一类带有阶段结构的扩散捕食系统的全局稳定性分析（英文）

本文研究一类带有反应扩散项、食饵具阶段结构的食饵捕食模型.通过运用Lyapunov直接法和构造合理的Lyapunov泛函,建立了系统边界平衡点和正平衡点的全局渐近稳定性,得到系统全局稳定的充分必要条件,提高已有的结论.     

食饵具有避难所效应的生态-传染病模型的分析

建立并分析了疾病在食饵中传播、食饵考虑避难所效应的捕食与被捕食模型,捕食者不仅捕食感染食饵而且捕食易感食饵.讨论了系统的有界性和各平衡点的存在性,利用Routh-Hurwitz判据分析各平衡点的局部渐进稳定性,通过构造Lyapunov函数证明了各平衡点的全局渐进稳定性,并进行数值模拟以验证结论的正确性.     

一类带无选择性捕获和时滞的捕食食饵系统的Hopf分支分析

本文主要研究了一个改进的带时滞和无选择捕获函数的捕食-食饵生态经济系统的稳定性和Hopf分支.利用微分代数系统的稳定性理论和分支理论,得到了系统正平衡点稳定性的条件,以及当时滞τ作为分支参数时系统产生Hopf分支的条件.对Leslie-Gower捕食-食饵模型进行了一定程度的完善,使得建立的模型更符合实际情况,因此得到的结论也更加科学.     

一类具有Allee效应的捕食系统的稳定性分析及模拟

建立了食饵具有Allee效应的捕食模型,讨论了系统的有界性和平衡点的存在性.并证明了平衡点的局部渐近稳定性,进而通过构造Lyapunov函数分析了正平衡点的全局渐近稳定性,利用数值模拟讨论了Allee效应对系统的影响:Allee效应是系统的不稳定因素.     

一类带无选择性捕获和时滞的捕食食饵系统的Hopf分支分析（英文）

本文主要研究了一个改进的带时滞和无选择捕获函数的捕食-食饵生态经济系统的稳定性和Hopf分支.利用微分代数系统的稳定性理论和分支理论,得到了系统正平衡点稳定性的条件,以及当时滞τ作为分支参数时系统产生Hopf分支的条件.对Leslie-Gower捕食-食饵模型进行了一定程度的完善,使得建立的模型更符合实际情况,因此得到的结论也更加科学.     

一类具有分段常数变量的三维食饵捕食者系统的稳定性和分支行为

本文研究一类具有分段常数变量的三维食饵-捕食者系统的稳定性和分支行为,该系统由一个捕食者和两个食饵构成,其中一个食饵可由捕食者对另一个食饵的捕食行为中获益.首先通过计算得到三维食饵-捕食者系统对应的差分模型,其次通过选择合适的参数讨论边界和正平衡点的存在性,进而利用线性稳定性理论讨论平衡点局部渐近稳定的充分条件.将两个食饵种群的出生率以及最大环境容纳量作为分支参数,使用分支理论研究差分模型在平衡点处产生翻转分支、Neimark-Sacker分支、折-翻转分支和1:2共振分支的充分条件.最后通过数值模拟验证了理论分析的正确性.     

改进了的捕食者-食饵系统的征税模型分析

探讨了Holling功能性反应的捕食者-食饵征税模型,修改了更合理的捕获函数.讨论了该系统生物经济平衡点的性态,正平衡点的局部渐近稳定性和全局渐近稳定性条件,并利用Pontrjagin最大值原理得到了最优税收策略.为可再生资源的合理开发利用提供了理论依据.     

具有时滞的生态-传染病模型的定性分析

针对一类疾病在食饵中传播而把食饵分为易感和染病的时滞生态-传染病模型,以时滞(即传染病在食饵种群中的潜伏期)作为分支参数,讨论了系统正平衡点在时滞τ=0时的局部渐近稳定性,在τ0时在一列临界值处发生了Hopf分支,并且对保持正平衡点稳定时时滞的范围也给出了估计.     

带有非线性收获和妊娠时滞的微分代数捕食者-食饵系统的稳定性及Hopf分支

本文研究了一类同时带有非线性食饵收获和捕食者妊娠时滞的微分代数捕食者-食饵系统的稳定性及Hopf分支问题.利用了分支理论和稳定性理论,以捕食者妊娠时滞作为系统的分支参数,获得了所提出的新系统在正平衡点处系统稳定性的相关判据条件和Hopf分支的产生条件.推广了一般带有线性收获和时滞的微分代数捕食者-食饵系统的结论.     

具有时滞的生态流行病模型的稳定性和Hopf分支

该文考虑一类食饵染病的时滞捕食被捕食模型. 作者分析了系统的非负不变性, 边界平衡点的性质和全局稳定性. 证明了当时滞τ=τ\-1+τ\-2适当小时, 正平衡点是局部渐近稳定的,随着时滞的增加, 正平衡点由稳定变为不稳定, 系统在正平衡点附近发生Hopf分支.     

基于模糊FNN-ELECTRE法的国有商业银行竞争力评价

随着金融业全方位开放,国有商业银行已成为国家经济命脉的核心,其竞争力强弱关系着国家经济的繁荣与衰退。本文基于模糊FNN-ELECTRE方法建立国有商业银行竞争力评价模型,以因素神经网络理论(FNN)与ELECTRE融合方法为基础,以现有商业银行竞争力评价指标为着眼,把国有商业银行竞争力的评价体系从现实竞争力和潜在竞争力两个因素抽取为一级指标,以规模、质量、业务结构、效率、成长性五个因素设为二级指标。从实证的角度对银行A、银行B、银行C、银行D、银行E五大国有银行进行分析验证,对其属性值进行和谐性与非和谐性检验得出,银行B竞争能力最强,银行E竞争能力最弱,五大国有银行均有改进空间。     

Wave parameter identification problem for ocean test structure data,part 2, discrete formulation

This paper deals with the solution of the wave parameter identification problem for ocean test structure data. A discrete formulation is assumed. An ocean test structure is considered, and wave elevation and velocities are assumed to be measured with a number of sensors. Within the frame of linear wave theory, a Fourier series model is chosen for the wave elevation and velocities. Then, the following problem is posed: Find the amplitudes of the various wave components of specified frequency and direction, so that the assumed model of wave elevation and velocities provides the best fit to the measured data. Here, the term best fit is employed in the least-square sense over a given time interval.At each time instant, the wave representation involves four indexes (frequency, direction, instrument, time); hence, four-dimensional arrays are required. This formal difficulty can be avoided by switching to an alternative representation involving only two indexes (frequency-direction, instrument-time); hence, standard vector-matrix notation can be used. Within this frame, optimality conditions are derived for the amplitudes of the assumed wave model.A characteristic of the wave parameter identification problem is that the condition number of the system matrix can be large. Therefore, the numerical solution is not an easy task and special procedures must be employed. Specifically, Gaussian elimination is avoided and advantageous use is made of the Householder transformation, in the light of the least-square nature of the problem and the discretized approach to the problem.Numerical results are presented. The effect of various system parameters (number of frequencies, number of directions, sampling time, number of sensors, and location of sensors) is investigated in connection with global or strong accuracy, local or weak accuracy, integral accuracy, and condition number of the system matrix.From the numerical experiments, it appears that the wave parameter identification problem has a unique solution if the number of directions is smaller than or equal to the number of sensors; it has an infinite number of solutions otherwise. In the case where a unique solution exists, the condition number of the system matrix increases as the size of the system increases, and this has a detrimental effect on the accuracy. However, the accuracy can be improved by proper selection of the sampling time and by proper choice of the number and location of the sensors.Generally speaking, the computations done for the discrete case exhibit better accuracy than the computations done for the continuous case (Ref. 5). This improved accuracy is a direct consequence of having used advantageously the Householder transformation and is obtained at the expense of increased memory requirements and increased CPU time.This work was supported by Exxon Production Research Company, Houston, Texas. This paper is based partly on Refs. 1–4.     

Formulation of linear problems and solution by a universal machine

Using the predicate language for ordered fields a class of problems referred to aslinear problems is defined. This class contains, for example, all systems of linear equations and inequalities, all linear programming problems, all integer programming problems with bounded variables, all linear complementarity problems, the testing of whether sets that are defined by linear inequalities are semilattices, all satisfiability problems in sentenial logic, the rank-computation of matrices, the computation of row-reduced echelon forms of matrices, and all quadratic programming problems with bounded variables. A single, one, algorithm, to which we refer as theUniversal Linear Machine, is described. It solves any instance of any linear problem. The Universal Linear Machine runs in two phases. Given a linear problem, in the first phase a Compiler running on a Turing Machine generates alinear algorithm for the problem. Then, given an instance of the linear problem, in the second phase the linear algorithm solves the particular instance of the linear problem. The linear algorithm is finite, deterministic, loopless and executes only the five ordered field operations — additions, multiplications, subtractions, divisions and comparisons. Conversely, we show that for each linear algorithm there is a linear problem which the linear algorithm solves uniquely. Finally, it is shown that with a linear algorithm for a linear problem, one can solve certain parametric instances of the linear problem.Research was supported in part by the National Science Foundation Grant DMS 92-07409, by the Department of Energy Grant DE-FG03-87-ER-25028, by the United States—Israel Binational Science Foundation Grant 90-00434 and by ONR Grant N00014-92-J1142.Corresponding author.     

A double-stage piecewise recursive filter for real-time applications

This paper examines the basic problem of estimating the state of a system described by a set of dynamical equations. The state estimation is performed by means of optimal filtering techniques in which the state observation is given by a set of nonlinear equations.The basic issue encountered in most engineering problems is the availability of more observable information than the processor can effectively process in real-time, while performing full optimal filtering on all available observable data. To alleviate this deficiency, an algorithm is developed in which the rate of information processing is kept at a high value, while the system statistics are evaluated at a much slower rate.The method utilizes a combination of fast and slow filtering loops, in which the observable data are processed at a high rate during the fast loop, while the system error covariance, gain computations, and all other system statistics are processed at a lower rate in the slow loop. Methods are provided to resolve any incompatibility in the system statistics resulting from this fast-loop/slow-loop processing combination.Applications describing problems pertaining to aircraft navigation are presented. Specifically, applications to aircraft navigation through a satellite network are studied. Appropriate simulation results from the above studies are shown.This work was performed under contract with the Department of the Air Force, Space and Missile Organization (SAMSO), Los Angeles, California, Contract No. F04-701-75-C-0180.The authors are indebted to Dr. C. Johnson, GPS System Engineer, Mr. G. Consolver, GPS Software Manager, and Mr. W. Riley, Communications/Navigation Department, Texas Instruments for their continuous encouragement in the course of this work. Also, they are indebted to Major M. Birnbaum, SAMSO, for his constructive criticism on the conceptual design of this work, and to Mr. A. Bierman, Aerospace Corporation, for kindly providing simulation data of aircraft trajectories. Finally, the authors would like to express their gratitude to Dr. N. Carlson, Intermetrics, for valuable consultation during the progress of this work.Portions of this paper were presented by the senior author at the GSP Conference, Plan 76, IEEE Position, Location, and Navigation Symposium, San Diego, California, 1976.     

考虑成本、等待时间和安全水平的分类安检模式研究

近年来,随着民航机场旅客吞吐量快速增加,机场安检部门的工作压力正不断加大,旅客等待时间也正在逐渐增加。针对该问题,引入了分类安检模式。然而,分类安检模式通常需要额外的投资成本,可能会产生较大的财务负担。因此,以成本为目标,综合考虑旅客等待时间和安全水平的要求,研究了分类安检模式和传统安检模式的比较以及最优决策性质等相关问题。首先,考虑安全水平和旅客等待时间的约束,分别为传统安检模式和分类安检模式建立了模型,并分析了其最优运营决策性质。其次,从成本的角度,对两种安检模式做了比较研究。研究结果表明,当旅客数量多、安检犯错容忍度较高或旅客等待敏感时,分类安检模式比传统安检模式表现更优;反之,传统安检模式更优。此外,在分类安检模式中,分配到高风险安检通道的旅客比例存在一个最优值,并且其通常在20%到30%之间取到。最后,通过数值分析验证了分类安检模式的最优服务配置。     

Representation of the solution to a model problem in semiconductor physics

We study a mixed type problem for the Poisson equation arising in the modeling of charge transport in semiconductor devices [V. Romano, 2D simulation of a silicon MESFET with a non-parabolic hydrodynamical model based on the maximum entropy principle, J. Comput. Phys. 176 (2002) 70-92; A.M. Blokhin, R.S. Bushmanov, A.S. Rudometova, V. Romano, Linear asymptotic stability of the equilibrium state for the 2D MEP hydrodynamical model of charge transport in semiconductors, Nonlinear Anal. 65 (2006) 1018-1038]. Unlike well-studied elliptic boundary-value problems in domains with smooth boundaries (see, for example, [O.A. Ladyzhenskaya, N.N. Uralceva, Linear and Quasilinear Elliptic Equations, Nauka, Moscow, 1973; D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1983]), our problem has two significant features: firstly, the boundary is not a smooth curve and, secondly, the type of boundary conditions is mixed (the Dirichlet condition is satisfied on the one part of the boundary whereas the Neumann condition on the other part). The well-posedness of the problem in Hölder and Sobolev spaces is proved. The representation of the solution to the problem is obtained in an explicit form.     

公众参与视角下的央地环境规制博弈分析

本文首先构建环境规制中中央政府和地方政府的两方演化博弈模型,并在此基础上将公众作为第三方参与主体,构建中央政府、地方政府和公众三方演化博弈模型,详细比较两方和三方博弈模型的区别,探究各个主体策略行为的影响因素。研究发现:(1)未有公众参与下,地方政府策略选择主要受地方政府积极执行成本、环境收益、经济损失,消极执行的环境政绩损失,中央政府监管力度、治理补贴和对地方政府的处罚等因素影响;中央政府的监管策略主要受到严格监管的成本以及对地方政府的治理补贴和处罚等因素影响。引入公众参与后,在央地两方博弈的基础上,地方政府环境规制执行策略的影响因素还增加了地方政府被举报后所受到的追加处罚,中央政府监管策略的影响因素还增加了中央政府监管力度、对地方政府的追加处罚以及中央政府的公信力损失。(2)未有公众参与下,中央政府严格监管的概率随地方政府积极执行概率的增大而减小。引入公众参与后,中央政府严格监管率随地方政府积极执行概率的增大而增大。说明在公众参与下,地方政府积极执行环境规制对中央政府严格监管产生的抑制作用转变成了促进作用。(3)地方政府积极执行的概率、中央政府严格监管的概率都随公众举报概率的增大而增大。说明公众参与不仅对地方政府承担环保责任具有促进作用,而且有利于促使中央政府落实环境治理政策。     

Personae at play. ‘Men of Mathematics’ in commentary

Mathematical writers, above all, Euclid, tend to present their theorems as decontextualized, abstract propositions, which has become the standard modus of textual presentation in theoretical mathematics. Mathematical commentators, however, provide their readers with personal names and historical facts in order to elucidate problems, provide contexts of discovery, or construct doxographies, among other things. Modern readers have used such information for the construction of histories of science. When we look at these passages, however, we see that personal names and information about mathematicians of the past can serve quite a range of different objectives, such as the strategic self-positioning of the commentator vis-à-vis the past or present of mathematics, the education of the reader, mathematical or moral, the construction of the history of the field, etc. Not only does the commentator present a persona of himself to the reader, he can also turn colleagues and predecessors into personae. This paper attempts to elucidate the practice, by offering four examples of such plays of and with personae, in Pappus, Eutocius, al-Nayrīzī, and Proclus.     

The generalized hierarchical product of graphs

A generalization of both the hierarchical product and the Cartesian product of graphs is introduced and some of its properties are studied. We call it the generalized hierarchical product. In fact, the obtained graphs turn out to be subgraphs of the Cartesian product of the corresponding factors. Thus, some well-known properties of this product, such as a good connectivity, reduced mean distance, radius and diameter, simple routing algorithms and some optimal communication protocols, are inherited by the generalized hierarchical product. Besides some of these properties, in this paper we study the spectrum, the existence of Hamiltonian cycles, the chromatic number and index, and the connectivity of the generalized hierarchical product.     

颤振分析中的特征值排序问题

颤振分析中判断颤振临界速度的重要依据是系统V-g和V-f图,即系统特征值随参数的变化曲线.在几乎所有商用软件及自编程序的输出结果中,有时会出现所谓的"窜支"现象,这给颤振临界速度和颤振穿越分支及耦合形式的判断带来很大不便.通过隐函数定理可以证明,除重特征值点以外,系统特征值连续依赖于系统参数变化.依据多元向量值函数连续性,建立对特征值的排列算法,给出系统特征根轨迹的正确曲线,再输出V-g和V-f图数据,从而避免"窜支"现象.编制应用程序,通过几个典型算例对算法进行了验证.该工作能够有效简化颤振分析的后处理工作,提高分析效率.