利用GAP研究一般线性群的抛物子群

A typical example for the algebraic groups is the general linear groups G = GL(n,F), we have studied the structure of such groups and paid special attention to its important substructures, namely the Parabolic subgroups.For a given G we computed all the Parabolic subgroups and determined their number, depending on the fact that any finite group has a composition series and the composition factors of a composition series are simple groups which are completely classified, we report here some investigations on the computed Parabolic subgroups. This has been done with the utility of GAP.     

On the edge-binding number of some plane graphs

1. IntroductionSince WOodall gave out the concept of biIldi11g Ilu1lJber in 1973[l] ! the bil1ding nunlber fOrsome specia1 classes have beeIl studied by Kane and WaIlg Jianfang[']. Mirolawa Skowronskahave studied the binding number of Halin-graph[']. ZI1ang Zhongfu, Liu Li1lzhong andZhang Jianxun have extended the bil1di11g nuInber to the edges and studied tlle edge-bindingnumber of path, cycle, coInplete grapl1. I1l this paper, we study the edge-binding number ofouter plane graph, Ha…     

A class of quasilinear elliptic hemivariational inequalities

1. IntroductionIn this paper we shall deal with the quasilinear elliptic hemivaxiational inequalitieswhere the symbol OJ designates Clarke's generalized gradiellt of a locally Lipschitz functionalJ (see [1, 2]). The discontinuity is assumed to be in the lower order term OJ(u(x)). If Ais a linear operator and the disconiinuity is monotone, the problems have been studied,for example, in [3-6]. If A is a linear opertor and the discolltinuity is nonmonotone, thiskind of problems have been inve…     

Gauss Sum of Index 4： （2） Non-cyclic Case

Assume that m ≥ 2, p is a prime number, （m,p（p - 1）） = 1,-1 not belong to 〈p〉 belong to （Z/mZ）^＊ and [（Z/mZ）^＊：〈p〉]=4.In this paper, we calculate the value of Gauss sum G（X）=∑x∈F^＊x（x）ζp^T（x） over Fq,where q=p^f,f=φ（m）/4,x is a multiplicative character of Fq and T is the trace map from Fq to Fp.Under our assumptions,G（x） belongs to the decomposition field K of p in Q（ζm） and K is an imaginary quartic abelian unmber field.When the Galois group Gal（K/Q） is cyclic,we have studied this cyclic case in anotyer paper：＂Gauss sums of index four：（1）cyclic case＂（accepted by Acta Mathematica Sinica,2003）.In this paper we deal with the non-cyclic case.     

Some Topological Relationships between Hyperspaces

Certain topological relationships between the topological spaces and the spaces of their subsets have heen studied in[1],[4]and[5].In this paper we Will discuss other topological relationships between the topological spaces and their hyperspaces with the Vietoris topology. Let (X,T) be a topological space,     

定曲率空间中闭凸超曲面的唯一性定理

Certain topological properties of the hyperspaces have been studied in [1], [2]and[3]. In this paper we will discuss some topological properties of hyperspace[,2~T], and will generalize related results of Z. Michael [1], A. Frank, Chimenti,[2],寿纪麟[4].     

Pseudomonotonicity of Nonlinear Transformations on Euclidean Jordan Algebras

In this paper, we have introduced the concepts of pseudomonotonicity properties for nonlinear transformations defined on Euclidean Jordan algebras. The implications between this property and other P-properties have been studied. More importantly, we have solved the solvability problem of the nonlinear pseudomonotone complementarity problems over symmetric cones.     

EFFECTS OF EXOTIC SPECIES ON ENDANGERED SPECIES THROUGH PREDATION

§1　IntroductionRare and endangered species face extinction through a variety of mechanisms,including destruction and fragmentation of their habitat and ecological invasion of exoticspecies[1 ,2 ] .In order to protectthese species,we should investigate the effects of diffusionand ecological invasion on the permanence and extinction of the native species.In[3 ] ,Cui and Chen have studied the effect of diffusion on the endangered speciesthat living in a weak patchy environment in the sense tha…     

On the Generalized Topological Degree for Perturbed Maximal Monotone Mappings

In recent years, F.E. Browder has constructed the topological degree for nonlinear monotone mappings.In the paper[1], we have introduced the classes of mappings of type (S)_ ~* and of type quasi-(S)_ ~* and the concept of weakly-demicontinuity and we have constructed the generalized topological degree for these classes of mappings. Some important results in [2] and [3] have     

A Hamiltonian Game

1. Introduction F.Harary(1)introduced achievement games and avoidance games on graphs. A. Papaioannou (2) studied the achievement games for Hamilton-path(H-path,for short) and Hamilton-cycle (H-cycle, for short). In this paper, we will study the avoidance game for H-path and get the following result: Ifp≥5, B can win in the game.     

一类Lienard方程的概周期解

By using exponential dichotomies and Liapunov function method, we have studied the existence of almost periodic solutions on a Lienard system and have obtained some simple sufficient condition.     

FIXED POINTS FOR WEAKLY INWARD MAPPINGS IN BANACH SPACES （II）

S. Hu and Y. Sun[1] defined the fixed point index for weakly inward mappings, investigated its properties and studied fixed points for such mappings. In this paper, following S. Hu and Y. Sun, we further investigate boundary conditions, under which the fixed point index for i（A, Ω, p） is equal to nonzero, where i（A, Ω, p） is the completely continuous and weakly inward mapping. Correspondingly, we can obtain many new fixed point theorems of the completely continuous and weakly inward mapping, which generalize some famous theorems such as Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem etc. in the case of weakly inward mappings. In addition, our conclusions extend the famous fixed point theorem of cone expansion and compression to the case of weakly inward mappings. Moreover, the main results contain and generalize the corresponding results in the recent work[2].     

An axiomatization of probabilistic Owen value for games with coalition structure

In the framework of games with coalition structure, we introduce probabilistic Owen value which is an extension of the Owen value and probabilistic Shapley value by considering the situation that not all priori unions are able to cooperate with others. Then we use five axioms of probabilistic efficiency, symmetric within coalitions, symmetric across coalitions applying to unanimity games, strong monotone property and linearity to axiomatize the value.     

Some Kinds of Bargaining Equilibria of Multi-objective Games

To solve the choice of multi-objective game's equilibria,we construct general bargaining games called self-bargaining games,and define their individual welfare functions with three appropriate axioms.According to the individual welfare functions,we transform the multi–objective game into a single-objective game and define its bargaining equilibrium,which is a Nash equilibrium of the single-objective game.And then,based on certain continuity and concavity of the multi-objective game's payoff function,we proof the bargaining equilibrium still exists and is also a weakly Pareto-Nash equilibrium.Moreover,we analyze several special bargaining equilibria,and compare them in a few examples.     

Necessary Maximum Principle of Stochastic Optimal Control with Delay and Jump Diffusion

In this paper, we have studied the necessary maximum principle of stochastic optimal control problem with delay and jump diffusion.     

THE LONG-TIME BEHAVIOR OF SPECTRAL APPROXIMATE FOR KLEIN-GORDON-SCHROEDINGER EQUATIONS

Klein-Gordon-Schroedinger (KGS) equations are very important in physics. Some papers studied their well-posedness and numerical solution [1-4], and another works investigated the existence of global attractor in R^n and Ω包含于R^n (n≤3) [5-6,11-12]. In this paper, we discuss the dynamical behavior when we apply spectral method to find numerical approximation for periodic initial value problem of KGS equations. It includes the existence of approximate attractor AN, the upper semi-continuity on A which is a global attractor of initial problem and the upper bounds of Hausdorff and fractal dimensions for A and AN,etc.     

BIFURCATION OF A CLASS OF CODIMENSION-TWO NONLINEAR HIGHER ORDER SYSTEM

We discuss a kind of codimension-tvro nonlinear higher order system, by normai form theory the system can be reduced into system equivalent toBogdanov, Takens, Carr have been studied it's local bifurcations for n - 2, after that, Wang Mingshu, Luo Dingjun, Li Jibin, Wang Xian and others studied the global bifurcations for n = 3. In this paper, we study the bifurcations for n - 4, and give all the local bifurcation curves of the system.     

A Kind of Cubic C~1—Interpolations in the n-dimensional Finite Element Method

As is well known that the multivariate spline function plays an important role in both theory and application. The paper [1]—[11] hove studied the multivariate spline functions and obtained a lot of results concerning this topic. Especially in [3], the existance theorem has been shown for the case of n-dim entional spline functions. A. Zeniek [10] and P. Alfeld [11] have established some of results about the tetrahedron partition. In this paper. we will show a kind of cubic C~1—interpolations for any n-simplicial partition in R~n. Of course, some of the subdivisions will be needed.     

On the Self-adjointness of the Product Operators of Two ruth-Order Differential Operators on [0, ＋∞）

In the present paper, the self-adjointness of the product of two mth-order differential operators on [0, ∞) is studied. By means of the construction theory of self-adjoint operators and matrix computation, we obtain a sufficient and necessary condition to ensure that the product operator is self-adjoint, which extends the results in the second order case.     

Some Properties of the Optimal Preconditioner and the Generalized Superoptimal Preconditioner

<正>The optimal preconditioner and the superoptimal preconditioner were proposed in 1988 and 1992 respectively.They have been studied widely since then.Recently, Chen and Jin[6]extend the superoptimal preconditioner to a more general case by using the Moore-Penrose inverse.In this paper,we further study some useful properties of the optimal and the generalized superoptimal preconditioners.Several existing results are extended and new properties are developed.