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Let and be a sufficiently large real number. In this paper, we prove that, for almost all , the Diophantine inequality is solvable in primes . Moreover, we also investigate the problem of six primes and prove that the Diophantine inequality is solvable in primes for sufficiently large real number . 相似文献
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Ye Wang 《Discrete Mathematics》2017,340(12):2782-2788
Let be the finite field of elements for prime power and let be the character of . For any positive integer , the linearized Wenger graph is defined as follows: it is a bipartite graph with the vertex partitions being two copies of the -dimensional vector space , and two vertices and being adjacent if , for all . In this paper, we show that for any positive integers and with , contains even cycles of length which is an open problem put forward by Cao et al. (2015). 相似文献
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Let p be an odd prime, and let x be a primitive root of p. Suppose that we write the elements of as and that, wherever we evaluate , we always write it as one of Let be a terrace for . Then is said to be a logarithmic terrace if , defined by , is also a terrace for . We study properties of logarithmic terraces, in particular investigating terraces which are simultaneously logarithmic for two different primitive roots. 相似文献
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We say a graph is -colorable with of ’s and of ’s if may be partitioned into independent sets and sets whose induced graphs have maximum degree at most . The maximum average degree, , of a graph is the maximum average degree over all subgraphs of . In this note, for nonnegative integers , we show that if , then is -colorable. 相似文献
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Neel Patel 《Journal of Differential Equations》2018,264(3):1841-1885
We consider continuation criteria for the three-dimensional relativistic Vlasov–Maxwell system. When the particle density, , is compactly supported at , we prove , where and is arbitrarily small, is a continuation criteria. Our continuation criteria is an improvement in the range to the previously best known criteria due to Kunze [7]. We also consider continuation criteria when has noncompact support. In this regime, Luk–Strain [9] proved that is a continuation criteria for . We improve this result to . Finally, we build on another result by Luk–Strain [8]. The authors proved boundedness of momentum support on a fixed two-dimensional plane is a sufficient continuation criteria. We prove the same result even if the plane varies continuously in time. 相似文献
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Very recently, Thomassé et al. (2017) have given an FPT algorithm for Weighted Independent Set in bull-free graphs parameterized by the weight of the solution, running in time . In this article we improve this running time to . As a byproduct, we also improve the previous Turing-kernel for this problem from to . Furthermore, for the subclass of bull-free graphs without holes of length at most for , we speed up the running time to . As grows, this running time is asymptotically tight in terms of , since we prove that for each integer , Weighted Independent Set cannot be solved in time in the class of -free graphs unless the ETH fails. 相似文献
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This paper is concerned with the quantitative homogenization of 2m-order elliptic systems with bounded measurable, rapidly oscillating periodic coefficients. We establish the sharp convergence rate in with in a bounded Lipschitz domain in as well as the uniform large-scale interior estimate. With additional smoothness assumptions, the uniform interior , and estimates are also obtained. As applications of the regularity estimates, we establish asymptotic expansions for fundamental solutions. 相似文献
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Let . We show how the fundamental theorem of surface theory for surfaces of class over a simply-connected open subset of established in 2005 by S. Mardare can be extended to surfaces of class when ω is in addition bounded and has a Lipschitz-continuous boundary. Then we establish a nonlinear Korn inequality for surfaces of class . Finally, we show that the mapping that defines in this fashion a surface of class , unique up to proper isometries of , in terms of its two fundamental forms is locally Lipschitz-continuous. 相似文献
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