无限级Dirichlet级数

本文研究了右半平面上无限级的Ｄｉｒｉｃｈｌｅｔ级数及随机Ｄｉｒｉｃｈｌｅｔ级数．这里我们给出一个较宽的系数条件,并证明在一定意义上是最好的;计算无限级Ｄｉｒｉｃｈｌｅｔ级数的精确级;把随机级数的研究引向一般得多的非同分布情况,并得到右半平面上非同分布的无限级随机Ｄｉｒｉｃｈｌｅｔ级数几乎必然（ａ．ｓ．）以虚轴上的每一点为没有有限例外值的Ｂｏｒｅｌ点的结论．     

半平面上随机Dirichlet级数的增长性

在较弱的系数条件下证明了右半平面上Dirichlet级数增长性定理,并应用到随机Dirich- let级数上去,得到了在一定条件下,两类级数a.s.有相同的增长级,从而推广和改良一系列定理,使相关问题的研究变得方便简洁．     

平面上随机级数的性质

研究了平面上系数{Xn,n≥0}为(?)-混合序列在满足,(q>1)等条件下的随机级数的增长性及值分布,得到了比较好的结果．     

简化原理及其应用

本文定量地阐明了简化原理。应用该原理,可以将许多以Rademacher序列为系数的随机Taylor级数和随机Dirichlet级数的结果推广到一般的具有独立对称分布系数的级数。本文特别讨论了Gauss系数的情形。 这些应用还包括:随机级数的收敛性,由该级数所定义的随机解析函数或随机整函数的值分布与增长性等。     

简化原理在Hilbert空间与可分Banach空间的一些应用

本文研究了简化原理在Hilbert空间与可分Banach空间中的一些应用,利用简化原理和独立随机元收敛准则获得了中分Banach空间随机级数的收缩原理和B-值随机Dirichlet级数简单收敛横坐标及一般随机整函数的增长性和值分布,将许多以Rademacher序列为系数的随机Tayor级数和随机Dirichlet级数的相关结果,推广到一般的具有独立对称分布系数的随机级数上去。     

右半平面无限级随机Dirichlet级数值的分布

该文主要研究了右半平面无限级随机Dirichlet级数值的分布.首先,在较宽的系数条件下证明了右半平面随机Dirichlet级数增长性和值的分布定理.其次,研究了系数的模为两两NQD列的随机Dirichlet级数的性质,得到与独立随机序列类似的结果.在一定的条件下,右半平面上随机级数Σ∞n=0X_ne~(-λ_ns)与级数Σ∞n=0σ_ne~(-λ_ns)a.s.有相同的收敛横坐标、增长级和型函数.     

半平面上随机Dirichlet 级数的增长性

在较弱的系数条件下证明了右半平面上Dirichlet级数增长性定理,并应用到随机Dirichlet级数上去,得到了在一定条件下,两类级数a.s.有相同的增长级,从而推广和改良一系列定理,使相关问题的研究变得方便简洁.     

随机Taylor级数

该文对一般的随机变量序列及相当弱的系数条件研究了随机级数定义的整函数的奈望里纳特征函数，并证明了它是几乎必然无有限例外值的．     

关于具有拟单调系数的三角级数L1-收敛性的注记

假设三角级数的系数具有拟单调性，给出了级数按L^1[0，2π]中的范数收敛于其和函数的一个判别条件，推广了文献中的有关结果．     

正弦级数L1- 收敛性确切条件的进一步研究和应用

已经对正弦级数的系数建立了一个本质上无法再推广的确切条件(对数有界变差条件) 保证其L¹- 收敛性成立. 然而, 一般来说, “全局性” 的条件在实际中是比较难以应用的. 本文进一步将条件推广到“分段性” 条件, 建立了正弦级数L¹- 收敛性的完整结果, 其重要意义在于: 第一, “全局性” 的对数有界变差条件是对单调递减条件的推广, 而本文中建立的“分段性” 的对数有界变差条件在每段中既可以推广单调递减条件, 还可以容纳单调递增条件; 第二, 可以允许所讨论的正弦级数的系数分段改变符号, 而全局性的条件要求系数不能变号; 第三, 可以允许所讨论的正弦级数的部分系数为零, 而这也是全局性的条件所无法做到的; 第四, 可用来实际构造可积的正弦级数, 这是全局性的条件比较难以做到的.     

系数的模为两两NQD序列的随机幂级数的增长性

本文研究了系数的模为两两NQD序列的B-值随机幂级数的增长性.利用两两NQD列推广的Borel-Cantelli引理及其它极限定理，在给定条件下得出其增长级和非随机幂级数的增长级有类似的性质.     

Tannaka-Krein duality for compact groupoids I, Representation theory

In a series of papers, we have shown that from the representation theory of a compact groupoid one can reconstruct the groupoid using the procedure similar to the Tannaka-Krein duality for compact groups. In this part we study continuous representations of compact groupoids. We show that irreducible representations have finite dimensional fibres. We prove Schur's lemma and Peter-Weyl theorem for compact groupoids.     

Extensions of the well-poised and elliptic well-poised Bailey lemma

We establish a number of extensions of the well-poised Bailey lemma and elliptic well-poised Bailey lemma. As application we prove some new transformation formulae for basic and elliptic hyper-geometric series, and embed some recent identities of Andrews, Berkovich and Spiridonov in a well-poised Bailey tree.     

Total positivity for loop groups II: Chevalley generators

This is the second in a series of papers developing a theory of total positivity for loop groups. In this paper, we study infinite products of Chevalley generators. We show that the combinatorics of infinite reduced words underlies the theory, and develop the formalism of infinite sequences of braid moves, called a braid limit. We relate this to a partial order, called the limit weak order, on infinite reduced words. The limit semigroup generated by Chevalley generators has a transfinite structure. We prove a form of unique factorization for its elements, in effect reducing their study to infinite products which have the order structure of ?. For the latter infinite products, we show that one always has a factorization which matches an infinite Coxeter element. One of the technical tools we employ is a totally positive exchange lemma which appears to be of independent interest. This result states that the exchange lemma (in the context of Coxeter groups) is compatible with total positivity in the form of certain inequalities.     

Schmitt-Vogel type lemma for reductions

The lemma given by Schmitt and Vogel is an important tool in the study of the arithmetical rank of squarefree monomial ideals. In this paper, we give a Schmitt-Vogel type lemma for reductions as an analogous result.     

The blocking lemma and group incentive compatibility for matching with contracts

This paper considers a general class of two-sided many-to-one matching markets, so-called matching markets with contracts. We study the blocking lemma and group incentive compatibility for this class of matching markets. We first show that the blocking lemma for matching with contracts holds if hospitals’ choice functions satisfy substitutes and the law of aggregate demand. The blocking lemma for one-to-one matching (Gale and Sotomayor, 1985) and that for many-to-one matching (Martínez et al., 2010) are special cases of this result. Then, as an immediate consequence of the blocking lemma, we show that the doctor-optimal stable mechanism is group strategy-proof for doctors if hospitals’ choice functions satisfy substitutes and the law of aggregate demand. Hatfield and Kojima (2009) originally obtain this result by skillfully using the strategy-proofness of the doctor-optimal stable mechanism. In this paper we provide a different proof for the group incentive compatibility by applying the blocking lemma.     

多复变Pang-Zalcman引理及应用

单复变中的Pang-Zalcman引理是研究亚纯函数正规族问题的重要工具.本文将该引理推广至多复变全纯函数的情形.作为应用建立了多复变全纯函数族的正规定则，改进和推广了相关结果.     

The snail lemma in a pointed regular category

In this paper we explore the snail lemma in a pointed regular category. In particular, we show that under the presence of cokernels of kernels, the validity of the snail lemma is equivalent to subtractivity of the category. As a corollary, this gives that in the more restrictive context of a normal category the validity of the snail lemma is equivalent to the validity of the snake lemma.     

非对称的Lax—Milgram引理对非关联塑性的一个应用

在塑性势和屈服面的广泛假设下,研究了非关联塑性的某些性质.对强化材料,通过使用非对称的Lax-Milgram引理,证明了当强化参数A>‖(?)F/(?)σ‖(?)Q/(?)σ‖-<(?)F/(?)σ,(?)Q/(?)σ>时,应力位移增量分布的存在唯一性.     

Abel's lemma on summation by parts and basic hypergeometric series

Basic hypergeometric series identities are revisited systematically by means of Abel's lemma on summation by parts. Several new formulae and transformations are also established. The author is convinced that Abel's lemma on summation by parts is a natural choice in dealing with basic hypergeometric series.