The Symmetry of Singular Hamiltonian Differential Operators and Properties of Deficiency Indices

The symmetry of singular Hamiltonian differential operators is proved under the standard ＂definiteness condition＂, which is strictly weaker than the densely definite condition used by A. M. Krall. Meanwhile, some properties of deficiency indices are given.     

Perturbation of Yamabe equation on Iwasawa N groups in presence of symmetry

Let G be a simple Lie group of real rank one and N be in the Iwasawa decomposition of G. Under the assumption of some symmetries, we obtain an existent result for the nonlinear equation △NU ＋ （1 ＋ ∈K（x, z））u2＊-1 = 0 on N, which generalizes the result of Malchiodi and Uguzzoni to the Kohn＇s subelliptic context on N in presence of symmetry.     

函数的对称性和周期性的关系

“函数”一章的内容贯穿于高中数学的始终,历来是数学高考考查的一个难点和热点,要求学生熟练掌握函数的性质．但在学习这一章过程中,许多同学被函数的若干性质弄的头昏脑涨．事实上,只要把握其中的关系,也就不困难了．     

The Elements in Crystal Bases Corresponding to Exceptional Modules

According to the Ringel-Green theorem, the generic composition algebra of the Hall algebra provides a realization of the positive part of the quantum group. Furthermore, its Drinfeld double can be identified with the whole quantum group, in which the BGP- reflection functors coincide with Lusztig＇s symmetries. It is first asserted that the elements corresponding to exceptional modules lie in the integral generic composition algebra, hence in the integral form of the quantum group. Then it is proved that these elements lie in the crystal basis up to a sign. Eventually, it is shown that the sign can be removed by the geometric method. The results hold for any type of Cartan datum.     

谈谈某些函数问题的处理

笔者在文[1]提出：处理抽象函数问题的根本方法是充分利用已知性质和挖掘未知性质（性质主要是指：单调性、奇偶性、周期性、对称性及某函数自身特有性质）,实际上,在处理某些具体函数试题时,上述方法也同样是很有用的,往往能收到意想不到的解题效果,现略举数例说明如下,供参考。     

C—H键核自旋耦合常数和伸缩频率的自然杂化轨道研究

利用PM3级别上的最大重迭对称性分子轨道法和自然杂化轨道方法,计算了系列碳氢化合物的杂化轨道,拟合出了计算C—H键核自旋耦合常数和伸缩频率的简单关系式.研究了系列碳氢化合物中不同的C—H键核自旋耦合常数和伸缩频率.结果表明,碳氢化合物中的C—H核自旋耦合常数和伸缩频率主要取决于C原子的轨道杂化作用,为从简单价键理论角度解释和计算1JCH和νCH提供了一种简便直观的方法.     

三旋理论展望

大量微观和宏观物理现象都表明基本粒子不是类点结构，但这并非是弦学说才有的特色，三旋理论利用类圈体存在三种内禀自旋的发现，会有助于对微观和宏观量子现象及场的一些难题的探索。     

Special Lie-Mei Symmetry and Conserved Quantities of Appell Equations Expressed by Appell Function

Special Lie-Mei symmetry and conserved quantities for Appell equations expressed by Appell functions in a holonomic mechanical system are investigated. On the basis of the Appell equation in a holonomic system, the definition and the criterion of special Lie-Mei symmetry of Appell equations expressed by Appell functions are given. The expressions of the determining equation of special Lie-Mei symmetry of Appell equations expressed by Appell functions, Hojman conserved quantity and Mei conserved quantity deduced from special Lie-Mei symmetry in a holonomic mechanical system are gained. An example is given to illustrate the application of the results.     

时空对称性与守恒律(下篇)——经典电动力学

本文从时空对称性导出经典电动力学中能量、动量、角动量三大守恒定律.