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Chapter 3 studies the compactness of product operators of a composition operator C〓 with the adjoint C〓 of another composition operator C〓 on weighted Bergman spaces A〓. We give some conditions in terms of angular derivatives of the inducing maps ψ and ψ for the operator C〓C〓 or C〓C〓 to be compact.
第三章研究了加权Bergman空间上的一个复合算子C〓与另一个复合算子C〓的共轭算子C〓的乘积C〓C〓与C〓C〓的紧性问题,我们用φ与ψ在〓D上的角导数的某种关系给出了C〓C〓与C〓C〓在A〓上为紧算子的一些判据。
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The characteristic of teeth meshing and,further,circumferential load distribution of non-conjugate crown gear coupling are analyzed,by which an effective method is given for analyzing the effect of obliqueness on the load distribution of engaged teeth in crown gear coupling .
分析了轧机用非共轭鼓形齿联轴器的齿面啮合特征,并在此基础上进一步研究齿间周向载荷的分配规律,给出一种分析非共轭鼓形齿联轴器工作倾角对其齿间载荷分配影响的有效方法。
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The research of matrixes is continuously an important aspect of the quaternion division algebra. The purpose of this paper is to discuss the property of skew self-conjugate matrix. The definition of skew self-conjugate matrix on real quaternion division algebra is given.
四元数体上矩阵的研究是四元数代数理论中的一个重要方面,本文研究实四元数体上斜自共轭矩阵的性质,给出实四元数体上斜自共轭矩阵的定义。
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Chapter 4,based on strong efficiency rather than efficiency or weak effi-ciency,discusses the similar problem to chapter 3.The concepts of strongsupremum and strong infimum for the set in finite-dimensionalEuclidean space are given,s-conjugate functions and s-subdifferentials theory is developed,by means of which,the duality problem ofmulitobjectivre programming for strong efficient solutions or called absoluteoptimal solutions is analysed,and a new duality theory-s-conjugateduality theory is proposed.
第四章,基于强有效性而不是有效性和弱有效性,给出了类似于第三章的结果,提出了有限维欧氏空间中集合的强上、下确界等概念,研究了点集映象的强共轭函数和强次微分问题,建立了点集映象的s-共轭函数及其s-次微分理论,并借助于这一理论,讨论了多目标规划关于绝对最优解或称强有效解的对偶性问题,建立了基于强有效性的s-共轭对偶理论。
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By extending the concepts of supremum and infimum in real space to the casein any finite-dimensional Euclidean space a weak supremum set and infimumset theory with respect to cones for the set in finite-dimensional Euclideanspace is developed,and several similar properties to the set in real space are ob-tained,with the concepts of this weak supremumset,w-D-conjugate maps and w-D-subdifferentials theory for the point-to-setmap are developed,and its several properties and its relationships with weakefficient solutions of the multiobjective programming are studied.
推广实空间中上、下确界的概念至任意有限维欧氏空间,建立了有限维欧氏空间中集合的锥弱上、下确界集理论,得到了与实空间中十分相似的性质。借助于这一理论,应用上、下确界的概念,给出了点集映象的w-D-共轭映象及w-D-次微分理论,并研究了它们的若干特性及其与弱有效解之间的关系,此外还讨论了弱鞍点问题。
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Necessary and sufficient conditions for the existence and the expressions of selfconjugate solution, perselfconjugate solution, centrosymmetric solution, bisymmetric solution, skewselfconjugate solution, skewperselfconjugate solution, skewcentrosymmetric solution, and skewbisymmetric solution to 4 kinds of systems of linear matrix equations over a regular ring with an involutorial antiautomorphism are given.
利用矩阵技巧和所建立的矩阵理论,给出了正则环上五类矩阵方程组有解的若干充要条件和一般解的表达公式。这些矩阵方程组除了它们在理论上有重要的意义外,还有重要的应用价值。在具有对合反自同构的正则环上,给出了四类矩阵方程组有双对称解,中心对称解,斜中心对称解,广自共轭解,斜广自共轭解,自共轭解以及斜自共轭解的充要条件及其这些解的具体表达式。
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In Chapter 2,we introduce the definition of adding machines,and give sev-eral equivalent conditions on the existence of several kinds of conjugacy and semi-conjugacy relations between adding machines.
第二章介绍了广义符号空间上的加法机器的定义,给出了加法机器之间存在着各种共轭及半共轭关系的多个充要条件,证明了加法机器之间的拓扑半共轭一定是一个群同态与一个平移映射的复合,并研究了此同态的核的构成。
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In [17], there is a theorem about the conjugacy of two words on the alphabet A . This chapter generalizes it to the partial words on the alphabet A.
在M.Lothaire主编的《Combinatorics on Words》[17]一书中,给出了关于字母表A上的字共轭定理,本章把它推广到部分字上。
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In chapter 3, characteristic paraments, focusing structure were discussed, the processing of double cell for phase conjugation was analyzed. Designing criteria of double cell phase conjugation mirror was given out. All phase aberrations could be compensated by using phase conjugation theoretically, but compensation is only effective to phase aberration of uniform polarizing state, it is not effective to aberration by thermally induced depolarization an diffractive effecting by aperture.
在第三章,我们讨论了SBS介质的特性参数,相位共轭镜的聚焦结构,分析了双池相位共轭镜的相互作用过程,给出了相位共轭镜的设计原则;从理论上讲相位共轭技术可以完全补偿热畸变以及因各种光学不均匀性造成的光束畸变,但是相位共轭技术只对偏振态均匀的相位畸变造成的光束畸变起补偿作用,而对由于热致双折射效应造成的退偏以及光束通过硬边光阑时的衍射效应造成的光束畸变无能为力。
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A conclusion that the symmetric product of a self-conjugate matrix is still a self-conjugate matrix was obtained.
给出实四元数体上矩阵对称积的定义,得到了自共轭矩阵的对称积仍是自共轭矩阵的结论。