粗糙子群和粗糙子环

文[1]研究了半群中的理想,首次提出了粗半群和粗理想的概念.本文继续研究了群中的粗糙子群和粗正规子群.同时,在环中引入了粗子环的概念.最后,研究了粗糙集的同态问题.     

粗糙集的拓扑基础

为了进一步研究粗糙集及其应用,本文介绍了一种关于粗糙集的新理论,即粗糙集的基本拓扑理论.主要研究了粗糙集的拓扑空间及其性质等.给出了一些新的定义和定理.并对未来的研究给予展望.     

树指标马氏链的等价定义

国内外关于树指标随机过程的研究已经取得了一定的成果.Benjamini和Peres首先给出了树指标马氏链的定义.Berger和叶中行研究了齐次树图上平稳随机场熵率的存在性.杨卫国与刘文研究了树上马氏场的强大数定律与渐近均分性.杨卫国又研究了一般树指标马氏链的强大数定律.为了以后更有效的研究树指标随机过程的一系列相关问题,本文在分析研究前人成果的基础上,给出了树指标马氏链的等价定义,并用数学归纳法证明了其等价性.     

半群的区间值反模糊子半群的性质

作为模糊代数的一个研究领域,区间值模糊子半群对模糊子半群的研究至关重要.引入了半群的区间值反模糊子半群的概念,对区间值反模糊子半群的性质进行了研究.讨论了半群的区间值反模糊子半群关于并运算的封闭性质.最后给出了半群的区间值模糊子半群的同态像和原像的相关性质.相关的研究结果丰富了半群的模糊理论.     

工程项目调度技术研究综述

研究了工程项目调度技术和求解算法的发展历程.首先概述了项目调度技术,并对近年来项目调度问题种类和算法的研究进行总结.最后就项目调度技术的新研究方向和应用作了简要探讨.     

2016年全国研究生数学建模竞赛E题赛题点评

首先阐明了2016年全国研究生数学建模竞赛E题"粮食最低收购价政策问题研究"的研究背景和问题研究的实际意义.接着,针对每一个问题,从研究思路、研究方法、研究结论等方面均作了详细的叙述.最后,对学生论文中出现的问题、难点以及创新性等方面做了点评.     

2014年全国研究生数学建模竞赛D题赛题点评

首先阐明了2014年全国研究生数学建模竞赛D题"人体营养健康角度的中国果蔬发展战略研究"的研究背景.接着,针对每一个问题,从研究思路、研究方法、研究结论等方面均作了叙述.最后,对学生论文出现的问题、难点以及创新性等方面均做了点评.     

具Michaelis-Menten型收获的Leslie-Gower捕食-食饵扩散模型的动力学和模式

该文研究了食饵具有Michaelis-Menten型收获的Leslie-Gower捕食-食饵扩散模型的动力学行为和稳态模式.首先证明了模型的一致持久性.其次研究了非负常数平衡解及其稳定性,分别利用Lyapunov函数和上下解两种方法证明得到了正常数平衡解全局渐近稳定的充分条件.最后利用度理论研究了稳态模式.研究结果表明:Michaelis-Menten型收项获对稳态模式的形成起着重要的作用,这与模型没有收获项的结果形成了鲜明的对比.     

Hardy空间上Fourier级数的Cesaro求和

研究了Hardy空间上Cesaro 算子的有界性.证明极大Cesaro算子的强型和弱型有界估计.其弱有界性估计是精确的.推广和加强了已有研究结果.     

Jeffrey流体流过有限长圆柱管时磁流体动力学的蠕动流

研究Jeffrey流体流过有限长管道时的蠕动流.在外加磁场作用时,流体呈导电性.分析是在长波长和低Reynolds数近似假设下完成.得到了压力梯度、体积流量、平均体积流量和局部壁面剪应力的表达式.研究了松弛时间、延迟时间和Hartman数,对压力、局部壁面剪应力以及蠕动泵机械效率的影响.还研究了回流现象,调查了沿管道壁波数非整倍数时的传播情况,研究有限长管道传播的内在特性.     

Hereditary crossed products

We characterize when a crossed product order over a maximal order in a central simple algebra by a finite group is hereditary. We need only concentrate on the cases when the group acts as inner automorphisms and when the group acts as outer automorphisms. When the group acts as inner automorphisms, the classical group algebra result holds for crossed products as well; that is, the crossed product is hereditary if and only if the order of the group is a unit in the ring. When the group is acting as outer automorphisms, every crossed product order is hereditary, regardless of whether the order of the group is a unit in the ring.

     

Long-term inventory policy-making through fuzzy decision-making models

The inventory policy, meant as a replenishment rule, has a considerable impact on most firms. The paper considers the determination of optimal inventory policy of firms from a global viewpoint of top management. The inventory is represented as a fuzzy system with the fuzzy inventory level as the output, the fuzzy replenishment as the input and fuzzy demand. The control problem is formulated in terms of decision-making in a fuzzy environment with fuzzy constraints imposed on replenishments, a fuzzy goal for preferable inventory levels to be attained and the fuzzy decision as the intersection of fuzzy constraints and the fuzzy goal at subsequent stages. The planning horizon is infinite. The problem is to find an optimal time-invariant strategy relating the optimal replenishments to the current inventory levels, maximizing the membership function of fuzzy decision. The existence of such a strategy is proved and an algorithm for its determination is given. The optimal time-invariant strategy obtained is represented as a fuzzy conditional statement equated with a fuzzy relation which is the firm's optimal fuzzy replenishment rule.     

关于集值优化问题的若干结果

引入了集值集值C-τ-半预不变凸概念，证明了集值集值C-τ-半预不变凸优化问题的局部弱有效元是弱有效元，给出了集值预不变凸变分不等式作为集值C-τ-半预不变凸优化问题的充分条件和必要条件，这些结果推广了文[1-4]的相应结果。     

Modeling and SPM-dependent control of multi-rate networked control system with long time delay

In this paper, an efficient approach of modeling and control is presented for Multi-Rate Networked Control System (MRNCS) with considering long time delay. Firstly, the system is modeled as a switched system with a random switching signal which is subject to random networked-induced delay. For this, time delay is defined as a Markov chain and the model of MRNCS is obtained as a Markovian jump linear system. Afterward, a dynamic output feedback controller is designed for output tracking as well as stabilization of closed-loop system. The modeling and control of MRNCS are presented for two structures. At first, a new model of single-side MRNCS is proposed and a mode-independent controller is designed for stabilizing the system. Then the proposed modeling method is generalized to double-side MRNCS and by introducing the Set of Possible Modes (SPM) concept, an SPM-dependent controller is proposed for double-side MRNCS. To show the effectiveness of the proposed methods, some numerical results are provided on the quadruple-tank process.     

Optimal design of multi-purpose beam-columns

The paper deals with the optimal design of an elastic pinended member of given volume that is to serve as a beam for a part of its design life and as a column for the rest. The optimal design can be interpreted in two ways. Firstly, it is the design that has the maximum Euler buckling load in column action, subject to a prescribed maximum deflection as a beam. Secondly, it is the design that has the least deflection as a beam under a midspan concentrated load, subject to a minimum permissible Euler buckling load in column action. The effectiveness of the optimal design is judged by comparing it with a prismatic bar of the same volume.     

Subspaces and quotients of Banach spaces with shrinking unconditional bases

The main result is that a separable Banach space with the weak* unconditional tree property is isomorphic to a subspace as well as a quotient of a Banach space with a shrinking unconditional basis. A consequence of this is that a Banach space is isomorphic to a subspace of a space with a shrinking unconditional basis if and only if it is isomorphic to a quotient of a space with a shrinking unconditional basis, which solves a problem dating to the 1970s. The proof of the main result also yields that a uniformly convex space with the unconditional tree property is isomorphic to a subspace as well as a quotient of a uniformly convex space with an unconditional finite dimensional decomposition.     

A bivariate non-homogeneous birth and death model for predator–prey interactions

We propose a bivariate non-homogeneous birth and death process as a model for predator–prey interactions. Its expectation is periodic, as it is a solution to the classical Lotka–Volterra system. Moreover, the mean age at extinction, as defined in Kendall (1948), is infinite.     

Optimal Release Times in Single-Stage Manufacturing Systems with Blocking: Optimal Control Perspective

This paper concerns a due-date matching problem in a single-stage manufacturing system. Given a finite sequence of jobs and their service order, and given the delivery due date of each job, the problem is to choose the jobs release (arrival) times so as to match as closely as possible their completion times to their respective due dates. The system is modelled as a deterministic single-server FIFO queue with an output buffer for storing jobs whose service is completed prior to their due dates. The output buffer has a finite capacity; when it is full, the server is being blocked. Associated with each job there is a convex cost function penalizing its earliness as well as tardiness. The due-date matching problem is cast as an optimal control problem, whose objective is to minimize the sum of the above cost functions by the choice of the jobs arrival (release) times. Time-box upper-bound and lower-bound constraints are imposed on the jobs output (delivery) times. The optimal-control setting brings to bear on the development of fast and efficient algorithms having intuitive geometric appeal and potential for online implementation.Communicated by W. B. GongResearch supported in part by the National Science Foundation under Grant ECS-9979693 and by the Georgia Tech Manufacturing Research Center under Grant B01-D06.     

Bayesian variable selection in generalized linear models using a combination of stochastic optimization methods

In this paper the usage of a stochastic optimization algorithm as a model search tool is proposed for the Bayesian variable selection problem in generalized linear models. Combining aspects of three well known stochastic optimization algorithms, namely, simulated annealing, genetic algorithm and tabu search, a powerful model search algorithm is produced. After choosing suitable priors, the posterior model probability is used as a criterion function for the algorithm; in cases when it is not analytically tractable Laplace approximation is used. The proposed algorithm is illustrated on normal linear and logistic regression models, for simulated and real-life examples, and it is shown that, with a very low computational cost, it achieves improved performance when compared with popular MCMC algorithms, such as the MCMC model composition, as well as with “vanilla” versions of simulated annealing, genetic algorithm and tabu search.