Constants in Kripke Models for Intuitionistic Logic

We present a technique to extend a Kripke structure (for intuitionistic logic) into an elementary extension satisfying some property (cardinality, saturation, etc.) which can be “axiomatized” by a family of sets of sentences, where, most often, many constant symbols occur. To that end, we prove extended theorems of completeness and compactness. Also, a section of the paper is devoted to the back-and-forth construction of isomorphisms between Kripke structures.     

Free Diffusions and Matrix Models with Strictly Convex Interaction

We study solutions to the free stochastic differential equation , where V is a locally convex polynomial potential in m non-commuting variables and S an m-dimensional free Brownian motion. We prove that such free processes have a unique stationary distribution μV. When the potential V is self-adjoint, we show that the law μV is the limit law of a random matrix model, in which an m-tuple of self-adjoint matrices are chosen according to the law exp. If V = V_β depends on complex parameters , we prove that the moments of the law μV are analytic in β at least for those β for which V_β is locally convex. In particular, this gives information on the region of convergence of the generating function for the enumeration of related planar maps. We prove that the solution X_t has nice convergence properties with respect to the operator norm as t goes to infinity. This allows us to show that the C* and W* algebras generated by an m-tuple with law μV share many properties with those generated by a semi-circular system. Among them is the lack of projections, exactness, the Haagerup property, and embeddability into the ultrapower of the hyperfinite II₁ factor. We show that the microstates free entropy χ(μV ) is finite when V is self-adjoint. A corollary of these results is the fact that the support of the law of any self-adjoint polynomial in under the law μV is connected, vastly generalizing the case of a single random matrix. We also deduce from this dynamical approach that the convergence of the operator norms of independent matrices from the GUE proved by Haagerup and Thorbjornsen [HT] extends to the context of matrices interacting via a convex potential. Received: February 2007, Revision: July 2007, Accepted: July 2007     

Two Game Models for Cooperation with Implicit Noncooperation

We propose two flexible game models to represent and analyze cases that cannot be modeled by current game models. One is called sharing creditability game (SCG) and the other is called bottomline game (BLG). The new models transform cooperative games into new games that incorporate auxiliary information (noncooperative in nature) usually neglected in previous theories. The new games will be solved only by traditional noncooperative game theory. When the new solutions are applied to the original games, the solutions can reflect the auxiliary information in addition to the original objectives of the decision makers or players. Generally, the new solutions are different from the cooperative and the noncooperative solutions of the original games. Existing transferable utility (TU) games and noncooperative games will coincide with special cases of the two new game models. Using SCG and BLG, the prisoner’s dilemma can be reformulated and a richer set of decisions can be considered for the players. The two new game models have potential applications in military and socioeconomic situations.This research was partly funded by the College Engineering, Ohio State University.     

政府投资治理污染的随机增长模型

本文设定了两种不同的带有污染的生产函数.在此两种生产函数情形下,利用随机最优化的方法分别分析了由政府投资治理污染的随机增长模型,得到了以下结论:在宏观均衡条件下,增大污染的外部性指标促进经济增长却降低福利;提高政府的环保投资增加福利,但对增长的影响却与污染的外部性指标和污染的负福利效用权数的大小有关.     

Persistence and Extinction in Two Species Models with Impulse

Both uniform persistence and global extinction are established for a two species predatorprey and competition system with impulse by appealing to theories of abstract persistence, asymptotically autonomous semiflows, and the comparison theorem.     

Nonlinear Physiologically Structured Population Models with Two Internal Variables

First-order hyperbolic partial differential equations with two internal variables have been used to model biological and epidemiological problems with two physiological structures, such as chronological age and infection age in epidemic models, age and another physiological character (maturation, size, stage) in population models, and cell-age and molecular content (cyclin content, maturity level, plasmid copies, telomere length) in cell population models. In this paper, we study nonlinear double physiologically structured population models with two internal variables by applying integrated semigroup theory and non-densely defined operators. We consider first a semilinear model and then a nonlinear model, use the method of characteristic lines to find the resolvent of the infinitesimal generator and the variation of constant formula, apply Krasnoselskii’s fixed point theorem to obtain the existence of a steady state, and study the stability of the steady state by estimating the essential growth bound of the semigroup. Finally, we generalize the techniques to investigate a nonlinear age-size structured model with size-dependent growth rate.

     

Locating Multiple Competitive Facilities: Spatial Interaction Models with Variable Expenditures

We develop a new framework for location of competitive facilities by introducing non-constant expenditure functions into spatial interaction location models. This framework allows us to capture two key effects – market expansion and cannibalization – within the same model.We develop algorithmic approaches for finding optimal or near-optimal solutions for several models that arise from choosing a specific form of the expenditure functions.     

Contact Interaction of Two Elastic Wedges

We consider the problem of contact of two elastic wedges and assume that only the vertices of the wedges touch before loading. After loading, the edges of both wedges come in contact near their common vertex. We reduce the constructed system of dual integral equations to a Fredholm integral equation of the second kind with difference kernel given on the semiaxis. We analytically solve the Fredholm equation by reducing it to the boundary-value Riemann problem for analytic functions. We obtain an analytic expression for contact stresses.     

多货栈及变质情形下两种可替代物品的经济订货批量模型

研究了多货栈及变质情形下两种可替代物品的经济订货批量问题.在计划期内,若某一种易变质物品发生缺货,则可以被另一种易变质物品以一定的替代率代替补充,不同物品有不同的变质率,且要决定租用货栈的数量.以库存系统的总费用最小为目标函数,分别对货栈容量无限与有限的情形建立模型,证明了最优策略存在的唯一性,并分别给出了求解最优订购策略的算法,最后通过一个算例验证了算法的最优性.     

两类加工时间是一般函数的单机排序问题

考虑了两类有一般加工时间函数的排序问题. 工件的加工时间分别为基本加工时间与开工时间函数、位置函数的和. 对加工时间依赖开工时间的模型,证明了一定条件下极小化最大完工时间和极小化总完工时间是多项式可解的. 对加工时间依赖开工位置的模型,给出极小化最大完工时间和极小化总完工时间的最优序,同时证明了极小化加权总完工时间的一个最优排序性质并给出一个贪婪算法.     

两个反问题的数学模型

本文考察了两个工业中的反问题 ,讨论了如何建立起这些问题的偏微分方程模型 ,并最终归结为变分问题 ,简述了这些模型的求解方法 .     

两个数学模型及其应用

给出了两个数学模型,模型Ⅰ—教学编制模型,模型Ⅱ—课时津贴模型,并结合实际问题进行了计算     

A Comparison of Two Stock Control Models

Two methods of computing re-order levels are compared under an assumed state of nature. The results indicate that the difference, measured in terms of the expected lost sales is significant.     

Ruin Probabilities in Cox Risk Models with Two Dependent Classes of Business

In this paper we consider risk processes with two classes of business in which the two claim-number processes are dependent Cox processes. We first assume that the two claim-number processes have a two-dimensional Markovian intensity. Under this assumption, we not only study the sum of the two individual risk processes but also investigate the two-dimensional risk process formed by considering the two individual processes separately. For each of the two risk processes we derive an expression for the ruin probability, and then construct an upper bound for the ruin probability. We next assume that the intensity of the two claim-number processes follows a Markov chain. In this case, we examine the ruin probability of the sum of the two individual risk processes. Specifically, a differential system for the ruin probability is derived and numerical results are obtained for exponential claim sizes.     

恒化器中两种群适应性生长模型

研究两种微生物基于恒化器培养的数学模型.微生物1因适应生存环境营养供给的变化而具有休眠特性,表现为活跃生长与休眠两种生存状态.微生物2不能休眠.经过数学分析和数值模拟,结论是当系统生产常数μ_0<1时,两种微生物不能在恒化器中生存.而当μ_0>1,会出现多种稳定的极限状态E_i,i=1,2,3,4,5.数值模拟也显示出当营养吸收转化率和定量输入的营养浓度确定时,两种微生物的最大生长率决定了竞争结果.     

关于两种DEA超效率模型的进一步探讨

对数据包络分析模型中的两种超效率模型——LJK模型和MAJ模型进行了分析和研究,通过变量替换,对原有模型进行了变形,在不变规模效益和非零输入条件下,分析了它们和AP模型之间的内在联系,得出并证明了若干重要性质,最后给了实例证明.     

Computing Normalizing Constants for Finite Mixture Models via Incremental Mixture Importance Sampling (IMIS)

This article proposes a method for approximating integrated likelihoods in finite mixture models. We formulate the model in terms of the unobserved group memberships, z, and make them the variables of integration. The integral is then evaluated using importance sampling over the z. We propose an adaptive importance sampling function which is itself a mixture, with two types of component distributions, one concentrated and one diffuse. The more concentrated type of component serves the usual purpose of an importance sampling function, sampling mostly group assignments of high posterior probability. The less concentrated type of component allows for the importance sampling function to explore the space in a controlled way to find other, unvisited assignments with high posterior probability. Components are added adaptively, one at a time, to cover areas of high posterior probability not well covered by the current importance sampling function. The method is called incremental mixture importance sampling (IMIS).

IMIS is easy to implement and to monitor for convergence. It scales easily for higher dimensional mixture distributions when a conjugate prior is specified for the mixture parameters. The simulated values on which the estimate is based are independent, which allows for straightforward estimation of standard errors. The self-monitoring aspects of the method make it easier to adjust tuning parameters in the course of estimation than standard Markov chain Monte Carlo algorithms. With only small modifications to the code, one can use the method for a wide variety of mixture distributions of different dimensions. The method performed well in simulations and in mixture problems in astronomy and medical research.     

一维可压缩Euler方程组的两个模型

作者考察了一维可压缩Euler方程组的两个模型.利用特征分解和Gronwall不等式,首先得到具有几何结构且绝热指数γ=3的一维可压缩Euler方程组L~∞模的一致有界性.进一步,考虑当绝热指数γ=-1时,一维非等熵可压缩Euler方程组的Cauchy问题.在适当的假设下,得到该系统的整体经典解.     

两极端值模型的比较和应用

极端值模型主要有分块样本极大值模型和阈顶点模型.从两模型极值分布的内在关系、尾部特征的角度作比较分析和证明.结果表明,它们的内在关系一致;随着形状参数的变化尾部各有不同特征,阈顶点模型更为具体和多样,更适合金融风险度量的应用.     

含有两个方差分量的多元混合效应模型方差分量矩阵的估计

考虑含有两个方差分量矩阵的多元混合模型,将一元混合模型下的谱分解估计推广到多元模型下.给出的方差分量矩阵的谱分解估计在均方误差意义下一致的优于ANOVA估计,最后还讨论了谱分解估计与ANOVA估计等价的条件.