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Measuring nonlinearity by means of static parameters in Bernoulli binary sequences distribution: a brief approach. International Journal of Modeling, Simulation and Scientific Computing - World Scientific

June 2020
International Journal of Modeling Simulation and Scientific Computing 11(3)

June 2020
11(3)

DOI:10.1142/S179396232050021X

Authors:

Secretaria de Estado da Educação do Paraná

The article analyzes Bernoulli's binary sequences in the representation of empirical nonlinear events, analyzing the distribution of natural resources, population sizes and other variables that influences the possible outcomes of resource’s usage. Considering the event as a nonlinear system, and the metrics of analysis consisting of two dependent random variables 0 and 1, with memory and probabilities in maximum finite or infinite lengths, constant and equal to ½ for both variables (stationary process). The expressions of the possible trajectories of metric space represented by each binary parameter remain constant in sequences that are repeated alternating the presence or absence of one of the binary variables at each iteration (symmetric or asymmetric). It was observed that the binary variables X1 and X2 assume on time T_k→∞ specific behaviors (geometric variable) that can be used as management tools in discrete and continuous nonlinear systems aiming at the optimization of resource’s usage, nonlinearity analysis and probabilistic distribution of trajectories occurring about random events. In this way, the article presents a model of detecting fixed-point attractions and its probabilistic distributions at a given population-resource dynamic. This means that coupling oscillations in the event occur when the binary variables X1 and X2 are limited as a function of time Y.

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International Journal of Modeling, Simulation, and Scientific Computing

 Imperial College Press

International Journal of Modeling, Simulation,

and Scientific Computing

Vol. 11, No. 1 (2020)

DOI: 10.1142/S179396232050021X

Measuring nonlinearity by means of static parameters in Bernoulli binary

sequences distribution: a brief approach

Charles Roberto Telles

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their multiple causalities: A case study." Journal of Economic and Administrative

Sciences 35, no. 1 (2019): 44-64.

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Comparative Assessment of Two Estimates of the Bernoulli Distribution Parameters in the Analysis of Short-Term Rainfall Intensity

Article

Full-text available

Apr 2023

This paper presents an application of the maximum likelihood method and the Bernoulli distribution of selected rainfall intensity data. The parameter of the density of Bernoulli distribution was estimated by the maximum likelihood method (MLM), and Microsoft Excel Solver (MES). The calculated probabilities using the estimated parameter were evaluated statistically (analysis of variance (ANOVA), relative error, model of' selection criterion (MSC), Coefficient of Determination (CD) and Correlation coefficient (R). The study revealed that the Bernoulli probability distribution’s parameter (p) is the mean of the natural logarithm of rainfall intensity using the MLM estimator. The parameter were 0.665 and 0.535 for Makurdi, 0.695 and 0.478 for Abeokuta using MLM and MES, respectively. The relative errors were 0.479 and 0.743, and 1.141 and 1.509 for Makurdi and Abeokuta using MLM and MES, respectively. The correlation coefficient for Makurdi and Abeokuta using MLM and MES were 0.876 and 0.800, and 0.269 and 0.341, respectively. It was concluded that the MLM parameter was better than MES based on the values of MSC, CD, relative error and R. MLM predicted Weibull probability of rainfall intensity better than MES. There is a need to evaluate MLM and other probability distributions

False Asymptotic Instability Behavior at Iterated Functions with Lyapunov Stability in Nonlinear Time Series

Chapter

Full-text available

Jul 2020

Charles Roberto Telles

Empirically defining some constant probabilistic orbits of iterated high-order functions, the stability of these functions in possible entangled interaction dynamics of the environment through its orbit’s connectivity (open sets) provides the formation of an exponential dynamic fixed point as a metric space (topological property) between both iterated functions for short time lengths. However, the presence of a dynamic fixed point can identify a convergence at iterations for larger time lengths (asymptotic stability in Lyapunov sense). Qualitative (QDE) results show that the average distance between the discontinuous function to the fixed point of the continuous function (for all possible solutions), might express fluctuations of on time lengths (instability effect). This feature can reveal the false empirical asymptotic instability behavior between the given domains due to time lengths observation and empirical constraints within a well-defined Lyapunov stability.

Geometrical Information Flow Regulated by Time Lengths: An Initial Approach

Article

Full-text available

Nov 2018

Charles Roberto Telles

The article analyzes Bernoulli's binary sequences in the representation of empirical events about water usage and continuous expenditure systems. The main purpose is to identify among variables that constitute water resources consumption at public schools, the link between consumption and expenditures oscillations. It was obtained a theoretical model of how oscillations patterns are originated and how time lengths have an important role over expenditures oscillations ergodicity and non-ergodicity.

Analysis of Oscillations in Continuous Expenditures and Their Multiple Causalities: A Case Study

Article

Full-text available

Sep 2018

Token eprint for free reading: https://www.emeraldinsight.com/eprint/SDCHW23F8VTZPJ968ZYX/full. (copy and paste the link - create account). Design/methodology/approach: Understand the dynamics of public spending in view of the oscillations between years that these expenses present, understanding the expenditure system as a non-linear and complex system in which the causes that generate oscillations in the annual expenses are originated by several random variables. Findings: It was found that several variables affect a public service. Many times policies or other actions try to achieve efficiency in controlling or containing public financial resources. It is not uncommon such actions do not have any determinant or robust effect at their prior objectives due to the nature of phenomena. Research limitations/implications: Government expenditures constitute an event of great complexity with respect to the magnitude of financial units and the budget flow involved in each of these units. In this sense, all the financial units that compose the great public expenditure scenario are inserted in heterogeneous contexts considering the dynamics of geographic, social, cultural and political administrative space of a State. Practical implications: The methods exposed in the paper are important tools to verify how policy, financial, administrative and other dimensions of actions taken influenced a continuous expenditure system. The main objective remained in identifying the strong influence of actions toward random variables that might affect the event.

Coupling functions: Universal insights into dynamical interaction mechanisms

Article

Full-text available

Nov 2017
REV MOD PHYS

The dynamical systems found in Nature are rarely isolated. Instead they interact and influence each other. The coupling functions that connect them contain detailed information about the functional mechanisms underlying the interactions and prescribe the physical rule specifying how an interaction occurs. Here, we aim to present a coherent and comprehensive review encompassing the rapid progress made recently in the analysis, understanding and applications of coupling functions. The basic concepts and characteristics of coupling functions are presented through demonstrative examples of different domains, revealing the mechanisms and emphasizing their multivariate nature. The theory of coupling functions is discussed through gradually increasing complexity from strong and weak interactions to globally-coupled systems and networks. A variety of methods that have been developed for the detection and reconstruction of coupling functions from measured data is described. These methods are based on different statistical techniques for dynamical inference. Stemming from physics, such methods are being applied in diverse areas of science and technology, including chemistry, biology, physiology, neuroscience, social sciences, mechanics and secure communications. This breadth of application illustrates the universality of coupling functions for studying the interaction mechanisms of coupled dynamical systems.

Usos finais de água em Habitações de Interesse Social no sul do Brasil

Conference Paper

Full-text available

Nov 2014

Knowing water consumption patterns in buildings is a key information for planning the needs of improvement and to encourage water conservation measures. This article aims to characterize the water consumption pattern and end-uses in low-income houses in the region of Florianopolis-SC. Data were collected by interviewing householders, as well as by measuring the flow rate of existing water fixtures and appliances. The results indicated that the shower was the fixture with the largest water consumption in households, i.e., about 33% of total water consumption on average. Households with incomes up to three minimum wages consumed 152 L/capita.day on average; while households with income between three and five minimum wages, 111 L/capita.day. Households with incomes over five minimum wages consumed 113 L/capita.day of water on average. The results of this study can be used to estimate the consumption of water for new buildings as well as to develop integrated water management strategies in low income developments in Florianopolis.

Potential for potable water savings in two schools in Florianópolis, SC

Article

Full-text available

Dec 2011

O objetivo deste artigo é apresentar os usos finais de água potável stimados e o potencial de economia de água potável obtido por meio e um sistema de aproveitamento de água pluvial, reúso de águas inzas, equipamentos economizadores, ou combinação deles, em duas nicípio de Florianópolis, Santa Catarina. Para isso, foi necessário obter informações sobre os hábitos de consumo dos ocupantes e realizar medições de vazão e levantamento de dados e aparelhos sanitários das escolas (uma estadual e outra municipal). Para o cálculo do potencial de economia obtido através do aproveitamento de água pluvial utilizou-se o programa Netuno 2.1. No reúso de águas cinzas, consideraram-se como oferta de água para a escola municipal os efluentes provenientes das torneiras de banheiros e da máquina de lavar roupas, e para a escola estadual foram considerados apenas os efluentes provenientes das torneiras de banheiros. Por último, as reduções de consumo de água potável, decorrentes da instalação de equipamentos economizadores, foram avaliadas para bacias sanitárias, mictórios, torneiras comuns e torneiras de fechamento automático. Como resultado, obteve-se um consumo de 28,8 litros/pessoa.dia na escola municipal, e de 25,3 litros/pessoa.dia na escola estadual. Com relação aos usos finais, as torneiras da cozinha e os mictórios destacaram-se como os maiores responsáveis pelo consumo de água. No que se refere ao potencial de economia de água, o resultado mais expressivo foi de 27,8% para a escola municipal e de 72,7% para a escola estadual, combinando equipamentos economizadores e aproveitamento de água pluvial.

Cours d'analyse de l'École Royale Polytechnique

Book

Aug 2010

Augustin-Louis Cauchy

In 1821, the French mathematician Augustin-Louis Cauchy published Cours d'Analyse de L'École Royale Polytechnique, a textbook designed to teach his students the basic theorems of calculus in as rigorous a way as possible. Cauchy was a pioneer of mathematical analysis, a branch of mathematics concerned with the idea of a limit, whether of a sequence or of a function. This book consists of 12 chapters that discuss real functions, infinitely small and large quantities, substitution groups, symmetrical functions, unknown variables, imaginary functions, and rational fractions in a recurrent series. It also provides formulas for solving various problems, such as converting the sine and cosine of a multiple polynomial arc and the Lagrange interpolation. Cauchy built on the work of Leibniz and Newton and is generally regarded as one of the greatest mathematicians in history. This is a reissue of one of his most important contributions.

From Newton to Navier–Stokes, or how to connect fluid mechanics equations from microscopic to macroscopic scales

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Isabelle Gallagher

In this survey we present an overview of some mathematical results concerning the passage from the microscopic description of fluids via Newton's laws to the macroscopic description via the Navier-Stokes equations.

Navier‐Stokes Equations

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