一种分解指数算符的简洁方法

提出一种新的分解指数算符的方法,这种方法不仅简单易懂,而且有助于找到更多的算符恒等式.     

MATLAB在光学界面发生反射时的分析与应用

基于MATLAB的计算功能及可视化功能计算并分析了光学中的菲涅耳公式,更加直观的揭示了光波在两介质界面发生反射时的变化规律。使学生更加深入、直观地掌握光波在界面发生变化的条件、实质及布儒斯特角与全反射临界角的物理意义,同时也学会了分析研究方法,且提高了学习的主动性和创造性。     

Stable local trace formula

Langlands program is the central concern of modern number theory. In general, we think that the main tool for studying this program is the trace formula. Arthur-Selberg’s trace formula is successful in solving the endoscopic case of Langlands program. Arthur stabilized the geometric side of the local trace formula in the general case, but did not stabilize the general spectral. This paper aims to solve the general case by different method in the Archimedean case, by directly stabilizing the spectral side of the local trace formula, and obtains the stable local trace formula.     

The Calculus of Moving Surfaces and Laplace Eigenvalues on an Ellipse with Low Eccentricity

Our goal is to demonstrate the utility of the calculus of moving surfaces (CMS) in boundary variation problems. We discuss the relative advantages of the CMS compared to the alternative approach of interior variations. We illustrate the technique by calculating the two leading terms of a power series for the Laplace eigenvalues on an ellipse with semi-axes 1 + a and 1 + b, where a and b are small. We compare the CMS estimates with those obtained by the conventional finite element method with Richardson extrapolation. The comparison confirms the cubic rate of convergence for the CMS estimates.     

CALCULATION FORMULAS FOR PRINCIPAL STRESSES

在前人工作的基础上,运用一元三次方程的理论直接求解应力状态的特征方程,得到了实用的主应力计算公式.     

三次Gauss和及二项指数和的混合均值

我们用三角和的性质研究一类三次Gauss和与两项指数和混合均值的计算问题,并给出一个精确的计算公式.     

Geometric derivation of the microscopic stress: A covariant central force decomposition

We revisit the derivation of the microscopic stress, linking the statistical mechanics of particle systems and continuum mechanics. The starting point in our geometric derivation is the Doyle–Ericksen formula, which states that the Cauchy stress tensor is the derivative of the free-energy with respect to the ambient metric tensor and which follows from a covariance argument. Thus, our approach to define the microscopic stress tensor does not rely on the statement of balance of linear momentum as in the classical Irving–Kirkwood–Noll approach. Nevertheless, the resulting stress tensor satisfies balance of linear and angular momentum. Furthermore, our approach removes the ambiguity in the definition of the microscopic stress in the presence of multibody interactions by naturally suggesting a canonical and physically motivated force decomposition into pairwise terms, a key ingredient in this theory. As a result, our approach provides objective expressions to compute a microscopic stress for a system in equilibrium and for force-fields expanded into multibody interactions of arbitrarily high order. We illustrate the proposed methodology with molecular dynamics simulations of a fibrous protein using a force-field involving up to 5-body interactions.