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).     

An exponentially fitted special second-order finite difference method for solving singular perturbation problems

An exponentially fitted special second-order finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer at one end (left or right) point. A fitting factor is introduced in a tri-diagonal finite difference scheme and is obtained from the theory of singular perturbations. Thomas Algorithm is used to solve the system and its stability is investigated. To demonstrate the applicability of the method, we have solved several linear and non-linear problems. From the results, it is observed that the present method approximates the exact solution very well.     

Weighted extended b-splines for one-dimensional electromagnetic problems

This paper considers the weighted extended b-splines as basis function for finite element method in electromagnetics and compares with the standard finite element method applied to the two-point boundary value problems with different boundary conditions. This new approach, which provides more accurate results than standard finite element method, is presented to compare other numerical techniques and applied to one-dimensional electromagnetic problems. Computed results are compared with other numerical results in literature.     

On a free group of transformations defined by an automaton

We prove that three automorphisms of the rooted binary tree defined by a certain 3-state automaton generate a free non-Abelian group of rank 3. Both authors are supported by the NSF grants DMS-0308985 and DMS-0456185. Yaroslav Vorobets is supported by a Clay Research Scholarship.     

几种约束广义逆矩阵的有限算法

1引言与引理众所周知，关于非奇异方阵的正则逆的有限算法是由Faddeev大给在1949年之前提出的，这就是著名的Faddeev算法[1，P…334-336]。自从五十年代中期广义逆矩阵的研究复兴与发展以来，有不少学者提出了关于广义逆矩阵的有限算法。第一个给出关于广义逆矩     

Studies on Three—electrode Semiconductor Lasers

Using the ray trace method,three-section semiconductor lasers are studied .An analytic expression of output power for the three-section semiconductor lasers is derived for the first time.Frome this expression,threshold condition is also obtained.     

Algebraic properties of cryptosystem PGM

In the late 1970s Magliveras invented a private-key cryptographic system calledPermutation Group Mappings (PGM). PGM is based on the prolific existence of certain kinds of factorization sets, calledlogarithmic signatures, for finite permutation groups. PGM is an endomorphic system with message space ℤ_|G| for a given finite permutation groupG. In this paper we prove several algebraic properties of PGM. We show that the set of PGM transformations ℐ _G is not closed under functional composition and hence not a group. This set is 2-transitive on ℤ_|G| if the underlying groupG is not hamiltonian and not abelian. Moreover, if the order ofG is not a power of 2, then the set of transformations contains an odd permutation. An important consequence of these results is that the group generated by the set of transformations is nearly always the symmetric group ℒ_|G|. Thus, allowing multiple encryption, any permutation of the message space is attainable. This property is one of the strongest security conditions that can be offered by a private-key encryption system. S. S. Magliveras was supported in part by NSF/NSA Grant Number MDA904-82-H0001, by U.S. West Communications, and by the Center for Communication and Information Science of the University of Nebraska.     

Time dependent analysis of finite buffer fluid flows and risk models with a dividend barrier

Based on the matrix-analytic approach to fluid flows initiated by Ramaswami, we develop an efficient time dependent analysis for a general Markov modulated fluid flow model with a finite buffer and an arbitrary initial fluid level at time 0. We also apply this to an insurance risk model with a dividend barrier and a general Markovian arrival process of claims with possible dependencies in successive inter-claim intervals and in claim sizes. We demonstrate the implementability and accuracy of our algorithms through a set of numerical examples that could also serve as test cases for comparing other solution approaches.      

The solution of a convection–diffusion–reaction equation arising from cathodic reduction in a pulsating crack

This paper derives the convection–diffusion-reaction equation governing the reaction between the dissolved oxygen in sea-water and the steel walls of a pulsating crack. By the neglect of the diffusion term it is shown that an exact solution of the convection-reaction equation can be obtained. A numerical method for the solution of the complete convection–diffusion-reaction equation is derived by the use of finite differences. The numerical computation of the initial transient and the final periodic steady-state values is also discussed.