在对称群中一类正则图所确定的极大子群

对称群的极大子群之确定,在多值逻辑理论和有限自动机理论中都有着重要而广泛的应用,同时也是置换群理论中的一个基本问题.本文提出了 k 次对称群中一类新的极大子群,k=h~m,m≥3,h≥7.设Γ=(Ω,E)是一个无向正则图,其中顶点集Ω={(α_1,…,α_m)|β_i∈Ω_h={10,1,…,h-1},i=1,…,m},边集 E={α,β〉|α=(α_1,…,α_m),β=(β_1,…,β_m)∈Ω,α_i≠β_i,i=1,….m}:G 是Γ的所自同构作成之群.于是,(1)G 是本原群,且G={g|g(x)=g(x_1,…,x_m)=(g_1(x_σ(1)),…,g_m(x_σ(m))),σ∈S_m(集合{1,…,m}上的对称群),g,∈S_h(Ω_h 上的对称群),i=1,…,m};(2)若 h 为奇数 h=2_n+1且 n 为偶数或 h-1>m,则 G 是 k 次对称群 S_k 中的极大子群;(3)若 k 为偶数且2(k-1)>m,则 G 是 k 次交代群 A_k 中的极大子群.     

在对称群中一类正则图所确定的极大子群

对称群的极大子群之确定,在多值逻辑理论和有限自动机理论中都有着重要而广泛的应用,同时也是置换群理论中的一个基本问题。本文提出了k次对称群中一类新的极大子群,k=h~m,m≥3,h≥7。 设Г=(Ω,E)是一个无向正则图,其中顶点集Ω={(α_1,…,α_m)|α_i∈Ω_h={0,1,…,h-1},i=1,…,m},边集E={<α,β>|α=(α_1…,α_m),β=(β_1,…,β_m)∈Ω,a_i≠β_i,i=1,…。m};G是Г的所自同构作成之群。于是,(1)G是本原群,且 G={g|g(x)=g(x_1,…x_m)=(g_1(x_(σ(1))),…,g_m(x_(σ(m))),σ∈S_m (集合{1,…,m}上的对称群),g_i∈S_h(Ω_h上的对称群),i=1,…,m};(2)若h为奇数h=2n+1且n为偶数或h-1>m,则G是k次对称群S_k中的极大子群;(3若h为偶数且2(h-1)>m,则G是k次交代群A_k中的极大子群。     

样条插值的最优误差界和宽度问题(Ⅰ)

我们在 J 及 J~2中分别定义偏序如下:设,Γ_1.Γ_2∈J,若γ_i(1)≤γ_i(2),i=1,…,m;则称Γ_1≤Γ_2.当上式中全部成立等号时,记Γ_1=Γ_2,否则,记Γ_1<Γ_2.设(Γ_1,(?)_1)、(Γ_2,(?)_2)∈J~2,若Γ_1≤Γ_2及(?)_1≤(?)_2同时成立,则记(Γ_1,(?)_1)≤(Γ_2,(?)_2).当上两式均为等式时,就记(Γ_1,(?)_1)=(Γ_2,(?)_2),否则记(Γ_1,(?)_1)(?)(Γ_1,(?)_2).今后,我们还令:     

几个有趣的不等式

一维情形设实数б_i(i=1,2,…,m,m≥2)满足б_1≥б_2≥…≥б_m,x=б_1-б_m,■则有如下定理。定理1 x≥y 证显然,若x=0则y=0,即x=y,定理成立。所以下面假定x>0。因x>0,所以y>0。于     

关于从属族的极值问题

设 U={z:|z|<1},H={f:f在U内解析},B={f∈H:f(U)=U},B_0={f∈B:f(0)=0},S(f)={g∈H:g f}。α_1…,α_m是U内不同的复数。给定正整数K_1,K_2,…K_m满足     

On Diophantine Approximation and Approximate Analysis (Ⅰ)

<正> We use γ=(γ_(11),…γ_(t1),…γ_(15)…,γ_(ts))to denote a point in st-dimensionalEuclidean space R_(st).We use the notations γ_i=(γ_(li)…γ_(ti)(1≤i≤s)and γ_i=(γ_i1,…,γ_(is))(1≤j≤t).q=(q_1,…,q_t),k=(k_1,…,k_s)and m=(m_1,…,m_s)will be     

常系数齐次线性差分方程的解的显式表示

<正> 根据经典方法,m 阶常系数齐次线性差分方程(?),满足初始条件Y_j(j=0,…,m-1)的解可表成 y_(n+m)=y_(n+m)(n,λ_1,…,λ_m,c_1,…c_m)之形,这里λ_i(i=1,…,m)是代数方程     

课外练习

高一年级1.(1)已知集合A={x|x2-3x 2=0},B={x|x2- mx 2=0},若A∩B=B,则实数m的取值范围是______.(2)已知集合A={x|m-1相似文献   

E^n中P维与q维平面间的夹角公式

本文将柯西不等式进一步推广为[α_1β,…,α_mβ][α_iα_j]~(-1)[α_1β,…,α_mβ]~T+(|α∧|β~2)/(|α|~2)≤β~2其中β=b_1∧…∧b_q,q≤p≤n,α_i 是从 p 个向量α_1,…,α_p 中任取 q 个作成的 q 重向量,m=c_p~q.接着给出了 n 维欧氏空间 E~n 中 p 维与 q 维平面间的夹角公式:cos~2θ=[α_1β,…,α_mθ][α_iα_j]~(-1)[α_1β,…,α_mβ]~T/β~2用它导出了 n-1维球面型空间 S_(n-1,1)中关于单形(顶点 P_n 到对面上)的高 h_n 的公式.     

活动受限制下的非协作对策

<正> 設Γ是一n人对策,第i人的策略空間是S_i,赢得函数是H_i(x_1,…,x_n),x_i∈S_i,i=1,…,n.命S_i为第i人的一个混合策略集,而H_i(μ_1,…,μ_n),μ_i∈S_i,为其相应数学期望.按Nash,策略組μ=(μ_1,…,μ_n)称为对策Γ=(这里I={1,…,n}是对策者集)的一个平衡局势,如果对每一μ_i∈S_i,i=1,…,n,有     

Convergence Conditions for Interpolation Fractions at the Nodes Distinct from the Singular Points of a Function

We consider an interpolation process for the class of functions with finitely many singular points by means of the rational functions whose poles coincide with the singular points of the function under interpolation. The interpolation nodes constitute a triangular matrix and are distinct from the singular points of the function. We find a necessary and sufficient condition for uniform convergence of sequences of interpolation fractions to the function under interpolation on every compact set disjoint from the singular points of the function and other conditions for convergence.Original Russian Text Copyright © 2005 Lipchinskii A. G.__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 822–833, July–August, 2005.     

A general recurrence interpolation formula and its applications to multivariate interpolation

Following the ideas of several papers by G. Mühlbach, a general recurrence interpolation formula is obtained that contains as particular cases some extended Newton and Aitken-Neville interpolation formulas. The exposition of the problem allows us to show the applications of this formula to multivariate interpolation. This is the principal aim of this work. Some simple examples are given to show the variety of applications.     

广义逆ATS^（2）的表示与逼近

给出了广义逆AT,S(2)的一个新的表示式．由此建立了基于两个特殊的Hermite插值多项式的广义逆迭代计算格式,数值例子说明方法是可行的．     

Certain Cuntz Semigroup Properties of Certain Crossed Product C*-algebras

We show that the following properties of the C^*-algebras in a class Ω are inherited by simple unital C-algebras in the class TAΩ:(1)(m,n)-decomposable,(2) weakly(m,n)-divisible,(3) weak Riesz interpolation.As an application,let A be an infinite dimensional simple unital C-algebra such that A has one of the above-listed properties.Suppose that α:G→Aut(A) is an action of a finite group G on A which has the tracial Rokhlin property.Then the crossed product C^*-algebra C^*(G,A,α) also has the property under consideration.     

Using a level set approach for image segmentation under interpolation conditions

In this paper, we propose a new 2D segmentation model including geometric constraints, namely interpolation conditions, to detect objects in a given image. We propose to apply the deformable models to an explicit function using the level set approach (Osher and Sethian [24]); so, we avoid the classical problem of parameterization of both segmentation representation and interpolation conditions. Furthermore, we allow this representation to have topological changes. A problem of energy minimization on a closed subspace of a Hilbert space is defined and introducing Lagrange multipliers enables us to formulate the corresponding variational problem with interpolation conditions. Thus the explicit function evolves, while minimizing the energy and it stops evolving when the desired outlines of the object to detect are reached. The stopping term, as in the classical deformable models, is related to the gradient of the image. Numerical results are given. AMS subject classification 74G65, 46-xx, 92C55     

一类含三角形图的伴随多项式的根

We denote h(G,x) as the adjoint polynomial of graph G. In [5], Ma obtained the interpolation properties of the roots of adjoint polynomial of graphs containing triangles. By the properties, we prove the non-zero root of adjoint polynomial of Dn and Fn are single multiple.     

一种二次保形插值参数曲面

1．引言保形插值是工业设计和制造中经常遇到的问题，有关这方面的研究已有许多文献【‘－u1．设n二Fx；，yi，人，川7一0，1，…；n；j＝0；l，…，。；x；＜x；＋1．l＝0，1，…．n—1；yi＜的十；，J二O，L…，。一卫｝是一给定的数据集，Cadson和［ltsch、Beatson和zejerJ－1985年分别提出的方法只保持被插数据集的轴向单调性；Dodd和Roulier等人于1983和1987年提出的方法只保持被插点集网格线上的轴向凸凹性和单调性；Constantini和FOntanella于1990年提出的方法可保持被插点集在所有于区域的边界及共内部的轴向凸凹性和单调性；…     

On the Nevanlinna-Pick interpolation problem for generalized stieltjes functions

The solutions of the Nevanlinna-Pick interpolation problem for generalized Stieltjes matrix functions are parametrized via a fractional linear transformation over a subset of the class of classical Stieltjes functions. The fractional linear transformation of some of these functions may have a pole in one or more of the interpolation points, hence not all Stieltjes functions can serve as a parameter. The set of excluded parameters is characterized in terms of the two related Pick matrices.Dedicated to the memory of M. G. Kreîn     

Node-based smoothed radial point interpolation method for electromagnetic-thermal coupled analysis

The node-based smoothed radial point interpolation method for solving the transient responses of magneto-electro-elastic structures in thermal environment is proposed. Considering the coupling relations between the elasticity, magnetism, electricity and heat, the generalized displacement (displacement, electric potential and magnetic potential) is calculated using the modified Newmark method. G space theory and the weakened weak formulation are applied to derive the equations of node-based smoothed radial point interpolation method for the magneto-electro-thermo-elastic multi-physics coupling problems. We use triangular background meshes as they could be generated more easily for structures with complex geometry. In some cases, they could even be created automatically. Detailed numerical study has shown that node-based smoothed radial point interpolation method not only successfully overcomes the overly-stiff behavior in the FEM and provides more accurate results, but also works well with distorted meshes. Therefore, the node-based smoothed radial point interpolation method could be adopted to solve the magneto-electro-thermo-elastic multi-physics coupling problems in practical engineering.