Prime Fano threefolds and integrable systems

For a general K3 surface S of genus g, with 2 ≤ g ≤ 10, we prove that the intermediate Jacobians of the family of prime Fano threefolds of genus g containing S as a hyperplane section, form generically an algebraic completely integrable Hamiltonian system. The first author is partially supported by grant MI1503/2005 of the Bulgarian Foundation for Scientific Research.     

Primes in quadratic progressions on average

In this paper, we establish a theorem on the distribution of primes in quadratic progressions on average.     

CAS based approach for discussing subset construction

This paper continues the discussion of teaching nondeterminism (see [6]) where we presented a didactic approach introducing the notion of nondeterministic automata. Although in this paper we use the same methodology we have to face up to new didactic challenges. Namely, teaching the subset construction requires answers to the question how can CAS be used in teaching the different phases of mathematical problem solving so that we can reach higher cognitive efficiency.     

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.     

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