Nonparametric estimation and adaptive control in a class of finite Markov decision chains

We consider a class of Markov decision processes withfinite state and action spaces which, essentially, is determined by the following condition: The state space isirreducible under the action of any stationary policy. However, except by this restriction, the transition law iscompletely unknown to the controller. In this context, we find a set of policies under which thefrequency estimators of the transition law are strongly consistent and then, this result is applied to constructadaptive asymptotically discount-optimal policies.Dedicated to Professor Truman O. Lewis, on the occasion of his sixtieth birthdayThis research was supported in part by the Third World Academy of Sciences (TWAS) under Grant TWAS RG MP 898-152, and in part by the Consejo Nacional de Ciencia y Tecnología (CONACYT) under Grant A128CCOEO550 (MT-2).     

Separable anisotropic differential operators and applications

The nonlocal boundary value problems for anisotropic partial differential-operator equations with a dependent coefficients are studied. The principal parts of the appropriate generated differential operators are nonself-adjoint. Several conditions for the maximal regularity and the fredholmness in Banach-valued Lp-spaces of these problems are given. These results permit us to establish that the inverse of corresponding differential operators belongs to Schatten q-class. Some spectral properties of the operators are investigated. In applications, the nonlocal BVP's for quasielliptic partial differential equations and for systems of quasielliptic equations on cylindrical domain are studied.     

Runge–Kutta interpolants for high precision computations

Runge–Kutta (RK) pairs furnish approximations of the solution of an initial value problem at discrete points in the interval of integration. Many techniques for enriching these methods with continuous approximations have been proposed. Here we construct C ¹ continuous, eighth and ninth order interpolation methods for a recently appeared RK pair of orders 9(8). These interpolants share a very small leading truncation error making them suitable for use at quadruple precision, i.e. 32–33 decimal digits of accuracy. Extended numerical results justify our effort.     

A parallel version of the preconditioned conjugate gradient method for boundary element equations

The parallel version of precondition techniques is developed for matrices arising from the Galerkin boundary element method for two-dimensional domains with Dirichlet boundary conditions. Results were obtained for implementations on a transputer network as well as on an nCUBE-2 parallel computer showing that iterative solution methods are very well suited for a MIMD computer. A comparison of numerical results for iterative and direct solution methods is presented and underlines the superiority of iterative methods for large systems.     

无穷区间上二阶微分方程的边值问题

利用Schauder不动点定理讨论了一类非线性二阶微分方程在无穷区间上的边值问题无界解的存在性，部分改进了郭大钧教授最近得到的结果。     

Fluorescent humic substances–arsenic complex in well water in areas where blackfoot disease is endemic in Taiwan

The relationship between the four components, (1) fluorescence intensity, (2) arsenic concentration, (3) pH and (4) total dissolved solids, (TDS) measured in well waters from areas in Taiwan where blackfoot disease (BFD) is endemic was studied, as well as the relationships between the four degrees of BFD and each of the above four symptomatic components, in order to evaluate the etiological factors of BFD more progressively. The following 95% confidence intervals were obtained in well water samples (n = 1189): fluorescence intensity, 26.837–32.570; arsenic concentration, 0.103–0.127 mg dm^?3; pH, 7.466–7.519; and TDS 733.063–801.647 mg dm^?3. Fluorescence intensities of the four degrees of BFD were not all the same (F = 64.54, P < 0.001), and nor were arsenic concentrations (F = 72.03, P < 0.001), pH values (F = 7.30, P < 0.001), nor TDS values (F = 10.76, P < 0.001). In addition, multiple comparisons indicate that the higher the epidemical degree, the higher the fluorescence intensities, arsenic concentrations and pH values become; however, such a relationship is not found for TDS values. Moreover, the fluorescence intensities have positive linear correlations with arsenic concentrations (r = 0.49, P < 0.001), pH (r = 0.25, P < 0.001), and TDS (r = 0.18, P < 0.001), as do the arsenic concentrations with pH (r = 0.22, P < 0.001). Of the four epidemical degree groups, pairs are not significantly different from one another in correlation coefficients between fluorescence intensity and arsenic concentration, which implies a steady relationship between fluorescent compounds and arsenic. We conclude that fluorescent compounds in well water, as possible etiological factors of BFD, are closely related to arsenic along with pH and TDS values in the areas where BFD is endemic. In addition, we infer that a complex is formed by fluorescent compounds, arsenic and other metals.     

Ranking Functions Induced by Weighted Average of Fuzzy Numbers

In this paper we present two definitions of possibilistic weighted average of fuzzy numbers, and by them we introduce two different rankings on the set of real fuzzy numbers. The two methods are dependent on several parameters. In the first case, the parameter is constant and the results generalize what Carlsson and Fuller have obtained in (2001). In the second case, the parameter is a function, not fixed a priori by the decision maker, but it depends on the position of the interval on the real axe. In all the two cases we call the parameter degree of risk, which takes into account of a risk-tendency or aversion of the decision maker.     

用于留数算术中的数值／留数／数值的转换

介绍用光学方法完成留数算术中的数值/留数/数值的转换,并附有实验结果。     

Anisotropic elastodynamics in a half space: An analytic method for polynomial data

An initial boundary value problem for the dynamic system of anisotropic elasticity in a half space is studied in the paper. A novel method of finding an exact solution of this problem for a special polynomial form of initial data and inhomogeneous term of the system is described. On the base of this method the simulation of elastic waves in different homogeneous anisotropic half spaces is implemented.     

Closed solution to electromagnetic scattering of a plane wave by an eccentric cylinder coated with metamaterials

Closed series solution of electromagnetic scattering by an eccentric coated cylinder is achieved in matrix form. Diffracted field patterns are examined for an incident plane transverse magnetic (TM) wave. The solution is found by the classical separation of variables technique and the translational addition theorems. Wave transformation and orthogonality of the complex exponentials are employed to produce an infinite series. Numerical results are then shown by shortening the infinite series to a limited number of terms. Solutions are discussed for a dielectric or a metamaterial coating.