Iterative solutions to coupled Sylvester-transpose matrix equations

This note studies the iterative solutions to the coupled Sylvester-transpose matrix equation with a unique solution. By using the hierarchical identification principle, an iterative algorithm is presented for solving this class of coupled matrix equations. It is proved that the iterative solution consistently converges to the exact solution for any initial values. Meanwhile, sufficient conditions are derived to guarantee that the iterative solutions given by the proposed algorithm converge to the exact solution for any initial matrices. Finally, a numerical example is given to illustrate the efficiency of the proposed approach.     

大学物理中几个常见超越方程解的渐近表示

简要介绍了布尔曼一拉格朗日级数,并推出了几个常见超越方程的解的渐近表示.     

A model of melting of rare gases within bubbles of crystalline metal matrix

Abstract

On the basis of experimental results obtained in the present and some other works a model of melting of rare gas solids within bubbles formed in a crystalline metal matrix as a result of ion implantation is proposed. Rare gas solid is supposed to melt on heating at the expense of the bubble volume expansion by emission of a dislocation loop. On this basis the melting temperature can be estimated as one which is enough to provide for a pressure inside a bubble sufficient for the initiation of the dislocation loop punching. Values of melting temperatures obtained in this way are in good agreement with available experimental data.     

An iterative starting method to control parasitism for the Leapfrog method

The Leapfrog method is a time-symmetric multistep method, widely used to solve the Euler equations and other Hamiltonian systems, due to its low cost and geometric properties. A drawback with Leapfrog is that it suffers from parasitism. This paper describes an iterative starting method, which may be used to reduce to machine precision the size of the parasitic components in the numerical solution at the start of the computation. The severity of parasitic growth is also a function of the differential equation, the main method and the time-step. When the tendency to parasitic growth is relatively mild, computational results indicate that using this iterative starting method may significantly increase the time-scale over which parasitic effects remain acceptably small. Using an iterative starting method, Leapfrog is applied to the cubic Schrödinger equation. The computational results show that the Hamiltonian and soliton behaviour are well-preserved over long time-scales.     

On a discretization process of fractional-order Logistic differential equation

In this work we introduce a discretization process to discretize fractional-order differential equations. First of all, we consider the fractional-order Logistic differential equation then, we consider the corresponding fractional-order Logistic differential equation with piecewise constant arguments and we apply the proposed discretization on it. The stability of the fixed points of the resultant dynamical system and the Lyapunov exponent are investigated. Finally, we study some dynamic behavior of the resultant systems such as bifurcation and chaos.     

求解Schrdinger方程的高阶紧致差分格式

基于Richardson外推法提出了一种求解Schrdinger方程的高阶紧致差分方法.该方法首先利用二阶微商的四阶精度紧致差分逼近公式对原方程进行求解,然后利用Richardson外推技术外推一次,得到了Schrdinger方程具有O(r~4+h~4)精度的数值解.通过Fourier分析方法证明了该格式是无条件稳定的.数值实验验证了该方法的高阶精度及有效性.     

Influence of temperature on thermodynamic properties of substituted aromatic compounds

This work presents experimental liquid densities and ultrasonic velocities for a collection of substituted aromatic compounds (isobutylbenzene, 1,3,5-trimethylbenzene, butylbenzene, isopropylbenzene, p-xylene, m-xylene and o-xylene) at the range of temperature 278.15–323.15 K and atmospheric pressure of a collection of halogenated and aromatic hydrocarbons. Fitting equations were applied to data in order to correlate for later computer-based design. The estimation of the studied properties was made by the application of different theoretical procedures. An equation of state based on the generalised Van der Waals theory which combines the Staverman–Guggenheim combinatorial term of lattice statistics with an attractive lattice gas expression and the free length theory (FLT) showed a good response at the studied conditions.