复杂非线性系统的控制综合与动态分析

随着当代科学和技术的发展,复杂非线性系统和控制理论研究不断深入,应用领域不断扩大,已影响了科技和社会领域的许多方面.针对当今该领域的研究难点和重点,本文集中讨论了复杂非线性系统控制研究中的3个关键问题,包括非光滑系统控制、网络化系统控制、临界态分析与控制.一方面是对在相关研究领域中的部分科研成果做一个简要的总结;另一方面,想借此机会在自动化学会控制理论专业委员会成立50周年之际向专业委员会表示感谢和祝贺.     

Making Statistics Significant in a Short Course for Graduates with Widely-Varying Non-Statistical Backgrounds

With reference to a short compulsory module for MBA students, this paper discusses how, despite a range of pressures and an extraordinary range of student backgrounds, fears and motivations, it is possible to quickly facilitate understanding and confidence in handling data and basic statistics for graduates in business and associated workplaces. Links and contrasts with a variety of undergraduate teaching scenarios help to enrich teaching and learning strategies, and the strategies and materials developed through interaction with the range of MBA students are transferable to other postgraduate coursework situations. In particular, the need for understanding and confidence in handling data and its presentation, in considering categorical and simple continuous data, and in understanding correlation and association, are common across many different workplaces and applications.     

基于产品生命周期的闭环供应链定价和协调策略研究

研究产品生命周期条件下一个制造商、一个零售商组成的闭环供应链的定价和协调策略:制造商第一周期只生产新品,从第二周期开始生产再制造品,并负责回收。建立了两周期、多周期和无限周期下的分散决策模型和多周期下的集中决策模型,得到最优定价和生产策略。结果表明:两周期中,制造商和零售商应根据不同的成本节约额制定不同的批发价、零售价和生产量。多周期中,当成本节约额比较小时,除第一和最后一个周期外,制造商和零售商应采取相同的定价和生产策略;当成本节约额比较大时,除第一和最后两个周期外,制造商和零售商应采取相同的定价和生产策略。无限周期中,除第一周期以外,制造商和零售商都应该采取相同的定价和生产策略。在有限周期情况下,制造商和零售商应通过在前期制定比较低的批发价和零售价,以提高生产量和销售量,使得后期的回收量增大,达到降低成本的目的。通过引入收益共享契约制定合适的批发价和销售收入及再制造收益共享比率可以协调整个闭环供应链。算例验证了上述结论。     

中美微积分教材比较研究

微积分课程的教学对高校创新型人才的培养具有重要的作用,其教材建设受到普遍关注.本文以微积分教学方法和教学理念为主线,从教材内容和案例选取、教材结构顺序以及教材表述方式等不同的角度,分析了国内外部分优秀微积分教材所具备的特色.依此为基础,以中美两部具有代表性的微积分教材为比较对象,着重对两本教材在知识点衔接、新知识的引入方式以及提出问题、分析问题的构思方法和阐述方式等具体方面进行了较细致的对比,力图从中展示出中美高等教育在教学思想和表现形式上的某些不同之处,由此得到一些有益的启示.最后,文章列举了美国微积分教材,在语言表达风格、教学案例和习题设计以及教材配套服务等诸多方面值得借鉴的经验和方法.     

GAMM Annual Meeting – Dresden 2004 Overview of the Sessions

Volume 4 (2004) of PAMM “Proceedings in Applied Mathematics and Mechanics” assembles the contributions to the GAMM Annual Meeting 2004, held 21–27 March 2004 in Dresden, Germany. The contributions are grouped according to the minisymposia and sessions of the conference. Minisymposia Mathematics MA1 Stochastic programming in energy and process engineering MA2 Numerical problems of stochastic dynamical systems MA3 Adaptive FEM MA4 PDE‐constrained optimization / optimization with PDEs MA5 Epitactic growth MA6 Nonlinear eigenvalue problems Minisymposia Mechanics ME1 Thin viscous films ME2 Drop–surface interactions ME3 Developments in auditory mechanics ME4 Microstructure of materials and scale bridging modeling ME5 Mechanics of smart structures and materials ME6 Micromagnetism Sessions 1–24 1 Linear and nonlinear oscillations 2 Stability and control theory 3 Multibody systems and kinematics 4 Elastic and viscoelastic materials and systems 5 Plasticity: constitutive equations and applications 6 Theory of materials and modelling of materials 7 Damage and fracture 8 Computational mechanics 9 Experimental methods and identification 10 Gas dynamics and rarefied gases 11 Viscous flows 12 Transition and turbulence 13 Heat and mass transfer, convective flows 14 Multiphase flows, flows of reactive fluids 15 Waves, acoustics 16 Applied analysis 17 Mathematical methods of the natural sciences and engineering 18 Computer algebra and computer analysis 19 Applied stochastics, operations research 20 Optimization 21 Numerical analysis 22 Applied and numerical linear algebra 23 Numerical treatment of ordinary and algebro‐differential equations 24 Numerical treatment of partial differential equations     

The NCTM Process Standards and the Five Es of Science: Connecting Math and Science

This study investigates defining characteristics among the process standards of the Principles and Standards for School Mathematics and the 5 Es from the National Science Education Standards and the Inquiry and the National Science Education Standards. These characteristics are used to demonstrate similarities and differences between the learning of mathematics and science, discuss implications from such, and argue for the integration of mathematics and science curriculum and instruction.     

基于不同产品质量安全水平的企业生产决策优化及相应消费者效用

基于消费者对产品平均质量安全水平的预期不同,在企业可以同时选择生产高、低质量安全水平产品的条件下,分别建立了完全垄断与完全竞争市场中的企业利润最大化模型,比较分析了企业供给产品的数量、利润及相应的消费者效用,得出消费者质量安全水平敏感度、产品需求价格敏感度及产品的高、低质量安全水平对上述决策的影响.据此,结合我国国情,为中国产品质量安全水平的提升提供了参考与启示.     

京沪文化创意产业发展比较研究

北京市和上海市的文化创意产业发展迅速,已经成为支柱性产业.北京形成文化创意产业发展的"一核、一带、两轴、多中心"的空间发展格局,而上海则形成"一轴、一带、两河、多圈"的空间格局.北京以京派文化、首都文化等为基础,形成"3+3+X"的文化创意产业发展模式,而上海以沪派文化、国际经济中心等为基础,形成"5+3+3"的文化创意产业发展模式.北京市和上海市都已经通过多元投融资渠道,在园区发展模式上由自发型走向政府导向型模式.     

A 3D modeling of static and forward smoldering combustion in a packed bed of materials

A three-dimensional (3D) model based on the first principles of mass, momentum and energy was developed that numerically simulates the processes of static and forward smoldering in a porous packed bed of plant materials. The packed bed contains cellulose material or tobacco (cigarette) wrapped in a porous paper and surrounded by an ambient air. Other major characteristics of the model are including the effects of buoyancy forces in the flow field, separate treatment of solid and gas in a thermally non-equilibrium environment, and use of multi-precursor kinetic models for the pyrolysis of staring material and oxidation of char. The changes in porosity due to pyrolysis and char oxidation and the effect of porosity on the bed permeability and gas diffusivity are included. The mass, momentum, energy, and species transport equations are solved in a discretized computational domain using a commercially available computational fluid dynamics (CFD) code. The simulation results show that the model reasonably reproduces the major features of a burning cigarette during smoldering and puffing and are in a good agreement with the existing experimental results for cigarettes. Results include the velocity profiles, gas and solid temperatures, coal shape, burn rates, profile and transport of gas and vapor species throughout the packed bed, dilution through the wrapper paper and ventilation in the filter section, and the mass fraction of some pyrolysis and oxidation products in the mainstream and sidestream flows.     

A Longitudinal Look at Attitudes and Perceptions Related to the Integration of Mathematics,Science, and Technology Education

The purpose of this study is to provide an in‐depth analysis of attitudes and perceptions related to the integration of mathematics, science, and technology education of preservice teachers preparing to teach STEM disciplines. Longitudinal data by individual cohort and across 7 years of the Integrated Mathematics, Science, and Technology (MSAT) Program are reported, analyzed, and interpreted to help design and improve preservice teacher education programs and improve teaching and learning in STEM classrooms. Results of quantitative analyses indicate that there was generally no change in preservice teacher attitudes and perceptions related to the value of the integration of mathematics, science, and technology education—they clearly valued integration at the onset and at the completion of the program. However, there was a significant change in preservice teacher attitudes and perceptions related to integration feasibility in terms of inefficiency and difficulty. Implications for teacher education programs include: (a) more exposure to concepts, processes, and skills in STEM that are similar, analogous, complementary, or synergistic; (b) familiarity with instructional strategies and access to resources; (c) deeper understanding of content across STEM; and (d) strategies for collaboration and team work to make integrated instruction time more efficient and less difficult to manage.     

The analytic hierarchy process in medical and health care decision making: A literature review

This paper presents a literature review of the application of the analytic hierarchy process (AHP) to important problems in medical and health care decision making. The literature is classified by year of publication, health care category, journal, method of analyzing alternatives, participants, and application type. Very few articles were published prior to 1988 and the level of activity has increased to about three articles per year since 1997. The 50 articles reviewed were classified in seven categories: diagnosis, patient participation, therapy/treatment, organ transplantation, project and technology evaluation and selection, human resource planning, and health care evaluation and policy. The largest number of articles was found in the project and technology evaluation and selection category (14) with substantial activity in patient participation (9), therapy/treatment (8), and health care evaluation and policy (8). The AHP appears to be a promising support tool for shared decision making between patient and doctor, evaluation and selection of therapies and treatments, and the evaluation of health care technologies and policies. We expect that AHP research will continue to be an important component of health care and medical research.     

Affine and degenerate affine BMW algebras: actions on tensor space

The affine and degenerate affine Birman–Murakami–Wenzl (BMW) algebras arise naturally in the context of Schur–Weyl duality for orthogonal and symplectic quantum groups and Lie algebras, respectively. Cyclotomic BMW algebras, affine and cyclotomic Hecke algebras, and their degenerate versions are quotients of the affine and degenerate affine BMW algebras. In this paper, we explain how the affine and degenerate affine BMW algebras are tantalizers (tensor power centralizer algebras) by defining actions of the affine braid group and the degenerate affine braid algebra on tensor space and showing that, in important cases, these actions induce actions of the affine and degenerate affine BMW algebras. We then exploit the connection to quantum groups and Lie algebras to determine universal parameters for the affine and degenerate affine BMW algebras. Finally, we show that the universal parameters are central elements—the higher Casimir elements for orthogonal and symplectic enveloping algebras and quantum groups.     

Ergodicity of Quasi-birth and Death Processes （Ⅰ）

Quasi-birth and death processes with block tridiagonal matrices find many applications in various areas. Neuts gave the necessary and sufficient conditions for the ordinary ergodicity and found an expression of the stationary distribution for a class of quasi-birth and death processes. In this paper we obtain the explicit necessary and sufficient conditions for/-ergodicity and geometric ergodicity for the class of quasi-birth and death processes, and prove that they are not strongly ergodic. Keywords ergodicity, quasi-birth and death process.     

Adult Education and Ethnomathematics: appropriating results, methods, and principles

This article aims at discussing the ways that Youth and Adult Education have been taking on the production, methods and principles of Ethnomathematics in the last decades, especially in Brazil. First, it focuses on how Youth and Adult educators found Ethnomathematics to be a resource to know their students and the mathematics they use and produce better. The second part discusses how intercultural studies undertaken by Ethnomathematics research offered a new perspective under which mathematics knowledge and educational practices of Youth and Adult Education are conceived. Finally, the interlocutive and interdiscursive dimensions of teaching and learning practices are approached to present a reflection about the relations among Youth and Adult Education, Ethnomathematics and the search for the meanings of teaching and learning mathematics at school into an Inclusion project.     

Time-linearized,compact methods for the inviscid GRLW equation subject to initial Gaussian conditions

The objective of this paper is three-fold. First, four time-linearization methods that are second- and fourth-order accurate in time and space, respectively, are presented and used to study the dynamics of the modified and generalized regularized-long wave equations (mRLW and GRLW equations, respectively). Two of the methods use the conservation-law form of the equations and treat the wave amplitude and its second-order spatial derivative and the linear and nonlinear advection fluxes as unknowns, whereas the other two employ the non-conservation-law form of the equations and consider the wave amplitude and its first- and second-order spatial derivatives as unknowns. The methods employ three-point fourth-order accurate Padé discretizations for the first- and second-order derivatives, are second-order accurate in time, and yield linear systems of blocktridiagonal matrices. Second, the accuracy of these methods is assessed by comparing their results with those of the exact solution of the mRLW equation. It is reported that the four methods predict nearly the same values of the three invariants and have the same accuracy, and that an accurate prediction of the invariants may not correspond to small errors in space and time. Third, the dynamics of the inviscid GRLW equation is studied first qualitatively in terms of length and time scales and then numerically as a function of the linear advection speed, the exponent of the nonlinear advection flux, the dispersion coefficient and the amplitude and width of the initial bell-shaped or Gaussian conditions. It is shown that wide initial conditions result in wave steepening and breakup and the formation of solitary waves whose amplitude and speed decrease as the time for their formation increases. For narrow initial conditions, it is shown that only a single solitary wave may form. Behind this wave and depending on the parameters that characterized the inviscid GRLW equation, rarefaction or negative amplitude waves that propagate towards the upstream boundary or a train of localized oscillatory waves that do not emerge from the trailing edge of the leading solitary wave may be formed. These oscillatory waves exhibit the characteristics of, but are not dispersive shock waves and their amplitude and frequency increases as the width of the initial conditions is decreased. The results presented here do not only complement previous work by the authors, they also show that the dynamics of the inviscid GRLW equation undergoes new and interesting phenomena as the width of the initial conditions is decreased.     

Further bounds for hardy type differences

In this paper we define a functional as a difference between the right-hand side and left-hand side of the refined Boas type inequality using the notation of superquadratic and subquadratic functions and study its properties, such as exponential and logarithmic convexity. We also, state and prove improvements and reverses of new weighted Boas type inequalities. As a special case of our result we obtain improvements and reverses of the Hardy inequality and its dual inequality. We introduce new Cauchy type mean and prove monotonicity property of this mean.     

The Supremum and Infimum of the Set of Fuzzy Numbers and Its Application

In this paper, we prove that the bounded set of fuzzy numbers must exist supremum and infimum and give the concrete representation of supremum and infimum. As an application, we obtain that the continuous fuzzy-valued function on a closed interval exists supremum and infimum and give the precise representation. We also show that the bounded fuzzy-valued function on a closed interval can define the lower and upper sums and the lower and upper integrals of Riemann and Riemann–Stieltjes by the usual way.     

Adapting Japanese Lesson Study to enhance the teaching and learning of geometry and spatial reasoning in early years classrooms: a case study

Increased efforts are needed to meet the demand for high quality mathematics in early years classrooms. Despite the foundational role of geometry and spatial reasoning for later mathematics success, the strand receives inadequate instructional time and is limited to concepts of static geometry. Moreover, early years teachers typically lack both content knowledge and confidence in teaching geometry and spatial reasoning. We describe our attempt to deal with these issues through a research initiative known as the Math for Young Children project. The project integrates effective features of both design research and Japanese Lesson Study and is designed to support teachers in developing content knowledge and new approaches for teaching geometry and spatial reasoning. Central to our Professional Development model is the integration of four adaptations to the Japanese Lesson Study model: (1) teachers engaging in the mathematics, (2) teachers designing and conducting task-based clinical interviews, (3) teachers and researchers co-designing and carrying out exploratory lessons and activities, and (4) the creation of resources for other educators. We present our methods and the results of our adaptations through a case study of one Professional Learning Team. Our results suggest that the adaptations were effective in: (1) supporting teachers’ content knowledge of and comfort level with geometry and spatial reasoning, (2) increasing teachers’ perceptions of young children’s mathematical competencies, (3) increasing teachers’ awareness and commitment for the inclusion of high quality geometry and spatial reasoning as a critical component of early years mathematics, and (4) the creation of innovative resources for other educators. We conclude with theoretical considerations and implications of our results.     

Some Joys and Trials of Mathematical Neuroscience

I describe the basic components of the nervous system—neurons and their connections via chemical synapses and electrical gap junctions—and review the model for the action potential produced by a single neuron, proposed by Hodgkin and Huxley (HH) over 60 years ago. I then review simplifications of the HH model and extensions that address bursting behavior typical of motoneurons, and describe some models of neural circuits found in pattern generators for locomotion. Such circuits can be studied and modeled in relative isolation from the central nervous system and brain, but the brain itself (and especially the human cortex) presents a much greater challenge due to the huge numbers of neurons and synapses involved. Nonetheless, simple stochastic accumulator models can reproduce both behavioral and electrophysiological data and offer explanations for human behavior in perceptual decisions. In the second part of the paper I introduce these models and describe their relation to an optimal strategy for identifying a signal obscured by noise, thus providing a norm against which behavior can be assessed and suggesting reasons for suboptimal performance. Accumulators describe average activities in brain areas associated with the stimuli and response modes used in the experiments, and they can be derived, albeit non-rigorously, from simplified HH models of excitatory and inhibitory neural populations. Finally, I note topics excluded due to space constraints and identify some open problems.