Gravitational Collapse of Self-Similar Perfect Fluid in 2 + 1 Gravity

Perfect fluid with kinematic self-similarity is studied in 2+1 dimensional spacetimes with circular symmetry, and various exact solutions to the Einstein field equations are given. These include all the solutions of dust and stiff perfect fluid with self-similarity of the first kind, and all the solutions of perfect fluid with a linear equation of state and self-similarity of the zeroth and second kinds. It is found that some of these solutions represent gravitational collapse, and the final state of the collapse can be either a black hole or a null singularity. It is also shown that one solution can have two different kinds of kinematic self-similarity.     

GA optimization on multi-segments muffler under space constraints

Whilst the space volume of muffler in noise control system is often constrained for maintenance in practical engineering work, the maximization on muffler’s performance becomes important and essential. In this paper, a novel approach genetic algorithms (GAs) based on the principles of natural biological evolution will be used to tackle this optimization of muffler design [M. Mitchell, An Introduction to Genetic Algorithms, The MIT Press, Cambridge, MA, 1996]. Here, the shape optimization of multi-segments muffler coupled with the GA searching technique is presented. The techniques of binary genetic algorithms (BGA) together with the commercial MATLAB package [G. Lindfield, J. Penny, Numerical Method Using Matlab, second ed., Prentice Hall, Englewood Cliffs, NJ, 2000] are applied in GA searching. In addition, a numerical case of pure tone elimination with 2-5 segments on muffler is introduced and fully discussed. To achieve the best optimization in GA, several GA parameters are on trial in various values. Results show that the GA operators, including crossover mutation and elitism, are essential in accuracy. Consequently, results verify that the optimal sound transmission loss at the designed frequency of 500 Hz is exactly maximized. The GA optimization on multi-segments muffler proposed in this study surely provides a quick and correct approach.     

Does the beam width affect the generalized M factor of hard-edged diffracted beams?

A detailed study of the generalized M² factor of hard-edged diffracted beams based on the truncated second-order moments method, asymptotic analysis and self-convergent beam width approach is performed. The dependence of the generalized M² factor on the parameters characterizing the spatial profile, and beam truncation, etc. is analyzed.     

Finite-Dimensional PT-Symmetric Hamiltonians

This paper investigates finite-dimensional PT-symmetric Hamiltonians. It is shown here that there are two ways to extend real symmetric Hamiltonians into the complex domain: (i) The usual approach is to generalize such Hamiltonians to include complex Hermitian Hamiltonians. (ii) Alternatively, one can generalize real symmetric Hamiltonians to include complex PT-symmetric Hamiltonians. In the first approach the spectrum remains real, while in the second approach the spectrum remains real if the PT symmetry is not broken. Both generalizations give a consistent theory of quantum mechanics, but if D>2, a D-dimensional Hermitian matrix Hamiltonian has more arbitrary parameters than a D-dimensional PT-symmetric matrix Hamiltonian.     

标度系统一致性矩阵容量的计算方法

本文研究正互反矩阵的变换性质 ,提出一种保持正互反矩阵一致性程度的等价分类 ,为计算各种标度系统下的一致矩阵容量提供了计算方法     

2‐connected 7‐coverings of 3‐connected graphs on surfaces

An m‐covering of a graph G is a spanning subgraph of G with maximum degree at most m. In this paper, we shall show that every 3‐connected graph on a surface with Euler genus k ≥ 2 with sufficiently large representativity has a 2‐connected 7‐covering with at most 6k ? 12 vertices of degree 7. We also construct, for every surface F² with Euler genus k ≥ 2, a 3‐connected graph G on F² with arbitrarily large representativity each of whose 2‐connected 7‐coverings contains at least 6k ? 12 vertices of degree 7. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 26–36, 2003     

Electrochemical characterization of poly(vinylidenefluoride)-zinc triflate gel polymer electrolyte and its application in solid-state zinc batteries

Gel polymer electrolyte (GPE) films comprising of poly(vinylidenefluoride), propylene carbonate, ethylene carbonate and zinc trifluoromethane sulfonate are prepared and characterized. The composition of GPE is optimized to contain minimum liquid components with a maximum specific conductivity of 3.94×10⁻³ S cm⁻¹ at (25±1) °C. A detailed investigation on the properties such as ionic conductivity, transport number, electrochemical stability window, reversibility of Zn/Zn²⁺ couple and Zn/gel electrolyte interfacial stability have been carried out. The ionic conductivity follows a VTF behaviour with an activation energy of about 0.0014 eV. Cationic transport number varies from 0.51 at 25 °C to 0.18 at 70 °C. Several cells have been assembled with GPE as the electrolyte, zinc as the anode, γ-MnO₂ as the cathode and their charge–discharge behaviour followed. Capacity values of 105, 82, 64 and 37 mAh/g of MnO₂ have been achieved at 10, 50, 100 and 200 μA/cm² discharge current densities, respectively. The discharge capacity values are almost constant for about 55 cycles for all values of current densities. Cyclic voltammetric study of MnO₂ electrode in Zn/GPE/MnO₂ cell clearly shows intercalation/deintercalation of Zn²⁺.     

The Asymptotics of Spectral Gaps of a 1D Dirac Operator with Cosine Potential

Letters in Mathematical Physics -     

二氧化碳和丙烯直接合成甲基丙烯酸的NiPMo/TiO2催化剂的研究

用溶胶 凝胶法以磷钼酸 (MPA)的镍盐溶液水解钛酸四丁酯制备了NiPMo/TiO2 催化剂 .使用ICP、XRD、TG DTA、IR、TPD MS和微反应技术研究了催化剂的化学组成、热稳定性、化学吸附性质和催化反应性能 .杂多钼酸盐与TiO2 通过O2 -在TiO2 表面发生了键合 .在 6 2 3K下 ,杂多阴离子仍保持原有的Keggin结构 .CO2 在Lewis酸位Ni(Ⅱ )和Lewis碱位Ni-O -Mo的桥氧协同作用下生成CO2 卧式吸附态Ni(Ⅱ )←O - (CO)← (O--Ni) .丙烯有多种吸附态在催化剂上吸附 .在 5 6 3K、1MPa和空速 15 0 0h-1的反应条件下 ,丙烯的摩尔转化率为 3.2 % ,产物MAA选择性为 95 % .