γ-稳定图

本文我们引进γ- 稳定图,γ 稳定图和γ稳定图的概念,图G是γ- 稳定图(γ 稳定图),若任意删去G(增加G)的一条边都不改变G的控制数γ(G).一个γ稳定图指既是γ- 稳定图又是γ 稳定图的图.我们给出一些γ-(γ ,γ) 稳定图的性质和实例.     

几类特殊θ-图的Laplacian谱唯一性问题研究

通过θ-图中除了含有一个4圈的θ-图外,其余的θ-图都是邻接谱唯一图的有关结论,研究了几类特殊θ-图的Laplacian谱唯一性问题.即:θ-图θ_(s_1,s_2,s_3)(|s_i-s_j|≤2,1≤i≤3)、圈长为3或4的θ-图以及θ-图θ_0,u,v(u+v=1(mod 2)).     

一类用于寻找欧拉生成子图边数的收缩子图

结合可折叠子图给出了可折叠α-子图的概念,得到可折叠α-子图一定为α-子图,并得到可折叠α-子图的顶点有交且边不交的并仍为可折叠α-子图.同时得到至多差1边具有3棵边不交的生成树的图和K_(l,m)(l≥3,m≥3)均是可折叠2/3-子图,并给出其在寻找欧拉生成子图极大边数的应用,同时也得到了一种寻找α-子图的方法.     

正则图的邻强边染色和全染色

如果~$k$-\-正则图~$G$~不含~5-\-圈的分支, 则猜测~$\chi''_{\mathrm{as}}(G) = \chi_{\mathrm t}(G)$. 证明这个猜想对很多图类都成立, 例如: 第1类型图、 $2$-\-正则图、$3$-\-正则图、$(|V(G)|-2)$-\-正则图、二部图、完全等多部图、$k$-\-方体以及一些特殊的联图类等.     

关于(ξ,k)-临界图

设 G为连通图 ,且ξ(G) =k≥ 1 ,若对 G中任意边 e,均有ξ(G\e) =k - 1 ,则称 G为 (ξ,k) -临界图 .本文刻划了ξ- 1 -临界图的若干性质 ,给出了一个图为ξ- 1 -临界图的一些充分或必要条件 ,以及一些ξ- 1 -临界图类 .     

不含悬挂点的A3-图

对于图方程 A( H) =n的讨论 ,重点是研究 A2 -图及 A3-图 H及其母图的性质 ,这就需要研究不同类型的 A3-图 .本文给出了不含悬挂点的 A3-图     

关于一类(g,f)-3-覆盖图的判据

本文首先给出了(g,f)-3-覆盖图的定义,即一个图G称为(g,f)-3-覆盖图,如果G的任何三条边都属于它的一个(g,f)-因子；其次,黄光鑫曾先后给出了当g＜f时一个二部图分别是(g,f)-2-覆盖图和(g,f)-3-覆盖图的充分必要条件,在此基础上,本文进一步得到了,当g≤f时一个二部图G=(X,Y)是(g,f)-3-覆盖图的一个充分必要条件；最后,研究了f(X)=f(Y)的情形,得到了当f(X)=f(Y)时一个二部图G=(X,Y)是f-3-覆盖图的一个充分必要条件．     

论两种2-棱-连通图

无自圈的极小2-棱-连通图构造已由[1]及[3]给出,最近朱必文又得到了临界2-棱-连通图的构造本文研究了极小2-棱-连通图与临界2-棱-连通图之间的转化关系,从而得到了由前者过渡到后者的一种方法。本文在极小2-棱-连通图构造的基础上首先研究了临界-极小2-棱-连通图的构造,由此得出临界2-棱-连通图的一种非常简洁的递归结     

关于Δ-临界图的构造

研究了 Δ-临界图的构造 ,并且给出了一种由给定 Δ-临界图构造新的 Δ-临界图的方法     

最小度和[a,b]-对等图

既是[a,b]-覆盖又是[a,b]-消去的图称为[a,b]-对等图.本文研究了最小度和[a,b]-对等图之间的关系,给出了一个图是[a,b]-对等图的关于最小度的充分条件.     

Linear programming with multiple objective functions: Step method (stem)

This paper describes a solution technique for Linear Programming problems with multiple objective functions. In this type of problem it is often necessary to replace the concept of optimum with that of best compromise. In contrast with methods dealing with a priori weighted sums of the objective functions, the method described here involves a sequential exploration of solutions. This exploration is guided to some extent by the decision maker who intervenes by means of defined responses to precise questions posed by the algorithm. Thus, in this man-model symbiosis, phases of computation alternate with phases of decision. The process allows the decision-maker to learn to recognize good solutions and the relative importance of the objectives. The final decision (best compromise) furnished by the man-model system is obtained after a small number of successive phases.This paper was presented at the 7th Mathematical Programming Symposium 1970, The Hague, The Netherlands.     

The martin boundary for harmonic functions on groups of automorphisms of a homogeneous tree

Consider a closed subgroup of the automorphism group of a homogeneous treeT, and assume that acts transitively on the vertex set. Suppose that is a probability measure on which has continuous density with respect to Haar measure and whose support is compact open and generates as a closed semigroup. It is shown that the Martin boundary of with respect to the random walk with law coincides with the space of ends ofT. This extends known results for free groups and applies, for example, to the affine group over a non archimedean local field.     

Functions with a finite dirichlet integral in a domain with cusp points on the boundary

Let be a domain in ⁿ, n >2, the boundary of which has a cusp point, pointing inside or outside the domain. The purpose of the paper is to characterize the traces on of the elements of the space H¹() of functions with a finite Dirichlet integral. As a consequence one establishes the existence of a linear continuous extension operator H¹ () H¹(ⁿ) under the presence of an interior cusp point on . Theorems on domains with cusps are proved with the aid of results on cylindrical domains. In the space of functions with a finite Dirichlet integral in the exterior or the interior of the cylinder one introduces the norm, depending on a small parameter and generating a norm of the trace on as an element of the quotient space. The latter is placed in correspondence with an explicitly described norm of functions on the boundary, uniformly equivalent relative to . One constructs an operator of extension of functions from the exterior of the cylinder to Rⁿ, preserving H¹, whose norm is uniformly bounded relative to . For the optimal operator of extension from the inside of the cylinder one finds the asymptotic behavior of the norm as 0. From these results there follow similar theorems on functions with a finite Dirichlet integral inside and outside a thin closed tube (of width ).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 126, pp. 117–137, 1983.     

A Computer-Assisted Proof of the Uniqueness of the Perkel Graph

The Perkel graph is a distance-regular graph of order 57, degree 6 and diameter 3, with intersection array (6, 5, 2; 1, 1, 3). We describe a computer assisted proof that every graph with this intersection array is isomorphic to the Perkel graph. The computer proof relies heavily on the fact that the minimal idempotents for , and their submatrices, are positive semidefinite.To minimize the risk of computer errors we have used two different methods to establish the same theorem and as an added precaution large parts of the corresponding programs were written by different authors.The first method generates plausible subgraphs induced by all vertices at distance 3 from a fixed vertex of and then tries to extend each of the generated graphs to a full graph with the given intersection array.The second method generates possible neighborhoods for a pentagon in . It turns out that every such pentagon can be extended to a Petersen graph in . We then prove mathematically that there is, up to isomorphism, only a single graph with this property.     

Perturbation from an elliptic Hamiltonian of degree four—III global centre

The paper deals with Liénard equations of the form , with P and Q polynomials of degree, respectively, 3 and 2. Attention goes to perturbations of the Hamiltonian vector fields with an elliptic Hamiltonian of degree four, exhibiting a global centre. It is proven that the least upper bound of the number of zeros of the related elliptic integral is four, and this is a sharp one.This result permits to prove the existence of Liénard equations of type (3,2) with a quadruple limit cycle, with both a triple and a simple limit cycle, with two semistable limit cycles, with one semistable and two simple limit cycles or with four simple limit cycles.     

Simple braids for surface homeomorphisms

Let S be a compact, oriented surface with negative Euler characteristic and let be a homeomorphism isotopic to the identity. If there exists a periodic orbit with a non-zero rotation vector , then there exists a simple braid with the same rotation vector.     

The CMP and Banach Spaces with unique metric lines

This paper is concerned with characterizing the class of Banach Spaces with unique metric lines in the class of complete metric spaces with unique lines.The concept utilized to prove the major theorem is theConsistent Midpoint Property (CMP). We define a binary operation (+) in metric spaces with unique lines and show that, under suitable assumptions, the space is a Banach Space with + as the vector addition and a=d(a, ) for some fixed .     

Antiplane deformation of an orthotropic body with a crack and elliptical cavities

A study was made of the stress distribution in an anisotropic body with a tunnel crack and one or two elliptical cavities. Examined as special cases were problems for a body with cavities and edge cracks with one or two sides, a body with cavities connected by a narrow slit, and a body with two or three longitudinal-transverse cracks. It is shown that anisotropy of the material has a substantial effect on the SIF and stresses around the cavities.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 61–66, 1988.     

A pascal theorem applied to Minkowski geometry

If on an oval in a projective plane a 4-point Pascal theorem, , with fixed points U and V holds, then the oval is {(x,y) ¦xy=c} (O) (), with c O, in some Hall coordinatization. If for every 3 distinct points P, Q, R (not on UV; neither U nor V collinear with two of P, Q, R) there is through them a certain point set satisfying an extended version of , then all these sets together with all lines not through U or V form the circles of a plane Minkowski (= pseudoeuclidean) geometry over a commutative field. may be expressed in terms of Minkowski geometry. Together with incidence axioms derived from the protective incidence axioms, the Minkowski version of characterizes the plane Minkowski geometry over a commutative field and is thus equivalent to Miquel's theorem.