# Ali TaghaviQom University Of Technology

Ali Taghavi

PHD

## About

17

Publications

10,612

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12

Citations

Introduction

"Je pense donc je suis"
Rene Descartes

Additional affiliations

September 2014 - September 2014

**Institut de Recherches Mathematiques Avancée**

Position

- A short vist

Description

- I presented a talk at IRMA, entitled: "What theories can be related to limit cycle theory" My talk was based on the second partof this note; http://arxiv.org/abs/1302.0001

September 2006 - December 2020

**Damghan University**

Position

- Professor (Assistant)

Description

- Some Graduate courses I have taught: Operator theory, Algebraic Topology, Differentiable Manifold, K-theory, Real Analysis. Functional Analysis.

September 1999 - June 2000

Education

September 1996 - September 2002

## Publications

Publications (17)

In this paper we give an alternative proof for a vanishing result about flat functions proved in G.Stoica, "When must a flat function be identically zero", The American Mathematical Monthly 125(7)648-649, 2018. With a dynamical approach we give a generalization of this result to multidimensional variables.

In this paper we give an alternative proof for a vanishing result about flat functions proved in G.Stoica, "When must a flat function be identically zero", The American Mathematical Monthly 125(7)648-649,2018. With a dynamical approach we give a generalization of this result to multidimensional variables.

We give a counter example to the MO question below. Despite of two MO bounties on this question, it was unanswered for more than 1 year
https://mathoverflow.net/questions/293197/a-complex-limit-cycle-not-intersecting-the-real-plane

Bulletin of Iran. math Society Vol 42 (2016) No 5 pp. 1169-1177

Using characteristic classes, we give an alternative proof for the fixed point property of CP2n

Let $A$ be a $C^{*}$ algebra and $T: A\rightarrow A$ be a symmetric linear
map which satisfies in functional equation $T(x)T(y)=T^{2}(xy)$. We prove that
under each of the following conditions, $T$ must be the trivial map
$T(x)=\lambda x$ for some $\lambda \in \mathbb{R}: $A$ is a simple
$C^{*}$-algebra.
$A$ is unital with trivial center and has a...

We study some properies of $Z^{*}$ algebras, thos C^* algebra which all
positive elements are zero divisors. We show by means of an example that an
extension of a Z* algebra by a Z* algebra is not necessarily Z* algebra.
However we prove that an extension of a non Z* algebra by a non Z* algebra is
again a Z^* algebra. As an application of our metho...

A consequence of the Gauss Bonnet theorem is interpreted in term of operator
theory by Alain Connes in his book, Non Commutative geometry. In this note we
explain in details about his method. We also introduce an operator theoretical
nature for limit cycle theory.

In this paper we concern with positive zero divisors in $C^{*}$ algebras. By
means of zero divisors, we introduce a hereditary invariant for $C^{*}$
algebras. Using this invariant, we give an example of a $C^{*}$ algebra $A$ and
a $C^{*}$ sub algebra $B$ of $A$ such that there is no a hereditary imbedding
of $B$ into $A$.
We also introduce a new co...

Using methods from the theory of commutative graded Banach algebras, we
obtain a generalization of the two dimensional Borsuk-Ulam theorem as follows:
Let $\phi:S^{2} \rightarrow S^{2}$ be a homeomorphism of order n and
$\lambda\neq 1$ be an nth root of the unity, then for every complex valued
continuous function $f$ on $S^{2}$ the function $\sum_{...

We present some questions and suggestion on the second part of the Hilbert 16th problem

Using Singular Rescaling We Prove Some Bifurcation Results. This note Presents short proofs for some Bifurcation results which had been appeared with other Authors

We prove that coexistence of two limit cycles with disjoint interior can not occur in certain quadratic systems

We Prove That The Uniform Upper Bound for the Number Of Limit Cycles Of The
Lienard Equation of Degree 4 Can not be equals to 2. Further We Suggest to
Embedding Planar Lienard Equations In Higher Dimension and Present question of
completly integrabiolity of Corresponding Hamiltonians. Actually this Question
Suggest To Look at to Limit Cycles Proble...

Problem asks for a uniform upper bound H(n) for the number of limit cycles of a polynomial vector field X of degree n on the Plane. More ever it seems that ”limit cycles ” are The only obstructions for solving the ”PDE ” X.g = f, globally in the plane The following observation about Lienard equation suggests to look at the Hilbert 16th problem as a...

It is conjectured by Pugh, Lins and de Melo in (7) that the system of equations ( ú x = y − F(x) ú y = −x

## Questions

Questions (53)

Dear colleagues,

I would appreciate if you give comment on the following question:

Best regards

Ali Taghavi

Dear colleagues,

I would appreciate if you give comments on the following question:

Best regards

Ali Taghavi

Dear colleagues I would appreciate if you give comment on the following question:

Best regards

Ali Taghavi

Dear colleagues.

In the following question i try to extend the concept of characters in group theory to a wilder class of functions. A character on a group G is a group homomorphism $\phi:G \to S^1$.

For every character $\phi=X+iY$ on a group $G$, we have $Cov(X.Y)=0$.

This is a motivation to consider all $\phi=X+iY: G\to S^1$ with $Cov(X,Y)=0$.

Please see this post:

So this question can be a starting point to translate some concepts in geometric group theory or theory of bamenability of groups in terms of notations and terminologies in statistics and probability theory.

Do you have any ideas, suggestions or comments?

Thank you

Dear colleagues,

I would appreciate if you give comments on the following question.

Best regards

Ali Taghavi

Dear colleagues I would appreaciate if you give comment on the following question:

Best regards

Ali Taghavi

Dear colleagues,

I would appreciate if you give comment on the following question:

In this question, the components of a vector field satisfy certain partial differential equation. then we guess that under this condition the vector field can not have any limit cycle:

Thank you for your attention

## Projects

Project (1)

In this project we search for some new interpretations for concept "limit cycle". Limit cycles are the main object of the second part of the Hilbert 16th problem. In foliation terminology, a limit cycle is a compact leaf of a one dimensional foliation ofa surface whose holonomy is different from the identity map.
Some questions in this directions:
https://mathoverflow.net/questions/219638/proposals-for-polymath-projects/264440#264440
http://mathoverflow.net/questions/160945/limit-cycles-as-closed-geodesicsin-negatively-curved-space
http://mathoverflow.net/questions/164059/codimension-of-the-range-of-certain-linear-operators
https://www.researchgate.net/deref/https%3A%2F%2Fmathoverflow.net%2Fquestions%2F335820%2Fa-cohomology-associated-to-a-not-necessarily-integrable-distribution-hilbert