scholarly journals Difference Equations and Sharing Values Concerning Entire Functions and Their Difference

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Zhiqiang Mao ◽  
Huifang Liu
Keyword(s):  
Difference Equations ◽  
Entire Functions ◽  
Value Distribution ◽  
Difference Operators ◽  
Sharing Values ◽  
Difference Analogue ◽  
The Difference ◽  
Brück Conjecture

The value distribution of solutions of certain difference equations is investigated. As its applications, we investigate the difference analogue of the Brück conjecture. We obtain some results on entire functions sharing a finite value with their difference operators. Examples are provided to show that our results are the best possible.

scholarly journals On Value Distribution of Difference Polynomials of Meromorphic Functions

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Zong-Xuan Chen
Keyword(s):  
Meromorphic Functions ◽  
Value Distribution ◽  
Difference Analogue ◽  
Difference Polynomials ◽  
The Difference

We study the value distribution of the difference counterpartΔf(z)−af(z)noff′(z)−af(z)nand obtain an almost direct difference analogue of results of Hayman.

scholarly journals Uniqueness Theorems on Entire Functions and Their Difference Operators or Shifts

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Baoqin Chen ◽  
Zongxuan Chen ◽  
Sheng Li
Keyword(s):  
Entire Function ◽  
Entire Functions ◽  
Difference Operators ◽  
Uniqueness Theorems ◽  
Difference Analogue ◽  
Function Sharing

We study the uniqueness problems on entire functions and their difference operators or shifts. Our main result is a difference analogue of a result of Jank-Mues-Volkmann, which is concerned with the uniqueness of the entire function sharing one finite value with its derivatives. Two relative results are proved, and examples are provided for our results.

scholarly journals Some details of proofs of theorems related to the quantum dynamical Yang-Baxter equation

2000 ◽  
Vol 24 (12) ◽  
pp. 793-806 ◽  
Author(s):  
Tom H. Koornwinder
Keyword(s):  
Quantum Groups ◽  
Difference Equations ◽  
Difference Operators ◽  
Baxter Equation ◽  
Quantum Dynamical ◽  
Intertwining Operator ◽  
The Difference ◽  
Exchange Matrix

This paper of tutorial nature gives some further details of proofs of some theorems related to the quantum dynamical Yang-Baxter equation. This mainly expands proofs given in “Lectures on the dynamical Yang-Baxter equation” by Etingof and Schiffmann, math.QA/9908064. This concerns the intertwining operator, the fusion matrix, the exchange matrix and the difference operators. The last part expands proofs given in “Traces of intertwiners for quantum groups and difference equations, I” by Etingof and Varchenko, math.QA/9907181. This concerns the dual Macdonald-Ruijsenaars equations.

scholarly journals Growth of meromorphic solutions of some difference equations

2010 ◽  
Vol 4 (2) ◽  
pp. 309-321 ◽  
Author(s):  
Xiu-Min Zheng ◽  
Zong-Xuan Chen ◽  
Tu Jin
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Higher Order ◽  
Meromorphic Solutions ◽  
Entire Solutions ◽  
Order Difference ◽  
Difference Analogue ◽  
Algebraic Difference ◽  
The Difference

We investigate higher order difference equations and obtain some results on the growth of transcendental meromorphic solutions, which are complementary to the previous results. Examples are also given to show the sharpness of these results. We also investigate the growth of transcendental entire solutions of a homogeneous algebraic difference equation by using the difference analogue of Wiman-Valiron Theory.

scholarly journals Degenerate Sklyanin algebras

Open Physics ◽  
2010 ◽  
Vol 8 (4) ◽  
Author(s):  
Andrey Smirnov
Keyword(s):  
Difference Operators ◽  
Baxter Equation ◽  
Quantum Algebras ◽  
Rational Solutions ◽  
R Matrix ◽  
Gauge Transformations ◽  
Sklyanin Algebras ◽  
Sklyanin Algebra ◽  
The Difference

AbstractNew trigonometric and rational solutions of the quantum Yang-Baxter equation (QYBE) are obtained by applying some singular gauge transformations to the known Belavin-Drinfeld elliptic R-matrix for sl(2;?). These solutions are shown to be related to the standard ones by the quasi-Hopf twist. We demonstrate that the quantum algebras arising from these new R-matrices can be obtained as special limits of the Sklyanin algebra. A representation for these algebras by the difference operators is found. The sl(N;?)-case is discussed.

scholarly journals Analytical Study of the Difference Equation xn+1 = xnxn-6 / xn-5 (±1 – xnxn-6)

2019 ◽  
pp. 1-12
Author(s):  
Abdualrazaq Sanbo ◽  
Elsayed M. Elsayed ◽  
Faris Alzahrani
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Analytical Study ◽  
Initial Conditions ◽  
Specific Form ◽  
Positive Real ◽  
Rational Difference Equations ◽  
Special Cases ◽  
The Difference

This paper is devoted to find the form of the solutions of a rational difference equations with arbitrary positive real initial conditions. Specific form of the solutions of two special cases of this equation are given.

scholarly journals A NOTE ON VALUE DISTRIBUTION OF DIFFERENCE POLYNOMIALS

2010 ◽  
Vol 81 (3) ◽  
pp. 353-360 ◽  
Author(s):  
K. LIU ◽  
I. LAINE
Keyword(s):  
Value Distribution ◽  
Difference Polynomials ◽  
Brück Conjecture

AbstractIn this paper, we investigate the value distribution of difference polynomials and prove some difference analogues of results of Hayman and the Brück conjecture.

Sign in / Sign up

Export Citation Format

Share Document