The classification of transversal multiplicity-free group actions

Multiplicity-free Hamiltonian group actions are the symplectic analogs of multiplicity-free representations, that is, representations in which each irreducible appears at most once. The most well-known examples are toric varieties. The purpose of this paper is to show that under certain assumptions multiplicity-free actions whose moment maps are transversal to a Cartan subalgebra are in one-to-one correspondence with a certain collection of convex polytopes. This result generalizes a theorem of Delzant concerning torus actions.Supported by an ONR Graduate Fellowship.     

复Grassmann流形中伪全纯曲线的结构

设Ｍ是黎曼曲面，ｆ：Ｍ→Ｇ（ｍ，Ｎ）是全纯映照，我们证明了：若ｆ完全分裂，则由ｆ生成的伪全纯曲线是完全分裂的以及两维球面到复Ｇｒａｓｓｍａｎｎ流形的伪全纯曲线是完全分裂的．     

An analogue of Hunt's representation theorem in quantum probability

In quantum mechanics certain operator-valued measures are introduced, called instruments, which are an analogue of the probability measures of classical probability theory. As in the classical case, it is interesting to study convolution semigroups of, instruments on groups and the associated semigroups of probability operators, which now are defined on spaces of functions with values in a von Neumann algebra. We consider a semigroup of probability operators with a continuity property weaker than uniform continuity, and we succeed in characterizing its infinitesimal generator under the additional hypothesis that twice differentiable functions belong to the domain of the generator. Such hypothesis can be proved in some particular cases. In this way a partial quantum analogue of Hunt's representation theorem for the generator of convolution semigroups on Lie groups is obtained. Our result provides also a closed characterization of generators of a new class of not norm continuous quantum dynamical semigroups.     

三因素完全巢式设计的分析

对于三因素完全巢式实验（the three-factor completely enstcd experiment），本就权向量的选取不依赖于样本容量的一般情形，建立了效应检验的公式，并证明了有关效应空间与权向量关系的两个基本结果。     

完全单的矩阵半群

引入矩阵型Rees矩阵半群的概念,证明完全单的矩阵半群等价于矩阵型Rees矩阵半群,进而给出矩阵拓扑半群的极小理想的刻画以及完全正则矩阵半群特别是一些重要类别的群带的刻画．     

A stability concept for matrix game optimal strategies and its application to linear programming sensitivity analysis

This paper studies a class of perturbations of a game matrix that alters each row by a different amount. We find that completely mixed optimal strategies are stable under these perturbations provided the norm of the vector of additive amounts is sufficiently small. Using this concept we give a new characterization of completely mixed grames. We also obtain a sensitivity result for a class of perturbations of the technological coefficient matrix of positive linear programs. The stability of an optimal strategy holds throughout at least a spherical neighborhood of the zero perturbation. We give a computational formula and equivalent programming formulations for the radius of this neighborhood.     

Wold decomposition in Banach spaces

We propose a natural analog of the Wold decomposition in the case of a linear noninvertible isometry V in a Banach space X. We obtain a criterion for the existence of such a decomposition. In a reflective space, this criterion is reduced to the existence of the linear projection P: X → VX with unit norm. Separately, we discuss the problem of the Wold decomposition for the isometry V _φ induced by an epimorphism φ of a compact set H in the space of continuous functions C(H). We present a detailed study of the mapping z → z ^m of the circle |z| = 1 with an integer m ≥ 2.     

An affine model for the actions in an integrable system with monodromy

We give a standard model for the flat affine geometry defined by the local action variables of a completely integrable system. We are primarily interested in the affine structure in the neighborhood of a critical value with nontrivial monodromy.      

Anisotropic temperature of charged particles in a variable electric field

The time dependence of the longitudinal and transverse temperatures in a completely ionized plasma immersed in a variable uniform electric field is analyzed by solving gas dynamics equations based on a bi-Maxwellian distribution. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 64–72, December, 2008.     

Continuous Approximations of Multivalued Mappings and Fixed Points

In the present paper, we prove a fixed-point theorem for completely continuous multivalued mappings defined on a bounded convex closed subset X of the Hilbert space H which satisfies the tangential condition , where T _X (x) is the cone tangent to the set X at a point x. The proof of this theorem is based on the method of single-valued approximations to multivalued mappings. In this paper, we consider a simple approach for constructing single-valued approximations to multivalued mappings. This approach allows us not only to simplify the proofs of already-known theorems, but also to obtain new statements needed to prove the main theorem in this paper.__________Translated from Matematicheskie Zametki, vol. 78, no. 2, 2005, pp. 212–222.Original Russian Text Copyright © 2005 by B. D. Gel’man.