New Temperature Integral Approximate Formula for Non-isothermal Kinetic Analysis

A new approximate formula for temperature integral is proposed. The linear dependence of the new fomula on x has been established. Combining this linear dependence and integration-by-parts, new equation for the evaluation of kinetic parameters has been obtained from the above dependence. The validity of this equation has been tested with data from numerical calculating. And its deviation from the values calculated by Simpson's numerical integrating was discussed. Compared with several published approximate formulae, this new one is much superior to all other approximations and is the most suitable solution for the evaluation of kinetic parameters from TG experiments. This revised version was published online in August 2006 with corrections to the Cover Date.     

Approximate formulae for calculation of the integral òT0Tmexp(-E/RT)dT

Summary In this paper two approximate formulae have been developed for calculation of the integral ò^T₀T^mexp(-E/RT)dT by using integration-by-parts approaches. They are in the following forms: I(m,T) = (RT^m+2)/(E+(m+2)RT)exp(-E/RT) I(m,T) = (RT^m+2)/(E+(m+2)(0.00099441E+0.93695599RT)exp(-E/RT) The validity of the two formulae has been confirmed and their accuracies have been tested with data from numerical calculating. In contrast to existing other integral methods, both the present approaches are simply used, accurate, and can be used for arbitrary values of m.     

Direct transformation of variational problems into Cauchy systems. I. Scalar-quadratic case

This series of papers addresses three interrelated problems: the solution of a variational minimization problem, the solution of integral equations, and the solution of an initial-valued system of integro-differential equations. It will be shown that a large class of minimization problems requires the solution of linear Fredholm integral equations. It has also been shown that the solution of a linear Fredholm integral equation is identical to the solution of a Cauchy system. In this paper, we bypass the Fredholm integral equations and show that the minimization problem directly implies a solution of a Cauchy system. This first paper in the series looks only at quadratic functionals and scalar functions.This research was sponsored by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant No. AFOSR-77-3383.     

三氮宾分子的磁性设计

采用量子化学ＧＡＵＳＳＩＡＮ９４ａｂｉｎｉｔｉｏＵＨＦ方法和ＳＴＯ－３Ｇ基组设计一系列三氮宾分子，讨论分子的几何结构和取代基对其磁性的影响，计算结果表明，这些分子都具有铁磁性并有高自旋基态，有效交换积分值随代基的变化而变化，其中一种具有较代的总能量和高的有效交换积分值的分子，可期望被合成。     

Monolayer adsorption isotherms and a disordered medium model

A model of disordered medium is proposed to describe the monolayer adsorption isotherm on heterogeneous surfaces. The model is based on the premise that adsorption medium consists of separate regions in each of which there is a permanent local equilibrium constant, the character of the changes of which is determined by the disorder parameter of the medium. __________ Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 42, No. 3, pp. 189–193, May–June, 2006.     

Fractional noise

Fractional noiseN(t),t 0, is a stochastic process for every , and is defined as the fractional derivative or fractional integral of white noise. For = 1 we recover Brownian motion and for = 1/2 we findf ^–1-noise. For 1/2 1, a superposition of fractional noise is related to the fractional diffusion equation.     

半平面多边缘裂纹反平面问题的奇异积分方程

利用复变函数和奇异积分方程方法,求解弹性范围内半平面多边缘裂纹的反平面问题．提出了满足半平面边界自由的由分布位错密度表示的单边缘裂纹的基本解,此基本解由主要部分和辅助部分组成．将半平面多边缘裂纹问题看作是许多单边缘裂纹问题的叠加,建立了一组Cauchy型奇异积分方程．然后,利用半开型积分法则求解该奇异积分方程,得到了裂纹端处的应力强度因子．最后,给出了几个数值算例．     

垂直磁压电材料界面三维裂纹的超奇异积分法

应用有限部积分概念和广义位移基本解,垂直于磁压电双材料界面三维复合型裂纹问题被转 化为求解一组以裂纹表面广义位移间断为未知函数的超奇异积分方程问题. 进而,通过主部 分析法精确地求得裂纹尖端光滑点附近的奇性应力场解析表达式. 然后,通过将裂纹表面 位移间断未知函数表达为位移间断基本密度函数与多项式之积,使用有限部积分法对超奇异 积分方程组建立了数值方法. 最后,通过典型算例计算,讨论了广义应力强度因子的变化规 律.     

分析力学初值问题的一种变分原理形式

明确了分析力学初值问题的控制方程,按照广义力和广义位移之间的对应关系,将 各控制方程卷乘上相应的虚量,代数相加,进而在 原空间中建立了分析力学初值问题的一种变分原理形式,即建立了分析力学初值问题的卷积 型变分原理和卷积型广义变分原理. 推导了分析力学初值问题卷积型变分原理和卷积型广义 变分原理的驻值条件. 在建立分析力学初值问题的一种变分原理形式的同时, 将变积方法推广为卷变积方法.