关于凸体覆盖的Hadwiger猜想的两个等价形式

令K是一个内部(记作intK)包含原点o的凸体,bdK为其边界,m为覆盖K所需的intK的平移的最小个数.本文证明,存在正实数η和含于η(bdK)的m元点集C1使得C1+int K覆盖K;存在正实数η′、实数γ∈(0,1)和含于η′(bd K)的m元点集C2使得C2+γK覆盖K.基于这两个事实,本文得到关于凸体覆盖的Hadwiger猜想的两个等价形式.本文还引入一个可以替代宗传明提出的攻克Hadwiger猜想的数量方案中的γm(K)的新泛函.     

可口革囊星虫三种同工酶表达初步分析

应用聚丙烯酰胺凝胶电泳法，对可口革囊星虫的收吻肌、吻、肠、肾管和体壁5种组织或器官进行了同工酶分析．共分析了酯酶、过氧化物酶和超氧化物歧化酶等三种同工酶．结果表明：酯酶具有显著的组织特异性，其余两种酶相对不明显；可口革囊星虫的肠除了行使消化功能外，还和吻、肾管一起在清除自由基方面起着重要作用；提出将EST分析作为星虫动物门的一个分类学依据。     

外平行凸体的平均值

本文研究了外平行凸体Kρ在任意(n-r)维平面上的正交投影( Kρ)′n-r,利用K的均质积分,得到了( Kρ)′n-r的面积平均值,体积平均值以及平均曲率的任意阶积分的平均值.     

A hypersingular integral equation for the floating body problem

A new boundary integral equation formulation for the floating body problem, which is defined on a bounded domain and includes a hypersingular and a nonlocal part, is proved to satisfy a Gärding inequality. Under the assunlption of uniqueness it is shown, that an approximating sequence of related semidiscrete integral operators is uniformly bounded invertible.     

Inequality constraints with elastic impacts in deformable bodies. The convex case

Summary The aim of the present paper is to present some new results for problems when impacts occur. We prove, in the framework of linear elastic body, certain equivalent form of the d'Alembert's principle, including velocity discontinuity. We show that the theorem of stationary action still holds as an inequality. The consideration of the variation of the unknown impact time implies for the impact problem certain new variational expressions in inequality form. Received 13 August 1998; accepted for publication 6 May 1999     

旋转液体中固体颗粒运动的进一步讨论

通过分析旋转液体中的压强分布,说明了浸在液体中的固体颗粒向轴心运动的原因,以及该规律的实际应用.     

Optimal rigid body motions,part 2: Minimum time solutions

The time-optimal control of rigid-body angular rates is investigated in the absence of direct control over one of the angular velocity components. The existence of singular subarcs in the time-optimal trajectories is explored. A numerical survey of the optimality conditions reveals that, over a large range of boundary conditions, there are in general several distinct extremal solutions. A classification of extremal solutions is presented, and domains of existence of the extremal subfamilies are established in a reduced parameter space. A locus of Darboux points is obtained, and global optimality of the extremal solutions is observed in relation to the Darboux points. The continuous dependence of the optimal trajectories with respect to variations in control constraints is noted, and a procedure to obtain the time-optimal bang-bang solutions is presented.This work was supported in part by DARPA under Contract No. ACMP-F49620-87-C-0016, by SDIO/IST under Contract No. F49620-87-C0088, and by Air Force Grant AFOSR-89-0001.     

投影体与U(P)的极值性质

为了研究著名的Schneider投影问题,E.Lutwak,D.Yang和张高勇最近引进了一个关于对称多胞形的新的仿射不变量U(P),并提出了关于U(P)下界的猜想.本文就二维、三维在一特定条件下的情形给予了此猜想的肯定回答并给出了严格的数学证明.