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关键词： Queueing theory   Congestion   Mathematical analysis   MATLAB   Queue  

摘要： We discuss various aspects of phase service queueingmodels. A large number of models have been developed in the area of queueing theory incorporating the concept of phase service. These phase service queueing models have been investigated for resolving the congestion problems of many day-to-day as well as industrial scenarios. In this survey paper, an attempt has been made to review the work done by the prominent researchers on the phase service queues and their applications in several realistic queueing situations. The methodology used by several researchers for solving various phase service queueing models has also been described. We have classified the related literature based on modeling and methodological concepts. The main objective of present paper is to provide relevant information to the system analysts, managers, and industry people who are interested in using queueing theory to model congestion problems wherein the phase type services are prevalent.

关键词： 数学分析   初中数学   微积分  

摘要： 在整个数学体系中,数学分析有着相当重要的作用,数学分析将极限、导数和微积分有机地结合起来,并发展到应用于其他科学,为其他科学的研究提供一种想法。本文着重探讨数学分析这种思想在初中数学的应用。

关键词： Extended trial equation method   Generalized benjamin equation   Generalized burger-kdv equation  

摘要： In this paper, using the Extended Trial Equation (ETEM), we get new traveling wave solutions of the Generalized Benjamin, the Generalized Burger-Kdv Equations (GBE, GBKE). The obtained solutions not only constitute a novel analytical viewpoint in nonlinear complex phenomena, but they also form a new stand alone basis from which physical applications in this arena can be comprehended further, and moreover investigated. Furthermore, to concretely enrich this research production, we provide illustrative, Mathematica Release 7 based, 3D graphics of the gotten solutions, with well chosen, yet structure revealing parameters. © 2013 .

关键词： Bioreactors   Cell growth   Mathematical modelling   Membrane bioreactor   Reaction engineering   Wastewater treatment  

摘要： The activated sludge process is widely used to treat domestic and industrial wastewater. A significant drawback of this process is the production of sludge, the disposal of which can comprise a significant proportion of the total operating costs of a wastewater treatment plant. We analyze the steady-state operation of a membrane bioreactor system (MBR) incorporating a sludge disintegration unit (SDU) to reduce sludge production. We provide a qualitative understanding of the model by finding analytically the steady-state solutions of the model and determining its stability as a function of the residence time. In practice a target value of the mixed liquor suspended solids (MLSS) content within the membrane reactor is specified. Applying the mathematical technique of singularity theory we show that if the sludge disintegration factor is sufficiently high then the MLSS content is guaranteed to be below the target value. This model prediction, of key interest from a practical perspective, was not identified in the original investigation of this model, which relied upon numerical integration of the governing equations.

关键词： accelerated molecular dynamics   temperature accelerated dynamics   Langevin dynamics   stochastic dynamics   metastability   quasi-stationary distributions   kinetic Monte Carlo  

摘要： We give a mathematical framework for temperature accelerated dynamics (TAD), an algorithm proposed by Sorensen and Voter in [J. Chem. Phys., 112 (2000), pp. 9599-9606] to efficiently generate metastable stochastic dynamics. Using the notion of quasi-stationary distributions, we propose some modifications to TAD. Then considering the modified algorithm in an idealized setting, we show how TAD can be made mathematically rigorous.

关键词： 高等教育   题解   数学分析  

ISBN: (纸本)9787560856193

摘要： 本书是编者30余年数学分析教学和考研辅导的经验总结。全书共选入600多个例题和200多个课后习题，它们基本上都是近年来国内各高校数学专业招收硕士研究生时的入学试题，涵盖了数学分析考研大纲要求的所有内容。

关键词： 塔桅   平衡方程   非线性分析   数学分析   单管塔   钢桅杆   软件   切线刚度   整体空间   动力分析法   钢塔架   二阶效应   线性静力分析  

摘要： 软件简介在大量工程实践的基础上,同济大学高耸结构研究室开发了钢塔桅设计系列软件MWT,MAST和SPT。MWT适用于多边形的钢塔架设计,按整体空间析架法进行结构静力分析及结构动力分析。MAST适用于三边形或四边形的结构式钢桅杆设计,采用简化动力分析法形成多质点弹性支座直立式计算模型对桅杆进行模态分析;采用基于修正的总体拉格朗日坐标描述法推导的空间索、杆单元大位移刚度矩阵,对桅杆进行非线性静力分析。SPT适用于单管通信塔设计,采用基于切线刚度的增量平衡方程对单管塔进行非线性分析,充分考虑了单管塔二阶效应。

关键词： 初中   数学   数学分析   微积分   三角函数  

摘要： 中学数学教学中关于数学课程知识点的掌握,一般会通过定义、运算法则、定理及公式等的掌握进行数学分析式教学。其中,数学分析应用在教学中通常比较抽象,难于理解。特别是数学分析教学中,基本都会涉及到一元函数微积分、证明不等式等教学内容。因此,为了让学生在逻辑推理、数形结合、语言表达等方面展现出良好的数学分析能力,在初中数学实践教学中应对数学分析予以高度重视。

关键词： HYBRID systems   DYNAMICAL systems   PREDATION (Biology)   VIRAL replication   MATHEMATICAL models   EPIDEMIOLOGY  

摘要： We consider an epidemic-species hybrid dynamical system. The disease is spread among the prey only and the infected prey can reproduce virus. The predator only eats the infected prey. Mathematical analyses are given for the system with regard to the existence of equilibria, local stability, Hopf bifurcation, and the orbital stability of the Hopf bifurcating limit cycle. We further analyse the system under impulsive releasing of virus and predator.

关键词： 数控车削   数控编程   二次曲线   数学分析   加工效率  

摘要： 数控编程是数控加工技术中的关键部分。编程的质量和效率是提高加工精度和生产效率的主要措施之一。本文中首先通过对比宏程序与CAD/CAM编程两者的优缺点，证明了宏程序的优势所在。其次又以实际生产零件为案例，详细分析了如何通过精度计算加工二次曲线类工件。然后分别编写了宏加工程序，最后以综合件的形式综合了各类二次曲线通过工艺编排、精度计算、宏程序编制、仿真加工、实际加工等充分证明了宏程序的优势。　　研究表明：　　(1)通过对各类二次曲线进行了数学分析和演算，并结合圆、正椭圆、斜椭圆、双曲线等相关例子介绍了具体的编程方法。为宏程序的使用和推广普及提供了初步的理论基础和编程源程序借鉴。　　(2)本文结合典型零件，通过精度计算，合理的编写了宏程序并利用宇龙仿真软件进行了验证。同时使用 CAXA数控车编程软件自动生成了加工程序，对两者进行了比对和相关分析，验证和证明了宏程序的优点。同时在研究和应用宏程序方面，有以下两点小结：　　①二次曲线的粗加工完全可以应用宏程序进行。　　②可通过精度计算使宏程序有效地控制加工精度。