完全椭圆积分和Hersch-Pfluger偏差函数

该文建立了Hersch-Pfluger偏差函数ψK(r)和第二类完全椭圆积分ε(r)之间的关系. 通过对完全椭圆积分及某些初等函数的组合的单调性和凹凸性的研究获得了完全椭圆积分的一些不等式, 并且藉此得到Hersch-Pfluger偏差函数ψK(r)的几个渐进精确的上界估计.     

完全区组设计下基于Aligned秩的有方向检验问题

本文基于Aligned秩给出了用于解完全区组设计有方向检验问题的, 我们称之为$C$-检验的检验方法. 本文分别对每个试验单元仅有一个观测值以及等重复观测值和不等重复观测值各种情形下的$C$检验进行了讨论, 并在原假设$H_0$成立时计算了上述各种情形下$C$检验统计量的数学期望和方差, 且证明了$C$检验统计量的渐近分布为正态分布.     

Testing monotonicity over graph products

We consider the problem of monotonicity testing over graph products. Monotonicity testing is one of the central problems studied in the field of property testing. We present a testing approach that enables us to use known monotonicity testers for given graphs G₁, G₂, to test monotonicity over their product G₁ × G₂. Such an approach of reducing monotonicity testing over a graph product to monotonicity testing over the original graphs, has been previously used in the special case of monotonicity testing over [n]^d for a limited type of testers; in this article, we show that this approach can be applied to allow modular design of testers in many interesting cases: this approach works whenever the functions are boolean, and also in certain cases for functions with a general range. We demonstrate the usefulness of our results by showing how a careful use of this approach improves the query complexity of known testers. Specifically, based on our results, we provide a new analysis for the known tester for [n]^d which significantly improves its query complexity analysis in the low‐dimensional case. For example, when d = O(1), we reduce the best known query complexity from O(log ²n/ε) to O(log n/ε). © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008     

Dimension of complete simple games with minimum

Weighted majority games have the property that players are totally ordered by the desirability relation (introduced by Isbell in [J.R. Isbell, A class of majority games, Quarterly Journal of Mathematics, 7 (1956) 183–187]) because weights induce it. Games for which this relation is total are called complete simple games. Taylor and Zwicker proved in [A.D. Taylor, W.S. Zwicker, Weighted voting, multicameral representation, and power, Games and Economic Behavior 5 (1993) 170–181] that every simple game (or monotonic finite hypergraph) can be represented by an intersection of weighted majority games and consider the dimension of a game as the needed minimum number of them to get it. They provide the existence of non-complete simple games of every dimension and left open the problem for complete simple games.     

Complete synchronization of Kuramoto oscillators with finite inertia

We present an approach based on Gronwall’s inequalities for the asymptotic complete phase-frequency synchronization of Kuramoto oscillators with finite inertia. For given finite inertia and coupling strength, we present admissible classes of initial configurations and natural frequency distributions, which lead to the complete phase-frequency synchronization asymptotically. For this, we explicitly identify invariant regions for the Kuramoto flow, and derive second-order Gronwall’s inequalities for the evolution of phase and frequency diameters. Our detailed time-decay estimates for phase and frequency diameters are independent of the number of oscillators. We also compare our analytical results with numerical simulations.     

The first eigenvalue of the p‐Laplace operator under powers of mean curvature flow

In this paper, we show the following main results. Let (Mⁿ,g(t)), t ∈ [0,T), be a solution of the unnormalized H^k ? flow on a closed manifold, and λ_1,p(t) be the first eigenvalue of the p‐Laplace operator. If there exists a nonnegative constant ε such that in M × [0,T) and in M × [0,T),then λ_1,p(t) is increasing and the differentiable almost everywhere along the unnormalized H^k ? flow on [0,T). At last, we discuss some useful monotonic quantities. Copyright © 2013 John Wiley & Sons, Ltd.     

Müntz-type theorems on the half-line with weights

We consider the linear span S   of the functions t^_ak$t^{a_k}$ (with some _ak>0$a_k>0$) in weighted L²$L^2$ spaces, with rather general weights. We give one necessary and one sufficient condition for S to be dense. Some comparisons are also made between the new results and those that can be deduced from older ones in the literature.     

Analysis of the convected Helmholtz equation with a uniform mean flow in a waveguide with complete radiation boundary conditions

In this paper, we propose complete radiation boundary conditions (CRBCs) for solutions of the convected Helmholtz equation with a uniform mean flow in a waveguide. We first study CRBCs for the Helmholtz equation in a waveguide. Noting that the convected Helmholtz equation is associated with the Helmholtz equation via the Prandtl–Glauert transformation, CRBCs for the convected Helmholtz equation is derived from CRBCs for the Helmholtz equation. We analyse well-posedness and convergence of approximate solutions satisfying CRBCs for the convected Helmholtz equation. In addition, simple numerical experiments will be presented to confirm the theoretical results.