紧性

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。

This paper mainly studied the semilinear biharmonic elliptic equation with multi-singularity and critical exponcnt,in which we mainly studied,where N≥5,k∈N,(λ_1,λ_2,…,λ_k)∈R~4,(a_1,a_2,"",a_k)∈R~(4n) and 2~*=2N/N-4 is the critical Sobolev exponent.

文章主要在有界域Ω中研究了如下含多奇性的半线形椭圆型问题其中N≥5，k∈N，(λ_1，λ_1，…，λ_k)∈R~k，(a_1，a_2，…，a_k)∈R~且2~*=2N/N-4是临界的嵌入指数，由于Sobolev嵌入失去紧性，所以文章将通过集中紧原理得到正解的存在性。

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。

We establish some connections between geometric properties, properties in analysis and analytic properties of the inducing map ψ and operatortheoretic properties of composition operator C〓: f〓fοψ on various analytic function spaces mentioned above, include the boundedness, compactness, weak compactness, collective compactness and the Schatten class operator ideal, etc. Our results extend some previous results, for instance, the Shapiro's Nevanlinna counting function condition and the MacCluer's Carleson measure condition for the compactness of C〓 on Hardy space.

本文建立了D上解析自映射φ：D→D的几何性质、分析性质和解析性质与复合算子C〓：f→foφ在上述各种解析函数空间上的限制的算子性质之间的联系，涉及到复合算子C〓的有界性、紧性、弱紧性、总体紧性及Schatten类算子理想等算子特征，推广了前人的一系列结果，如Shapiro关于C〓的紧性的Nevanlinna计数函数条件，MacCluer关于C〓的紧性的Carleson测度条件等。

In this paper, based on local compactness in topological spaces, local N-compactness and connectedness in L—topological spaces, we have studied local paxacompactness in topological spaces, local paxacompactness and δ—connectedness in L—topological spaces.

本文以拓扑空间的局部紧性、L-拓扑空间的局部良紧性以及连通性为基础，研究拓扑空间的局部仿紧性、L-拓扑空间的局部仿紧性以及δ-连通性。

Some properties of the closed sets, separation and compactness are discussed, so the advantages of nonstandard analysis is showed.

在此基础上，定义了闭集、分离性及紧性，讨论了闭集、分离性及紧性的一些相关性质。

Since the solutions of this problem are the critical points of the associated energy function. One generally needs some compactness such as PScondition or C-condition to prove the existence of critical points of the energy func-tion, but when we study the elliptic equation in R~N, the compactness condition does not always hold since the imbedding of the Sobolev space H_0~(1,2)into L~(2*) is not compact. In this chapter, based on the nonsmooth critical point theory, and by using the approximation technique with periodic function, the existence of nontrivial solution is obtained.

由于该方程的解就是其所对应的能量泛函的临界点，通常都要在一些紧型条件的基础上来证明其所对应的能量泛函临界点的存在性，但当我们在无界域上考虑该椭圆方程解的存在性时，Sobolev空间H_0~(1，2)到L~(2*)的嵌入非紧，从而导致所对应的能量泛函失去紧性，本章在非光滑临界点理论的基础上，应用周期逼近的方法证明该问题非平凡解的存在性。

We also introduce the countable compactness and sequential compact-ness for a De Morgan algebra of topology and study the relations between any two of theseconcepts and compactness.

同理还在德摩根拓扑代数中引进了可列紧和序列紧，研究了可列紧和序列紧之间的关系以及这两种紧性与紧之间的关系。

As the layer structure of lattice, relative separation properties and relative compactness in L-fuzzy topological spaces are more complex than that in general topological spaces.

由于层次结构的存在，L-fuzzy拓扑空间中的相对分离性和相对紧性较一般拓扑学中的相对分离性与相对紧性复杂得多。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。