Extension of covariant derivative(Ⅱ): From flat space to curved space

This paper extends the classical covariant deriva tive to the generalized covariant derivative on curved sur faces. The basement for the extension is similar to the pre vious paper, i.e., the axiom of the covariant form invariabil ity. Based on the generalized covariant derivative, a covari ant differential transformation group with orthogonal duality is set up. Through such orthogonal duality, tensor analy sis on curved surfaces is simplified intensively. Under the covariant differential transformation group, the differential invariabilities and integral invariabilities are constructed on curved surfaces.

Generalized covariant differentiation and axiom-based tensor analysis

This paper reports the new progresses in the axiomatization of tensor anal- ysis, 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 differentia- tions. These progresses strengthen the tendency of the axiomatization of tensor analysis.

Extension of covariant derivative(Ⅲ): From classical gradient to shape gradient

This paper further extends the generalized covari ant derivative from the first covariant derivative to the sec ond one on curved surfaces. Through the linear transforma tion between the first generalized covariant derivative and the second one, the second covariant differential transformation group is set up. Under this transformation group, the sec ond class of differential invariants and integral invariants on curved surfaces is made clear. Besides, the symmetric struc ture of the tensor analysis on curved surfaces are revealed.

Generalized Covariant Derivative with Respect to Time in Flat Space(Ⅰ):Eulerian Description

This paper reports a new derivative in the Eulerian description in flat space-the generalized covariant derivative with respect to time. The following contents are included:(a) the restricted covariant derivative with respect to time for Eulerian component is defined;(b) the postulate of the covariant form invariability in time field is set up;(c) the generalized covariant derivative with respect to time for generalized Eulerian component is defined;(d) the algebraic structure of the generalized covariant derivative with respect to time is made clear;(e) the covariant differential transformation group in time filed is derived. These progresses reveal the covariant form invariability of Eulerian space and time.

Generalized Covariant Derivative with Respect to Time in Flat Space(Ⅱ):Lagrangian Description

The previous paper reported a new derivative in the Eulerian description in flat space—the generalized covariant derivative of generalized Eulerian component with respect to time. This paper extends the thought from the Eulerian description to the Lagrangian description:on the basis of the postulate of covariant form invariability in time field, we define a new derivative in the Lagrangian description in flat space—the generalized covariant derivative of generalized Lagrangian component with respect to time. Besides, the covariant differential transformation group is set up. The covariant form invariability of Lagrangian space-time is ascertained.

仿射对称变换与对称性原理

给出了物理空间的一种仿射对称变换 ,并论证了拉普拉斯方程、热传导方程、波动方程及连续性方程对于这个变换的协变性 ,由此得出对称性原理 ,为研究自然界普遍存在的仿射对称现象提供了数学物理依据 ,从理论上揭示了仿射对称现象 .

多群核截面协方差矩阵转群方法研究

分析多群核截面协方差矩阵信息特点,采用平源近似研究多群核截面协方差矩阵转群方法并自主开发核截面协方差矩阵转群通用程序T-COCCO。以SCALE6.1程序自带44群核截面协方差矩阵信息为基础,通过T-COCCO对235U、238U、239Pu等核素的不同核反应进行核截面协方差矩阵能群结构转换,分别得到33群、47群和70群核截面协方差矩阵,并与NJOY程序制作的响应能群核截面协方差矩阵信息进行对比。对比研究及分析矩阵特性参数信息可知:在能群结构差异不大时(能群数目的变化在两倍以内),本文研究的转群方法是合理的,开发的程序可以方便、快捷、高效获得所需能群结构的核截面协方差矩阵信息,该信息可以用于开展核数据计算不确定性和敏感性分析。