Why an infinite product of metrics are not metric spaces? Any counter Example?

Dear Researchers,

I am reaching out to seek insights and opinions on the potential connections between chaotic dynamics, arithmetic functions, and open conjectures in analytic number theory. My interest lies in exploring the derivation of chaotic operators from mathematical constructs such as L-Dirichlet functions and conjectures like those presented by Yitang Zhang in 2022 on Landau-Siegel zeros, as well as the Montgomery conjecture on the distribution of zeros.

Specifically, I am intrigued by the possibility of deriving chaotic dynamics from these mathematical frameworks and understanding their implications for questions related to the Riemann Hypothesis.

I also want to inform you that I have recently derived a chaotic operator from Yitang Zhang's latest theorem on Landau-Siegel zeros. The work has been accepted for publication in the European Physical Journal.

My ultimate goal is to further investigate the derivation of chaotic operators from these mathematical foundations and to understand the conditions under which ζ(0.5+iH)=0. welcome any insights, suggestions, or collaboration opportunities that may arise from your expertise in these areas.

Thank you for your time and consideration. I look forward to engaging in fruitful discussions with the research community.

Irina Zvina stated the corresponding statement in the proof of Lemma 2.3

[On i-topological spaces: generalization of the concept of a topological space via ideals,

Appl. Gen. Top. 7(2006), 51--66] without proof.

I asked Irina and some other mathematicians, but nobody has given me a proof. Irina,

impolitely enough, has not even answered my letter. For your convenience, her paper is attached below.

Actually, I am interested in the corresponding problem in relator (generalized uniform) spaces. Namely, all reasonable generalizations of closures can be derived from relators,

and thus they need not be studied separately.

No longer available

Is there a connection between fixed point theory and algebric topology

Hello everyone,

I'm using ABAQUS to calculate some variables, which I use to run my topology optimization. I finally have a vector of element densities. I have the Connectivity Matrix, and the Coordinates of every node on Matlab (and I could get other data).

I want to Plot the 3D results (density of every element) in Matlab.

Now, I can transition from an element-wise density to a node-wise density (by performing a weighted average based on the volume of the element, but I would like to plot directly the element-wise results).

Reassuming: I need to obtain a colored mesh where each element has a color based on its density.

Thanks

I encountered a situation where I submitted an article to BMC, but unexpectedly, my preprint was published on ResearchSquare instead. However, I have since withdrawn my article from BMC, and now I need to remove the preprint from ResearchSquare as well, as requested by the new journal. I would appreciate any guidance or advice from individuals who have faced a similar issue on how to handle this situation

Does anyone have any experience or feedback regarding SciTube? They reached out, but I'm not sure what to make of it. While their “about us” page looks promising, I easily get a dozen or more invites for predatory services each week (although some are legit) so I wanted to ask before I give it any more consideration. Nevertheless, I know these types of services are becoming increasingly popular overseas so I didn't necessarily want to dismiss it outright if there is some merit to it. Ultimately, I'm just hoping to learn more whether I choose to do it now or not.

Thanks!

As a researcher, often, it comes to my mind why do we require measure theory and what is the significance and applications of measure theory, measurable set, space and function in real life. Can anyone help me and enlighten me in this direction.

Polynomials have many applications in science.

Let p(x) be a polynomial of degree n. What is the form of its companion matrix M?

What are some applications of this matrix M?

See an attached file, for p(x)!

Thanks!