Hyperbolic positive mass theorem under modified energy condition

We provide two new positive mass theorems under respective modified energy conditions allowing T00 negative on some compact set for certain modified asymptotically hyperbolic manifolds. This work is analogous to Zhang’s previous result for modified asymptotically ?at initial data sets.     

A constructive proof of Ky Fan’s coincidence theorem

We present a constructive proof for the well-known Ky Fan’s coincidence theorem through a simplicial algorithm. In a finite number of steps the algorithm generates a simplex containing an approximate coincidence point. In the limit, when the mesh size converges to zero, the sequence of approximations converges to a coincidence point. This research was carried out while the second author was visiting the CentER for Economic Research, Tilburg University. He would like to thank both CentER and the Netherlands Organization for Scientific Research (NWO) for their financial support.     

Some new results on transition probability

In this paper, we study the basic properties of stationary transition probability of Markov processes on a general measurable space （E, δ）, such as the continuity, maximum probability, zero point, positive probability set,standardization, and obtain a series of important results such as Continuity Theorem, Representation Theorem, Levy Theorem and so on. These results are very useful for us to study stationary tri-point transition probability on a general measurable space （E, δ）. Our main tools such as Egoroff＇s Theorem, Vitali-Hahn-Saks＇s Theorem and the theory of atomic set and well- posedness of measure are also very interesting and fashionable.     

一类三阶非线性伪抛物方程的初边值问题

非线性伪抛物方程由于其来源于一些重要的物理过程而成为研究热点.对于一类三阶非线性伪抛物方程的初边值问题,给出了Hilbert空间中相应的强制不等式,利用同胚理论及推广的反函数定理,得到了非线性方程初边值问题解的大范围存在定理.对于相应的半线性方程给出了初边值问题解的大范围存在性、唯一性定理.     

Normalizers of subsystem subgroups in finite groups of Lie type

Finite groups of Lie type form the greater part of known finite simple groups. An important class of subgroups of finite groups of Lie type are so-called reductive subgroups of maximal rank. These arise naturally as Levi factors of parabolic groups and as centralizers of semisimple elements, and also as subgroups with maximal tori. Moreover, reductive groups of maximal rank play an important part in inductive studies of subgroup structure of finite groups of Lie type. Yet a number of vital questions dealing in the internal structure of such subgroups are still not settled. In particular, we know which quasisimple groups may appear as central multipliers in the semisimple part of any reductive group of maximal rank, but we do not know how normalizers of those quasisimple groups are structured. The present paper is devoted to tackling this problem. Supported by RFBR (grant No. 05-01-00797) and by SB RAS (Young Researchers Support grant No. 29 and Integration project No. 2006.1.2). __________ Translated from Algebra i Logika, Vol. 47, No. 1, pp. 3–30, January–February, 2008.     

Boundary Value Problems of the Theory of Analytic Functions with Displacements

Integral representations are constructed for functions holomorphic in a strip. Using these representations an effective solution of Carleman type problem is given for a strip.     

双原子分子能量的一种简明推导

对非刚性双原子分子的能量表达式给出一种简明的推导。     

A new method for estimating bounds of eigenvalues

A new method for estimating the bounds of eigenvalues is presented. In order to show that the method proposed is as effective as Qiu's, an undamping spring-mass system with 5 nodes and 5 degrees of freedom is given. To illustrate that the present method can be applied to structures which cannot be treated by non-negative decomposition, a plane frame with 202 nodes and 357 beam elements is given. The results show that the present method is effective for estimating the bounds of eigenvalues and is more common than Qiu's. Project supported by the National Natural Science Foundation (No. 19872028) and the Mechanical Technology Development Foundation of China.     

完整有势力学系统的高阶Lagrange方程

首先提出力学系统高阶速度能定理,阐明了系统高阶速度能量的物理意义;然后提出力学系统有势的一般判据.在此基础上,引入高阶Lagrange函数,得出完整有势力学系统的高阶Lagrange方程,并得到系统高阶循环积分和高阶广义能量积分. 关键词： 高阶速度能定理 有势力学系统 高阶Lagrange方程 高阶Lagrange函数