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61.
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Noga Alon 《Journal of Number Theory》2007,126(1):110-118
For a prime p, a subset S of Zp is a sumset if S=A+A for some A⊂Zp. Let f(p) denote the maximum integer so that every subset S⊂Zp of size at least p−f(p) is a sumset. The question of determining or estimating f(p) was raised by Green. He showed that for all sufficiently large p, and proved, with Gowers, that f(p)<cp2/3log1/3p for some absolute constant c. Here we improve these estimates, showing that there are two absolute positive constants c1,c2 so that for all sufficiently large p,
63.
本文讨论机器具有准备时间的双目标平行机排序问题,目标函数为完工时间和最优条件下极小化最大完工时间.通过对SPT排序的性质的分析,给出了最优排序的下界.在此基础上证明了SPT排序的误差界为3/2,并且是紧界. 相似文献
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The Henstock integral in ℝn and its relation to the n-dimensional improper Riemann integral are studied. A Hake-type theorem for the Henstock integral in ℝn is proved.__________Translated from Matematicheskie Zametki, vol. 78, no. 2, 2005, pp. 251–258.Original Russian Text Copyright © 2005 by P. Muldowney, V. A. Skvortsov. 相似文献
66.
By using divided differences, we derive two different ways of representing the Lauricella function of n variables FD(n)(a,b1,b2,...,bn;c;x1,x2,...,xn) as a finite sum, for b1,b2,...,bn positive integers, and a,c both positive integers or both positive rational numbers with c–a a positive integer.
AMS subject classification 33D45, 40B05, 40C99Jieqing Tan: Research supported by the National Natural Science Foundation of China under Grant No. 10171026 and Anhui Provincial Natural Science Foundation under Grant No. 03046102.Ping Zhou: Corresponding author. Research supported by NSERC of Canada. 相似文献
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We consider the iterative solution of linear systems arising from four convection–diffusion model problems: scalar convection–diffusion problem, Stokes problem, Oseen problem and Navier–Stokes problem. We design preconditioners for these model problems that are based on Kronecker product approximations (KPAs). For this we first identify explicit Kronecker product structure of the coefficient matrices, in particular for the convection term. For the latter three model cases, the coefficient matrices have a 2 × 2 block structure, where each block is a Kronecker product or a summation of several Kronecker products. We then use this structure to design a block diagonal preconditioner, a block triangular preconditioner and a constraint preconditioner. Numerical experiments show the efficiency of the three KPA preconditioners, and in particular of the constraint preconditioner that usually outperforms the other two. This can be explained by the relationship that exists between these three preconditioners: the constraint preconditioner can be regarded as a modification of the block triangular preconditioner, which at its turn is a modification of the block diagonal preconditioner based on the cell Reynolds number. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
69.
Flavia Bonomo Guillermo Durán Javier Marenco Mario Valencia-Pabon 《Discrete Applied Mathematics》2011,159(5):288-294
In this paper, we study the minimum sum set coloring (MSSC) problem which consists in assigning a set of x(v) positive integers to each vertex v of a graph so that the intersection of sets assigned to adjacent vertices is empty and the sum of the assigned set of numbers to each vertex of the graph is minimum. The MSSC problem occurs in two versions: non-preemptive and preemptive. We show that the MSSC problem is strongly NP-hard both in the preemptive case on trees and in the non-preemptive case in line graphs of trees. Finally, we give exact parameterized algorithms for these two versions on trees and line graphs of trees. 相似文献
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This article is concerned with solving the high order Stein tensor equation arising in control theory. The conjugate gradient squared (CGS) method and the biconjugate gradient stabilized (BiCGSTAB) method are attractive methods for solving linear systems. Compared with the large-scale matrix equation, the equivalent tensor equation needs less storage space and computational costs. Therefore, we present the tensor formats of CGS and BiCGSTAB methods for solving high order Stein tensor equations. Moreover, a nearest Kronecker product preconditioner is given and the preconditioned tensor format methods are studied. Finally, the feasibility and effectiveness of the new methods are verified by some numerical examples. 相似文献