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.     

A local search approach to a circle cutting problem arising in the motor cycle industry

This paper is concerned with the development of a customized circle packing algorithm for a manufacturer of sprockets for the motor cycle industry. Practical constraints mean that the problem differs somewhat from those tackled elsewhere in the literature. In particular, the layouts need to conform to a given structure. This is achieved by using a local search algorithm with an appropriate starting solution and a series of neighbourhoods designed to preserve the layout structure. Empirical evidence based on real data shows that the quality of the resulting solutions closely matches that of cutting patterns currently produced by human experts. Computation times average around 20–30?s per order as compared to several hours for an equivalent manual solution.     

Controllability of Functional Integro-Differential Inclusions with an Unbounded Delay

In this paper, a sufficient condition is established for the controllability of neutral functional integro-differential inclusions with an unbounded delay in Banach spaces. The approach used is a fixed-point theorem for condensing maps due to Martelli and the theory of analytic semigroup of linear operators. Communicated by F. Zirilli Research supported by NNSF of China, by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of the Ministry of Education of China, and by the Qing Lan Talent Engineering Fund QL-05-164 of Lanzhou Jiaotong University. The authors are grateful to Professor F. Zirilli and two anonymous referees for valuable suggestions improving this paper.     

Game theoretic analysis of the bargaining process over a long-term replenishment contract

This paper presents supplier–buyer models to describe the bargaining process between a supplier and a buyer over a long-term replenishment contract. Two different models are developed: one for the situation where the supplier has superior bargaining power over the buyer, and the other for the reverse situation. For each model, a method is derived that employs game theory-based analysis to determine the best strategy for each agent. A computational experiment is conducted to estimate the efficiency of the methods and to determine the economic implications of the results. The result indicates that each algorithm is very efficient compared to other strategies. We also verify that the solutions derived from each model are Nash equilibrium. Significantly improved outcomes are obtained for both agents by agreeing to the terms generated by the algorithms over the terms selected in the usual manner.     

Tunneling radiation of a Gibbons-Maeda dilaton black hole

We use the Parikh-Wilczek method to treat Hawking radiation as a tunneling process across the event horizon and calculate the emission rate of a Gibbons-Maeda dilaton black hole. We show that if self-gravitation is taken into account, then the radiation deviates from the purely thermal spectrum, and the corrected spectrum is consistent with an underlying unitary theory. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 1, pp. 172–175, April, 2007.     

Asymptotic and boundary integral formulae for the computational reconstruction of small conductivity imperfections

In this paper we investigate the electrostatic problem of determining conductivity profiles from the knowledge of boundary currents and voltages. We obtain an improved estimate for the voltage potential of a two-dimensional conductor having finitely many circular inclusions and piecewise constant conductivity profile. We derive an asymptotic expansion for the voltage potential in terms of the reference voltage potential and the location, size, and conductivity of the inhomogeneities. This representation is used to formulate the nonlinear least squares problem for estimating the location and size of the inhomogeneities. Required boundary data for the voltage potential are generated numerically by solving a system of integral equations. Computational experiments are presented to demonstrate the effectiveness of our identification procedure.     

Theory of Valuations on Manifolds: A Survey

This is a non-technical survey of a recent theory of valuations on manifolds constructed in [A10], [A11], [AF] and [A12], and actually a guide to this series of articles. We also review some recent related results obtained by a number of people. Received: February 2006, Revision: June 2006, Accepted: June 2006     

UPML formulation for truncating conductive media in curvilinear coordinates

This work presents a formulation based on UPML for truncating conductive media by using a local and non-orthogonal coordinate system to solve Maxwell’s equations by the FDTD method. The detailed procedure for obtaining the UPML equations for this case is shown and the complete equation set is provided.     

Charge density fluctuation of low frequency in a dusty plasma

The charge density fluctuation of low frequency in a dusty plasma, which is derived from the longitudinal dielectric permittivity of the dusty plasma, has been studied by kinetic theory. The results show that theP value, which describes the relative charge density on the dust in the plasma, and the charging frequency of a dust particle Ω _c , which describes the ratio of charge changing of the dust particles, determine the character of the charge density fluctuation of low frequency. For a dusty plasma ofP≪1, when the charging frequency Ω _c , is much smaller than the dusty plasma frequency ω_d, there is a strong charge density fluctuation which is of character of dust acoustic eigenwave. For a dusty plasma ofP≫1, when the frequency Ω _c , is much larger than ω _d there are weaker fluctuations with a wide spectrum. The results have been applied to the ionosphere and the range of radius and density of dust particles is found, where a strong charge density fluctuation of low frequency should exist.     

泛代数的二次扩张

在本文中引入了泛代数的二次扩张的概念，解决了ＴＵ－ＥＣ（Ａ）和ＵＴ－ＥＣ（Ａ）的存在、真类和基数问题，范畴ＴＵ－ＥＣ（Ａ）（及ＵＴ－ＥＣ（Ａ）），并得到了有关二次扩张的几个同构定理，还对一点二次扩张作了讨论。