Results 1 to 10 of about 601,525 (187)
Uniqueness of difference polynomials
AIMS Mathematics, 2021 Let $ f(z) $ be a transcendental meromorphic function of finite order and $ c\in\Bbb{C} $ be a nonzero constant. For any $ n\in\Bbb{N}^{+} $, suppose that $ P(z, f) $ is a difference polynomial in $ f(z) $ such as $ P(z, f) = a_{n}f(z+nc)+a_{n-1}f(z+(n-1)
Xiaomei Zhang , Xiang Chen
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Uniqueness of entire functions whose difference polynomials share a polynomial with finite weight
Cubo, 2022 In this paper, we use the concept of weighted sharing of values to investigate the uniqueness results when two difference polynomials of entire functions share a nonzero polynomial with finite weight.
Goutam Haldar
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Meromorphic solutions of three certain types of non-linear difference equations
AIMS Mathematics, 2021 In this paper, the representations of meromorphic solutions for three types of non-linear difference equations of form $ f^{n}(z)+P_{d}(z, f) = u(z)e^{v(z)}, $ $ f^{n}(z)+P_{d}(z, f) = p_{1}e^{\lambda z}+p_{2}e^{-\lambda z} $ and $
Min Feng Chen +2 more
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Multivariate polynomial values in difference sets
Discrete Analysis, 2021 Multivariate polynomial values in difference sets, Discrete Analysis 2021:11, 46 pp. A well known theorem of Furstenberg and Sárközy states that every dense set of integers must contain two elements that differ by a perfect square.
John R. Doyle, Alex Rice
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Zeros of difference polynomials
Journal of Approximation Theory, 1992 Studies --- both analytic and numerical --- on polynomials have been of immense interest for long. Here the authors deal in detail with various questions relating to the zeros of difference polynomials. Particularly, defining the difference operator by \(\Delta f(x)=f(x+1)-f(x)\), the polynomial \(\Delta^ mx^ n\) of degree \((n-m)\) having \((n-m ...
John J. Warvik, Ronald J. Evans
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Polynomial Differences in the Primes [PDF]
, 2014 We establish, utilizing the Hardy-Littlewood Circle Method, an asymptotic formula for the number of pairs of primes whose differences lie in the image of a fixed polynomial. We also include a generalization of this result where differences are replaced with any integer linear combination of two primes.
Alex Rice, Neil Lyall
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Manifolds of Difference Polynomials [PDF]
Transactions of the American Mathematical Society, 1948 1. It is the purpose of this paper to develop in some detail the structure of the manifolds determined by systems of difference polynomials. Our results will necessarily be confined to the case of polynomials in an abstract field, since a suitable existence theorem for analytic difference equations is not available. The ideal theory, developed by J. F.
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Results on the uniqueness of difference polynomials of entire functions
Revista de Matemática: Teoría y Aplicaciones, 2015 In this paper, we study the uniqueness of two difference polynomials of entire functions sharing one value, polynomial and small function. Our results of this paper are improvement of the previous theorems given by Chen and Chen [2], Liu, Liu and Cao [22]
Hua Wang, Hong Yan Xu
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Conditions for asymptotic stability of first order scalar differential-difference equation with complex coefficients [PDF]
Archives of Control Sciences, 2023 We investigate a scalar characteristic exponential polynomial with complex coefficients associated with a first order scalar differential-difference equation.
Rafał Kapica, Radosław Zawiski
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On difference polynomials and hereditarily irreducible polynomials
Journal of Number Theory, 1980 AbstractA difference polynomial is one of the form P(x, y) = p(x) − q(y). Another proof is given of the fact that every difference polynomial has a connected zero set, and this theorem is applied to give an irreducibility criterion for difference polynomials. Some earlier problems about hereditarily irreducible polynomials (HIPs) are solved.
Lee A. Rubel, Helge Tverberg, A Schinzel
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