Quantum dynamics of dissociative adsorption of H_2 on Ni(100) using the dynamical Lie algebraic method

A dynamical Lie algebraic method has been applied to treating the quantum dynamics of dissociative adsorption of H_2 on a static flat metal surface. An LEPS potential energy surface has been used to describe the interaction of H_2 with Ni(100) surface. The dependence of the initial state-selected dissociation probability was obtained analytically on the initial kinetic energy and time. A comparison with other theoretical calculations and experiments is made. The results show that the method can be effectively used to describe the dynamics of reactive gas-surface scattering.     

Bounded Algebraic Geometry over a Free Lie Algebra

Bounded algebraic sets over a free Lie algebra F over a field k are classified in three equivalent languages: (1) in terms of algebraic sets; (2) in terms of radicals of algebraic sets; (3) in terms of coordinate algebras of algebraic sets.Supported by RFBR grant No. 02-01-00192a.__________Translated from Algebra i Logika, Vol. 44, No. 3, pp. 269–304, May–June, 2005.     

矩形校正公式的误差分析

This paper presents truncation errors among Corrector Formula for left Rectangular rule and Corrector Formula for middle Rectangular rule respectively.It also displays an analysis on convergence order of compound corrector formulas for rectangular rule.Examples of numerical calculation have validated theoretical analysis.     

渐变折射率波导传播特性微扰计算的代数递推公式

应用量子力学的超位力定理（HVT）和赫尔曼－费恩曼（Hellmann-Feynman）定理（HFT），导出了用微扰法计算渐变折射率平面波导传播常数各级近似值的代数递推公式，并给出了由传播常数近似值计算模场近似表达式的代数式。计算了几个典型实例，此法的特点是便于直接计算任意级近似的传播常数及模场分布，且可推广到二维波导的计算。     

Systematic calculation of molecular vibrational spectra through a complete Morse expansion

We propose an accurate and efficient method to compute vibrational spectra of molecules, based on exact diagonalization of an algebraically calculated matrix based on powers of Morse coordinate. The present work focuses on the 1D potential of diatomic molecules: as typical examples, we apply this method to the standard Lennard‐Jones oscillator, and to the ab initio potential of the H₂ molecule. Global cm^?1 accuracy is exhibited through the H₂ spectrum, obtained through the diagonalization of a 30 × 30 matrix. This theory is at the root of a new method to obtain globally accurate vibrational spectral data in the context of the multi‐dimensional potential of polyatomic molecules, at an affordable computational cost. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

On matrix analogs of Fermat’s little theorem

The theorem proved in this paper gives a congruence for the traces of powers of an algebraic integer for the case in which the exponent of the power is a prime power. The theorem implies a congruence in Gauss’ form for the traces of the sums of powers of algebraic integers, generalizing many familiar versions of Fermat’s little theorem. Applied to the traces of integer matrices, this gives a proof of Arnold’s conjecture about the congruence of the traces of powers of such matrices for the case in which the exponent of the power is a prime power.     

基于代数等价变换下的凸二次规划不可行内点算法

基于代数等价变换和在KMM算法的框架基础上,在原始-对偶内点方法的牛顿方程里嵌入一种自调节功能.从而对凸二次规划提出了一种新的迭代方向的不可行内点算法,并证明了算法的全局收敛性.