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  开集
     Suppose {X_i,i∈N} is a stationary NA random variables such thatψ_(1)>0. Define the empirical measure■,ψ≥1.This article,proves that {P{δ_n∈·},n→∞} satisfies the large deviation principle on (M_1(R),■) by the relation between the open set under the weak convergence topology and the open sphere under the metricβ.
     设{X_i,i∈N)是平稳N A随机变量序列且ψ_(1)>0.记经验测度δ_n=1/n■,借助于弱收敛拓扑下的开集与β度量下的开球之间的关系,证明了{P{δ_n∈·},n→∞}在(M_1(R),■)上满足大偏差原理.
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     By using the variational method, we discuss the existence of solution of the boundary value problem-△pu=μQ(x)|u|p-2u+f(x,u), u∈D01,p(Ω), where Ω is an open set of RN, 10 and both functions Q and f may change sign.
     本文利用变分方法研究如下边值问题的可解性:-△pu=μQ(x)|u|p-2u+f(x,u),u∈D_0~1,p(Ω),其中Ω是RN中的开集,1
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     A general Sierpinski block generated by normal tetrahedron is constructed by making use of the contraction of identical mapping which meets the open set conditions,and finds out its Hausdorff dimension s=ln[4+6(n-1)]/ln(1/ε).
     构造了正四面体生成的一般Sierpinski块,利用满足开集条件的压缩自相似映射的性质,给出它们的Hausdorff维数s=ln[4+6(n-1)] ln(1 ε)。
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     Some properties of Z-Scott open set,Z-Lawson open set,Z-Scott topology and Z-Lawson topology are studied.
     研究了Z-连续偏序集上的Z-Scott开集,Z-Lawson开集,Z-Scott拓扑及Z-Lawson拓扑的一些性质。
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     Let E and F be Banach spaces, and f:UE→F be a C 1 map where U is an open set in E .
     设 E和 F是 Banach空间 ,让 f是定义在 E中开集 U到 F的一个 C1映射。
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  “open set”译为未确定词的双语例句
     Integral Solution Operators for the Cauchy-Riemann Equations on an Open Set with Piecewise C ̄1-Boundary
     Integral Solution Operators for the Cauchy-Riemann Equations on an Open Set with Piecewise C~1-Boundary
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     Local C ̄k---boundary Regularity of Integral Solution Operators of the equations on Open Set with Piecewise C ̄1---boundary
     Local C~k──boundary Regularity of Integral Solution Operators of the ──equations on Open Set with Piecewise C~1──boundary
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     Mian results:If X is a S cmpactness space,and X has finite semi open set interrection property then(1)If X is a S 2 space, then X is a S 3 * space;
     主要结论 :设X是 -S紧空间 ,且具有有限半开集可交性 ,则 (1)若是S2 -空间 ,则X是S3 -空间 ;
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     (1) where (x,t)=(x~1, ……x~m, t) is the variable in an open set Ω of R~(m+1), I_N is the N×N identity matrix, A_j(x,t) (0≤j≤m) are N×N complex matrices, and their entries are analytic functions.
     其中I_N是N×N单位矩阵,A_j(x,t)(0≤j≤m)是元素为解析函数的N×N矩阵.
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     If E satisfies the strong separation open set condition (SSC), then there exists a series of contracting-copy-group {Ui} and a compact set U(|U| > 0) such that Hs(U) = |U|s and moreover, {Ui} converges to U with respect to Hausdorff metric.
     利用部分估计原理得到了本文的主要结果:若E满足强分离开集条件,则在E中存在一个压缩拷贝串序列{Ui}和紧集U(|U|>0),使得Hs(U)等于|U|s,并且{Ui}按Hausdorff度量收敛到U,进而证明了由U可以构造一个数列,使得该数列正好收敛到Hs(E);
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  相似匹配句对
     open;
     评价的开放性问题;
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     set with (?)
     集且(?)
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     (L) and set
     (L),证明了范畴Set_0(L)与(?)
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     L-FUZZY SEMI-OPEN SET
     L—Fyzzy半开集
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     the other is to set up open access journals.
     二是创办开放存取期刊。
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  open set
We show that the (open) set $\Omega^+\subset{\mathcal A}$ of all division algebra structures on $A$ has four connected components.
      
A functionf∶G→?n, whereG is an open set in ?n, has theN-1-property if for allE??n we have {|E|=0?|f-1(E)|=0} (|·| is the Lebesgue measure).
      
The Pólya conjecture and its connection with the weak Weyl-Berry conjecture are studied Specifically let Ω?Rn (n≥1) be a non-empty bounded open set with boundary ?Ω.
      
It is also shown that under these necessary and sufficient conditions, all the generalized regularizing feedback controllers form a Zarisky open set.
      
Let Ω?Rn(n≥2) be a bounded open set;QT=Ω×[0,T],ST=δΩ×[0,T],S1,S2 be the partial boundaries of Ω andS1∪S2=δΩ,S1∩S2=Φ.
      
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Let F be a sufficiently smooth functional on an open set in a Banach space. The equationcan be solved by the iterationwith where

设F是Banach空间中一个开集上的充分光滑泛函.对方程F″(x_0)=0可由下述迭代来求解,其中A=F″(x)~(-1). 同时有估计式

In this paper the notions of semi-open set and semi-continuous mapping,defined as in fuzzy topological space,are extended into the fuzzy topological space.Some of their primary properties are discussed.Main definitions and results are as follows.Def.2.1 A fuzzy set A in a fuzzy topological space s termed fuzzy semi-open if and only if there exists a set O∈t such that O(?)A(?)O,where O denotes the closure of O.Prop.2.1 A fuzzy set A in a fuzzy topological space is semi-open...

In this paper the notions of semi-open set and semi-continuous mapping,defined as in fuzzy topological space,are extended into the fuzzy topological space.Some of their primary properties are discussed.Main definitions and results are as follows.Def.2.1 A fuzzy set A in a fuzzy topological space s termed fuzzy semi-open if and only if there exists a set O∈t such that O(?)A(?)O,where O denotes the closure of O.Prop.2.1 A fuzzy set A in a fuzzy topological space is semi-open ifand only if A(?)A0),where A0 denotes the interior of AProp.2.3 Let {Aαa}α∈A be a collection of semi-open sets in a fuzzytopological space,then Uα∈A Aα is semi-open.Prop.2.6 Let J={Ba}a∈A be a collection of fuzzy subsets in a fuzzytopological space uch that (1) t(?)J and (2) if B∈J and S(?)D(?)B,where D is fuzzy set in X,then Z∈J.It follows that T(?)J,where T denotes the class of all semi-open sets in X.Prop.2.7 If A is any fuzzy sets in a fuzzy topological space,then A(?)AThe semi-closure of A,denoted by A,is the intersection of all fuzzysemi-closed sets in X that contains A.Def.3,1 Let f:X→Y be single valued where X and Y are fuzzy topological spaces,then f:X→Y is termed fuzzy semi-continuous if and only if f-1(O) is a fuzzy semi-open set in X for fuzzy semi-open O in Y.Prop,3.5 Let f be a fuzzy semi-continuous function from a separable fuzzy topological space X onto a fuzzy topological space Y,then Y is also separable.Prop.3.6 Let f be a fuzzy semi-continuous function from a fuzzy S-closed space onto a fuzzy topological space Y,then Y is also fuzzy S-closed space.Prop.3.7 Let f be a fuzzy semi-continuous funiction from an α-compact space X onto a fuzzy topological space Y,then Y is also α-compact [4]A fuzzy topological space is fuzzy S-closed if and only if every semi-open cover of X has a finite subcollection whose closure covers X

本文在弗晰拓扑空间中引入了弗晰半开集概念,以及定义在弗晰拓扑空间上的半连续映射概念。并且初步地探讨了它们的一些性质,得到了一个映射为弗晰半连续映射的条件。

In [4] and [5], E. Albrecht has shown that every operator with spectral decomposition property is a decomposable operator and has constructed an example of decomposable operator which is not strongly decomposable respectively.In §1 of this paper, by virtue of the integral round a contour of the maximal analytic extension x(λ),a brief proof of the above theorem is given. In §2, we give a necessary and sufficient condition of operator with spectral decomposition property. That is.Theorem. TεB(X) has the spectral...

In [4] and [5], E. Albrecht has shown that every operator with spectral decomposition property is a decomposable operator and has constructed an example of decomposable operator which is not strongly decomposable respectively.In §1 of this paper, by virtue of the integral round a contour of the maximal analytic extension x(λ),a brief proof of the above theorem is given. In §2, we give a necessary and sufficient condition of operator with spectral decomposition property. That is.Theorem. TεB(X) has the spectral decomposition property if and only if for every open set of the complex plane there exists YεInv(T) such thatBy means of this theorem, the example in [5] is simplified.

本文利用围道积分对Albrecht定理:有谱分解性质的算子是可分解算子,给出了一个简单证明,同时给出了一个具有可分解性质的算子的充要条件.利用这一充要条件,简化了Albrecht的可分解而不强可分解的例子.

 
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