Primes in quadratic progressions on average

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

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.     

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     

高等师范学校物理专业课程结构改革研究

为解决高等师范院校物理专业学生的知识结构和实际能力与社会需要明显不相适应的矛盾，我们对四年制物理专业的课程结构进行了全面改革。改革后，毕业生不仅能胜任普通中学或职业中学（职业中专）的教学，而且有能力参与厂矿企业的技术工作，具有更广泛的适应性和更强的竞争力。     

The Existence of Periodic Orbits for Higher Dimensional Autonomous Systemswith Small Perturbations

ＴｈｅＥｘｉｓｔｅｎｃｅｏｆＰｅｒｉｏｄｉｃＯｒｂｉｔｓｆｏｒＨｉｇｈｅｒＤｉｍｅｎｓｉｏｎａｌＡｕｔｏｎｏｍｏｕｓＳｙｓｔｅｍｓｗｉｔｈＳｍａｌｌＰｅｒｔｕｒｂａｔｉｏｎｓＪｉａｎｇＬｉｑｉｎｇ（蒋里强）；ＺｈｏｕＹｉ（周毅）；ＦａｎＹｅ（范晔）（...     

α－萘甲酰呋喃甲酰甲烷的合成及谱学性质的研究

本文用Ｃｌａｉｓｅｎ缩合反应合成了未见文献报道的一种新的β－二酮，α－萘甲酰呋喃甲酰甲烷（α－ＮＦＭ），考察了该化合物的红外光谱、质谱及核磁共振氢谱。确定其存在着互变异构。