共查询到20条相似文献,搜索用时 31 毫秒
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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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Quốc Anh Ngô 《Comptes Rendus Mathematique》2017,355(5):526-532
In this note, we mainly study the relation between the sign of and in with and for . Given the differential inequality , first we provide several sufficient conditions so that holds. Then we provide conditions such that for all , which is known as the sub poly-harmonic property for u. In the last part of the note, we revisit the super poly-harmonic property for solutions to and with in . 相似文献
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Nguyen Tien Tai 《Journal of Differential Equations》2018,264(6):3940-3975
Our main task in this note is to prove the existence and to classify the exact growth at infinity of radial positive -solutions of in , where and p is bounded from below by the sixth-order Joseph–Lundgren exponent. Following the main work of Winkler, we introduce the sub- and super-solution method and comparison principle to conclude the asymptotic behavior of solutions. 相似文献
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《Journal of Mathematical Analysis and Applications》2014,419(2):783-795
We study restriction estimates for algebraic varieties in d-dimensional vector spaces over finite fields. Unlike the Euclidean case, if the dimension d is even, then it is conjectured that the Stein–Tomas restriction result can be improved to the estimate for both spheres and paraboloids in finite fields. In this paper we show that the conjectured restriction estimate holds in the specific case when test functions under consideration are restricted to d-coordinate functions or homogeneous functions of degree zero. To deduce our result, we use the connection between the restriction phenomena for our varieties in d dimensions and those for homogeneous varieties in dimensions. 相似文献
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Zuoshunhua Shi 《Journal of Differential Equations》2018,264(3):1550-1580
In this paper, we mainly study the existence of self-similar solutions of stationary Navier–Stokes equations for dimension . For , if the external force is axisymmetric, scaling invariant, continuous away from the origin and small enough on the sphere , we shall prove that there exists a family of axisymmetric self-similar solutions which can be arbitrarily large in the class . Moreover, for axisymmetric external forces without swirl, corresponding to this family, the momentum flux of the flow along the symmetry axis can take any real number. However, there are no regular () axisymmetric self-similar solutions provided that the external force is a large multiple of some scaling invariant axisymmetric F which cannot be driven by a potential. In the case of dimension 4, there always exists at least one self-similar solution to the stationary Navier–Stokes equations with any scaling invariant external force in . 相似文献
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