Results 51 to 60 of about 8,973,715 (361)
Non-linear difference polynomials sharing a polynomial with finite weight
Ratio MathematicaThe uniqueness theory of meromorphic function mainly studies the conditions under which there exists only one function satisfying these conditions. The uniqueness theory of entire and meromorphic functions has grown up as an extensive sub-field of value ...
Harina Pandit Waghamore +1 more
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, 2004 We complete the construction of raising and lowering operators, given in a previous work, for the orthogonal polynomials of hypergeometric type on non-homogeneous lattice, and extend these operators to the generalized orthogonal polynomials, namely ...
Alvarez-Nodarse R +24 more
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Advanced Materials Interfaces, EarlyView., 2023 This review discusses the use of Surface‐Enhanced Raman Spectroscopy (SERS) combined with Artificial Intelligence (AI) for detecting antimicrobial resistance (AMR). Various SERS studies used with AI techniques, including machine learning and deep learning, are analyzed for their advantages and limitations.
Zakarya Al‐Shaebi +4 more
wiley +1 more source
AIMS MathematicsWe construct a new type of Genocchi polynomials using degenerate quantum exponential functions and find various forms of $ (q, h) $-difference equations with these polynomials as solutions. This paper includes properties of the symmetric structures of $ (
Jung Yoog Kang , Cheon Seoung Ryoo
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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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Classes of Bivariate Orthogonal Polynomials [PDF]
, 2016 We introduce a class of orthogonal polynomials in two variables which generalizes the disc polynomials and the 2-$D$ Hermite polynomials. We identify certain interesting members of this class including a one variable generalization of the 2-$D$ Hermite ...
Ismail, Mourad E. H., Zhang, Ruiming
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On a characterization of polynomials by divided differences [PDF]
Aequationes Mathematicae, 1994 We consider the functional equationf[x1,x2,⋯, xn] =h(x1 + ⋯ +xn) (x1,⋯,xn ∈K, xj ≠xk forj ≠ k), (D) wheref[x1,x2,⋯,xn] denotes the (n − 1)-st divided difference off and ...
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On the value distribution and uniqueness of difference polynomials of meromorphic functions
Advances in Differential Equations, 2013 In this paper, we study the zeros of difference polynomials of meromorphic functions of the forms (P(f)∏j=1df(z+cj)sj)(k)−α(z),(P(f)∏j=1d[f(z+cj)−f(z)]sj)(k)−α(z), where P(f) is a nonzero polynomial of degree n, cj∈C∖{0} (j=1,…,d) are distinct ...
H. Xu
semanticscholar +2 more sources
$q$-Classical orthogonal polynomials: A general difference calculus approach
, 2009 It is well known that the classical families of orthogonal polynomials are characterized as eigenfunctions of a second order linear differential/difference operator.
A.F. Nikiforov +26 more
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Discriminants and Functional Equations for Polynomials Orthogonal on the Unit Circle [PDF]
, 2001 We derive raising and lowering operators for orthogonal polynomials on the unit circle and find second order differential and $q$-difference equations for these polynomials.
Ismail, Mourad E. H., Witte, Nicholas S.
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