关于对称方程组非零解的判定与解法

给出对称方程组{x_1+x_2+…+x_n=0,……,x_1~(i-1)+x_2~(i-1)+…+x_n~(i-1)=0,x_1~(i+1)+x_2~(i+1)+…+x_n~(i+1)=0,……,x_1~(n+1)+x_2~(n+1)+…x_n~(n+1)=0.(1)非零解的判别条件、求解方法以及严格的证明．     

方形对称传输线TE模的色散特征曲线的数值计算

本文提出了一种计算方形对称传输线TE模的各模式的截止波数,以及根据各模式的截止波数计算各模式的色散曲线的方法。     

Curie’s principle and causal graphs

Curie’s Principle says that any symmetry property of a cause must be found in its effect. In this article, I consider Curie’s Principle from the point of view of graphical causal models, and demonstrate that, under one definition of a symmetry transformation, the causal modeling framework does not require anything like Curie’s Principle to be true. On another definition of a symmetry transformation, the graphical causal modeling formalism does imply a version of Curie’s Principle. These results yield a better understanding of the logical landscape with respect to the relationship between Curie’s Principle and graphical causal modeling.     

Target space ≠ space

This paper investigates the significance of T-duality in string theory: the indistinguishability with respect to all observables, of models attributing radically different radii to space—larger than the observable universe, or far smaller than the Planck length, say. Two interpretational branch points are identified and discussed. First, whether duals are physically equivalent or not: by considering a duality of the familiar simple harmonic oscillator, I argue that they are. Unlike the oscillator, there are no measurements ‘outside’ string theory that could distinguish the duals. Second, whether duals agree or disagree on the radius of ‘target space’, the space in which strings evolve according to string theory. I argue for the latter position, because the alternative leaves it unknown what the radius is. Since duals are physically equivalent yet disagree on the radius of target space, it follows that the radius is indeterminate between them. Using an analysis of Brandenberger and Vafa (1989), I explain why—even so—space is observed to have a determinate, large radius. The conclusion is that observed, ‘phenomenal’ space is not target space, since a space cannot have both a determinate and indeterminate radius: instead phenomenal space must be a higher-level phenomenon, not fundamental.     

真空中的中心对称引力场的空间曲率

本文给出在真空中中心对称引力场的空间曲率的详尽证明.     

面心立方基体内B2结构沉淀相间的界面结构

从面心立方基体的对称性出发，我们确定了该基体内固态沉淀反应所致Ｂ２结构沉淀相之间的界面取向；基于稳定界面结构应具有最低能量的考虑，提出了几种可能的沉淀相间界面结构模型；实验观察表明，Ｎｉ－Ｂｅ合金中沉淀相间界面取向满足对称性要求，β／β界面结构跟自由β相的＜１１０＞｛１１２｝孪晶界面相同，但界面附近存在应变场。     

无结点线位移刚架在结点集中力作用下的简化

一般刚架在一般外力作用下，它的每一截面都要产生弯矩、剪力和轴向力，计算量很大。但无结点位移刚架在结点集中作用下，却只产生轴向力，如果分析得法，将会为计算带来很大的方便。     

八元向量代数及其在电动力学中的应用

本文建立了八元向量代数,它既是一种方阵代数,又作为一个更加完备的运算系统而包含了复数、矢量和四元数.应用八元向量代数,可以十分方便地导出 Maxwell 方程组的对称变换,并将其拓展成为一个更加完整而对称的电磁场结构定律,从而构成进一步发展经典电动力学的理论基础.     

正规类中遗传根的一个性质

在结合环中，Amitsur证明了：设R是遗传根，对环A的任意两个理想Ii，令Ii^-是由Ii^-/Ii=R（A/I）所唯一确定的A的理想，i=1,2,则有（I1∩I2^-)=I1^-∩I2^-。本文在更广泛的意义下证明此定理，推广了Amitsur的结果，同时给出它的几个应用。     

势论

从从传统文化到现代科学，有关势的论述比比皆是，但却没有“势”的统一的科学定义。笔者在给出势概念的逻辑定义的基础上，论述了造势的基本原理：使系统中的元素差别最大联系最紧。由于这样的元素只能是对称性元素，而对称性元素构成“群”，从而揭示了“造势”必然“成群”的基本规律。在此基础上，探讨了科学找势、管理造势、文学造势、教育造势和创新造势的造势普适性机制。