Related papers: About a conjecture for uniformly isochronous polyn…
In this paper, we give a direct method to study the isochronous centers on center manifolds of three dimensional polynomial differential systems. Firstly, the isochronous constants of the three dimensional system are defined and its…
In this paper we investigate the problem of linearizability for a family of cubic complex planar systems of ordinary differential equations. We give a classification of linearizable systems in the family obtaining conditions for…
This paper focuses on isochronicity of linear center perturbed by a polynomial. Isochronicity of a linear center perturbed by a degree four and degree five polynomials is studied, several new isochronous centers are found. For homogeneous…
The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].
We study the conjecture of Jarque and Villadelprat stating that every center of a planar polynomial Hamiltonian system of even degree is nonisochronous. This conjecture is proved for quadratic and quartic systems. Using the correction of a…
We announce numerous new results in the theory of orthogonal polynomials on the unit circle.
We study the isochronicity of centers at $O\in \mathbb{R}^2$ for systems $\dot x=-y+A(x,y), \dot y=x+B(x,y)$, where $A, B\in \mathbb{R}[x,y]$, which can be reduced to the Lienard type equation. Using the so-called C-algorithm we have found…
We study the isochronicity of centers at $O\in \mathbb{R}^2$ for systems $$\dot x=-y+A(x,y),\;\dot y=x+B(x,y),$$ where $A,\;B\in \mathbb{R}[x,y]$, which can be reduced to the Li\'enard type equation. When $deg(A)\leq 4$ and $deg(B) \leq 4$,…
We construct explicit non-isotrivial families of polynomials over $\mathbb{Q}$ satisfying uniform boundedness for their rational preperiodic points.
We study two families of orthogonal polynomials. The first is a finite family related to the Askey-Wilson polynomials but the orthogonality is on the real line. A limiting case of this family is an infinite system of orthogonal polynomials…
We give an alternative proof for the celebrated Bertrand's theorem as a corollary of the isochronicity of a certain family of centers.
The purpose of this work is to analyse a family of mutually orthogonal polynomials on the unit ball with respect to an inner product which includes an additional term on the sphere. First, we will get connection formulas relating classical…
We study the discrete semiclassical orthogonal polynomials of class s=1. By considering all possible solutions of the Pearson equation, we obtain five canonical families. We also consider limit relations between these and other families of…
An open problem about two new families of orthogonal polynomials was posed by Alhaidari. Here we will identify one of them as Wilson polynomials. The other family seems to be new but we show that they are discrete orthogonal polynomials on…
In this paper we investigate the isochronicity and linearizability problem for a cubic polynomial differential system which can be considered as a generalization of the Riccati system. Conditions for isochronicity and linearizability are…
The problem when the order polytope and the chain polytope of a finite partially ordered set are unimodularly equivalent will be solved.
Condition numbers of random polynomial systems have been widely studied in the literature under certain coefficient ensembles of invariant type. In this note we introduce a method that allows us to study these numbers for a broad family of…
Several results about the union-closed sets conjecture are presented.
In this paper, I have proved that for a class of polynomial differential systems of degree n+1 ( where n is an arbitrary positive integer) the composition conjecture is true. I give the sufficient and necessary conditions for these…
This work is a study of polynomial compositions having a fixed number of terms. We outline a recursive method to describe these characterizations, give some particular results and discuss the general case. In the final sections, some…