A Generalization of Strongly Regular Graphs

Motivated from an example of ridge graphs relating to metric polytopes, a class of connected regular graphs such that the squares of their adjacency matrices are in certain symmetric Bose-Mesner algebras of dimension 3 is considered in this paper as a generalization of strongly regular graphs. In addition to analysis of this prototype example defined over (MetP₅)^*, some general properties of these graphs are studied from the combinatorial view point.AMS Subject Classification: 05E30.     

A note on equilibrium of eventually strongly monotone skew-product semiflows

In this paper, we show that for an eventually strongly monotone skew-product semiflow τ, the strict ordering on Ec （the set consisting of continuous equilibria of τ） implies the strong one.     

A Class of Strongly Decomposable Abelian Groups

Let G be a completely decomposable torsion-free Abelian group and G= G_i, where G _i is a rank 1 group. If there exists a strongly constructive numbering of G such that (G,) has a recursively enumerable sequence of elements g _i G _i , then G is called a strongly decomposable group. Let pi, i, be some sequence of primes whose denominators are degrees of a number p _i and let . A characteristic of the group A is the set of all pairs ‹ p,k› of numbers such that for some numbers i ₁,...,i _k . We bring in the concept of a quasihyperhyperimmune set, and specify a necessary and sufficient condition on the characteristic of A subject to which the group in question is strongly decomposable. Also, it is proved that every hyperhyperimmune set is quasihyperhyperimmune, the converse being not true.     

On strong pseudomonotonicity and (semi)strict quasimonotonicity

An example in Ref. 1 is corrected to show that indeed a strongly pseudoconvex function, which is only once but not twice differentiable, does not necessarily have a strongly pseudoconvex gradient.     

序半群的一类正则同余

设S是有向序半群,本文给出了S上的一类正则同余,称为强序同余的定义及性质.证明了S的强序同余是强正则同余,但反之不成立.同时证明了强序同余格SOC(S)是S的同余格C(S)关于通常集合的交和传递积的V-完备的分配子格.     

An Analog of the Krein--Mil'man Theorem for Strongly Convex Hulls in Hilbert Space

We prove the following theorem: in Hilbert space a closed bounded set is contained in the strongly convex R-hull of its R-strong extreme points. R-strong extreme points are a subset of the set of extreme points (it may happen that these two sets do not coincide); the strongly convex R-hull of a set contains the closure of the convex hull of the set.     

Cyclotomy and Strongly Regular Graphs

We consider strongly regular graphs defined on a finite field by taking the union of some cyclotomic classes as difference set. Several new examples are found.     

关于强Armendariz环和强拟Armendariz环

提出了强拟Armendariz环的概念,给出了强Armendariz环和强拟Armendariz环上的一些结果.     

模糊自动机的强连通性及群自动机

为了更好地研究模糊自动机的结构和性质,采用代数的方法,在传统的模糊有限状态自动机的基础上,通过定义状态集合为代数群的自动机,讨论了这一类自动机的连通性和正则性,这丰富了模糊自动机理论．     

2一致凸Banach空间中均衡问题、变分不等式问题和不动点问题的一个弱收敛定理

In this paper,we introduce a new iterative scheme for finding the common element of the set of solutions of an equilibrium problem,the set of solutions of variational inequalities for an α-inversely strongly monotone operator and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and 2-uniformly convex Banach space.Some weak convergence theorems are obtained,to extend the previous work.     

A note on correlated equilibrium

The set of correlated equilibria for a bimatrix game is a closed, bounded, convex set containing the set of Nash equilibria. We show that every extreme point of a maximal Nash set is an extreme point of the above convex set. We also give an example to show that this result is not true in the payoff space, i.e. there are games where no Nash equilibrium payoff is an extreme point of the set of correlated equilibrium payoffs.     

Approximating a Zero of Sum of Two Monotone Operators Which Solves a Fixed Point Problem in Reflexive Banach Spaces

Abstract

The purpose of this paper is to introduce an iterative method for approximating a point in the set of zeros of the sum of two monotone mappings, which is also a solution of a fixed point problem for a Bregman strongly nonexpansive mapping in a real reflexive Banach space. With our iterative technique, we state and prove a strong convergence theorem for approximating an element in the intersection of the set of solutions of a variational inclusion problem for sum of two monotone mappings and the set of solutions of a fixed point problem for Bregman strongly nonexpansive mapping. We give applications of our result to convex minimization problem, convex feasibility problem, variational inequality problem, and equilibrium problem. Our result complements and extends some recent results in literature.     

A Generic relation on Recursively Enumerable Sets

We introduce the concept of a generic relation for algorithmic problems, which preserves the property of being decidable for a problem for almost all inputs and possesses the transitive property. As distinct from the classical m-reducibility relation, the generic relation under consideration does not possess the reflexive property: we construct an example of a recursively enumerable set that is generically incomparable with itself. We also give an example of a set that is complete with respect to the generic relation in the class of recursively enumerable sets.     

强正则自补图的一个注记

Kotzig put forward a question on strongly-regular self-complementary graphs, that is, for any natural number k, whether there exists a strongly-regular self- complementary graph whose order is 4k 1, where 4k 1=x2 y2, x and y are positive integers; what is the minimum number that made there exist at least two non-isomorphic strongly-regular self-complementary graphs. In this paper, we use two famous lemmas to generalize the existential conditions for strongly-regular self-complementary circular graphs with 4k 1 orders.     

Can a large cardinal be forced from a condition implying its negation?

In this note, we provide an affirmative answer to the title question by giving two examples of cardinals satisfying conditions implying they are non-Rowbottom which can be turned into Rowbottom cardinals via forcing. In our second example, our cardinal is also non-Jonsson.

     

Regularization of a two-dimensional strongly damped wave equation with statistical discrete data

In this paper, we consider an inverse problem for a strongly damped wave equation in two dimensional with statistical discrete data. Firstly, we give a representation for the solution and then present a discretization form of the Fourier coefficients. Secondly, we show that the solution does not depend continuously on the data by stating a concrete example, which makes the solution be not stable and thus the present problem is ill-posed in the sense of Hadamard. Next, we use the trigonometric least squares method associated with the Fourier truncation method to regularize the instable solution of the problem. Finally, the convergence rate of the error between the regularized solution and the sought solution is estimated and also investigated numerically.     

关于5-正则图的强协调性

构造了若干个 5 -正则图的强协调值 ,从而证明它们都是强协调的     

A Liouville-Type Theorem for Strongly Subharmonic Functions on Complete Non-compact Riemannian Manifolds and Some Applications

We prove that if Mis a complete non-compact Riemannian manifold and ₁(M)=0, then any C ²solution of uk> 0 is unbounded. We apply this result to obtain an estimate for the size of the image set of some types of maps between Riemannian manifolds.     

二面体群上构作的结合方案

本文研究了二面体群的元素的等价划分问题。利用群在集合上的作用,在二面体群上构造了一类新的结合方案,并且计算了这类结合方案的所有参数。进一步,得到了一类强正则图。所得到的结果丰富了结合方案理论。     

函数强伪凸性与映射强伪单调性

1　引　　言Schaible在[1]中引入七类单调映射,并证明对其中六类,函数的某种广义凸性都和相应的梯度单调性等价,只有函数强伪凸和梯度强伪单调的等价性是否成立作为公开问题.其后,Schaible又在[2]中通过一个例子否定了两者的等价性,并引入了较弱的函数强伪凸和映射强伪单调的概念,在函数二次可微的条件下证明了函数强伪凸和梯度强伪单调等价.我们将引入强于[2]中概念的强伪凸和强伪单调性,对给出的定义,不附加条件便可保证函数强伪凸性和梯度强伪单调性等价.同时,对[2]中的一个错误予以指出,并给出正确的反例.还就[1]中问题给出远比[2]中简…