New star discrepancy bounds for (t,m,s)-nets and (t,s)-sequences

In this paper, we derive new general upper bounds on the star discrepancy of $(t,m,s)$ -nets and $(t,s)$ -sequences. These kinds of point sets are among the most widely used in quasi-Monte Carlo methods for numerical integration. By our new results, we improve on previous discrepancy bounds and prove a conjecture stated by the second author in an earlier paper.     

On controllability of systems of the form\dot x=A(t)x+g(t,u)

In an earlier paper, the author established a sufficient condition for controllability of systems of the form =A(t)x+g(t, u). This condition is a growth condition which generalizes the concept of an asymptotically proper system introduced by LaSalle for linear systems. The purpose of this paper is examine and apply this growth condition. We first show that the condition is also necessary for controllability. Then, we use these results to consider the controllability of perturbations of the above system. The main result of the paper is a class of systems which in many applications can be assumed to be controllable.During the writing of this paper, the author held a Junior Faculty Summer Fellowship from the Research Council of the University of Nebraska.     

x'=g(x,t)+h(t)型方程的拓扑动力系统与Kurzweil-Henstock积分

本文借助Sell等人建立的局部动力系统理论,利用Kurzweil-Henstock积分,建立了x′=g(x,t)+h(t)型非自治微分方程的拓扑动力系统,为进一步讨论这种方程解的渐近行为作了基础性的工作.本文的工作也是Sell等人工作中有关结论的推广.     

x''''=g(x,t)+h(t)型方程的拓扑动力系统与Kurzweil-Henstock积分

本文借助Sell等人建立的局部动力系统理论,利用Kurzweil-Henstock积分,建立了x′=g(x,t)+h(t)型非自治微分方程的拓扑动力系统,为进一步讨论这种方程解的渐近行为作了基础性的工作.本文的工作也是Sell等人工作中有关结论的推广.     

Quelques propriétés génériques en analyse

We consider some classical genericity results in the sense of Baire categories, and we study whether they can be extended to the settings supplied by prevalence and by HP-residual sets. To cite this article: A. Fraysse et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

x′=g(x,t)+h(t)型方程的拓扑动力系统与Kurzweil-Henstock积分

本文借助Sell等人建立的局部动力系统理论,利用Kurzweil-Henstock积分,建立了x′=g(x,t)+h(t)型非自治微分方程的拓扑动力系统,为进一步讨论这种方程解的渐近行为作了基础性的工作.本文的工作也是Sell等人工作中有关结论的推广(参见文[1-12]).     

Domination of cyclic monotone (s, t)-graphs

The conjecture of zero domination of 0-cyclic monotone graphs is proved (anr-cyclic graph is a cyclic monotone (s, t)-graph exactlyr minimal paths of which have cycles). As a corollary, a formula for computing the reliability of an arbitrary 0-cyclic monotone graph is obtained. It is proved that the problem of determining the domination in the class ofr-cyclic monotone graphs is #P-complete for any fixed integerr≥1. Translated fromMatematicheskie Zametki, Vol. 67, No. 2, pp. 288–294, February, 2000.     

Formula for a solution ofu t +H(u,Du) =g

We study the continuous as well as the discontinuous solutions of Hamilton-Jacobi equationu _t +H(u,Du) =g in ℝ ⁿ x ℝ₊ withu(x, 0) =u ₀(x). The HamiltonianH(s,p) is assumed to be convex and positively homogeneous of degree one inp for eachs in ℝ. IfH is non increasing ins, in general, this problem need not admit a continuous viscosity solution. Even in this case we obtain a formula for discontinuous viscosity solutions.     

Variétés de Kummer généralisées

Re?u le 22 mars 2001; forme finale: 18 juin 2001 / Published online: 1 February 2002     

微分方程x+g(x)=p(T)的调和解

通过估计方程x+g(x)=p(t)之解绕原点一周的时间,讨论了周期解存在的条件及调和解的存在唯一性。