The Study of Minimax Inequalities, Abstract Economics and Applications to Variational Inequalities and Nash Equilibria

In this survey, a new minimax inequality and one equivalent geometricform are proved. Next, a theorem concerning the existence of maximalelements for an LC-majorized correspondence is obtained.By the maximal element theorem, existence theorems of equilibrium point fora noncompact one-person game and for a noncompact qualitative game withLC-majorized correspondences are given. Using the lastresult and employing 'approximation approach', we prove theexistence of equilibria for abstract economies in which the constraintcorrespondence is lower (upper) semicontinuous instead of having lower(upper) open sections or open graphs in infinite-dimensional topologicalspaces. Then, as the applications, the existence theorems of solutions forthe quasi-variational inequalities and generalized quasi-variationalinequalities for noncompact cases are also proven. Finally, with theapplications of quasi-variational inequalities, the existence theorems ofNash equilibrium of constrained games with noncompact are given. Our resultsinclude many results in the literature as special cases.     

Optimal observation network in geostatistics and underground hydrology

Mathematical models and algorithms for the optimal design of data collection for regionalized variables are presented. The topics considered subsume as a special case optimal drilling strategies in hydrology, the mining industries and other geostatistical applications. In these disciplines an optimal design is a critical consideration since data, can only be obtained through an expensive drilling process.The methods given here are based on the theory of regionalized variables and of kriging. The basis of the methods for locating a single additional data point, and for locating multiple points, is the theory of minimizing uncertainty in parameter estimation. That is, the possible locations of additional points must be determined on the basis of surface analysis with respect to the projected costs of obtaining this data.After a summary of basic kriging techniques, four models are discussed. The first deals with the optimal location problem for a single experimental point, and the second, third and fourth models pertain to the case of multiple additional points. (Unfortunately the repeated application of the single-point model leads only to approximations of the global optima, since the global optima are usually unobtainable as a simple sum of the partial optima.) In the second model, an optimal regular observation network is to be designed to minimize the uncertainty of the estimation process subject to either the given number of additional data, or an upper bound for the cost of the additional data. In the fourth model, the number or cost of additional points is minimized subject to bounded uncertainty conditions. Finally, a numerical example will be used to illustrate the models and algorithms.     

Symmetrization of matrix technique in a finite element context

A finite element Galerkin-based formulation of the mass conservation and momentum equations can require, if convective type terms are retained in the coefficient matrix, a non-symmetric solver. The resulting increase in core storage for efficient utilization of CPU time can be considerable. The current paper advocates a simple symmetrization of matrix technique, at element level which results in a considerable reduction in core requirement. The increase in CPU time required when solving linear systems of equations is considerable. However, for nonlinear systems the penalty can be negligible.     

Spatial exponential fitting scheme for the solution of steady and unsteady diffusion-convection problems in two-dimensions

Using a spatial exponential fitting scheme, the steady diffusion-convection problem in two-dimensions is reduced to a system of linear equations, while the unsteady problem is reduced to a system of ordinary-differential equations that may be solved by a fully-implicit time scheme. Also, a predictor-corrector fitting scheme is presented for solving the unsteady problem. Numerical results for the Raithby steady problem and the unsteady dispersion in a shallow sea problem are shown.     

Modelling of discontinuities through dipole distribution

An indirect boundary element method using dipole distribution is employed in order to model discontinuities inside the flow region. The problem of flow under a dam is treated with a sheet-pile in its foundation. The discontinuity across the sheet-pile is demonstrated, a general boundary element procedure for a mixed problem is outlined and the coefficients of the linear system are given in analytical form. Very good agreement with existing analytical results is obtained.     

A multi-objective optimization model for aquifer management under transient and steady-state conditions

A multiple objective waste-disposal model is developed and analysed. The model is a modification of the single objective waste-disposal model of Alley, Aguado and Remson. The solution structure is obtained using the method of constraints so that dual variables (shadow prices) are available with the solutions.     

船舶碰撞危险度模型的构建

运用模糊数学的综合评判理论,把会遇中目标船的DCPA、TCPA两船距离、相对方位、船速比5个因素作为基本评判参数,建立碰撞危险度的评价模型．而将其它因素,如航行区域状况、能见度情况和船舶的操纵性能等,作为对上述因素的危险隶属度函数的修正加以考虑．引入了船舶领域、动界等概念,以对来船构成的本船危险度进行客观有效地评价,为安全避碰提供合理依据．     

$\Phi $-functions for complex 2D-objects

Within two-dimensional cutting and packing problems with irregular shaped objects, the concept of -functions has been proven to be very helpful for several solution approaches. In order to construct such -functions a previous work, in which so-called primary objects are considered, is continued. Now -functions are constructed for pairs of objects which can be represented as a finite combination (union, intersection, complement) of primary objects which allows the handling of arbitrary shaped objects by appropriate approximations of sufficient accuracy.Received: October 2002, Revised: October 2003, AMS classification: 65K05, 90C26, 90B06All correspondence to: Guntram Scheithauer     

The Laguerre polyhedral decomposition: application to protein folds

An extension of the Voronoi tessellation, the Laguerre polyhedral decomposition, is introduced and applied to the analysis of the packing geometry of amino-acids in folded proteins. This method considers an ensemble of points with different weights and therefore it is well suited for a geometrical analysis of a set of objects with a wide size distribution. With this method it is shown that the true volumes occupied by the amino-acids inside a protein is better described than with the standard Voronoi procedure. This method allows defining unambiguously (without cut-off distance) the neighborhood for each amino-acid in a given protein and contact matrices can be established which contain all topological informations on the internal structure. Finally, a statistical analysis of the geometrical characteristics of the polyhedra attached to each amino-acid is done over a collection of 35 proteins. Received 20 November 2002 / Received in final form 26 March 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: sadoc@lps.u-psud.fr     

Convergence Acceleration of Some Continued Fractions

The tails of a continued fraction satisfy a bilinear recurrent equation. Transforming iteratively these tails (in a special manner) as well as these equations one may obtain finally, for a given fraction, a new, so-called diagonal continued fraction (DF) having the same value. For many important classes of continued fractions the DF has a calculable analytical form and converges qualitatively faster. Using the same method one may transform some hypergeometrical series directly into fast convergent DFs.