Uniqueness of the positive solution for a non-cooperative model of nuclear reactors

We prove the uniqueness of the positive solution for a non-cooperative reaction–diffusion model of nuclear reactors, by converting the system to an equivalent cooperative one.     

A non-cooperative interpretation of the kernel

The purpose of the paper is to propose a bargaining game to interpret the kernel non-cooperatively. Based on the idea of the Davis-Maschler reduced game, a bilateral bargaining procedure is provided in our game model. We show that the set of all subgame perfect equilibrium outcomes of our non-cooperative game coincides with the kernel for transferable utility games.     

A system of equilibria for non-cooperative games

We develop the foundations of a new theory of non-cooperative games based on natural equilibrium concepts (without any artificial behavioral norms) and dispensing with the use of the characteristic function, which is the basis for all known theories that (as practical experience shows) have no relevance in applications. __________ Translated from Nelineinaya Dinamika i Upravlenie, No. 3, pp. 167–178, 2003.     

A continuous time solution for optimal claim limits in vehicle insurance

The traditional method of obtaining optimal claim limits for vehicle insurance is to discretise the state space and use successive approximations. In this paper we show how the stochastic dynamic programming equations reduce to a set of differential equations, in which these are easily solved to provide exact continuous time solutions. The resulting model can be used for evaluating alternative levels of excess.     

A general MPCC model and its solution algorithm for continuous network design problem

This paper formulates the continuous network design problem as a mathematical program with complementarity constraints (MPCC), with the upper level a nonlinear programming problem and the lower level a nonlinear complementarity problem. Unlike in most previous studies, the proposed framework is more general, in which both symmetric and asymmetric user equilibria can be captured. By applying the complementarity slackness condition of the lower-level problem, the original bilevel formulation can be converted into a single-level and smooth nonlinear programming problem. In order to solve the problem, a relaxation scheme is applied by progressively restricting the complementarity condition, which has been proven to be a rigorous approach under certain conditions. The model and solution algorithm are tested for well-known network design problems and promising results are shown.     

A non-cooperative approach to the cost spanning tree problem

We associate to each cost spanning tree problem a non-cooperative game, which is inspired by a real-life problem. We study the Nash equilibria and subgame perfect Nash equilibria of this game. We prove that these equilibria are closely related with situations where agents connect sequentially to the source.Finicial support from the Ministerio de Ciencia y Tecnologia and FEDER, and Xunta de Galicia through grants BEC2002-04102-C02-01 and PGIDIT03PXIC30002PN is gratefully acknowledged.     

Comparison principle for non-cooperative elliptic systems

This paper presents some sufficient conditions for the validity of the comparison principle for weak and classical solutions of non-cooperative weakly-coupled systems of elliptic second-order PDE.     

A solution algorithm for non-convex mixed integer optimization problems with only few continuous variables

Geometric branch-and-bound techniques are well-known solution algorithms for non-convex continuous global optimization problems with box constraints. Several approaches can be found in the literature differing mainly in the bounds used.     

Infinitely many solutions for non-cooperative elliptic systems

In this paper, we consider the existence of infinitely many solutions of noncooperative elliptic systems perturbed from odd cases.     

Wave-front solution behaviour for continuous neural networks with lateral inhibition

^** Email: rsittipong{at}yahoo.com^*** Corresponding author. Email: jbell{at}math.umbc.edu^**** Email: scylb{at}mahidol.ac.th In this paper we discuss the shape of travelling wave-frontsolutions to a model for a single continuous layer of nervecells originally introduced by Amari (1977, Dynamics of patternformation in lateral inhibition-type neural fields. Biol. Cybern.,27, 77–87). The neural field is homogeneous and isotropic,and the connection function is one of lateral inhibition type,meaning that nearby connecting cells have an excitatory influence,while more spatially distant cells impose an inhibitory influence.We give results on the shape of the wave-front solutions, whichare non-monotone and exhibit different shapes depending on thesize of a threshold parameter. For a layer of excitatory cellsindirectly inhibited by a second layer of cells, we derive resultson the qualitative behaviour of wave-fronts for changes in parametersrepresenting the inhibitory firing threshold and the time-scaleof the inhibition process. This study shows how intrinsic celland network parameter can interact to shape global responseproperties.     

Energy method as solution for deformation of geosynthetic-reinforced embankment on Pasternak foundation

To more accurately analyze the settlement of geosynthetic-reinforced embankments on soft soil foundation, we simplified the ground surface structures as an Euler–Bernoulli beam, and the geosynthetic-reinforced layer as a Timoshenko beam. The granular fill and the soft soil foundation were both modelled using two-parameter Pasternak foundation models. We used energy method to establish energy balance equations for the system, and then we used the principle of resident potential energy to derive the governing differential equations of the settlement of the ground surface structures and the geosynthetic-reinforced layer. The MATLAB solver bvp4c was used to obtain numerical solutions for the settlement of the ground surface structures and the geosynthetic-reinforced layer on Pasternak foundations. By comparing to test results and existing models, the validity of the proposed solution is verified. This study analyzed the effects of parameters, such as flexural rigidity of the geosynthetic-reinforced layer, shear modulus of the granular fill, thickness of the soft soil foundation, and horizontal shear modulus of the Timoshenko beam, on the settlement of the ground surface structures and the geosynthetic-reinforced layer. The results showed that the model using a Pasternak foundation and a Timoshenko beam is more accurate at predicting settlement than that using a Winkler foundation and an Euler–Bernoulli beam.     

Analytical solution considering the tangential effect for an infinite beam on a viscoelastic Pasternak foundation

In this study, the dynamic response of an infinite beam resting on a Pasternak foundation subjected to inclined travelling loads was developed in the form of the analytical solution wherein the tangential effect between the beam and foundation and the damping were taken into consideration. Three parameters were used to model the mechanical resistance of the viscoelastic Pasternak foundation, one of them accounts for the compressive stress in the soil, the other accounts for the shearing effect of soils, and the last one accounts for the damping of the foundation. By contrast, the Pasternak model is more realistic than the Winkler model that just considers the compressive resistance of soil. In the paper, the tangential effect between the beam and foundation was simulated by a series of separate horizontal springs, the damping was also considered to obtain the dynamic response under forced vibration. The theory of elasticity and Newton's laws were used to derive the governing equation. To simplify the partial-differential equation to an algebraic equation, the double Fourier transformation was used wherein the analytical solution in the frequency domain for the dynamic response of the beam is obtained. And its inversion was adopted to convert the integral representation of the solution into the time domain. The degraded solution was then utilized to verify the validity of the proposed solution. Finally, the Maple mathematical software was used for further discussion. The solution proposed in this study can be a useful tool for practitioners.     

A foundation for competence set analysis

For each decision problem, there is a competence set consisting of knowledge, information and skills for its effective solution. How the decision-maker acquires and expands his/her competence set plays a key role in the process and quality of decision-making. This paper provides a mathematical foundation for studying competence sets, their expansion processes and stability. Time and cost functions for expansion, reachable domains, effective expansion using minimal spanning trees, random set decomposition of competence sets, marginal analysis, connectivity, metrization and stability of competence sets are some key concepts introduced.     

Analytical solution for general nonlinear continuous systems in a complex form

In this paper, the method of multiple scales is used to study free vibrations and primary resonances of geometrically nonlinear spatial continuous systems with general quadratic and cubic nonlinear operators in a complex form. It is found that in the free vibrations of general continuous systems in a complex form, both forward and backward modes are excited. This situation is in contrast to the primary resonances in which only forward modes are excited. Consequently, one may determine the form of solution before applying the multiple scales method to the equation. This analysis is applicable to general continuous systems with gyroscopic and Coriolis effects and includes many nonlinear problems as a special case. As an example of application of this general solution, free vibrations and primary resonances of a simply supported rotating shaft with stretching nonlinearity are considered.     

Distributions for which div v = F has a continuous solution

The equation div v = F has a continuous weak solution in an open set U ? ?^m if and only if the distribution F satisfies the following condition: the F(φ_i) converge to 0 for every sequence {φ_i} of test functions such that the support of each φ_i is contained in a fixed compact subset of U, and in the L¹ norm, {φ_i} converges to 0 and {?φ_i} is bounded. © 2007 Wiley Periodicals, Inc.     

A continuous linear optimization model for the exact solution of travelling-salesman-problems in connexion with expansion planning of ring networks

Summary This work describes a subproblem in connexion with a newly developed optimization model for dynamic expansion planning of ring networks serving for electric power distribution in urban supply areas. This subproblem is the exact solution of a Travelling-salesman-problem by a continuous linear optimization model. A short survey over the complete planning model is given too. The model is created by a problem specific, flexibly applicable matrix generator and solved by a powerful commercial standard programming package. The symmetric Travelling-salesman-problems under consideration are characterized as follows: The set of potential ways is determined by the public streets of a city and the nodes to be connected are distributed uniformly over the supply area. The new optimization model allows the exact solution of problems up to about 60 nodes. The practical application is demonstrated by two examples.

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Zusammenfassung Diese Arbeit beschreibt ein Teilproblem im Zusammenhang mit einem neu entwickelten Optimierungsmodell zur dynamischen Ausbauplanung von Ringnetzen für die Verteilung elektrischer Energie in städtischen Versorgungsgebieten. Dieses Teilproblem betrifft die exakte Lösung des Problems des Handlungsreisenden mittels eines kontinuierlichen linearen Optimierungsmodells. Auch das Gesamtmodell wird kurz beschrieben. Es wird von einem problemspezifischen, flexibel anwendbaren Matrixgenerator erstellt, die Lösung erfolgt mit Hilfe leistungsfähiger kommerzieller Standardsoftware. Die vorliegenden symmetrischen Rundreiseprobleme sind dadurch charakterisiert, daß als Wege die städtischen Straßen zur Verfügung stehen und daß die zu verbindenden Punkte relativ gleichmäßig verteilt sind. Das neu entwickelte Optimierungsmodell gestattet die exakte Lösung von Aufgaben bis zu etwa 60 Knoten. Die Anwendung in der Praxis wird an zwei Beispielen demonstriert.

     

Existence theorems of nash equilibria for non-cooperative n-person games

In this paper, we first obtain existence theorems of Nash equilibria for non-cooperative n-person games which generalize a corresponding result of Nikaido and Isoda (1955). As applications, we give two new existence theorems of -equilibrium points which generalize that of Tijs (1981). Finally, a saddle point theorem of Komiya (1986) is deduced from one of our existence theorems of -equilibrium points.     

A minimalist two-level foundation for constructive mathematics

We present a two-level theory to formalize constructive mathematics as advocated in a previous paper with G. Sambin.One level is given by an intensional type theory, called Minimal type theory. This theory extends a previous version with collections.The other level is given by an extensional set theory that is interpreted in the first one by means of a quotient model.This two-level theory has two main features: it is minimal among the most relevant foundations for constructive mathematics; it is constructive thanks to the way the extensional level is linked to the intensional one which fulfills the “proofs-as-programs” paradigm and acts as a programming language.     

不确定条件下n人非合作博弈均衡点集的通有稳定性

基于经典博弈模型的Nash均衡点集的通有稳定性和具有不确定参数的n人非合作博弈均衡点的概念,探讨了具有不确定参数博弈的均衡点集的通有稳定性.参照Nash均衡点集稳定性的统一模式,构造了不确定博弈的问题空间和解空间,并证明了问题空间是一个完备度量空间,解映射是上半连续的,且解集是紧集（即usco（upper semicontinuous and compact-valued）映射）,得到不确定参数博弈模型的解集通有稳定性的相关结论.