An algorithm based on the regularization and integral mean value methods for the Fredholm integral equations of the first kind

In this paper, an algorithm based on the regularization and integral mean value methods, to handle the ill-posed multi-dimensional Fredholm equations, is introduced. The application of this algorithm is based on the transforming the first kind equation to a second kind equation by the regularization method. Then, by converting the first kind to a second kind, the integral mean value method is employed to handle the resulting Fredholm integral equations of the second kind. The efficiency of the approach will be shown by applying the procedure on some examples.     

Heuristics for multi-attribute vehicle routing problems: A survey and synthesis

The attributes of vehicle routing problems are additional characteristics or constraints that aim to better take into account the specificities of real applications. The variants thus formed are supported by a well-developed literature, including a large variety of heuristics. This article first reviews the main classes of attributes, providing a survey of heuristics and meta-heuristics for Multi-Attribute Vehicle Routing Problems (MAVRP). It then takes a closer look at the concepts of 64 remarkable meta-heuristics, selected objectively for their outstanding performance on 15 classic MAVRP with different attributes. This cross-analysis leads to the identification of “winning strategies” in designing effective heuristics for MAVRP. This is an important step in the development of general and efficient solution methods for dealing with the large range of vehicle routing variants.     

Two-player simultaneous location game: Preferential rights and overbidding

Competitive location problems can be characterized by the fact that the decisions made by others will affect our own payoffs. In this paper, we address a discrete competitive location game in which two decision-makers have to decide simultaneously where to locate their services without knowing the decisions of one another. This problem arises in a franchising environment in which the decision-makers are the franchisees and the franchiser defines the potential sites for locating services and the rules of the game. At most one service can be located at each site, and one of the franchisees has preferential rights over the other. This means that if both franchisees are interested in opening the service in the same site, only the one that has preferential rights will open it. We consider that both franchisees have budget constraints, but the franchisee without preferential rights is allowed to show interest in more sites than the ones she can afford. We are interested in studying the influence of the existence of preferential rights and overbidding on the outcomes for both franchisees and franchiser. A model is presented and an algorithmic approach is developed for the calculation of Nash equilibria. Several computational experiments are defined and their results are analysed, showing that preferential rights give its holder a relative advantage over the other competitor. The possibility of overbidding seems to be advantageous for the franchiser, as well as the inclusion of some level of asymmetry between the two decision-makers.     

Multiple solutions of a quasilinear elliptic system involving the nonlinear boundary conditions on exterior domain

In this paper, we consider the multiplicity results of nontrivial nonnegative solutions of the quasilinear p‐Laplacian system with the nonlinear boundary conditions: (0.1) where Ω is a smooth exterior domain in is the outward normal derivative on the boundary Γ = ?Ω, and . By the Nehari manifold and variational methods, we prove that the problem (0.1) has at least two nontrivial nonnegative solutions when the pair of the parameters (λ,μ) belongs to a certain subset of . Copyright © 2012 John Wiley & Sons, Ltd.     

Upper (lower) bounds of the eigenvalues,spread and the open problems for the real symmetric interval matrices

This work is concerned with exploring the upper bounds and lower bounds of the eigenvalues of real symmetric matrices of order n whose entries are in a given interval. It gives the maximum and minimum of the eigenvalues and the upper bounds of spread of real symmetric interval matrices in all cases. It also gives the answers of the open problems for the maximum and minimum of the eigenvalues of real symmetric interval matrices. Copyright © 2012 John Wiley & Sons, Ltd.     

EQUIVALENCIES IN THE FISHERY

Abstract We consider the management of a resource by a sole owner whose utility depends on income and leisure. Income is generated from time spent harvesting the resource and time spent working for a wage in the nonfishing sector. Our analysis produces two results. (i) The sole owner maximizing discounted utility will seek to achieve the same steady‐state optimum as a manager seeking to maximize discounted net revenue. (ii) The approach paths to the common steady‐state optimum will be the same if the utility function is linear in income and separable in income and leisure. These equivalencies are illustrated in a numerical example.     

The unknown object problem in a sea with sloping bottom

This article considers the acoustic unknown object problem for a shallow ocean with a sloping seabed. The incident waves are sent from point sources along a s raight line parallel to the sea surface, and the corresponding scattered fields are measured from a line above the unknown object. We prove a uniqueness theorem for the inverse problem,and describe a generalizeddual space indicator method for numerical solution.Numerical results are given in Section 4.     

Innovative solution of a 2D elastic transmission problem¶

This article is concerned with a boundary-field equation approach to a class of boundary value problems exterior to a thin domain. A prototype of this kind of problems is the interaction problem with a thin elastic structure. We are interested in the asymptotic behavior of the solution when the thickness of the elastic structure approaches to zero. In particular, formal asymptotic expansions will be developed, and their rigorous justification will be considered. As will be seen, the construction of these formal expansions hinges on the solutions of a sequence of exterior Dirichlet problems, which can be treated by employing boundary element methods. On the other hand, the justification of the corresponding formal procedure requires an independence on the thickness of the thin domain for the constant in the Korn inequality. It is shown that in spite of the reduction of the dimensionality of the domain under consideration, this class of problems are, in general, not singular perturbation problems, because of appropriate interface conditions.     

一类带积分边界条件的三阶微分方程边值问题的解

运用Banach压缩映射原理以及Leray-Schauder连续性原理,在非线性项为L1-Caratheodory函数的条件下,研究了一类带积分边界条件的三阶微分方程边值问题解的唯一性、存在性以及解集的紧性.     

一维p-Laplace二阶脉冲微分方程的奇异边值问题

脉冲现象作为一种瞬时突变现象,在现代科技各领域的实际问题中是普遍存在的.本文研究具有奇异边值的一维p-Laplace二阶微分方程在脉冲影响下的正解的存在性,介绍了解的一般性存在定理,并用A-A定理和不动点定理证明了一维p-Laplace二阶脉冲微分方程的奇异边值问题的正解存在性定理.