紧拓扑半群上概率测度卷积序列的极限性质

本文讨论紧拓扑半群上概率测度卷积序列的若干重要极限性质．在第１节中，我们讨论测度集的代数结构与其支撑集代数结构的关系．第２节的定理１，通过支撑集的代数结构给出组合收敛测度序列的一个极限定理．在定理２中我们讨论独立同分布时的情形，建立了一类紧半群上的Ｋａｗａｄａ－Ｉｔ型结果．这些定理推广了紧群、紧交换半群、紧Ｌ－Ｘ半群上一些相应的结论．     

上单调部分单位半群

某些类型的抽象拓扑单位半群的理论是研究概率论中某些具体半群的结构的有力工具。本文用序列条件代替拓扑条件，用部分单位半群，而定义了上单调部分单位半群和上单调Ｄｅｌｐｈｉｃ部分单位半群，证明它们在类似于Ｄｅｌｐｈｉｃ半群的某些性质，且应用这些结果于测度环理论的研究。     

Г—纯整半群

印度数学家Ｍ．Ｋ． Ｓｅｎ和Ｍ．Ｋ．Ｓａｈａ在１９８６年给出了Г－半群的概念和讨论了Г－半群的若干性质。本文引入了Г－正则半群和Г－纯整半群的概念。     

Γ-纯整半群

印度数学家Ｍ．Ｋ．Ｓｅｎ和Ｍ．Ｋ．Ｓａｈａ在１９８６年给出了Γ－半群的概念和讨论了Γ－半群的若干性质．本文引入了Γ－正则半群和Γ－纯整半群的概念．并讨论了这两种重要的Γ－半群类的若干特性，最后通过三个有趣的实例说明了纯整Γ－半群类和Γ－纯整半群类是互不包合的及交是非空的．     

U-纯正半群

型彬半群是正则半群类中纯正半群的一个自然推广．这类半群最先由E1-Qallali和Fountain研究．本文定义了U-纯正半群．这类半群是纯正半群和型W半群二者在U-半富足半群类中的一个共同推广．首先我们确定了U-纯正半群上包含在关系HU中的最小允许同余．借此,证明了半群S为U-纯正半群,当且仅当S可以表示为一个Hall半群和一个V—ample半群的织积．这一结果不仅推广了关于纯正半群结构的著名Hall—Yamada定理,而且推广了E1-Qallali和Fountain建立的型W半群的结构定理．     

右Clifford左商半群

本文讨论了右Ｃｌｉｆｆｏｒｄ左商半群．利用所谓的可适对刻划了右Ｃｌｉｆｆｏｒｄ半群中的左次半群,因此扩展了商半群的研究范围．     

双格半群

本文给出格半群上对偶同构、双格半群、ST-格半群等概念,讨论了格上半群构成格群的几组充要条件,从而解决了格在什么情况下具有格群结构这一至今未解决的问题.同时研究了ST-格半群等的一些性质、指出格群类是双格半群类的一个真子类.     

局部紧拓扑半群上概率测度卷积幂的若干极限定理

我们通过研究极限测度的不变性质，讨论了局部紧拓扑半群上概率测度卷积幂的若干极限性状．推广了[1]－[3]中的若干结果．     

半群上Rees矩阵半群的半格的结构

推广了Ｍ．Ｐｅｔｒｉｃｈ在文［１］中所用的方法，得到了幺半群上Ｒｅｅｓ矩阵半群的半格的一个结构定理．研究了单幂幺半群上Ｒｅｅｓ矩阵半群的半格的性质并给出了矩形单幂幺半群的半格的若干等价刻划．     

一类abundant半群的构造

本文讨论ａｂｕｎｄａｎｔ半群上中间幂等元的性质，研究具有正规中间幂等元的ｑｕａｓｉ－ａｄｅｑｕａｔｅ半群及若干极端情形，并分别给出各类半群的构造．     

Designing a call center with an IVR (Interactive Voice Response)

A call center is a service operation that caters to customer needs via the telephone. Call centers typically consist of agents that serve customers, telephone lines, an Interactive Voice Response (IVR) unit, and a switch that routes calls to agents. In this paper we study a Markovian model for a call center with an IVR. We calculate operational performance measures, such as the probability for a busy signal and the average wait time for an agent. Exact calculations of these measures are cumbersome and they lack insight. We thus approximate the measures in an asymptotic regime known as QED (Quality and Efficiency Driven) or the Halfin–Whitt regime, which accommodates moderate to large call centers. The approximations are both insightful and easy to apply (for up to 1000’s of agents). They yield, as special cases, known and novel approximations for the M/M/N/N (Erlang-B), M/M/S (Erlang-C) and M/M/S/N queue.     

THE RANDOM BATCH METHOD FOR N-BODY QUANTUM DYNAMICS

This paper discusses a numerical method for computing the evolution of large inter-acting system of quantum particles.The idea of the random batch method is to replace the total interaction of each particle with the N-1 other particles by the interaction with p ＜＜ N particles chosen at random at each time step,multiplied by (N-1)/p.This re-duces the computational cost of computing the interaction potential per time step from O(N2) to O(N).For simplicity,we consider only in this work the case p =1 — in other words,we assume that N is even,and that at each time step,the N particles are orga-nized in N/2 pairs,with a random reshuffling of the pairs at the beginning of each time step.We obtain a convergence estimate for the Wigner transform of the single-particle reduced density matrix of the particle system at time t that is both uniform in N ＞ 1 and independent of the Planck constant h.The key idea is to use a new type of distance on the set of quantum states that is reminiscent of the Wasserstein distance of exponent 1 (or Monge-Kantorovich-Rubinstein distance) on the set of Borel probability measures on Rd used in the context of optimal transport.     

Theorems on convergence of stochastic integrals distributions to signed measures and local limit theorems for large deviations

We study properties of symmetric stable measures with index α > 2, α ≠ 2m, m ? \mathbbN m \in \mathbb{N} . Such measures are signed ones, and hence they are not probability measures. For this class of measures, we construct an analogue of the Lévy–Khinchin representation. We show that, in some sense, these signed measures are limit measures for sums of independent random variables. Bibliography: 11 titles.     

Controllability for some integrodifferential equations driven by vector measures

In this work, we consider the question of controllability of a class of integrodifferential equations on Hilbert space with measures as controls. We assume that the linear part has a resolvent operator in the sense given by R. Grimmer. We generalize the original work of N. Ahmed on vector measures, and we use it to develop necessary and sufficient conditions for weak and the exact controllability of the integrodifferential equation. Using the latter, we prove that exact controllability of the integrodifferential equation implies exact controllability of a perturbed integrodifferential equation. Controllability problem for the perturbed system is formulated fixed point problem in the space of vector measures. Our results cover impulsive controls as well as regular controls. Copyright © 2016 John Wiley & Sons, Ltd.     

Stability Properties for Feynman’s Operational Calculus in the Combined Continuous/Discrete Setting

We establish some stability theorems for Feynman’s operational calculus in the setting where the time-ordering measures are allowed to have both continuous and discrete parts. In particular, we investigate stability in a number of special cases of this blended approach to the operational calculus.Mathematics Subject Classifications (2000) Primary: 46J15, 47A56, 47A60, 60B10; secondary: 46N50, 47N50.     

截超泊松排队:具有阻碍、放弃和不同服务员H_k/M/2/N系统(英文)

本文讨论具有阻碍、放弃，不同服务员Ｋｋ／Ｍ／２／Ｎ排队系统的解析解．对经典的一种先入先出的修改排队规则在较一般的条件下被采用了，得到了稳态概率和一些有效度量的显式．一些特殊情况也被化简了。     

基于排队模型的电动汽车充电桩数量优化设计

通过对电动汽车充电行为的分析,采用顾客带有不耐烦和止步行为的有限容量M/M/C/N排队模型对充电场所充电服务系统进行建模.通过求解模型的平衡方程,获得系统稳态下的队长分布及其它多项性能指标.以系统性能指标为基础,从经济效益与社会效益的角度提出了充电服务系统优化设计的目标函数,并通过数字例子对优化模型进行了说明.分析了模型参数对系统充电桩最优配置数的影响,从中可看出,系统容量、顾客的不耐烦率及顾客的止步概率等参数对充电桩数量的优化设计都会产生不可忽视的影响.     

Addendum to: Comparison between different types of abstract integrals in riesz spaces

In [3] we did not give explicitly the definition of measurability for realvalued functions, with respect to finitely additive measures with values in a Dedekind complete Riesz space. We note that, in [3], all involved functions are intended to be measurable. We now report the definition of measurability, which we gave in [2] (Definition 3.2). Lavoro svolto nell’ ambito dello G.N.A.F.A. del C.N.R.     

A concentration inequality and a local law for the sum of two random matrices

Let ${H_{N}=A_{N}+U_{N}B_{N}U_{N}^{\ast}}$ where A _N and B _N are two N-by-N Hermitian matrices and U _N is a Haar-distributed random unitary matrix, and let ${\mu _{H_{N}},}$ ${\mu_{A_{N}}, \mu _{B_{N}}}$ be empirical measures of eigenvalues of matrices H _N , A _N , and B _N , respectively. Then, it is known (see Pastur and Vasilchuk in Commun Math Phys 214:249?C286, 2000) that for large N, the measure ${\mu _{H_{N}}}$ is close to the free convolution of measures ${\mu _{A_{N}}}$ and ${\mu _{B_{N}}}$ , where the free convolution is a non-linear operation on probability measures. The large deviations of the cumulative distribution function of ${\mu _{H_{N}}}$ from its expectation have been studied by Chatterjee (J Funct Anal 245:379?C389, 2007). In this paper we improve Chatterjee??s concentration inequality and show that it holds with the rate which is quadratic in N. In addition, we prove a local law for eigenvalues of ${H_{N_{N}},}$ by showing that the normalized number of eigenvalues in an interval approaches the density of the free convolution of??? _A and??? _B provided that the interval has width (log N)^?1/2.