Is there a connection between fixed point theory and algebric topology?

More Taieb. Hamaizia's questions See All

Poincare Section from phase space?

Hi all, I want to plot Poincare Section from phase space. i don't get how obtained the time series , but I obtained phase space, now I don't know how to plot Poincare section. by this way, my aim...

26 May 2021 2,981 1 View

Time it takes to publish papers on the Journal of Advanced Manufacturing Systems by the publisher World Scientific

I wanted to know how long did it take for you to publish a paper on the Journal of Advanced Manufacturing Systems (JAMS) which is published by World Scientific, Meaning the time it took since you...

01 January 1970 2,440 0 View

Can you connect an HPLC to a Mass Spec only at a certain time point?

Can anyone explain this method? Especially the last statement where it says only at 1.5 to 2.5mins was the MS/MS connected to the UPLC. How is that possible, is it a feature in this specific...

11 August 2024 8,140 3 View

Is it possible to plot the atom-projected band structure using GPAW?

Hi, I'm currently working on a project where I need to plot the atom-projected band structure using GPAW. I've been able to calculate the band structure for my material, but I'm having trouble...

07 August 2024 266 3 View

Should I include H atom into C3N5 when i am doing DFT modelling?

Hi all, my experimental XPS results shown that my C3N5 sample consists of N-H bond, hence in this case I should incorporate the N-H bond into my DFT modelling. However, I do notice several papers...

07 August 2024 8,414 2 View

Why does my protein refolded to beta sheet during thermal denaturation analysis?

Hi! So i attempted to understand a novel protein behavior towards heat application by analyzing its secondary structure change. I subjected the protein to a thermal denaturation analysis using...

06 August 2024 1,986 3 View

Are there any good simple systems or platforms to recommend?

In order to show people the beauty of control and enhance enthusiasm for learning control theories, are there any good simple systems or platforms to recommend?

05 August 2024 10,033 1 View

How can major oxides determined by ICP-MS/ES be normalized to 100% volatile free? How does this connect with LOI?

I am analyzing cherts from different sources found within one specific geologic formation using ICP-MS/ES. My committee was asking this question about my analysis. I was not sure how to answer this

05 August 2024 7,902 3 View

Why do exism movements become permanent dictatorship threats within liberal democracy thinking under majority rule-independent rule of law system?

Exism movements after gaining power within liberal democracies under majority rule and independent rule of law system become permanent dictatorship threats, but why this is the case is not clear...

04 August 2024 8,125 3 View

How to use Density Functional Theory to calculate carrier mobilities of solid system?

Hello, everyone. I have tried to determine carrier motilities of some materials, by Density Functional Theory, using Quantum ESPRESSO. There are a few methods to do it, like a package called...

04 August 2024 8,890 1 View

How do environmental toxins interact with genetic predispositions to increase cancer risk?

I am currently researching the impact of environmental toxins on children's health and would greatly appreciate insights from experts in the field. If you are an expert or researcher working on...

02 August 2024 2,626 1 View

Why is nonpoint source pollution potentially more harmful and difference between point and nonpoint sources of water pollution?

01 August 2024 1,180 2 View

Taras Radul

I recommend the book "Algebraic topology" by Allen Hatcher where the Brouwer fixed point theorem is proved using homotopy and homology groups.

Federica Pasqualone

Yes, Taras Radul !

Taieb. Hamaizia you may want to have a look also at this great book:

Kosniowski C. A First Course in Algebraic Topology. Cambridge: Cambridge University Press; 1980. doi:10.1017/CBO9780511569296

On page 141 for instance. It is very basic, but my favorite to start with. Hope this helps! Let me know if you need anything else.

Alun Wyn-jones

The Lefschetz (or Lefschetz-Hopf) Fixed-Point Theorem comes to mind.