一类泛圈图

本证明了如果G是2连通无爪图,G不是圈,n=|V(G)1≥9,G的每个导出子圈A都满足φ（a1,a2),且G中不含同构于Z^ 2的导出子图,则G是泛圈图。     

K1,4-自由的模κ泛圈图

设G是2-连通的K1，4自由图．本文证明了当δ(G)≥κ 1时，G是模κ泛圈图．这一结果肯定了猜想2，继而也肯定了Thomassen猜想在2-连通图中的正确性．     

Hamiltonian图的泛圈性一个充分条件

根据Bondy在[4]中的想法：几乎任何一个Hamiltonian图的非平凡的充分条件都可能蕴含着图的泛圈性质,自然有如下猜测,设图G满足定理A的条件,则G是泛圈图或者n=2t,G=Kt,t.[2]证明了这一猜测在t=3时成立,[3]对t=4得到子了一个更强的结果,本文证明此猜测对一般情形(t≥3)均成立。     

3—连通局部连通无爪图是泛连通图

本文证明了若G是连通、局部连通的无爪图,则G是泛连通图的充要条件为G是3-连通图.这意味着H.J.Broersma和H.J.Veldman猜想成立.     

关于简单MCD图

设G是阶为n的简单图，若G中没有两个等长圈且具有最大可能的边数，则称G为简单MCD图。本文通过引进路分解概念给出了两个关于图中圈数的结果并应用它们证明了下述定理：若G是简单MCD图，则G不是2连通可平面图且对所有整数n，除七个例外，G不是阶为n的含有同胚于K4的2连通图。     

一类泛圈图

本文证明了如果 Ｇ 是 ２ 连通无爪图, Ｇ 不是圈,ｎ＝ ｜ Ｖ（ Ｇ）｜≥９, Ｇ 的每个导出子图 Ａ都满足φ（ａ１,ａ２ ）,且 Ｇ 中不含同构于 Ｚ＋２ 的导出子图,则 Ｇ是泛圈图     

Bondy的泛圈图定理的改进

记G=(V,E)是简单图,1971年Bondy得到O re条件下的泛圈图的著名结果:若2连通n阶图G的不相邻的任两点x、y均有d(x) d(y)≥n,则G是泛圈图或G=Kn/2,n/2.这里进一步研究条件d(x) d(y)≥n-1,得到:若2连通n阶图G的不相邻的任两点x、y均有d(x) d(y)≥n-1,则G是泛圈图或G∈{K(Cn 1)/2∨G(n-1)/2,Kn/2,n/2}.本文作者得知最近国际著名权威专家Ho lton等人也得到完全相同的结果,但本证明更简捷.     

无K1,r图中的哈密顿圈（英文）

本文借助对图的本质独立集和图的部分平方图的独立集的研究，对于K1,r图中哈密顿圈的存在性给出了八个充分条件。我们将利用T－插点技术对这八个充分条件给出统一的证明，本文的结果从本质上改进了C－Q.Zhang于1988年利用次形条件给出的k-连通无爪图是哈密顿图的次型充分条件，同时。G.Chen和R.H.Schelp在1995年利用次型条件给出的关于k-连通无K1，4图是哈密顿图的充分条件也被我们的结果改进并推广到无K1,r图。     

K(1,4)-自由的模k泛圈图(英文)

设G是2-连通的K1,4自由图.本文证明了当δ(G)≥k 1时,G是模k泛圈图.这一结果肯定了猜想2,继而也肯定了Thomassen猜想在2-连通图中的正确性.     

关于无爪Hamilton图的一个泛圈性结果

一个图Ｇ是泛圈的，如果它含有长为３，４，…，ｎ（＝｜Ｖ（Ｇ）｜）的圈．本文探讨了一类无爪Ｈａｍｉｌｔｏｎ图的圈结构，主要结果为：设Ｇ＝（Ｖ，Ｅ）是ｎ阶无爪Ｈａｍｉｌｔｏｎ图．如果Ｇ中有节点ｘ使ｄ（ｘ）≧ｎ／２且Ｎ（ｘ）连通，则除少数几个例外，Ｇ是泛圈的．     

Distribution of types of symmetry of tensors of high degree

The asymptotic distribution of tensors of degree N in symmetry types is studied in this paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 181–186, 1986.     

Estimates of stability of characterization of additive types of distributions

An estimate of stability of characterization of distribution types is obtained for the case of additive types. Under some conditions, the estimate has the order ε^1/3L(ε), where L(ε) is a slowly varying function. Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part I.     

Study of the blow-up of solutions of systems of equations of hydrodynamic type

Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from...     

Characterization of types of asymptotic discernibility of families of hypotheses

We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987.     

一类完全正则半群簇子簇格的性质

本文研究了完全正则半群簇的子簇格［Ｖ＋∩ＰＶ，Ｖ＋∩ＰＶ］的某些格运算性质，我们证明了簇Ｖ＋∩ＰＶ可分解为Ｖ与Ｖ＋∩ＰＶ的并；对任意完全正则半群簇Ｗ，有Ｗ∩（Ｖ∨Ｖ＋∩ＰＶ）＝（Ｗ∩Ｖ）∨（Ｗ∩Ｖ＋∩ＰＶ）．特别地，我们得到了等式Ｖ＋∩ＰＶ＝Ｖ成立的若干条件．     

Bases of the identities of products of certain varieties of groups

The following theorem is proved: The product of any variety of two-step solvable groups and a variety having a finite basis of identity relations has a finite basis of identity relations.Translated from Matematicheskie Zametki, Vol. 5, No. 1, pp. 137–144, January, 1969.     

Birational aspects of the geometry of Varieties of Sums of Powers

Varieties of Sums of Powers describe the additive decompositions of a homogeneous polynomial into powers of linear forms. The study of these varieties dates back to Sylvester and Hilbert, but only few of them, for special degrees and number of variables, are concretely identified. In this paper we aim to understand a general birational behavior of VSP. To do this we birationally embed these varieties into Grassmannians and prove the rational connectedness of many VSP in arbitrary degrees and number of variables.