新型高速光发射模块的设计与分析

介绍了用于高速、宽带光纤通信系统的铌酸锂(LiNbO3)光发射模块的优化设计方法。分析比较了半导体器件与铌酸锂波导器件在作为光纤通信光发射模块时的优缺点。对光发射模块的两个主要器件———掺铒铌酸锂(Er∶LiNbO3)波导激光器和LiNbO3电光调制器进行了结构设计和分析。分析和讨论了电光调制器带宽及半波电压随器件主要参数的变化关系。用BPM软件模拟了所设计的模块的结构特征。该发射模块的发射峰值波长为1531nm,调制速率为10Gbits/s。     

On simple modules of Hecke algebras of type Dn

This is a continuation of our previous work. We classify all the simple ℋ_q(D _n )-modules via an automorphismh defined on the set { λ | D^λ ≠ 0}. Whenf _n(q) ≠ 0, this yields a classification of all the simple ℋ ^q (D _n)- modules for arbitrary n. In general ( i. e., q arbitrary), if λ⁽¹⁾ = λ⁽²⁾,wegivea necessary and sufficient condition ( in terms of some polynomials ) to ensure that the irreducible ℋ_q,1(B _n )- module D^λ remains irreducible on restriction to ℋ_q(D _n ).     

Quasitilted extensions of algebras I

Let be a connected finite dimensional -algebra, and let be a nonzero decomposable -module such that the one-point extension is quasitilted. We show here that every nonzero indecomposable direct summand of is directing and is a tilted algebra.

     

随机度量理论及其应用在我国最近进展的综述

本旨在全面综述随机度量理论及其应用过去十年在我国发展过程中所获得的主要结果与思想方法。全由十节组成,第一节对我们工作的背景－概率度量空间与随机度量空间理论和一简单的介绍;第二节给出某些有关随机泛函分析及取值于抽象空间的可测函数的预备知识;第三节阐明随机泛函分析与原始随机度量理论（本称之为F－随机度量理论）的整体关系：主要结果是在随机元生成空间给出自然且合理的随机度量与随机范数的构造,从而将随机元与随机算子理论的研究纳入随机度量理论框架;主要思想是将随机泛函分析视为随机度量空间体系上的分析学而统一地发展,从而形成了发展随机泛函分析的一个新的途径－空间随机化途径;除此之外,在本节我们也从随机过程理论观点出发首次提出对应于随机度量理论原始版本的一种新的随机共轭空间理论（叫作F－ 随机共轭空间理论）,它的突出优点是能保持象随机过程的样本性质这样更精细的特性（本节由作的工作构成）;在第四节,基本作最近提出的随机度量理论的一个新的版本（本称之为E－随机度量理论）,从传统泛函分析的角度对过去已被发展起来的随机共轭空间理论（本称之为E－随机共轭空间理论）,从传统泛函分析的角度对过去已被发展起来的随机共轭空间理论（本称之为E－随机共轭空间理论）的基本结果进行系统整理并给以全新的处理（本节内容整体上由作最近后篇论构成,也尤其提到朱林户等人的重要工作）;在本节我们也相当的篇幅论述F－随机共轭空间理论与E－随机共轭空间理论的内存关系与本质差异。在下紧跟的两节,致力于E－随机共轭空间理论深层次的结果,尤其突出了E－随机赋范模与传统的赋范空间、E－随机共轭空间与经典共轭空间之间的内存联系;在第五节给出了几类E－随机赋范模的E－随机共轭空间的表示定理（主要由作的工作,作与游兆永及林熙合作的工作,还有巩馥州与刘清荣合作的工作组成）;在第六节给出完备E－随机赋范模为随机自反的特征化定理（主要由作及合作的工作组成）;在第六节给出完备E－随机赋范模为随机自反的特征化定理（主要由作及合作的工作组成）。尤其在第五及第六节中,我们给出随机度量理论在随机泛函分析及经典Banach空间中若干实质性的应用;第七节简要给出E－随机赋半范模及E－随机对偶系理论初步;第八节简单阐明随机度量理论与泛函分析的关系;第九节阐明了随机度量理论与概率度量空间理论的关系。最后在第十节结合随机度量理论,Banach空间理论及随机泛函分析对发展随机泛函分析的空间随机化途径的合理性与优越性作了进一步的分析。     

Cotorsion theories and splitters

Let be a subring of the rationals. We want to investigate self splitting -modules (that is . Following Schultz, we call such modules splitters. Free modules and torsion-free cotorsion modules are classical examples of splitters. Are there others? Answering an open problem posed by Schultz, we will show that there are more splitters, in fact we are able to prescribe their endomorphism -algebras with a free -module structure. As a by-product we are able to solve a problem of Salce, showing that all rational cotorsion theories have enough injectives and enough projectives. This is also basic for answering the flat-cover-conjecture.

     

Quasi-Whittaker modules over the conformal Galilei algebras

In this paper, we study quasi-Whittaker modules over the conformal Galilei algebras. We determine all quasi-Whittaker vectors and the simplicities of the universal quasi-Whittaker modules. For the reducible ones, we determine the corresponding simple quotient modules. Thus we classify all simple quasi-Whittaker modules for the conformal Galilei algebras.     

Memory estimation of inverse operators

We use methods of harmonic analysis and group representation theory to estimate the memory decay of the inverse operators in Banach spaces. The memory of the operators is defined using the notion of the Beurling spectrum. We obtain a general continuous non-commutative version of the celebrated Wiener's Tauberian Lemma with estimates of the “Fourier coefficients” of inverse operators. In particular, we generalize various estimates of the elements of the inverse matrices. The results are illustrated with a variety of examples including integral and integro-differential operators.     

A note on quasi-Frobenius rings

It is shown that a semiperfect ring is quasi-Frobenius if and only if every closed submodule of is non-small, where denotes the direct sum of copies of the right -module and is the first infinite ordinal.

     

On the Szegő–Radon projection of monogenic functions

We define a version of the Radon transform for monogenic functions which is based on Szegő kernels. The corresponding Szegő–Radon projection is abstractly defined as the orthogonal projection of a Hilbert module of left monogenic functions onto a suitable closed submodule of functions depending only on two variables. We also establish the inversion formula based on the dual transform.     

完备随机内积模上稠定模同态的共轭算子

对定义在完备随机内积模的稠子模上的模同态引入了共轭算子的概念并讨论其基本性质,尤其证明了共轭算子的闭性.