具反馈控制的一方不能独立生存偏利合作系统的稳定性

研究具反馈控制的一方不能独立生存的两种群偏利合作系统正平衡点和边界平衡点的稳定性,通过构造适当的Lyapunov函数分别得到保证正平衡点和边界平衡点全局渐近稳定的充分性条件,并通过MATLAB进行数值模拟.研究结果表明,在原系统存在正平衡点时,适当的反馈控制变量仅改变正平衡点的位置,不会改变正平衡点的稳定性;但不适当的反馈控制变量将导致系统中不能独立生存的种群绝灭.     

一类带有一般接触率和常数输入的流行病模型的全局分析

借助极限系统理论和构造适当的Liapunov函数,对带有一般接触率和常数输入的SIR型和SIRS型传染病模型进行讨论．当无染病者输入时,地方病平衡点存在的阈值被找到A·D2对相应的SIR模型,关于无病平衡点和地方病平衡点的全局渐近稳定性均得到充要条件;对相应的SIRS模型,得到无病平衡点和地方病平衡点全局渐近稳定的充分条件．当有染病者输入时,模型不存在无病平衡点．对相应的SIR模型,地方病平衡点是全局渐近稳定的;对相应的SIRS模型,得到地方病平衡点全局渐近稳定的充分条件．     

向量对策理想-Nash平衡点的存在性

本文采用向量优化问题中理想解的概念,定义向量对策理想-Nash平衡点,并证明这一平衡点的存在性．这一结果一方面体现了向量对策Pareto-Nash平衡点和弱Pareto-Nash平衡点的存在性,同时,还给出了特殊的Pareto-Nash平衡点的存在性．     

一类具有时滞的流行病模型分析

讨论了一类带有时滞的SE IS流行病模型,并讨论了阈值、平衡点和稳定性.模型是一个具有确定潜伏期的时滞微分方程模型,在这里我们得到了各类平衡点存在条件的阈值R0;当R0<1时,只有无病平衡点P0,且是全局渐近稳定的;当R0>1时,除无病平衡点外还存在唯一的地方病平衡点Pe,且该平衡点是绝对稳定的.     

一类具有离散双时滞的SEIR传染病模型的稳定性与持久性

针对一类潜伏期和恢复期描述为离散双时滞的SEIR传染病模型,给出无病平衡点和地方病平衡点存在条件,证明了无病平衡点和地方病平衡点的稳定性,以及疾病的持久性.应用数值模拟验证了疾病的持久性与灭绝性,分析了接触率对疾病流行趋势的影响.     

具反馈控制的单方不能独立生存合作系统稳定性研究

研究具有反馈控制的单方不能独立生存两种群合作系统正平衡点和边界平衡点的稳定性.通过构造适当的Ly印unov函数分别得到一组保证正平衡点和边界平衡点全局吸引的充分性条件.我们的结果表明在原系统存在唯一的全局吸引的正平衡点时,反馈控制变量控制在一定的范围,则所研究系统仍然具有唯一的全局吸引的正平衡点;反馈控制变量足够大,则第二个种群将最终绝灭;在原系统只有一个全局稳定的边界平衡点时,反馈控制变量仅改变正平衡点的位置,而不会改变边界平衡点的稳定性.     

一类带有潜伏期和部分免疫的传染病模型的全局分析

通过假设被接种者具有部分免疫,建立了一类具有潜伏期和接种的SEIR传染病模型,借助再生矩阵得到了确定此接种模型动力学行为的基本再生数.当基本再生数小于1时,模型只有无病平衡点;当基本再生数大于1时,除无病平衡点外,模型还有唯一的地方病平衡点.借助Liapunov函数,证明了无病平衡点和地方病平衡点的全局稳定性.     

一类含有非线性传染率的传染病模型的全局稳定性

讨论了一类带有非线性传染率的SIRS型传染病模型,得到了无病平衡点和地方病平衡点存在的阈值条件,借助构造Dulac函数和Liapunov函数,找到了两类平衡点全局渐近稳定的充要条件.     

一类具免疫控制的SIR传染病模型的稳定性

利用微分方程理论研究了一类具有常数输入和免疫控制的数学模型,讨论了模型无病平衡点和地方病平衡点的存在性以及局部稳定性.构造Dulac函数的方法,得到了无病平衡点和地方病平衡点的全局稳定性充分条件,同时利用Matlab软件进行了数值模拟.     

一类具有非线性传染率的时滞SIR模型的分析

分析并建立具有时滞及非线性传染率的SIR传染病模型.通过分析在无病平衡点和正平衡点处的特征方程,可得到在这两个平衡点处的局部渐近稳定性,然后我们得到了系统在两个平衡点处的全局渐近稳定性,最后我们证明了系统的持久性.     

乡村绿色生态旅游适宜等级VIKOR评估方法

针对乡村绿色生态旅游特征,并考虑旅游者个体感受与群体效益,本文从乡村绿色生态旅游开发与适宜评级概念出发,提出乡村绿色生态旅游适宜等级VIKOR评估模型与方法。首先,从等级评估的概念与内涵出发,刻画乡村绿色生态旅游适宜评级问题,避免混淆旅游适宜评级和排序两个本质不同的问题。然后,构建乡村绿色生态旅游适宜等级评估指标及隶属函数,提出评估指标的熵权确定方法。其次,提出乡村绿色生态旅游适宜等级VIKOR评估模型与二元语义等级评估方法。最后,通过案例研究和比较分析,说明本文所提模型与方法的合理性、可行性与实用性。     

A system-theoretic model for cooperation, interaction and allocation

A system-theoretic approach to cooperation, interaction and allocation is presented that simplifies, unifies and extends the results on classical cooperative games and their generalizations. In particular, a general Weber theory of linear values is obtained and a new theory for local cooperation and general interaction indices is established. The model is dynamic and based on the notion of states of cooperation that change under actions of agents. Careful distinction between “local” states of cooperation and general “system” states leads to a notion of entropy for arbitrary non-negative and efficient allocations and thus to a new information-theoretic criterion for fairness of allocation mechanisms. Shapley allocations, for instance, are exhibited as arising from random walks with maximal entropy. For a large class of cooperation systems, a characterization of game symmetries in terms of λ-values is given. A concept for cores and Weber sets is proposed and it is shown that a Weber set of a game with selection structure always contains the core.     

Mechanics of Delaminations in Laminate Composite Structures

A survey of the literature and state of the art of the mechanical aspects of delaminations in laminate composite structures is presented. Surface and internal delaminations of various origin, shape, and location are discussed. The origination, stability, and postcritical behavior of delaminations under quasi-static, cyclic, and dynamic loads are analyzed. Some problems for further investigations are discussed.     

On the use of history of mathematics: an introduction to Galileo's study of free fall motion

In this paper, we report on an experimental activity for discussing the concepts of speed, instantaneous speed and acceleration, generally introduced in first year university courses of calculus or physics. Rather than developing the ideas of calculus and using them to explain these basic concepts for the study of motion, we led 82 first year university students through Galileo's experiments designed to investigate the motion of falling bodies, and his geometrical explanation of his results, via simple dynamic geometric applets designed with GeoGebra. Our goal was to enhance the students’ development of mathematical thinking. Through a scholarship of teaching and learning study design, we captured data from students before, during and after the activity. Findings suggest that the historical development presented to the students helped to show the growth and evolution of the ideas and made visible authentic ways of thinking mathematically. Importantly, the activity prompted students to question and rethink what they knew about speed and acceleration, and also to appreciate the novel concepts of instantaneous speed and acceleration at which Galileo arrived.     

Semicorings and Semicomodules

In this paper, we introduce and investigate semicorings over associative semirings and their categories of semicomodules. Our results generalize old and recent ones on corings over rings and their categories of comodules. The generalization is not straightforward and even subtle at several places due to the nature of the base category of commutative monoids which is neither Abelian (not even additive) nor homological, and has no nonzero injective objects. To overcome these and other difficulties, a combination of methods and techniques from categorical, homological and universal algebra is used including a new notion of exact sequences of semimodules over semirings.     

房地产业对中国经济真的那么重要吗？

为恰当评估房地产业对中国经济的重要性,通过编制2002、2007和2012年中国社会核算矩阵,进行乘数分解和结构化路径分析的结果表明:房地产业对行业总产出、劳动力和资本报酬、居民和企业收入的拉动作用极低。房地产业主要对金融业、租赁和商务服务业、建筑业以及金属冶炼与压延加工业四个行业的产出影响比较显著,对前三个行业主要是直接的一步式影响,与房地产业紧密相关的产业链条并不长。房地产业对要素报酬和机构收入的拉动总效应极小,且主要是开环效应,与此同时,房地产业主要通过自身和金融业影响要素报酬进而影响机构收入,特别是对资本报酬和企业收入的影响简单、直接,高度依赖这两条基础路径。土地出让金和房地产有关税收已成为地方政府的主要收入来源。房地产开发和运营商、金融机构和地方政府已成为房地产业发展过程中最主要的利益相关方。     

On effectiveness of wiretap programs in mapping social networks

Snowball sampling methods are known to be a biased toward highly connected actors and consequently produce core-periphery networks when these may not necessarily be present. This leads to a biased perception of the underlying network which can have negative policy consequences, as in the identification of terrorist networks. When snowball sampling is used, the potential overload of the information collection system is a distinct problem due to the exponential growth of the number of suspects to be monitored. In this paper, we focus on evaluating the effectiveness of a wiretapping program in terms of its ability to map the rapidly evolving networks within a covert organization. By running a series of simulation-based experiments, we are able to evaluate a broad spectrum of information gathering regimes based on a consistent set of criteria. We conclude by proposing a set of information gathering programs that achieve higher effectiveness then snowball sampling, and at a lower cost. Maksim Tsvetovat is an Assistant Professor at the Center for Social Complexity and department of Public and International Affairs at George Mason University, Fairfax, VA. He received his Ph.D. from the Computation, Organizations and Society program in the School of Computer Science, Carnegie Mellon University. His dissertation was centered on use of artificial intelligence techniques such as planning and semantic reasoning as a means of studying behavior and evolution of complex social networks, such as these of terrorist organizations. He received a Master of Science degree from University of Minnesota with a specialization in Artificial Intelligence and design of Multi-Agent Systems, and has also extensively studied organization theory and social science research methods. His research is centered on building high-fidelity simulations of social and organizational systems using concepts from distributed artificial intelligence and multi-agent systems. Other projects focus on social network analysis for mapping of internal corporate networks or study of covert and terrorist orgnaizations. Maksim’s vita and publications can be found on Kathleen M. Carley is a professor in the School of Computer Science at Carnegie Mellon University and the director of the center for Compuational Analysis of Social and Organizational Systems (CASOS) which has over 25 members, both students and research staff. Her research combines cognitive science, social networks and computer science to address complex social and organizational problems. Her specific research areas are dynamic network analysis, computational social and organization theory, adaptation and evolution, text mining, and the impact of telecommunication technologies and policy on communication, information diffusion, disease contagion and response within and among groups particularly in disaster or crisis situations. She and her lab have developed infrastructure tools for analyzing large scale dynamic networks and various multi-agent simulation systems. The infrastructure tools include ORA, a statistical toolkit for analyzing and visualizing multi-dimensional networks. ORA results are organized into reports that meet various needs such as the management report, the mental model report, and the intelligence report. Another tool is AutoMap, a text-mining systems for extracting semantic networks from texts and then cross-classifying them using an organizational ontology into the underlying social, knowledge, resource and task networks. Her simulation models meld multi-agent technology with network dynamics and empirical data. Three of the large-scale multi-agent network models she and the CASOS group have developed in the counter-terrorism area are: BioWar a city-scale dynamic-network agent-based model for understanding the spread of disease and illness due to natural epidemics, chemical spills, and weaponized biological attacks; DyNet a model of the change in covert networks, naturally and in response to attacks, under varying levels of information uncertainty; and RTE a model for examining state failure and the escalation of conflict at the city, state, nation, and international as changes occur within and among red, blue, and green forces. She is the founding co-editor with Al. Wallace of the journal Computational Organization Theory and has co-edited several books and written over 100 articles in the computational organizations and dynamic network area. Her publications can be found at: http://www.casos.cs.cmu.edu/bios/carley/publications.php     

Dynamics of coupled systems

A survey in the form of a review of the author’s research results in the area of dynamics of coupled rotations and coupled systems is presented. The theorem on the existence of a trigger of the coupled singularities and the separatrix in the form of the number eight is presented with a few examples of coupled rotations of the simple systems with debalances. Also, a survey of models and dynamics of coupled systems composed of a number of deformable bodies (plates, beams or belts) with different properties of materials and discrete layer properties is presented and mathematically described. The constitutive stress–strain relations for materials of the coupled sandwich structure elements are presented for different properties: elastic, viscoelastic and creeping. The characteristic modes of the coupled system vibrations are obtained and analyzed for different kinds of materials and structure composition. The visualization of the characteristic numbers and modes and eigenamplitude forms are presented. Structural analysis of sandwich structure vibrations is done.     

Organizational implications of systems thinking: Multidimensional modular design

Despite a well recognized systemic principle that parts of an organization are interdependent and the nature of their interaction defines the behavior of the whole, we have stubbornly held to the illusion that each function is more or less self-contained and can be treated independently. For a majority of managers the unidimensional mode of organization based on structurally defined tasks, segmentation and hierarchical coordination of functions seems to be the only acceptable way of organizing the work. A predominant management culture continues to value narrow specialization very dearly and considers any forms of redundancy in the organizational structure as wasteful and inefficient. However, the ability to adapt requires some forms of flexibility and responsiveness, which in turn demands that some degree of redundancy be built into the system.The required level of interaction and flexibility in an organization can be achieved by creating a modular structure embedded in a multidimensional scheme. The resulting mode of organization is capable of redesigning its structure and redefining its functions, so that it can exhibit different behaviors and produce different outcomes in the same or different environments.     

Schreier rewriting beyond the classical setting

Using actions of free monoids and free associative algebras, we establish some Schreiertype formulas involving ranks of actions and ranks of subactions in free actions or Grassmann-type relations for the ranks of intersections of subactions of free actions. The coset action of the free group is used to establish a generalization of the Schreier formula in the case of subgroups of infinite index. We also study and apply large modules over free associative and free group algebras. This work was supported by Natural Sciences and Engineering Research Council of Canada (Grant No. 227060-04), Yuri Bahturin, National Science Foundation (Grant No. DMS-0700811) and Russian Fund for Basic Research (Grant No. 08-01-00573), Alexander Olshanskii