查询词典 compactness theorem

In addition, by utilizing Jacobi two square numbers theorem and Lagrange four square numbers theorem and some theta function identities, we also prove the known results of number theory: two triangular number theorem, four triangular number theorem, and the number of representations of a positive integer by various quadratic forms in terms of divisor functions

包括Jacobi二平方数定理，Lagrange四平方数定理等，然后利用这些结果结合几个theta函数恒等式，我们获得了把任意一个正整数表示成两个三角数或四个三角数的和以及其他的二次形式的方法数，这些方法数都是用因子函数来表示的。

And guided by Schur theorem, many of the Schur theorem inference arises, formed a complete theoretical system Schur theorem. Schur theorem and put many of its reasoning applied to the unitary matrix and the similarity matrix eigenvalue of proof onto.

在Schur定理的指导下，许多关于Schur定理的推论便产生了，并且形成了一个完整的Schur定理理论体系，把Schur定理和它的许多推论推广到了酉矩阵的相似和矩阵的特征值的证明上来。

As a particular of Rado's theorem and the compactness theorem one obtains the following result.

作为Rado定理和紧致性定理的一种特殊情形，我们得到下面的结果。

Firstly, the eigenvalue problem of a class of second order elliptic equation with critical potential and indefinite weights is considered. Then, using critical point theory, Trudinger-Moser inequality and the properties of the first eigenvalue, we prove the existence of a nontrivial solution for a class of nonlinear elliptic with critical potentialand indefinite weights in R~2. Secondly, we prove the existence of nontrivial solutions for a class of subcritical and critical elliptic systems with indefinite part in R~2 byusing a generalized linking theorem, Trudinger-Moser inequality and concentration-compactness principle.5. The existence of at least three weak solutions for discrete boundary value problem is established by using a three critical point theorem introduced by Ricceri.

首先，讨论了R~2中一类带不定权且含临界位势的二阶椭圆型方程的特征值问题，并借此特征值问题的第一特征值性质，利用山路引理及Trudinger-Moser不等式，证明了R~2中一类带不定权且含临界位势的非线性椭圆型方程非平凡解的存在性；其次，利用广义环绕定理，Trudinger-Moser不等式及集中列紧原理，得到了R~2上一类具有强不定部分的半线性椭圆型方程组在非线性项分别为次临界增长和临界增长情形下非平凡解的存在性。

In this research report, we mainly study the boundedness, compactness, weak compactness and other properties of composition operators on some analytic function spaces.

在本报告中，我们主要研究了一些全纯函数空间上复合算子的有界性，紧性，弱紧性和这种算子的一些其它性质。

In this paper,Laterite soil adjacent to some stake of the highway in Chenzhou, Hunan section from Xiamen to Chengdu was used to investigate the deformation characteristics and protection methods of the Laterite soil subgrade under the influence of environment factors.Properties like water-holding capacity,capillary rise, coupled heat-moisture transfer and wetting deformation of samples under different compactness were studied through a series of laboratory tests.In addition,by using meteorological data of two consecutive years in Chenzhou,coupled process of moisture transfer and subgrade deformation was stimulated under the impacts of groundwater and the atmosphere.Specific work done in this paper is as follows:(1) Samples under different compactness were subjected to a series of conventional laboratory tests,such as permeability,consolidation,contraction,shear test and etc.

论文以厦门至成都高速公路湖南郴州段的红粘土为研究对象，以环境因素作用下红粘土路基的变形特征与防护方法为研究目的，通过室内试验研究了不同压实度红粘土的持水性能、毛细上升、湿热耦合迁移及湿化变形等特征，借助郴州地区连续两年的气象数据，模拟在地下水和大气的共同作用下路基内部红粘土水分迁移与路基变形的耦合过程，主要研究内容及结论如下：(1)针对不同压实度的红粘土，系统开展了其渗透、固结、收缩、剪切等试验研究。

Ii Base on the compactness of C〓, we study the compactness of product operators of a composition operator with another one's adjoint on weighted Bergman spaces.

第二，在考虑单个复合算子C〓的紧性的基础上，进一步讨论了乘积算子C〓C〓和C〓C〓在加权Bergman空间A〓上的紧性问题。

Although many results have been obtained, there are still a number of very interesting questions about composition operators unsolved. There is much more to be learned about the collective compactness and convergence of composition operator sequences, compactness of various product of composition operators, cyclicity, closed range and spectra of composition operators in various settings. Commutants of composition operators seem to be very difficult to characterize. Only a little is known about their reducing invariant subspaces. There has been no work on C〓 algebras generated by composition operators.

尽管已取得如此丰富的结果，但是关于复合算子仍然有大量非常有意义的问题值得研究，例如：复合算子序列的总体紧性及收敛性、复合算子的各种乘积的紧性、复合算子的闭值域问题、复合算子在各种解析函数空间上的谱的描述、换位复合算子的刻画、复合算子诱导的不变子空间问题、循环复合算子的研究、由复合算子生成的C〓-代数的研究、不同解析函数空间之间的加权复合算子及复合算子半群等等问题。

Iii By using the well-known properties of the dela vallee-poussin summability kernels and the pass principle of weakly compact operator, we study the weak compactness of C〓 on vector-valued analytic function spaces H〓, B〓, N and N〓, establish some connections between the weak compactness of composition operators and the structure properties of Banach spaces. These generalize and unify the corresponding results in the scalar-valued setting and enrich the content of the study of composition operator in another way.

第三，利用著名的de la Vallee-poussin可和核及有关算子的弱紧性的传递原理给出了向量值解析函数空间H〓、B〓、N及N〓上的复合算子的弱紧性的刻画，建立了复合算子的弱紧性与Banach空间的结构性质之间的联系，统一和推广了对应的数量值解析函数空间上的复合算子的弱紧性，这从另一种途径极大地丰富了复合算子的研究内容。

Furthermore,inspired by〓and the study of compactness in chapter four,wediscuss the boundedness and compactness of integral operator〓.

受〓及第四章关于紧算子的研究的启发，本章还讨论了积分算子〓的有界性和紧性。

So it was last week in Selma , alabama.

上星期在亚拉巴马州塞尔马市发生的事件也是这样一个转折点。

The group also spearheads various social programs in China.

该组织还带头参与中国的各种社会活动。