scholarly journals Some Identities Involving the Derivative of the First Kind Chebyshev Polynomials

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Tingting Wang ◽  
Han Zhang
Keyword(s):  
Open Problem ◽  
Chebyshev Polynomials ◽  
Combinatorial Method ◽  
Power Sums

We use the combinatorial method and algebraic manipulations to obtain several interesting identities involving the power sums of the derivative of the first kind Chebyshev polynomials. This solved an open problem proposed by Li (2015).

scholarly journals An Identity Involving the Integral of the First-Kind Chebyshev Polynomials

2018 ◽  
Vol 2018 ◽  
pp. 1-5
Author(s):  
Xiao Wang ◽  
Jiayuan Hu
Keyword(s):  
Open Problem ◽  
Chebyshev Polynomials ◽  
Power Sums ◽  
Interesting Identity

We used the algebraic manipulations and the properties of Chebyshev polynomials to obtain an interesting identity involving the power sums of the integral of the first-kind Chebyshev polynomials and solved an open problem proposed by Wenpeng Zhang and Tingting Wang.

scholarly journals A STRUCTURED DESCRIPTION OF THE GENUS SPECTRUM OF ABELIAN p-GROUPS

2018 ◽  
Vol 61 (2) ◽  
pp. 381-423
Author(s):  
JÜRGEN MÜLLER ◽  
SIDDHARTHA SARKAR
Keyword(s):  
Finite Group ◽  
Riemann Surface ◽  
Open Problem ◽  
Compact Riemann Surface ◽  
General Description ◽  
Combinatorial Method ◽  
A Finite Group ◽  
Almost All

AbstractThe genus spectrum of a finite group G is the set of all g such that G acts faithfully on a compact Riemann surface of genus g. It is an open problem to find a general description of the genus spectrum of the groups in interesting classes, such as the Abelian p-groups. Motivated by earlier work of Talu for odd primes, we develop a general combinatorial method, for arbitrary primes, to obtain a structured description of the so-called reduced genus spectrum of Abelian p-groups, including the reduced minimum genus. In particular, we determine the complete genus spectrum for a large subclass, namely, those having ‘large’ defining invariants. With our method we construct infinitely many counterexamples to a conjecture of Talu, which states that an Abelian p-group is recoverable from its genus spectrum. Finally, we give a series of examples of our method, in the course of which we prove, for example, that almost all elementary Abelian p-groups are uniquely determined by their minimum genus, and that almost all Abelian p-groups of exponent p2 are uniquely determined by their minimum genus and Kulkarni invariant.

scholarly journals On Power Sums Involving Lucas Functions Sequences

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Stefano Barbero
Keyword(s):  
Chebyshev Polynomials ◽  
Power Sums ◽  
Polynomial Sequences ◽  
Divisibility Properties

We present some general formulas related to sum of powers, also with alternating sign, involving Lucas functions sequences. In particular, our formulas give a synthesis of various identities involving sum of powers of well-known polynomial sequences such as Fibonacci, Lucas, Pell, Jacobsthal, and Chebyshev polynomials. Finally, we point out some interesting divisibility properties between polynomials arising from our results.

scholarly journals Some Identities Involving Chebyshev Polynomials

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Xiaoxue Li
Keyword(s):  
Chebyshev Polynomials ◽  
Combinatorial Method ◽  
Sums Of Powers ◽  
Divisibility Properties

The main purpose of this paper is using the combinatorial method and algebraic manipulations to study some sums of powers of Chebyshev polynomials and give several interesting identities. As some applications of these results, we obtained several divisibility properties involving Chebyshev polynomials.

The Yukawa Potential Function and Reciprocal Univalent Function

2013 ◽  
Vol 3 (2) ◽  
pp. 197-202
Author(s):  
Amir Pishkoo ◽  
Maslina Darus
Keyword(s):  
Mathematical Model ◽  
Unit Disk ◽  
Potential Function ◽  
Univalent Function ◽  
Open Problem ◽  
Yukawa Potential ◽  
Reciprocal Theorem ◽  
Problem Statement ◽  
Fundamental Forces

This paper presents a mathematical model that provides analytic connection between four fundamental forces (interactions), by using modified reciprocal theorem,derived in the paper, as a convenient template. The essential premise of this work is to demonstrate that if we obtain with a form of the Yukawa potential function [as a meromorphic univalent function], we may eventually obtain the Coloumb Potential as a univalent function outside of the unit disk. Finally, we introduce the new problem statement about assigning Meijer's G-functions to Yukawa and Coloumb potentials as an open problem.

On the Security of Public-Key Algorithms Based on Chebyshev Polynomials over the Finite Field $Z_N$

2010 ◽  
Vol 59 (10) ◽  
pp. 1392-1401 ◽  
Author(s):  
Xiaofeng Liao ◽  
Fei Chen ◽  
Kwok-wo Wong
Keyword(s):  
Finite Field ◽  
Chebyshev Polynomials ◽  
Public Key
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