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1.
设(Ω,)是一可测空间,X是一拓扑空间,(X)为X中的Borel集合类,即X中包含全体开集的最小一代数。我们称从Ω到X的映射U为取值于X的一随机变量[1],[2],如果对任意B∈(X) U~(-1)(B)={ω:U(ω)∈B}∈ 取值于X的随机变量也称为Ω→X的随机元或简称为X中的随机元。  相似文献   

2.
John Jones,Jr.在[1]中证明了一个关于半连通映射的定理:设f是拓扑空间(X,)到半局部连通空间(Y,)上的1—1半连通映射,则f是连续的。以后并被别的文献所引用。本文把Jones定理中映射是1—1的条件去掉,并使原文中定理的证明得到简化。 定义 1 空间(x,)到(Y,)中的映射f称为半连通的,如果对(Y,)的任一连通闭子集A,f~(-1)(A)为(X,)中的连通子集。  相似文献   

3.
双拓扑群     
由J.C.Kelley首创的双拓扑空间理论七十年代中期以来得到迅速发展。在此背景下,本文建立双拓扑群概念,以拓广拓扑群的研究。 定义 设(X,·)为群,(X,)为双拓扑空间。(X,·,)关于为拓扑群系指函数f(x,y)=xy~(-1)视为f:(X,)×(X,)→(X,)是连续的,平行地可定义(X,)关于为拓扑群。若上述两者皆成立,则称(X,·,)为双拓扑群。  相似文献   

4.
Fuzzy拓扑空间中的仿紧性与紧性   总被引:4,自引:0,他引:4  
罗懋康 《数学学报》1987,30(4):548-552
<正> 本文中,以q记相重关系,以Q(A)记Fuzzy集A的重域系,以X记特征函数.其他未经定义的概念均取自[2—5]。简记Fuzzy拓扑空间为fts.在不致混淆时,常径称Fuzzy集,Fuzzy点为集和点,对分明集与其特征函数不加区别.恒以(X,)表-fts. 定义1 设,为(X,)中集族.称为的加细,若A∈,B∈  相似文献   

5.
吕播 《数学学报》1979,22(5):633-635
<正> 在随机测度一文中有这样的结果,任意抽象可测空间(E,)上的一族两两关系正常的S.M.(O)可以扩充成一个极大族是Hilbert空间,而且封闭于随机不定积分运算,即本身是一个完全子空间.在对半鞅的积分一文中考察了可料可测空间(R_+×Ω,)和可选可测空间(R_+×Ω,),并指出所有平方可积鞅在上所产生的S.M.(O)构成一个两两关系正常的S.M.(O)的极大族在{}左拟连续的情况下,全体平方可积鞅在上所产生的S.M.(O)也构成一个两两关系正常的S.M.  相似文献   

6.
薛行鸿 《数学学报》1986,29(3):389-392
<正> 设(Ω,■,P)是一概率空间,E(E)是Banach(共轭)空间,(■)是■的递增子σ-代数列,T是简单停时全体.一个E-值适应序列(x_n,)(x_n关于强可测)称为Pramart,若称(x_n,)属于(B)类,若称(x_n,)L_B~1-  相似文献   

7.
§1 引言设 X={x(t,ω),t<σ(ω)}是定义在完备概率空间上的齐次可列标准马尔可夫过程(以下简称马氏过程或过程),其相空间 E=(0,1,2,…,)其转移概率为 p_(ij)(t),i,j∈E,t≥0,它们是一组满足下列条件的实值函数  相似文献   

8.
郑权 《应用数学》1991,4(1):116-117
本文设(X,)是Banach空间,L(X)是X的非空有界闭子集族,H是导出的Hausdorff度量.此外,∧是一指标集.作为准备,我们有以下Chen和Shin的结果对集值映象情形的推广: 引理设T_λ:X→L(X)(λ∈∧),使得这里函数φ满足(φ):φ:[0,∞)→[0,∞)不减,φ(t)0),且(?)α≥0,存在β>1及收敛序列{t_k}:t_0=0,t_1≥α,t_(k 1)=t_(k φ)(β(t_k-t_(k-1))(k=1,2,…),则存在  相似文献   

9.
关于Lowen空间指数对象的一点注记   总被引:1,自引:0,他引:1  
L-拓扑空间(X,△)称为一Lowen空间若△有一组由层特征函数构成的基,即△中形如a∧U,a∈L,U∈X的元素构成△的一组基.若L=[0,1],则(X,△)是一Lowen空间当且仅当(X,△)是一Lowen意义下的fzzy邻域空间.通过在函数空间上引入适当的L-拓扑结构,证明了若0∈L是一素元并且Lowen空间(X,△)的开集格是一连续格,则(X,△)是Lowen空间范畴中一指数对象.特别地,若一fuzzy邻域空间的开集格连续,则它是FNS中一指数对象.  相似文献   

10.
Rl日1.弓旨石人.,.『刁设X~凡,,。哟,刀~。,欢,J和D相互独立,凡。,尹是未知参数.令F一工矛x尽D 夕/帕则尸‘F,.。:,,这里钾,一吞协/。, 定义1称氏F)X为压缩估计,若民F)一1一从刃/P尸,称,为压缩估计a(刃了的,函数.今后相仿地用于,,.分别作为压缩估计瓦,)X和毓伊)x的,函数,而不再另加说明. 本文取风险函数为R,(a(F)了;0,砂)一刀(a(,’)X一的’W(a口)X一沙)/砂这里平是任意给定的正定阵. 定义,若民。x,瓦。了是二个压缩估计,且对任何沙,。祝 丑二(占(,)x;沙,a,)喊五,(熟F)x;口,。,)则称氏扔x一致地优于气;,X. 定义8若存在氏刃了一致地…  相似文献   

11.
通过不同观测数据研究捕食者—被捕食者生态系统参数确定问题.研究了四种情形1.观察数据无误差,并已知一个参数值.这种情况下,参数可由其相轨线和最小二乘法精确确定.2.观察数据无误差,但所有参数未知.此时仅靠相轨线的研究,无论给出多少组精确数据,都无法精确确定这些参数.通过原非线性模型的数值计算和网格搜索法,至少需要4组数据,同样得到了精度较高的参数值.3.当观测数据有误差时,根据解的周期性,引入标准周期的概念,在一个标准周期里讨论参数的确定问题,并利用标准周期内的捕食者与被捕食者的数量均值与系统的平衡点的关系对参数进行修正,然后使用网格法进行搜索,进一步提高了参数的精度.4.当观测时间也有误差时,先选取相对最优的随机正态数对观测时刻进行修正,然后再利用3.的方法估计参数.  相似文献   

12.
We show that if the Hamiltonian is locally semiconvex with respect to the state variables and strictly convex with respect to the gradient then every viscosity solution of the eikonal equation is locally semiconcave. Furthermore, in the 1D case, we show that every viscosity solution of the eikonal equation is semiconcave if and only if the Hamiltonian is Lipschitz continuous with respect to the state variable.  相似文献   

13.
We consider an optimal control problems for the chemotherapy process on the base of a known dynamical model. The solution technique is connected with a combination of control modes determined in accordance with the Pontryagin maximum principle. We propose extremal control procedures with particular components supplementing the known therapy strategies within the considered model.  相似文献   

14.
An infinite (complete) convex polyhedron with equiangular faces, that is, such that all the angles of each of its faces are equal to one another, is called irreducible if the number of monogonal faces belonging to it cannot be decreased (by identifying their sides) while preserving the equiangularity of all of the other faces and the convexity of the polyhedron itself (a lack of conditional edges). Any infinite convex polyhedron with equiangular faces can be obtained from the corresponding irreducible one by pasting in the missing number of monogons. It is proved that the number of combinatorially different irreducible polyhedra is finite, not counting three infinite series of frusta of cones with finite or infinite bases and right prisms with infinite bases. It is also established that, without exception, all infinite convex polyhedra with equiangular faces and total curvature 2are the derivatives of closed convex polyhedra with equiangular faces. The proof is carried out with the help of A. D. Milka's method from Ross. Zh. Mat., 1988, 3A830. Translated from Ukrainskii Geometricheskii Sbornik, No. 35, pp. 75–83, 1992.  相似文献   

15.
本文利用对数函数变换简便地解决了积分上、下限互为倒数的一类定积分计算问题.  相似文献   

16.
The best members of the Kim family, in terms of stability, are obtained by using complex dynamics. From this elements, parametric iterative methods with memory are designed. A dynamical analysis of the methods with memory is presented in order to obtain information about the stability of them. Numerical experiments are shown for confirming the theoretical results.  相似文献   

17.
In [2] it was shown with reference to the cylindrical bending of a plate that the Kirchhoff-Love hypothesis is asympototically accurate for determining the critical load irrespective of the properties of the material. However, the question of the dependence of the critical load on the material properties was left unexplored. This question is now numerically investigated. Curves characterizing the variation of the critical load with relative shear modulus are presented.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 355–357. March–April, 1969.  相似文献   

18.
Under study is the class of ring Q-homeomorphisms with respect to the p-module. We establish a criterion for a function to belong to the class and solve a problem that stems from M. A. Lavrentiev [1] on the estimation of the measure of the image of the ball under these mappings. We also address the asymptotic behavior of these mappings at a point.  相似文献   

19.
We obtain improved regularity criteria for the axisymmetric weak solutions of the three dimensional Navier-Stokes equations with nonzero swirl. In particular we prove that the integrability of single component of vorticity or velocity fields, in terms of norms with zero scaling dimension give sufficient conditions for the regularity of weak solutions. To obtain these criteria we derive new a priori estimates for the axisymmetric smooth solutions of the Navier-Stokes equations. Received: 11 April 2000; in final firm: 26 November 2000 / Published online: 28 February 2002  相似文献   

20.
Kashchenko  S. A. 《Mathematical Notes》2018,104(1-2):231-243
Mathematical Notes - The delay logistic equation with rapidly oscillating coefficients is studied. An averaged equation is constructed, and its dynamics is investigated. Algorithms relating the...  相似文献   

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