Generalized covariant differentiation and axiom-based tensor analysis

This paper reports the new progresses in the axiomatization of tensor analysis, including the thought of axiomatization, the concept of generalized components, the axiom of covariant form invariability, the axiomatized definition, the algebraic structure, the transformation group, and the simple calculation of generalized covariant differentiations. These progresses strengthen the tendency of the axiomatization of tensor analysis.     

归纳环及归纳域

提出了归纳环的概念(即:含1且适合1阶Peano归纳公理的环),指出其意义并提出下列关于确定归纳环代数结构的问题:是否每一归纳环都与由整数环的一族剩余类环及特征数0的代数闭域所作的一个超积初等等价?首先给出了有关归纳环及归纳域的一些基本事实.然后着重在代数范围内进行讨论,得到下列的结果:每个有限次实代数数域都不是归纳域;代数整数环的每个子环都不是归纳环.还证明了很多有限次代数数域不与上述的超积初等等价.     

代数替换公理与对偶原理

提出和阐明了两个普遍的逻辑规律——代数替换公理与对偶原理．通过这两个规律，极大地简化和统一了布尔代数中的运算规律和运算公式．在布尔代数中，A的非与A的对偶本质上是一回事．对偶本质上是一种对称的关系．一个代数表达式（这里的表达式是一个广义的概念，它可以是一个变量，一个常量，一个逻辑函数，一个集合表达式等）的对偶，等于该表达式中的每个元素（如变量、常量、运算符、关系符等，对偶算子除外）分别同时取其对偶，并保持原来的运算次序不变（也即原表达式中的对偶算子和括号位置不变）；对于关系表达式而言，原表达式与其对偶表达式必然同时正确或同时错误，这一规律叫做对偶原理．     

关于L-相对T_0与相对T_1分离性

定义了L-fuzzy拓扑空间的相对T0与相对T1分离性.给出了相对T0与相对T1分离性等价刻画.研究了相对T0与相对T1分离性的性质,包括遗传性、可乘性,传递性与L-好的推广,对相对T0与相对T1分离性与其他分离性进行了比较.     

Strict regular completions of Cauchy spaces

A diagonal condition is defined and used in characterizing the Cauchy spaces which have a strict, regular completion.

     

传递过程的统一描述

提出了传递公理,即任何形式的传递过程都是在相应基本强度量差推动下,基本广延量的流动过程;基本广延量的传递过程也同时是与之对应的能和(火用)的传递过程。定义了热力学流密度和热力学力的数学表达式,在传递公理的基础上,利用能和(火用)的普遍化表达式,分别建立了三类广延量的传递定律。利用传递定律,结合广延量的平衡方程,导出了传递方程的普遍化表达式。     

On L-Tychonoff spaces II

This paper is a sequel to the 1995 paper On L-Tychonoff spaces. The embedding theorem for L-topological spaces is shown to hold true for L an arbitrary complete lattice without imposing any order reversing involution (·)^′ on L. Some results on completely L-regular spaces and on L-Tychonoff spaces, which have previously been known to hold true for (L,^′) a frame, are exhibited as ones holding for (L,^′) a meet-continuous lattice. For such a lattice an insertion theorem for completely L-regular spaces is given. Some weak forms of separating families of maps are discussed. We also clarify the dependence between the sub-T₀ separation axiom of Liu and the L-T₀ separation axiom of Rodabaugh.     

a-石英晶体和铜块间手性不对称宏观力的研究

研究a-石英晶体和无手性物质间由Moody提出的有效势所产生的宏观力,发现这种宏观力是手性依赖的．根据a-石英晶的非简单群P3-21的表示,分析宏观力表达式中的矩阵元．结果表明,a-石英晶体中价电子的不对称分布和选择定则不能使这种宏观力相消为零．因此得出结论,存在一种新的宏观力,可能使等效原理破坏．最后讨论它的量级．     

Quantum Hamilton mechanics: Hamilton equations of quantum motion, origin of quantum operators, and proof of quantization axiom

This paper gives a thorough investigation on formulating and solving quantum problems by extended analytical mechanics that extends canonical variables to complex domain. With this complex extension, we show that quantum mechanics becomes a part of analytical mechanics and hence can be treated integrally with classical mechanics. Complex canonical variables are governed by Hamilton equations of motion, which can be derived naturally from Schrödinger equation. Using complex canonical variables, a formal proof of the quantization axiom p → pˆ = −i, which is the kernel in constructing quantum-mechanical systems, becomes a one-line corollary of Hamilton mechanics. The derivation of quantum operators from Hamilton mechanics is coordinate independent and thus allows us to derive quantum operators directly under any coordinate system without transforming back to Cartesian coordinates. Besides deriving quantum operators, we also show that the various prominent quantum effects, such as quantization, tunneling, atomic shell structure, Aharonov–Bohm effect, and spin, all have the root in Hamilton mechanics and can be described entirely by Hamilton equations of motion.