Results 21 to 30 of about 601,525 (187)
Differential Galois Theory of Linear Difference Equations [PDF]
, 2008 We present a Galois theory of difference equations designed to measure the differential dependencies among solutions of linear difference equations.
Hardouin, Charlotte, Singer, Michael F.
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On the Intersections of the Components of a Difference Polynomial [PDF]
Proceedings of the American Mathematical Society, 1955 The purpose of this note is to prove the following theorem: Solutions common to two distinct components' of the manifold of a difference polynomial annul the separants of the polynomial. We begin by considering a field I, not necessarily a difference field, and a set of polynomials F,, F2,, * * *, Fp in K[ul, * , u.; xl, * *I* xp], the ui and xj being ...
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On uniform polynomial splitting of variational nonautonomous difference equations in Banach spaces
Annals of the West University of Timisoara: Mathematics and Computer Science, 2022 In this paper we consider a concept of uniform polynomial splitting for a discrete cocycle over a discrete semiflow in Banach spaces. We obtain some characterizations of Datko type and also in terms of Lyapunov functions. The study is made from the point
Biriş Larisa Elena +3 more
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On the Uniqueness of Certain Type of Shift Polynomial Sharing a Small Function
Annals of the West University of Timisoara: Mathematics and Computer Science, 2017 The purpose of the paper is to study the uniqueness problems of certain type of difference polynomial sharing a small function. We point out and rectify some gaps in the proof of the main results in [8]. In addition to this we obtain our main result as a
Majumder Sujoy
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Exponential Polynomials and Nonlinear Differential-Difference Equations
Journal of Function Spaces, 2020 In this paper, we study finite-order entire solutions of nonlinear differential-difference equations and solve a conjecture proposed by Chen, Gao, and Zhang when the solution is an exponential polynomial.
Junfeng Xu, Jianxun Rong
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Difference equation of the colored Jones polynomial for torus knot
, 2004 We prove that the N-colored Jones polynomial for the torus knot T_{s,t} satisfies the second order difference equation, which reduces to the first order difference equation for a case of T_{2,2m+1}.
Andrews G. E. +2 more
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A high order $q$-difference equation for $q$-Hahn multiple orthogonal polynomials [PDF]
, 2009 A high order linear $q$-difference equation with polynomial coefficients having $q$-Hahn multiple orthogonal polynomials as eigenfunctions is given. The order of the equation is related to the number of orthogonality conditions that these polynomials ...
Abramowitz M. +10 more
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On the Finite Differences of a Polynomial [PDF]
The Annals of Mathematical Statistics, 1935 In this paper an apparently new and convenient method of finding the successive finite differences of a polynomial is considered. If operationally 4(u + rjr2) = Er7r2 4(u) = (1 + Ari)r2 4o(u) then for any polynomial f(x) of degree "n" f(x) = po xn + P, Xn-1 +--+ Pn = po(x + a)n + qll(x + a)n-I + + qln Eaf(x) = po(x + a)n + pl(x + a)n-' + + Pn Aaf(X) = (
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On a characterization of polynomials by divided differences [PDF]
Aequationes Mathematicae, 1994 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Positive Polynomials on Riesz Spaces
, 2016 We prove some properties of positive polynomial mappings between Riesz spaces, using finite difference calculus. We establish the polynomial analogue of the classical result that positive, additive mappings are linear.
Cruickshank, James +2 more
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