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.     

Selection of Planar Chiral Conformations between Pillar[5,6]arenes Induced by Amino Acid Derivatives in Aqueous Media

Chiral α-amino acids play critical roles in the metabolic process in nearly all life forms. So far, chiral recognition of α-amino acids has mainly focused on the determination of l /d enantiomers. Herein, selection of planar chiral conformations between water-soluble pillar[5]arene WP5 and pillar[6]arene WP6 was observed due to α-side chain or ethyl ester moieties of l -α-amino acid ethyl ester hydrochlorides binding with WP5 and WP6 , respectively. Therefore, α-side chain and ethyl ester moieties of l -α-amino acid ethyl ester hydrochlorides were recognized by observing the induced CD signal and its inversion. This is a rare example of being able to detect the chiral region around α-carbon of a chiral α-amino acid molecule.     

An empirical formula for scattered neutron components in fast neutron radiography

Scattering neutrons are one of the key factors that may affect the images of fast neutron radiog- raphy. In this paper, a mathematical model for scattered neutrons is developed on a cylinder sample, and an empirical formula for scattered neutrons is obtained. According to the results given by Monte Carlo methods, the parameters in the empirical formula are obtained with curve fitting, which confirms the logicality of the empirical formula. The curve-fitted parameters of common materials such as <'6>LiD are given.     

Meromorphic functions on compact Riemann surfaces and value sharing

Let X be a smooth and connected Riemann surface of genus g 0 and f: X P1, h: X P1 non-constant meromorphic functions on X. Fix an integer n 4 and assume the existence of n distinct points a1, , an P1 such that [image omitted] (set-theoretically) for every i. Here we prove that either f = h or [image omitted].     

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.     

Bilevel convex programming models

Bilevel convex models are studied after being cast into a parametric programming form. This form has a lexicographic inner-outer structure where the optimal value of the outer model is optimized on the set of optimal solutions of the inner model. Optimal solutions are characterized using a Lagrangian saddle-point approach and a marginal value formula is given for the outer model. These are used to formulate a general method for finding an optimal solution by input optimization.     

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。