共查询到20条相似文献,搜索用时 31 毫秒
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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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Let . The daisy cube is introduced as the subgraph of induced by the union of the intervals over all . Daisy cubes are partial cubes that include Fibonacci cubes, Lucas cubes, and bipartite wheels. If is a vertex of a graph , then the distance cube polynomial is introduced as the bivariate polynomial that counts the number of induced subgraphs isomorphic to at a given distance from the vertex . It is proved that if is a daisy cube, then , where is the previously investigated cube polynomial of . It is also proved that if is a daisy cube, then holds for every vertex in . 相似文献
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The tensor product of graphs , and is defined by and Let be the fractional chromatic number of a graph . In this paper, we prove that if one of the three graphs , and is a circular clique, 相似文献
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《Stochastic Processes and their Applications》2020,130(4):2127-2158
Let be an ergodic diffusion with invariant distribution . Consider the empirical measure where is an Euler scheme with decreasing steps which approximates . Given a test function , we obtain sharp concentration inequalities for which improve the results in Honoré et al. (2019). Our hypotheses on the test function cover many real applications: either is supposed to be a coboundary of the infinitesimal generator of the diffusion, or is supposed to be Lipschitz. 相似文献
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《Discrete Mathematics》2019,342(10):2834-2842
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An independent broadcast on a connected graph is a function such that, for every vertex of , the value is at most the eccentricity of in , and implies that for every vertex of within distance at most from . The broadcast independence number of is the largest weight of an independent broadcast on . Clearly, is at least the independence number for every connected graph . Our main result implies . We prove a tight inequality and characterize all extremal graphs. 相似文献
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《Stochastic Processes and their Applications》2020,130(7):4358-4391
We consider a critical superprocess with general spatial motion and spatially dependent stable branching mechanism with lowest stable index . We first show that, under some conditions, converges to 0 as and is regularly varying with index . Then we show that, for a large class of non-negative testing functions , the distribution of , after appropriate rescaling, converges weakly to a positive random variable with Laplace transform 相似文献
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《Discrete Mathematics》2021,344(12):112589
Let be the set of positive integers. For a nonempty set A of integers and every integer u, denote by the number of with such that . For a sequence S of positive integers, let be the counting function of S. The set is called a perfect difference set if for every positive integer u. In 2008, Cilleruelo and Nathanson (2008) [4] constructed dense perfect difference sets from dense Sidon sets. In this paper, as a main result, we prove that: let be an increasing function satisfying for any positive integer n, then for every Sidon set B and every function , there exists a set such that for every positive integer u and for all . 相似文献
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The paper investigates longtime dynamics of the Kirchhoff wave equation with strong damping and critical nonlinearities: , with . The well-posedness and the existence of global and exponential attractors are established, and the stability of the attractors on the perturbation parameter ? is proved for the IBVP of the equation provided that both nonlinearities and are of critical growth. 相似文献
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Let be a rational expression of degree three over the finite field . We count the irreducible polynomials in , of a given degree, that have the form for some . As an example of application of our results, we recover the number of irreducible transformation shift registers of order three, which were computed by Jiang and Yang in 2017. 相似文献