On the identification of Wiener-Hopf factors

This note is concerned with the identification of the Wiener-Hopf factors of a function 1–f, wheref generates an aperiodic distribution on the integers with a negative mean. The general and rational cases are addressed. We give a concise summary of the main practical facts needed for calculations involving the Wiener-Hopf factors. The basic facts are cited from the literature, but a few aspects are briefly proven here.Supported by the European grant BRA-QMIPS of CEC DG XIII.     

关于序列覆盖s映射

本文定义了两类序列覆盖映射，讨论了度晴空间的序列覆盖ｓ映象，特别地，我们证明了空间Ｘ具有点可数弱当且仅当Ｘ是度量空间的１序列覆盖的商ｓ映象，这回答了１９７０年Ｔ．Ｈｏｓｈｉｎａ提出了一个问题。     

无限维空间中的实零点定理

在本文中，我们建立了无限维空间中的实零点定理，同时从仿射空间的拓扑结构和域的序结构两个方面，分别刻划了适合无限维实零点定理的序域．此外，本文有例子表明，对任意的基数α，确实存在适合α维实零点定理的序域．     

Ideal version of Egorov's theorem for analytic P-ideals

We introduce the notion of equi-ideal convergence and use it to prove an ideal variant of Egorov's theorem. We also show that this variant usually cannot be strengthen to a direct analogue of Egorov's theorem.     

RANK t ℋ-PRIMES IN QUANTUM MATRICES

ABSTRACT

Let 𝕂 be a (commutative) field and consider a nonzero element q in 𝕂 that is not a root of unity. Goodearl and Lenagan (2002 Goodearl , K. R. , Lenagan , T. H. ( 2002 ). Prime ideals invariant under winding automorphisms in quantum matrices . Internat. J. Math 13 : 497 – 532 . [CROSSREF]  [Google Scholar]) have shown that the number of ?-primes in R = O _q (? _n (𝕂)) that contain all (t + 1) × (t + 1) quantum minors but not all t × t quantum minors is a perfect square. The aim of this paper is to make precise their result: we prove that this number is equal to (t!) ² S(n + 1, t + 1)2, where S(n + 1, t + 1) denotes the Stirling number of the second kind associated to n + 1 and t + 1. This result was conjectured by Goodearl, Lenagan, and McCammond. The proof involves some closed formulas for the poly-Bernoulli numbers that were established by Kaneko (1997 Kaneko , M. ( 1997 ). Poly-Bernoulli numbers . J. Théorie Nombres Bordeaux 9 : 221 – 228 . [Google Scholar]) and Arakawa and Kaneko (1999 Arakawa , T. , Kaneko , M. ( 1999 ). On poly-Bernoulli numbers . Comment Math. Univ. St. Paul 48 ( 2 ): 159 – 167 . [Google Scholar]).     

On residually ideals and projective dimension one modules

We prove that certain modules are faithful. This enables us to draw consequences about the reduction number and the integral closure of some classes of ideals.

     

结构动力重分析的子结构有理逼近

在基于子结构灵敏度综合的结构动力重分析方法的基础上,应用向量值函数有理逼近,提出了一种新的结构动力重分析方法。子结构方法的应用,有效减少了结构自由度数目,达到了减少计算量的目的。将向量值函数有理逼近应用于截断的Taylor级数,提高了计算精度,扩大了收敛范围,适用于结构作大修改的情形。数值算例表明,所提出的方法对结构参数发生大修改能够有效降低Taylor级数截断的误差,给出高精度的逼近结果。     

MODAL SYNTHESIS METHOD FOR NORM COMPUTATION OF H∞ DECENTRALIZED CONTROL SYSTEMS (Ⅱ)

When using H ∞ techniques to design decentralized controllers for large systems,the whole system is divided into subsystems, which are analysed using H∞ control theory before being recombined. An analogy was established with substructural analysis in structural mechanics, in which H ∞ decentralized control theory corresponds to substructural modal synthesis theory so that the optimal H ∞ norm of the whole system corresponds to the fundamental vibration frequency of the whole structure. Hence, modal synthesis methodology and the extended Wittrick-Williams algorithm were transplanted from structural mechanics to compute the optimal H∞ norm of the control system. The orthogonality and the expansion theorem of eigenfunctions of the subsystems H∞ control are presented in part (Ⅰ)of the paper. The modal synthesis method for computation of the optimal H ∞ norm of decentralized control systems and numerical examples are presented in part (Ⅱ).