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an open set
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  开集
     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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     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。
短句来源
     INTEGRAL SOLUTION OPERATORS FOR THE CAUCHY-RIEMANN EQUATIONS ON AN OPEN SET PIECEWISE C ̄1-BOUNDARY
     具有逐片C~1-边界开集上Cauchy-Riemann方程的积分算子解
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     INTEGRAL OPERATOR SOLUTIONS OF -EQUATIONS IN AN OPEN SET WITH PIECEWISE C 2 -BOUNDARIES
     -方程在逐片C~2-边界开集上的积分算子解
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     Let X be normed space, ψ: X→X be a operator. Then this paper demonstrates that under certain conditions, there exist in ψ(X) some interior points; ψ(X) is an open set;
     设Ψ是线性赋范空间X→X的算子,本文研究了在某些条件下,Ψ(X)存在内点、Ψ(X)为开集、Ψ为满映射及Ψ为开映射.
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  “an 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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     (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.
短句来源
     Let Ω be an open set of R n . Based on isoperimetric inequality and Morrey′s lemma,an apriori interior estimate with H o ·lder exponent 1/K for (K,K′) quasiconformal mappings is established.
     设Ω是Rn上的一个开区域,对于Ω上的一个(K,K′)拟共形映射f(x)∈W1,nloc(Ω),通过等周不等式和Morrey引理,建立了指数为1/K的Ho··lder连续内估计.
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     S-harmonic function and the Dirichlet prolem on an open set D are defined for supeHunt process. Any bounded function f defined on the complement of D extends to a function h cuRd such that F(P) = exp(-- h,μ} is S-harmonic in D and satisfies the Dirichlet boundary condition at any regular boundary points of D.
     本文定义了超Hunt过程的S-调和函数与Dirichlet问题.定义在Dc上的有界函数f可以扩张到Rd上的函数h使得F(P)=exp<-h,μ>为D内S-调和函数并且在D的规则边界点上满足Dirichlet边界条件
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     In this paper, he proved a global Implicit function theoremTheorem Let Dt be an open set of a first countable toplogical space, D2 an open set of a Banach space E2. f:Di X D2 - F CI E is continuous on first variable and satisfiesR+ continuous.
     得到两个全局性隐函数定理:定理1设D_1是第一可数的拓扑空间E_1的开子集. D_2是Banach空间E_2的开子集.
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  相似匹配句对
     Hypertopologies on an Open-set Noose Space
     开集套空间上的超拓扑
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     3. to set up an open and modern agricultural system;
     ③建立开放型的现代农业体系;
短句来源
     Note on an Open Problem
     关于一个Open问题的注记
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     In an X.
     X.
     C~(An)(?)
     C~(An)A~(B(?)
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  an open set
We prove that if the indicator-function1E of a measurable setE ?? is a Fourier multiplier in the spaceEp(?) for somep≠2 thenE is an open set (up to a set of measure zero).
      
We prove the existence of infinitely many vector-valued Lipschitz-continuous functions u on an open set satisfying suitable Dirichlet boundary conditions such that the singular values of the gradient matrix u, i.e.
      
Our examples are obtained by conformal change of the metric on an open set of the complex space form.
      
We demonstrate that there is always an open set of linear transformations such that the image curves have at least six vertices.
      
The third problem for the Laplace equation is studied on an open set with Lipschitz boundary.
      
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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 analytic hypoellipticity (at a point) is considered by means of the first-order systems of the kind ??(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. A necessary and sufficient condition for the analytic hypoelliptic first-order systems(1) is obtained.As an application, the sufficient condition for analytic hypoellipticity of a class of second...

In this paper, the analytic hypoellipticity (at a point) is considered by means of the first-order systems of the kind ??(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. A necessary and sufficient condition for the analytic hypoelliptic first-order systems(1) is obtained.As an application, the sufficient condition for analytic hypoellipticity of a class of second order linear partial differential operators is also given.

本文考虑如下的一阶线性偏微分算子组?? 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. 我们给出了一阶算子组L是解析亚椭圆的一个充分必要条件,并由此得出一类二阶线性偏微分算子是解析亚椭圆的一个充分条件.

In this paper we have studied the continuity of functions defined on the generalized number system defined in[1], which is a subfield of the formal power series studied in[3]-[10].If y-f(x)is a generalized function with(m,n)-derivative at point x~0∈E, the field of generalized numbers, then d_ny/d_mx(x~0)=(…, 0,(?)y_n(x~0)/(?)x_m, 0,…).If y=f(x) has(m,n)-derivative on each point in a open set G(?)E.I=(a,b)(?)G,[f(a)]_n=[f(b)]_n, where a(?)=b_i,when i

In this paper we have studied the continuity of functions defined on the generalized number system defined in[1], which is a subfield of the formal power series studied in[3]-[10].If y-f(x)is a generalized function with(m,n)-derivative at point x~0∈E, the field of generalized numbers, then d_ny/d_mx(x~0)=(…, 0,(?)y_n(x~0)/(?)x_m, 0,…).If y=f(x) has(m,n)-derivative on each point in a open set G(?)E.I=(a,b)(?)G,[f(a)]_n=[f(b)]_n, where a(?)=b_i,when iset[a,b]has weak derivative, and there exists k∈Z,set of all integers,so that y_m=0 for each m∈Z and m≠k, then y=f(x) is monotonic increasing(decreasing), if, and only(?),for each x∈[a,b],weak derivative df(x)/dx(weak)≥0(≤0), where[a,b] is the the box closed interval determined by a and b defined in[11]

此文中我们研究广义数域E上的连续函数。如果y=f(x)是一广义数函数,在点x~0s∈E处具有(m、n)-导数,则d_ny/d_mx(x~0)=(…,0,(?)y_n(x~0)/(?)再x_m,0,…)。如果y=f(x)在开集G(?)E上的每点具存(m,n)一导数,I=[a,b](?)G,[f(a)]_n=[t(b)]_n,并且当i

 
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