The 1/N expansion in the two-dimensional supersymmetric O(N)xO(K)-invariant O(N)/O(N−K) model and dynamical generation of massive vector particles

Republication Engineering and Technical Center for the Renewal and Strengthening of Parts of Machines and Mechanisms, Tomsk, Siberian Branch, USSR Academy of Sciences; Erevan Physics Institute; State University, Tomsk. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 76, No. 3, pp. 371–378, September, 1988.     

An O(n2) algorithm for a controllable machine scheduling problem

A single-machine scheduling problem with controllable processingtimes is discussed in this paper. For some jobs, the processingtime can be crashed up to u units of time with the additionalcost c per unit of time crashed. The object is to find an optimalprocessing sequence as well as crash activities to minimizetotal costs of completion and crash. This problem is shown tobe polynomially solvable, and an O(n²) algorithm is given togetherwith the theoretical proof.     

循环图C_(2n)(1,(2n+1)/3)的匹配可扩性

称图G是k-偶匹配可扩的,是指G的每一个基数不大于k(1≤k≤(|V(G)|-2)/2)的偶匹配M都可以扩充为G的一个完美匹配.根据循环图的性质研究了图C_(2n)(1,(2n+1)/3)的匹配可扩性,证明了对于任意的n(n≥4),C_(2n)(1,(2n+1)/3)是3-偶匹配可扩的.     

齐性空间SU(2n)/Sp(n)的H-同伦指数

令p为大于3的素数.在一定维数限制下,通过把齐性空间SU(2n)/Sp(n)分解为若干个同伦可结合,同伦可交换的H-空间的乘积,进而得到了SU(2n)/Sp(n)的p素H-同伦指数的一个上界.     

空间Sp(n)/U(n)上的特征值与特征函数

本文利用群表示论研究了对称空间SP（n）/U（n）的特征值与特征函数.     

对称空间SU~*(2n)/sp(n)上的Busemann函数

Busemann函数在对完备Riemann流形上的拓扑与几何问题的研究中起作十分重要的作用。而显式求出一个域上的Busemann函数将有助于一些问题的解决。在本文中,我们显式求出了对称空间SU~*(2n)/sp(n)上的Busemann函数。     

n-1／n（G）表决系统中的可靠性分析

本文通过补充变量法研究了n-1/n(G)表决系统中可靠度,可用度,以及故障频度等可靠性的一系列指标.     

Locally smooth SU(n + 1)-actions on SU(n + 1)/S(U(n - 1) × U(2)) are unique

If the Lie group SU(n + 1) acts nontrivially and in a locally smooth way on the Grassmannian G_n+1,2, then the action is conjugate to the standard action by left translation. We prove this theorem using a former result of the author on the nonexistence of fixed points for actions of SU(n + 1) on generalized flag manifolds.     

O(n2.5) time algorithms for the subgraph homeomorphism problem on trees

The complexity of the subgraph homeomorphism problems have been open. We show O(n^2.5) time algorithms when the problems are restricted to trees, directed or undirected. The algorithm can be applied to the subtree isomorphism problem for unrooted trees with the same complexity, and improves over Reyner's O(n^3.5) algorithm for the subtree isomorphism problem.     

Automorphisms of groupGL n(o) for dim Max(o)⩽n-2

We describe the automorphisms of group GL_n+(o), where (o) is a commutative ring with unity and with an invertible element 2, not generated by the divisors of zero, while the space Max (o) is Noetherian of dimension ≤ n?2.     

关于Diophantine方程(n+1)+(n+2)y=nz

设n是正整数.本文证明了:方程(n+1)+(n+2)y=nz仅当n=3时有正整数解(y,z)=(1,2).     

Affine immersion ofn-dimensional manifold intoR n+n(n+1)/2 and affine minimality

We formulate an affine theory of immersions of ann-dimensional manifold into the Euclidean space of dimensionn+n(n+1)/2 and give a characterization of critical immersions relative to the induced volume functional in terms of the affine shape operator.