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《Indagationes Mathematicae》2022,33(2):421-439
We prove the irreducibility of integer polynomials whose roots lie inside an Apollonius circle associated to two points on the real axis with integer abscissae and , with ratio of the distances to these points depending on the canonical decomposition of and . In particular, we obtain irreducibility criteria for the case where and have few prime factors, and is either an Eneström–Kakeya polynomial, or has a large leading coefficient. Analogous results are also provided for multivariate polynomials over arbitrary fields, in a non-Archimedean setting. 相似文献
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Li-Mei Wang 《Journal of Mathematical Analysis and Applications》2022,505(1):125448
In this paper, the order of convexity of is given under certain conditions on the positive real parameters a, b and c. We show also that the image domains of the unit disc under some shifted zero-balanced hypergeometric functions are convex and bounded by two horizontal lines. This solves a problem raised by Ponnusamy and Vuorinen in [10]. 相似文献
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《Discrete Mathematics》2020,343(1):111640
For any graph with , a shortest path reconfiguration graph can be formed with respect to and ; we denote such a graph as . The vertex set of is the set of all shortest paths from to in while two vertices in are adjacent if and only if the vertex sets of the paths that represent and differ in exactly one vertex. In a recent paper (Asplund et al., 2018), it was shown that shortest path graphs with girth five or greater are exactly disjoint unions of even cycles and paths. In this paper, we extend this result by classifying all shortest path graphs with no induced 4-cycles. 相似文献
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Ilpo Laine 《Journal of Mathematical Analysis and Applications》2019,469(2):808-826
Given an entire function f of finite order ρ, let be a shift polynomial of f with small meromorphic coefficients in the sense of , . Provided α, β, are similar small meromorphic functions, we consider zero distribution of , resp. of . 相似文献
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In this article, we obtain a sufficient condition related to toughness for a graph to be all fractional -critical. We prove that if for some nonnegative integers , then is all fractional -critical. Our result improves the known results in Liu and Zhang (2008) and Liu and Cai (2009). 相似文献
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We prove several improved versions of Bohr’s inequality for the harmonic mappings of the form , where is bounded by 1 and . The improvements are obtained along the lines of an earlier work of Kayumov and Ponnusamy, i.e. (Kayumov and Ponnusamy, 2018) for example a term related to the area of the image of the disk under the mapping is considered. Our results are sharp. In addition, further improvements of the main results for certain special classes of harmonic mappings are provided. 相似文献
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The paper presents a number of new exact solutions to nonlinear reaction–diffusion equations with delay of the form where is the delay time, and is an arbitrary function of two arguments. Solutions are sought in the form of a generalized traveling-wave, with . It is shown that one of the two functional coefficients and of the equation considered can be specified arbitrarily. Examples of delay reaction–diffusion equations and their solutions are given. New exact solutions of few other nonlinear delay PDEs are also obtained. 相似文献
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A non-empty -regular graph on vertices is called a Deza graph if there exist constants and such that any pair of distinct vertices of has either or common neighbours. The quantities , , , and are called the parameters of and are written as the quadruple . If a Deza graph has diameter 2 and is not strongly regular, then it is called a strictly Deza graph. In the present paper, we investigate strictly Deza graphs whose parameters satisfy the conditions and . 相似文献
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Michael Skotnica 《Discrete Mathematics》2019,342(12):111611
Let denote the maximal number of points on the discrete torus (discrete toric grid) of sizes with no three collinear points. The value is known for the case where is prime. It is also known that . In this paper we generalize some of the known tools for determining and also show some new. Using these tools we prove that the sequence is periodic for all fixed . In general, we do not know the period; however, if for prime, then we can bound it. We prove that which implies that the period for the sequence is , where is at most . 相似文献
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Qichun Wang 《Discrete Mathematics》2019,342(12):111625
It was proved by J. Schatz that the covering radius of the second order Reed–Muller code is 18 (Schatz (1981)). However, the covering radius of has been an open problem for many years. In this paper, we prove that the covering radius of is 40, which is the same as the covering radius of in . As a corollary, we also find new upper bounds for the covering radius of , . 相似文献
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《Discrete Mathematics》2020,343(7):111888
For any sequence , the extremal function is the maximum possible length of a -sparse sequence with distinct letters that avoids . We prove that if is an alternating sequence of length , then for all and , answering a question of Wellman and Pettie (2018) and extending the result of Roselle and Stanton that for any alternation of length (Roselle and Stanton, 1971).Wellman and Pettie also asked how large must be for there to exist -block sequences of length . We answer this question by showing that the maximum possible length of an -block sequence is if and only if . We also show related results for extremal functions of forbidden 0–1 matrices with any constant number of rows and extremal functions of forbidden sequences with any constant number of distinct letters. 相似文献
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《Discrete Mathematics》2019,342(5):1275-1292
A discrete function of variables is a mapping , where , and are arbitrary finite sets. Function is called separable if there exist functions for , such that for every input the function takes one of the values . Given a discrete function , it is an interesting problem to ask whether is separable or not. Although this seems to be a very basic problem concerning discrete functions, the complexity of recognition of separable discrete functions of variables is known only for . In this paper we will show that a slightly more general recognition problem, when is not fully but only partially defined, is NP-complete for . We will then use this result to show that the recognition of fully defined separable discrete functions is NP-complete for .The general recognition problem contains the above mentioned special case for . This case is well-studied in the context of game theory, where (separable) discrete functions of variables are referred to as (assignable) -person game forms. There is a known sufficient condition for assignability (separability) of two-person game forms (discrete functions of two variables) called (weak) total tightness of a game form. This property can be tested in polynomial time, and can be easily generalized both to higher dimension and to partially defined functions. We will prove in this paper that weak total tightness implies separability for (partially defined) discrete functions of variables for any , thus generalizing the above result known for . Our proof is constructive. Using a graph-based discrete algorithm we show how for a given weakly totally tight (partially defined) discrete function of variables one can construct separating functions in polynomial time with respect to the size of the input function. 相似文献