Smart Geodesic Tracing in GRworkbench

We have developed a new tool for numerical work in General Relativity: GRworkbench. We discuss how GRworkbench's implementation of a numerically-amenable analogue to Differential Geometry facilitates the development of robust and chart-independent numerical algorithms. We consider, as an example, geodesic tracing on two charts covering the exterior Schwarzschild space-time.     

On the Reality of the Eigenvalues for a Class of -Symmetric Oscillators

 We study the eigenvalue problem with the boundary conditions that decays to zero as z tends to infinity along the rays , where is a real polynomial and . We prove that if for some we have for all , then the eigenvalues are all positive real. We then sharpen this to a larger class of polynomial potentials. In particular, this implies that the eigenvalues are all positive real for the potentials when with , and with the boundary conditions that decays to zero as z tends to infinity along the positive and negative real axes. This verifies a conjecture of Bessis and Zinn-Justin. Received: 16 January 2002 / Accepted: 1 May 2002 Published online: 6 August 2002     

Two inequalities involving Hadamard products of positive semi-definite Hermitian matrices

We extend two inequalities involving Hadamard products of positive definite Hermitian matrices to positive semi-definite Hermitian matrices. Simultaneously, we also show the sufficient conditions for equalities to hold. Moreover, some other matrix inequalities are also obtained. Our results and methods are different from those which are obtained by S. Liu in [J. Math. Anal. Appl. 243:458–463(2000)] and B.-Y. Wang et al. in [Lin. Alg. Appl. 302–303: 163–172(1999)].     

Large set of P3‐decompositions

Let G=(V(G),E(G)) be a graph. A (n,G, λ)‐GD is a partition of the edges of λK_n into subgraphs (G‐blocks), each of which is isomorphic to G. The (n,G,λ)‐GD is named as graph design for G or G‐decomposition. The large set of (n,G,λ)‐GD is denoted by (n,G,λ)‐LGD. In this work, we obtain the existence spectrum of (n,P₃,λ)‐LGD. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 151–159, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10008     

Every diassociative A-loop is Moufang

An A-loop is a loop in which every inner mapping is an automorphism. A problem which had been open since 1956 is settled by showing that every diassociative A-loop is Moufang.

     

MODEL COMPARISON FOR ACOUSTIC SCATTERING BY A SPHERICAL AIR BUBBLE IN WATER

The oscillation of a bubble has many vibrational modes, contributing to different portions in acoustic scattering. Without approximations a priori, an hydrodynamic approach is applied to investigate acoustic scattering by a bubble in water, taking into account the heat exchange and viscosity. The scattering function is derived for a wide range of frequencies. Examples are shown to illustrate the thermal and viscous effects on sound scattering. Comparison is made with three existing models. While these models are known not to be applicable for high frequencies, it is shown here that even in the low-frequency region, there are also noticeable discrepancies between the exact solution and the three existing models with regard to the scattering properties such as the scattering cross-section, and the quality factor of resonant peaks. By numerical simulation, we claim that the discrepancies may be due to the incomplete consideration of the thermal exchange process in the previous models. The approach presented here is valid for any other fluid enclosure in liquids.     

一种新型彩色三维光学成像系统

提出一种新型三维彩色光学数字成像系统。此系统利用投影结构光对现实世界中的物体进行数字化，同时得到对应的彩色纹理。详细介绍了系统的硬件设计和软件体系结构设计，得到物体彩色纹理的两种不同方法；直接获取和从编码条纹中提取，给出了用该系统得到的实验结果并简单评价了系统的性能。此系统在反求工程、影视制作、三维游戏制作、医学应用等方面有远大的应用前景。     

Magnetic properties of oxygenated carbon nitride films from RF-discharge in an acetylene, nitrogen, and oxygen mixture environments

Properties of oxygenated carbon nitride films have attracted the attention of physics researchers due to their magnetic and physical properties, as well as for their usefulness in the industry. The free radicals were investigated using electron paramagnetic resonance applied in the study of spin concentration due to the different mechanism of preparation of carbon nitride films by RF-discharge with different kinds of plasma. Unpaired spin concentrations, in the order of 10²⁰ per cm³, were measured and their time recombination dependency was important in those films. The films were grown by plasma enhanced chemical vapor deposition using mixtures of hydrocarbons, N₂ and O₂ in different proportions.     

A comprehensive study of the long pulse Nd:YAG laser drilling of multi-layer carbon fibre composites

The results of an extensive experimental study of the free running Nd:YAG laser drilling of a multi-layer carbon fibre composite, where adjacent layers have differently orientated fibres, are reported. For holes drilled with the laser operating in fixed-Q mode at 1064 nm, parallel sections of blind holes illustrating discontinuities in the hole size along a given section direction will be shown to occur at the interface between adjacent layers. An explanation for this effect is proposed. Detailed single pulse drilling characteristics will be presented illustrating the exit hole diameter as a function of pulse energy and material thickness. These characteristics illustrate a ‘stable' drilling regime in which the exit hole diameters are least sensitive to changes in pulse energy or material thickness and a less ‘stable' regime in which they are more strongly dependent on these parameters. Drilling characteristics will be given for two different beam qualities, illustrating the greater drilling depth and reduced hole size achievable with an improved beam quality. Finally holes drilled through a 2 mm thick sample of material with multiple pulses are considered. Size distribution curves for entrance and exit holes will be presented. The total energy required (number of pulses × pulse energy) to drill through 2 mm thick material will be reported as a function of pulse energy in stationary air and argon atmospheres and in a partial vacuum, illustrating a threshold energy which is dependent upon the drilling atmosphere. The threshold energies will be discussed with reference to plasma formation and the reactivity of the drilling atmosphere.