Radiation bursts from particles in the field of compact, impenetrable, astrophysical objects

The radiation emitted by charged, scalar particles in a Schwarzschild field with maximal acceleration corrections is calculated classically and in the tree approximation of quantum field theory. In both instances the particles emit radiation that has characteristics similar to those of gamma-ray bursters.     

关于左手性介质几何光学的研究（一）

根据几何光学中的费马原理和完善成像原理研究了光线经过正负折射率界面时的传播特性，推导了单负折射率完善成像的曲面方程，讨论了单块负折射率透镜成像特性的一些缺陷及改进方案，依此指出了最短时间原理的适用范围的局限性和利用左手性介质制作光学器件的优越性，为进一步研究左手性介质的光学特性和相关光学器件设计提供了理论基础.     

Minimal Ellipsoid Circumscribing a Polytope Defined by a System of Linear Inequalities

In this paper, we will propose algorithms for calculating a minimal ellipsoid circumscribing a polytope defined by a system of linear inequalities. If we know all vertices of the polytope and its cardinality is not very large, we can solve the problem in an efficient manner by a number of existent algorithms. However, when the polytope is defined by linear inequalities, these algorithms may not work since the cardinality of vertices may be huge. Based on a fact that vertices determining an ellipsoid are only a fraction of these vertices, we propose algorithms which iteratively calculate an ellipsoid which covers a subset of vertices. Numerical experiment shows that these algorithms perform well for polytopes of dimension up to seven.     

Irregularities of distribution with respect to strips

Summary A lower bound is established for the strip discrepancy of a broad class of point distributions. The bound implies unbounded strip discrepancy for equally weighted point distributions under favorable conditions. The methods of proof use notions from integral geometry.     

Geometry of Differential Equations: A Concise Introduction

A short introduction to geometrical theory of nonlinear differential equations is given to provide a unified overview to the collection 'Symmetries of differential equations and related topics'.     

The Kissing Triangles: The Aesthetics of Mathematical Discovery

Papert's (1978) appeal to reconsider the power and possibilities of the aesthetic in mathematics learning is often ignored in mathematics education research. This paper begins with the premise, put forth by Dewey (1934), that the aesthetic structures many dimensions of inquiry and experience. In the same way that using particular paintings, musical compositions, or even everyday experiences has been instrumental to attempts by philosophers to understand the aesthetic dimensions of meaning and experience in artistic domains, I propose that analysing a particular encounter with mathematics may help reveal the nature and role of the often nebulous responses of elegance, beauty, and `fit' to which mathematicians lay claim in their mathematical activity. To achieve this, I draw on and adapt the defining features of the aesthetic character of experience set forth by the aesthetician Beardsley (1982). This, in turn, sheds light on the role thataesthetics can play in mathematical inquiry and experience, and provides initial categories and conjectures that can be used to investigate the potential roles of aesthetics in mathematics learning contexts.This revised version was published online in September 2005 with corrections to the Cover Date.     

转移矩阵法在负折射率介质材料平板波导中的应用研究

利用严格电磁理论，推导出了适用于负折射率介质材料光波导的转移矩阵，分析讨论了转移矩阵的性质和应用.利用转移矩阵方法，推导出导波层为负折射率介质材料、覆盖层和衬底为右手材料的三层对称介质光波导的本征色散方程.用图解法研究了负折射率介质波导中TE波的异常色散特性.在负折射材料介质波导中没有零阶模，最低阶为1阶模，并且有截止频率,只有波导参量满足一定条件的时候才会存在，导模的横向波数可以为实数和纯虚数，而正折射率介质波导导模的横向波数只能为实数.     

Projective geometry and special relativity

Some concepts of real and complex projective geometry are applied to the fundamental physical notions that relate to Minkowski space and the Lorentz group. In particular, it is shown that the transition from an infinite speed of propagation for light waves to a finite one entails the replacement of a hyperplane at infinity with a light cone and the replacement of an affine hyperplane – or rest space – with a proper time hyperboloid. The transition from the metric theory of electromagnetism to the pre‐metric theory is discussed in the context of complex projective geometry, and ultimately, it is proposed that the geometrical issues are more general than electromagnetism, namely, they pertain to the transition from point mechanics to wave mechanics.     

Spectroscopic Studies of a Three-dimensional, Five-coordinated Copper(Ⅱ) Complex via Hydrogen Bonds: [Cu(PDA)(H_2O)_2](H_2PDA=Pyridine-2,6-dicarboxylic Acid)

IntroductionFive- coordinated complexes with d9- configuredcations have received much attention stereochemi-cally,spectrochemically and biologically,and havebeen comprehensively discussed[1] . Usually thereare two stable configurations for the copper( )complexes with five equal coordinating atoms:anapically elongated square pyramid( SP) and a com-pressed trigonal bipyramid( TBP) ,with an obviousenergetic preference for the latter coordination.When the ligands are rigid and provide angular d…     

A Kind of Electrode Enhanced the Electrochemiluminescence

Electrochemiluminescence (ECL), like other chemiluminescence technique, offers high signal-to-noise ratio. Furthermore, it has the advantage over other chemiluminescence techniques of being initiated by a voltage potential. Thus, it provides a better-controlled luminescence. This technique has been used in measuring many kinds of organic and inorganic matters, and analyzing many kinds of antigen, antibody and hapten, such as carcinoembryonic antigen and alpha-fetoprotein, etc1-6. The ele…