图的(g,f)—因子分解

设Ｇ是一个图，ｇ和ｆ是定义在图Ｇ的顶点集上的两个整数值函数，且ｇ≤ｆ．图Ｇ的一个（ｇ，ｆ）—因子是Ｇ的一个支撑子图Ｈ，使对任意ｘ∈Ｖ（Ｈ）有ｇ（ｘ）≤ｄＨ（ｘ）≤ｆ（ｘ）．若图Ｇ的边集能划分为若干个边不相交的（ｇ，ｆ）—因子，则称Ｇ是（ｇ，ｆ）—可因子化的．给出了一个图是（ｇ，ｆ）—可因子化的一个充分条件，改进了有关结果．     

图的正交(g,f)-因子分解

设ｇ和ｆ分别是定义在图Ｇ的顶点集合Ｖ（Ｇ）上的整数值函数且对每一个ｘ∈Ｖ（Ｇ）有２≤ｇ（ｘ）≤ｆ（ｘ）．证明了若Ｇ是（ｍｇ＋ｍ－１,ｍｆ－ｍ＋１）—图,则对Ｇ中任意一个给定的有ｍ条边的子图Ｈ,Ｇ有一个（ｇ,ｆ）—因子分解与Ｈ正交．     

关于图的(g,f)-因子分解的若干结果

对目前关于图的因子分解研究中的3个问题进行了讨论,得到了以下结果(1)设Z= {x∈V(G) dG(x) - mg(x)≤t(x), 或mf(x) - dG(x)≤t(x);t (x) = f (x)– g (x) > 0}.当Z≠SymbolFCp时,g和f可以不全为偶数,能使(mg, mf)-图有(g, f)-因子分解.(2)G是具有2n个顶点的m-正则图,m ≥n.若(P1,P2,…,Pr)是m的一个划分,则G的边集E(G)能划分成r个部分E1,E2,…,Er,使G[Ei]是G的Pi-因子,其中Pi ≡ 0 (mod 2),I= 2,…, r;P1 ≡m (mod 2).(3)G是具有2n个顶点的m-正则图,m≥n.若G不含有K3,则G有1-因子分解.     

K_(m,n)~*的(?)_(2k)——因子分解

给出了完全二部对称有向图K_(m,n)~*存在—因子分解的充分必要条件为m=n≡0(mod k(2k-1))。     

具有(k,r)-正交的(g,f)-因子分解的子图

研究了图的正交因子分解，通过构造函数p(x)和q(x)，证明了(mg k，mf-k)-图具有子图，该图有(g，f)-因子分解与kr-星(k，r)-正交，从而推广了原晋江教授的关于(mg m-1，mf-m 1)-图，存在(g，f)-因子分解与星(m，r)-正交的结论．     

m<50时完全二部图K_(n,n)的循环m-圈分解

设Kn,n表示每部分具有n个顶点的完全二部图,本文利用差集的方法来构造Kn,n的循环m-圈分解,讨论了30相似文献   

m≡0(mod8)时完全二部图Kn,n的循环m-圈分解

研究完全二部图Kn,n的循环m-圈分解的存在性问题．利用差的方法构造完全二部图Kn,n的循环m-圈分解的初始圈．对于m≡0（mod8）且m≥8这种情况,证明当n≡0,m／2,m,3m／2（mod2m）时完全二部图Kn,n存在循环m-圈分解;对于m≡0（mod8）,m≥8且m／4无平方因子这种情况,证明了完全二部图Kn,n存在循环m-圈分解的充分必要条件是n≡0,m／2（modm）．     

Lorentz群的换位子

本文证明了Lorentz群的换位子群中每一个元素皆为换位子。     

有限域上奇异辛群的Sylow子群及其正规化子

设Ｆｑ表示特征ｐ的ｑ元有限域,ｑ＝ｐ＾α,ｐ为素数。给出了Ｆｑ上奇异辛群Ｓｐ２ｖ＋ｔ（Ｆｑ）的Ｓｙｌｏｗ子群的结构并讨论了其正规化子的性质。     

Decomposition of almost Poisson structure of non-self-adjoint dynamical systems

Non-self-adjoint dynamical systems, e.g., nonholonomic systems, can admit an almost Poisson struc-ture, which is formulated by a kind of Poisson bracket satisfying the usual properties except for the Jacobi identity. A general theory of the almost Poisson structure is investigated based on a decompo-sition of the bracket into a sum of a Poisson one and an almost Poisson one. The corresponding rela-tion between Poisson structure and symplectic structure is proved, making use of Jacobiizer and symplecticizer....     

Geometric structure of generalized controlled Hamiltonian systems and its application

The main purpose of this paper is to provide a systematic geometric frame for generalized controlled Hamiltonian systems. The pseudo-Poisson manifold and the co-manifold are proposed as the statespace of the generalized controlled Hamiltonian systems. A Lie group, called N-group, and its Lie algebra, called N-algebra, are introduced for the structure analysis of the systems. Some properties, including spectrum, structure-preservation, etc. are investigated. As an example the theoretical results are applied to power systems. The stabilization of excitation systems is investigated.     

整数环上一些典型群的二元生成

研究了整数环上一些典型群的二元生成问题．考虑典型群中元素的矩阵形式，将典型群中一个特殊元素对其另外的元素进行共轭作用，证明了整数环上m≥4时的辛群SP（2m，Z）、特殊线性群SL（m，Z）和一般线性群GL（m，Z）均可由两个元素生成，并决定了它们的生成元素．     

f(x,y)在点(x,y)可微的一个充分条件

提出了二元函数在某点可微的一个充分条件，与传统的判别方法相比，这个充分条件更加减弱了判别条件，进一步阐明了二元函数偏导数与可微性的关系，使适用范围扩大，适用性加强．     

Phase stability in an austenitic Fe—Cr—Mn（W,V） alloy

By means of deformation and long term aging,the stability and phase equilibrim characteristic of the C N synthetically strengthening austenitic Fe-Cr-Mn(W,V) alloy were investigated.Experimental results indicate that the austenitic alloy remains stability and no γ→α transformation occurs under 500℃.Synthetic addition of C and N causes the grains to refine and powerfully retards formation of ε martensite and precipition of σ phase.Ms point is elevated with long term aging at elevated temperature (500-700℃） due to a large number of strain induced carbides precipitate.Along with accelerated decomposition of strain induced α′ martenstie and occurrence of recrystallization.γ→α transformation and σ phase precipitation are promoted so that austenite becomes unstable.