-
tion raised by some power. Figure 1 claims odd integer
spin bosonic or half-spin fermionic string fields possess
open strings whose vibratory modes satisfy solely Di-
richlet boundary conditions; the strings, called D-
branes, about such fields, have endpoints that are fixed
in spacetime [83,86,87]. Thus, GFT implies the odd in-
teger spin bosonic or half-spin fermionic string field’s
are equal to null. On the contrary, Figure 1 sug-
gests that other string fields, such as fields that com-
prise even integer spin bosonic strings (excluding those
that describe scalar particles), can be closed or open
strings [76,85,86,87]. They possess vibratory modes
that satisfy solely Neumann boundary conditions; these
fields have string endpoints that are free to roam in
80 Slovak international scientific journal # 84, (2024)
spacetime [76,85,86,87]. In short, open string fields
that behave like gauge bosons, such as photons and glu-
ons, have
equal to null and
exist as a 4 X 1
vector, while open string fields that behave like pseu-
doscalar and vector mesons retain a equal to null.
On the contrary, closed string fields that behave like
tensor bosons possess
equal to null and
exist
as a 4 X 4 matrix. The endpoints of the open string
fields are fermions.
Figure 1: examples of relativistic strings.
For this paper’s purposes,
,
, and
can
be expressed as
,
,
and
.
Finally, most operations involve Hadamard multi-
plication, mainly if limited to two vectors.
3.2.) On- and off-shell rest mass assessment via
renormalization
The expression for renormalization within a vol-
ume V was:
where was the mass-energy equivalence for a
compound effective or string field U and its conjugate
U*. Assuming the spherical volume, using Manhat-
tan/taxicab-like distance , for compound effective or
string field U was equal to the following expression
[75]:
the formula for renormalization became the fol-
lowing:
or
If the field pertains to either a vector or tensor
boson, an individual must find the (root) mean (square)
of for the former and implement a trace on , then
divided by four to the latter.
4.) Examples
This section explores and expands upon two basic
Lagrangian equations needed to solve the effective and
string fields associated with this paper. One Lagrangian
density formalism for either a fermion or gauge boson
field involving the Dirac equation, with its complex
conjugate field:
or .
Either equation obeys canonical commutation re-
lations and is converted to the Schrodinger equation if
the process is Markovian or the quantum telegraph
equation if the process is not Markovian [105]. For this
paper’s intentions, all functional derivatives of the
above equations will not involve a Markov process,
yielding the quantum telegraph equation. On the other
hand, the inhomogeneous Klein-Gordon equations for
a (pseudo)scalar, vector, and tensor mesons/boson are
,
,
and
,
respectively. (Note: If a gauge boson is a constit-
uent of another particle, one should use the quantum
telegraph Lagrangian formalism. On the contrary, if a
vector meson is considered a composite particle, then
(s)he should use the inhomogeneous Klein-Gordon La-
grangian equation.) The values is an interaction
Slovak international scientific journal # 84, (2024) 81
constant generally equal to unity, while the value
equals a positive integer if the particle/string is pre-
sented initially or a negative integer if the parti-
cle/string is a by-product [16,44]. Also, the number
equals the coefficient associated with a specific term in
the inhomogeneous Klein-Gordon Lagrangian. The
principles of least action have several bold Lagrangian
terms: represents the set of scalar bosonic effective
or string fields, represents the set of vector-based
bosonic effective or string fields, represents the set
of tensor bosonic effective or string fields. On the other
hand, and signify the initial and final fermionic
effective or string fields, respectively. Also, symbol-
izes the conjugate fields.
Supplementary material included with this study
is Mathematica® spreadsheets of the following exam-
ples of EFT solved by GFT. The supplementary mate-
rial also contains an instance of linearized gravitational
waves solved via GFT. Finally, the results between
EFT and SFT were equal!
4.1.) The cause of the deviation in the muon g-2
experiment
The muon g-2 experiment attempts to measure a
muon's magnetic dipole moment or g-factor accurately,
and Fermilab is currently conducting it [17,55]. The ex-
periment involves injecting the muons from the decay
of pseudoscalar pions into a storage ring and then meas-
uring the muon’s g-factor. Theoretically, the strength of
the magnetic dipole moment is supposed to be exactly
two. Any deviation from this, the latter value claims
there are likely additional particles in the standard
model in the storage ring.
So far, the laboratory has experimented two times.
The results of the first two experiments suggested that
the anomalous magnetic moment, which is
,
had deviated by a factor of 0.00116592 [33]. Ulti-
mately, this data implied there was likely at least one
additional particle that is a by-product of a pion but not
currently listed in the standard model.
Assuming the additional particle is a vector boson
and the Lagrangian term for interactions is as fol-
lows:
then the principle of least action for pion decay is as defined as:
.
Claiming is the pionic effective or string field, is the unknown bosonic effective or string field, and
is one of the valence muonic effective or string fields, while is the valence muon neutrino-based effective or
string field associated with the decay of the pion, the functional derivative of the principle of least action yields at
least four transformed Hamiltonian equations:
,
,
,
and
.
After solving for any arbitrary parameters/coefficients and constants whenever possible and setting and
to unity, then assuming the self and mixing interaction mass-energy equivalence equation, one can derive the
following mass-energy equivalences:
,
,
,
and
.
After using the three most former expressions and
the known rest masses for the particles or relativistic
strings of interest, one can solve for the arbitrary pa-
rameters/coefficients , , and constant using
known values for items of interest. Next, the rest mass
of the unknown particle or relativistic string is calcu-
lated to be 1.70 X 107 eV or 17 MeV.
4.2.) Glueball estimations
A glueball is a hypothetical particle solely com-
prised of gluons [58]. Particle physics theories suggest
contemporary colliders should detect them. Although
there is anecdotal evidence pointing to the existence of
these particles, they have not been explicitly identified
[47,58].
Since a gluon is a vector boson and the Lagran-
gian terms for interactions of the entanglement type are
as follows:
,
82 Slovak international scientific journal # 84, (2024)
then, the principle of least action for the decay of a meson should be as follows:
.
Suggesting is the mesonic effective or string
field, is the gluonic effective or string field, and
is one of the valence quark effective or string fields,
while is the other valence quark effective or string
field present in the decay of the meson, the functional
derivative of the principle of least action yields at least
four transformed Hamiltonian equations:
,
,
,
and
.
After solving for any arbitrary parameters/coeffi-
cients and constants whenever possible and setting
and to unity, and using the self and mixing interac-
tion mass-energy equivalence equation, one can derive
the following mass-energy equivalences:
,
,
,
and
.
One may also assume that the gluonic effective or
string field forms a glueball. In other words, the
mass of a glueball would constitute the mass-energy
equivalence of gluonic effective or string field. After
using the three most former expressions and the known
rest masses for the particles or relativistic strings of in-
terest, one can solve for the arbitrary parameters/coef-
ficients , , and constant using known val-
ues for items of interest. Check the table for calcula-
tions of glueballs.
A table of predicted glueball masses derived from
various meson decays is featured below:
Quark 1/
(eV)
Quark 2/
(eV)
Meson/
(eV)
Glueball/
(eV)
charged pion
2.20*107
4.70*106
1.40*108
1.49*109 [65]
neutral pion
(pair)
2.20*106
4.70*106
1.35*108
1.39*109 [65]
neutral kaon
4.70*106
9.60*107
4.98*108
1.72*109 [65]
J/psi meson
1.28*109
1.28*109
3.10*109
1.87*109 [66,67]
4.3.) Assessment of tetraquarks mass via decay
by-products.
Recently, LHC at CERN found that the four
charmed tetraquark , which had a rest mass of 6.9
GeV, decayed into the vector meson and sigma glueball
[98,99,100].
Assuming the tetraquark is a scalar bosonic entity
and the Lagrangian term for entanglement interac-
tion is as follows:
,
then the principle of least action for decay
into vector J/y mesons and s glueball is defined as:
.
One may also deem that the tetraquark effective or string field is comprised of the vector meson or
glueball effective or string fields
and
, respectively. The functional derivatives of the Lagrangian yields
three evolution equations:
,
,
and
.
After solving for any arbitrary parameters/coeffi-
cients and constants whenever possible and setting
and to unity, then assuming the self and mixing in-
teraction mass-energy equivalence equation, one can
derive the following mass-energy equivalences:
,
,
and
Slovak international scientific journal # 84, (2024) 83
.
After using the two latter expressions and the
known rest masses for the particles or relativistic
strings of interest, one can solve for the arbitrary pa-
rameters/coefficients and constant using
known values for the vector meson or glueball .
Plugging in the value into the former expression
claims, the mass of the four-charm tetraquark is
6.90*109 eV.
4.4.) Photon analysis linked to a binary black hole
merger
Black holes (BH) were objects in the universe that
had much speculation and excellent study. In the 18th
century, Pierre-Simon Laplace and John Michell pro-
posed that the universe possessed objects whose gravi-
tational fields were so intense that light could not es-
cape them [31]. Two centuries later, David Finkelstein
and Karl Schwarzschild could make primitive solutions
that were used to define such entities [69,70,93] ini-
tially. It was not until the 1960s that BH became a reg-
ular prediction in the general theory of relativity [37].
While undergoing mergers in spacetime, BH was
known to emit gravitational waves (GW) and possibly
some forms of light [49,94]. In 1916, Albert Einstein
postulated that BH created ripples in spacetime in his
great work, the General Theory of Relativity [46]. Be-
fore Einstein pinpointed the primary source of GW,
Poincare, and Heaviside stated there were gravity’s
equivalent to electromagnetic waves [71,72]. In 2015,
the first GW was detected by LIGO gravitational wave
detectors. Finally, Atura Tanikawa and associates
claimed that g-ray bursts were also emitted during the
BH merger [74].
Quantum entanglement (QE) may be the primary
mechanism for merging BHs. Leonard Susskind and
Juan Maldacena generated a conjecture stating BH
were like two entangled particles, or Einstein-Po-
dolsky-Rosen pair, connected by a wormhole or Ein-
stein-Rosen bridge [13]. Thus, they established the fol-
lowing relationship: ER = EPR. For this study, we used
the previous equation to signify BH-QE.
In the first section of this study, we generate a La-
grangian to define BH-QE. Upon functional differenti-
ation of this Lagrangian, we derive three quantum tele-
graph equations and two inhomogeneous nonlinear
Klein-Gordon equations, or QT-KG. Assuming the
three quantum telegraph equations described the two
BH associated via ER = EPR and the merged BH while
the inhomogeneous Klein-Gordon equations repre-
sented GW and photons, we used the generating func-
tion technique (GFT) to solve for the three BH, GW,
and photons. Then, we try to predict the mass equiva-
lents for photon emission, given we know the values of
the three BH and GW. Ultimately, we concluded that
population III stars were the source of BH mergers
since they produced g-ray photons predicted via BH-
QE system of equations.
84 Slovak international scientific journal # 84, (2024)
Assuming black holes are vector boson-like and the Lagrangian term for interactions, such as entanglement,
is as follows:
,
then the principle of least action for the merger of a binary black hole system is as follows:
.
Deeming is the gravitational wave/gravitonic
practical or string field involved in the merger, is the
photonic effective or string field,
is the first black
hole, and
is the second black hole effective or string
fields involved in the merger, and is the residual
black hole effective or string field, the functional deriv-
ative of the principle of least action yields at least six
transformed Hamiltonian equations:
,
and
,
,
,
And
,
where
and
,
is the Ansatz transform tensor, and is the
metric tensor. After solving for any arbitrary parame-
ters/coefficients whenever possible and constants, set-
ting and to unity, and applying the mass-energy
equivalence equation to one element of the transformed
solutions, assume the following relationships for deter-
mining the mass-energy equivalents of fermion and
bosonic effective or string fields associated with the
BH-QE system of equations were true:
,
,
and
After using the four most former expressions and
the known rest masses for the large-scale structures or
relativistic strings of interest, one can solve for the ar-
bitrary parameters/coefficients , , and
constant using known values for items of interest.
Ultimately, (s)he obtained the following table of pho-
tons for the first several GWs detected by LIGO:
Specific GW
BH 1/
(solar masses)
BH 2/
(solar masses)
Residual BH/
(solar masses)
GW/
(solar masses)
Photons/
(erg)
GW150914
35.6
30.6
63.1
3.1
4.40*1055
GW151012
23.3
13.6
35.7
1.5
2.60*1055
GW151226
13.7
7.7
20.5
1.0
1.47*1055
GW170104
31.0
20.1
49.1
2.2
3.54*1055
GW170608
10.9
7.6
17.8
0.9
1.25*1055
GW170729
50.6
34.3
80.3
4.8
5.26*1055
GW170809
35.2
23.8
56.4
2.7
3.99*1055
GW170814
30.7
25.3
53.4
2.6
3.69*1055
GW170818
35.4
26.7
59.4
2.7
4.24*1055
GW170823
39.5
29.0
65.4
3.3
4.56*1055
Slovak international scientific journal # 84, (2024) 85
5.) Conclusion
Via EFT and SFT, one will likely identify particle
X17 as the culprit causing the deviation in the muon g-
2 experiment. The additional by-product from pion de-
cay that coexists with the muons in the Fermilab stor-
age ring has a rest mass of 17 MeV. This is the same
mass as particle X17, a hypothetical protophobic spin-
0 boson first captured by the ATOMKI and then JINR
[101,102,103].
EFT and SFT might provide an accurate means to
calculate glueballs derived from the decay of mesons.
The rest of the masses of glueballs, condensed gluonic
particles, or relativistic stings, established from the de-
cay of pions and kaons, derived in this paper were con-
sistent with CERN data [65]. Therefore, the theories
discussed in this study could adequately estimate the
masses of glueballs derived from the decay of other me-
sons.
EFT and SFT claimed that the initial gravitational
waves detected by VIRGO/LIGO were generated from
binary black hole mergers and were likely accompanied
by g-ray bursts, or GRB. The theories in this study
claimed the earliest observed binary black hole mergers
likely emitted g-ray bursts at ~ 1055 erg. It is well
known that many cosmological phenomena emit g-ray
bursts. However, this range of energy for photons sug-
gested the merging BH likely existed in the first gener-
ation or hypothetical population III stars [8].
Establishing a Triality between Quantum Infor-
mation Theory (QIT), EFT, and SFT. Information the-
ory is known as the study of uncertainty in the quantum
realm, and its basic unit of information is the qubit, a
two-state quantum mechanical system [104]. If an indi-
vidual lets , then (s)he obtains:
or .
This expression is associated with the exponential
map of a qubit [104]. Also, if one applies Euler’s for-
mula to the above expression, (s)he obtains the sinusoi-
dal wave function discussed in section 3. The above
statements imply there is an intimate link between a
qubit, physical body/particle, and string.
Conflicts of Interests
The author of this paper has no conflicts of inter-
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ZOOLOGY
SPECIES COMPOSITION AND NUMBER OF RODENT CARRIERS OF THE PLAGUE PATHOGEN
IN THE (MOYINKUM DESERT PLAGUE FOCUS IN 2021
Bely D.,
Head of the laboratory of epizootology of especially dangerous infections
Republican State Institution "Zhambyl Anti-Plague Station" of the Committee of Sanitary and Epidemio-
logic Control of the Ministry of Health of the Republic of Kazakhstan, Taraz city
Niyazaliev K.,
zoologist
Republican State Institution "Zhambyl Anti-Plague Station" of the Committee of Sanitary and Epidemio-
logic Control of the Ministry of Health of the Republic of Kazakhstan, Taraz city
Nurbaev K.,
zoologist
Republican State Institution "Zhambyl Anti-Plague Station" of the Committee of Sanitary and Epidemio-
logic Control of the Ministry of Health of the Republic of Kazakhstan, Taraz city
Kopkova A.,
zoologist
Republican State Institution "Zhambyl Anti-Plague Station" of the Committee of Sanitary and Epidemio-
logic Control of the Ministry of Health of the Republic of Kazakhstan, Taraz city
Sayakova Z.
Candidate of Biological Sciences, Senior Scientific Associate
Republican State Enterprise "Institute of Zoology", Ministry of Science and Higher Education of the Repub-
lic of Kazakhstan,
Almaty city
DOI: 10.5281/zenodo.11624546
Abstract
The work was carried out taking into account the specific epizootic situation of plague in 2020, on the territory
where the course of plague among mammals has been observed for more than 40 years, which is a constant poten-
tial threat of epidemic of this infection among the population. Taking into account the fact that plague epizootic
was detected by bacteriological method during rodent plague testing in spring 2015, and in the fall of the same
year local low-intensity plague epizootic was detected by serological method in the tract "Shynyrau kudyk", indi-
cating the continuation of the epizootic, as well as intensive human economic activity in the active Moyinkum
desert plague focus, in the spring season of 2021. studies of the state of fauna and rodent abundance in the Western
Remnant Landscape-Epizootologic Region (LER) were conducted. During the research period, the territory on the
area of 3000 km2, which is a part of the Moyinkum desert plague focus, was surveyed. Among rodents, large and
small gerbils, yellow gopher and small marmoset were studied, among predators - fox, skogpa, buzzard and harrier.
Rodent abundance was low.
Keywords: rodents, natural plague focus, landscape-epizootologic region, carriers of the plague pathogen,
great gerbil, small gerbils.
Introduction. The plague epizootic in the study
area was detected in spring 2012 at the following
points: "Satybaldy" 1 culture of plague was isolated
from the greater sandfly and 1 seropositive greater
sandfly was detected, "Kadyrbek" 1 culture of plague
was isolated from the greater sandfly; "Shynyrau
kudyk" 1 seropositive greater sandfly was detected;
plague epizootic was detected at the following points:
"Satybaldy" ur. "Kadyrbek" 1 culture of plague was
isolated from the great sandfly; "Shynyrau kudyk" - 1
seropositive great sandfly was found; the plague epizo-
otic was characterized as local, intensive, occurred on a
total area of 300 km2 [1]. In the fall of 2012, no epizo-
otic process was registered in this territory.
In spring 2013 local low-intensity epizootic of
plague was detected by serologic method in tracts
"Kokdala", Baikozha, headquarters Bekmurat,
Sadykzhal, Kuzendidala, Suzhal-1. The plague epizo-
otic at all sites was characterized as local, low-intensity
and occurred on a total area of 600 km2 [1]. From the
fall of 2013 to the fall of 2014, despite the survey of the
territory, no plague epizootics were registered.
In spring 2015, the epizootic process was regis-
tered by bacteriological method on the area of 500 km2
in the tract "Shokai" isolated 5 strains of Y. pestis from
fleas of the great gerbil burrows of the plague pathogen
from the flea of the burrows of the great gerbil
Xenopsylla gerbilli minax. In the tract "Koizhigit" 1
culture of the plague pathogen was isolated from the
suspension of the great gerbil in the tract "Zhaylybek"
1 culture of the plague pathogen was isolated from the
red-tailed gerbil and in the tract "Kokdala" 1 culture of
the plague pathogen was isolated from the great gerbil,
around the settlement "Kishi Kokdala" 1 culture of the
plague pathogen was isolated from the flea of the great
gerbil burrows: Xenopsylla gerbilli minax. The plague
epizootic was characterized as local low-intensity. In
the fall of 2015, local low-intensity plague epizootic
was detected by serological method in Shynyrau kudyk.
The plague epizootic at all sites was characterized as
90 Slovak international scientific journal # 84, (2024)
local, low-intensity and flowed over a total area of 100
km2 [1]. From 2016 to the fall of 2017, despite the sur-
vey of the territory, the plague epizootic was not de-
tected.
In spring 2018, a local low-intensity plague epizo-
otic was detected in the tracts "Satybaldy" (1 seroposi-
tive great sandfly was isolated), "Kadyrbek" 2 seroposi-
tive great sandflies were isolated; The plague epizootic
at all sites was characterized as local, low-intensity and
flowed over a total area of 200 km2. An inter-epizootic
period was observed from fall 2019 to spring 2021.
The main host of the plague pathogen is the great
gerbil. Great Sandpiper settlements are mostly sporadic
and occur in small groups [2-4]. The density of settle-
ments is very low. Only in the extreme northwest in a
relatively small area and in some places in the southeast
along the southern edge of the sands, colony density is
somewhat higher. Numbers of the Greater Sandpiper in
these areas averaged 3.0 individuals per 1 ha, varying
from 0.5 to 4.5 individuals per year [5-7]. In addition,
the Noon Sandpiper, Grebeschik's Sandpiper and Red-
tailed Sandpiper inhabit the area. The Noon Sandpiper
dominates among the Small Sandpipers. The abun-
dance of the Yellow Gopher is also low. Other rodents
are rare. The vectors are fleas of sandflies, mainly of
the Greater Sandpiper [8-9]. According to long-term
averages, their number in the habitat of the Greater
Sandpiper is 140 specimens per 1 ha, with annual vari-
ations from 24 to 535 [10-12].
The purpose of our research was to study the state
of the fauna and to conduct an inventory of the number
of rodents in the Western Remnant Landscape-Epizo-
otologic Area, as well as their natural enemies - preda-
tory animals.
Materials and Methods.
Great Sandpiper was captured from 10-12 rodent
colonies. Traps were placed 1.5 km apart. On one col-
ony 2-3 traps were placed, for a more uniform survey
of the territory, 1-2 gerbils were captured from each
colony on average, after which the traps were moved to
colonies that had not been trapped. First of all, the sur-
vey was conducted in the vicinity of settlements, by
sectors and was aimed at searching for local epizootics
in the places of plague pathogen establishment and ad-
jacent areas.
During the spring season of 2021, 500 rodents, in-
cluding the greater sandfly, were captured.
The population of the greater sandfly was counted
using the route-colonial method, while the lesser sand-
flies and other small rodents were counted using the
trap-night method.
The trapping of Greater Red-tailed Sandpipers
was carried out with special traps placed at the entrance
to the burrows of these rodents. No more than 2 gerbils
were captured per colony, after which the traps were
moved to other colonies.
Small Sandpipers were counted by placing 100
traps with standard bait (bread moistened with vegeta-
ble oil) in a line at 5-meter intervals in the main habi-
tats, as well as traps placed on colonies of large sandpi-
pers.
Counts of Yellow Gophers were carried out on au-
toroutes (number of sightings per 1 km). Small gopher
tortoises were counted at dusk in the light of car head-
lights (number of sightings per 1 or 10 km of route).
Numbers of rodents were determined by the trap-
night method. When counting in settlements, at least
20% of the total number of objects were surveyed.
Small settlements with up to 20 houses were surveyed
completely. At the same time with counting the number
of rodents, four-legged predators were counted by trap-
ping them in traps placed on colonies of Great Sandpi-
pers.
The number of raptors was judged by the number
of birds seen per daylight hours.
To conduct stationary observations of the Greater
Sandpiper, 3 fixed points were selected, which most
fully reflect the landscape-ecological peculiarity of the
surveyed area. The following ecological observations
were carried out at the stationary points of permanent
record:
a/ observations of rodent population composition
and breeding intensity;
b/ counting the number of embryos in pregnant fe-
males;
c/ registration of repeated pregnancy and embryo
resorption;
d/ study of multi-year population dynamics of the
great gerbil;
e/ change of colonies, interspecific contacts, ro-
dent mobility, etc.
Results
During the period of work from 28.05.2020 to
16.07.2021 the survey was conducted on the area of -
3000 sq. km2. The abundance of Great Sandpiper
(Rhombomys opimus (Lichtenstein, 1823)) in the
whole LER per 1 km2 amounted to 228 individuals,
with colony occupancy of 37.6 %. Colony density av-
eraged 146 per 1 km2. The average number of Greater
Sandpipers per colony was 4.6 individuals. The per-
centage of minor rodents caught in traps was 0 % per
100 l/n.
Counting of the number of the main carrier of the
plague pathogen is carried out before the release of
young animals. In the study area, 51.8% of animals sur-
vived the winter period, which stabilized the number of
the main carrier in most parts of the LER.
In general, the number of Great Sandpipers per 1
km2 in spring 2021 was 256, with a range of 77 to 384,
and 141 in spring 2020, with colony occupancy rates of
37.6 % and 43.6 %, respectively.
During the 2021 summer season, 196 Great Sand-
pipers were captured in the Western Remnant LER, of
which 67 (34.2 %) were sexually mature males and 112
(57.1 %) were sexually mature females. Of the sexually
mature females: 35 (31.3 %) were yearlings, 67 (59.8
%) were littered, and only 7 (6.3 %) were pregnant.
Young were captured 17 (8.7 %), of which 10 (58.8 %)
were young males and 7 (41.2 %) were young females.
The ratio of sexually mature females to males, was
1.7:1. The percentage of females participating in repro-
duction was 66.1%.
The number of embryos per pregnant female was
2.7, ranging from 1 to 5. The breeding intensity index
was 22.
Slovak international scientific journal # 84, (2024) 91
Numbers of the Noon Sandpiper (Meriones merid-
ianus (Pallas, 1773)) are generally low in the area. For
example, the percentage of their occurrence per 600 l/n
was 0% in the LER.
Numbers of Red-tailed Sandpiper (Meriones liby-
cus (Lichtenstein, 1823)) are generally low in the area.
The percentage of their occurrence per 600 l/n in the
LER was - 0.
Numbers of Grebe Sandpiper (Meriones tamaris-
cinus (Illiger, 1811)) are generally very low in the area.
For example, in the LER the percentage of their occur-
rence per 500 l/n was - 0%.
In the Western Remnant LER this summer, num-
bers of Ruffs remain at a low level. No geese were
caught in fishing gear. At dusk single animals were en-
countered on the routes, and 10 Little Ruffs (Allactaga
elater (Lichtenstein, 1825)) were recorded per 10 km of
the auto-route (or 1.0% per 1 km of the route). Their
numbers may increase slightly in the fall of 2021.
Numbers of yellow gophers (Spermophilus fulvus
(Lichtenstein, 1832)) on the territory of the Western
Remnant LRR were below average. Gophers were not
specifically captured during material sampling.
Three routes were established to record the abun-
dance of yellow gophers:
The total area of these routes was 3 km2, 15 yel-
low gophers were encountered, with an average of 0.15
animals per 1 km2.
Numbers of terrestrial predators (weasels, band-
ages, ferrets) in the area were counted visually and by
trapping. Four-legged predators were not specifically
captured. Their numbers are still low. A total of 2 Red
Foxes (Vulpes vulpes (Linnaeus, 1758)) were recorded.
Among raptors, an average of 2 birds were seen
per daylight hours, mainly Buzzards (Buteo rufinus
(Cretzschmar, 1827)). Nests of buzzards contained
mainly 2 eggs, but not more than 3 eggs. In addition to
Buzzards, Osprey Pandion haliaetus (Linnaeus, 1758),
Harrier (Circus pygargus (Linnaeus, 1758)) were rec-
orded, approximately 1 - 4 birds of prey per 10 km of
the vehicle route.
Weather conditions are characterized according to
the data of the weather station located in Oyyk settle-
ment. The winter of 2020-2021 was snowy with rare
precipitation in the form of snow (18 days). The winter
temperature background was close to the average long-
term data and was -8.4. Spring was relatively cool and
prolonged.
In the 1st decade of March the temperature back-
ground was +4.10 С, in the 2nd decade of the month -
1.10 С. In the 3rd decade of the month and average air
temperature amounted to +8.30 С. The average
monthly air temperature was +3.80, last year +7.00 C,
with a norm of +1.7 0C. Precipitation in the form of rain
fell in the 1st, 2nd, 3rd decade (11 days). Snow cover
on the soil surface was recorded until March 20, while
last year it was until February 7. The transition from
00°C to above zero temperatures was recorded on
March 19 (February 13 last year).
In April, the weather was stable, within multiyear
values. Air temperature in the first ten-day period was
+ 10.70 С, in the second ten-day period + 15.10 С, in
the third ten-day period + 16.70С. Precipitation fell in
the form of rain in the second and third ten-day periods
of the month (accompanied by strong easterly winds in
the first and second ten-day periods). Rare flowering of
tulips was observed in the first, second and third ten-
day periods of April. Rare flowering of poppies was ob-
served in the third decade of April. The vegetation con-
dition assessment was low due to weak vegetation of
ephemerals and ephemeroids. In general, weather con-
ditions in April were favorable for rodent activity.
In May, the weather was stable, moderately warm
but windy, with strong easterly winds prevailing. Pre-
cipitation fell in the first and second decades of the
month (3 times). Air temperature was +21.30 C in the
first decade, +23.00 C in the second and +28.40 C in
the third. Assessment of vegetation condition was un-
satisfactory, ephemerals and ephemeroids vegetated
poorly, wormwood and sagebrush grew poorly, meager
flowering of poppies continued until the third decade of
May.
In general, it can be said that the spring of 2021
was late and drier than the spring of the previous year.
The forage base for rodents was insufficient due to
weak vegetation of desert vegetation, climatic condi-
tions were satisfactory and sufficient for rodent activity
(Table 1).
Thus, the abundance of the Greater Sandpiper here
remains below average. Thus, the number of animals in
summer of this year was 266 animals per 1 km2, with
an average colony occupancy rate of 38.2%. The index
of intensity of the main carrier remained at the last
year's level and amounted to 22. The average number
of embryos per pregnant female was 2.7. Taking into
account the above-mentioned data, it can be assumed
that by the fall of 2021 the number of the greater sand-
fly in the whole territory under favorable weather and
climatic conditions will be higher than last year's data,
therefore, the possibility of a local epizootic of plague
in the fall of 2021 is not excluded in this territory.
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