A Determinantal Formula for Supersymmetric Schur Polynomials

We derive a new formula for the supersymmetric Schur polynomial s (x/y). The origin of this formula goes back to representation theory of the Lie superalgebra gl(m/n). In particular, we show how a character formula due to Kac and Wakimoto can be applied to covariant representations, leading to a new expression for s (x/y). This new expression gives rise to a determinantal formula for s (x/y). In particular, the denominator identity for gl(m/n) corresponds to a determinantal identity combining Cauchy's double alternant with Vandermonde's determinant. We provide a second and independent proof of the new determinantal formula by showing that it satisfies the four characteristic properties of supersymmetric Schur polynomials. A third and more direct proof ties up our formula with that of Sergeev-Pragacz.     

Development of the Evans Wave Equation in the Weak-Field Limit: The Electrogravitic Equation

The Evans wave equation [1-3] is developed in the weak-field limit to give the Poisson equation and an electrogravitic equation expressing the electric field strength E in terms of the acceleration g due to gravity and a fundamental scalar potential ⁽⁰⁾ with the units of volts (joules per coulomb). The electrogravitic equation shows that an electric field strength can be obtained from the acceleration due to gravity, which in general relativity is non-Euclidean spacetime. Therefore an electric field strength can be obtained, in theory, from scalar curvature R. This inference is supported by recent experimental data from the patented motionless electromagnetic generator [5].     

傅里叶思想的精髓及其伟大之处

介绍了傅里叶级数和傅里叶变换的基本思想,从哲学、物理学和数学的角度阐述了其深刻涵义和伟大之处.指出了傅里叶的思想和牛顿-莱布尼茨的思想的不同之处.导出了四维协变的傅里叶变换公式.简要介绍了傅里叶级数和变换在物理学中的应用.     

Contribution of matter fields to the Gell-Mann-Low function for the $$\mathcal{N} = 1$$ supersymmetric Yang-Mills theory regularized by higher covariant derivatives

We use the Schwinger-Dyson equations and Slavnov-Tailor identities to obtain the contribution of matter fields to the Gell-Mann-Low function for the supersymmetric Yang-Mills theory regularized by higher covariant derivatives. We discuss the possible deviation of the result from the corresponding contribution to the exact Novikov-Shifman-Vainshtein-Zakharov β-function. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 3, pp. 441–460, March, 2007.     

Comparison of using Cartesian and covariant velocity components on non-orthogonal collocated grids

In this paper, the Cartesian velocity components and the covariant velocity components are adopted respectively as the main variables in solving the momentum equations in the SIMPLE-like method to calculate a lid-driven cavity flow on non-orthogonal collocated grids. In total, more than 400 computer runs are carried out for a two-dimensional problem. The accuracy and convergence performance of using Cartesian and covariant velocity components are compared in detail. Comparisons show that both the Cartesian and covariant velocity methods have the same numerical accuracy. The convergence rate of the covariant velocity method can be faster than that of the Cartesian velocity method if the relaxation factor for pressure is small enough. However, the convergence range of the relaxation factor for pressure in the covariant velocity method is quite narrow. When the cross-derivatives in the pressure-correction equation are retained approximately, its convergence performance can be greatly improved. Copyright © 1999 John Wiley & Sons, Ltd.     

Wt-approximation representations over quasik-Gorenstein algebras

The notions of quasik-Gorenstein algebras and W ^t -approximation representations are introduced. The existence and uniqueness (up to projective equivalences) of W ^t -approximation representations over quasi k-Gorenstein algebras are established. Some applications of W ^t -approximation representations to homologically finite subcategories are given.     

Conformally and Projective Covariant Differential Operators

Motivated by the structure of conformal anomalies in two-dimensional gravity and its generalizations, the projective and conformal covariance properties of linear, bilinear and trilinear differential operators are investigated in some detail and the triviality of the covariant trilinear operators is demonstrated.     

整数自旋粒子的方程和波函数

从高自旋态的Bargmann-Wigner方程出发,建立了整数自旋粒子的运动方程,通过求解方程得到了一套整数自旋粒子波函数,并建立了等效Largrange形式.     

从球面到光滑流形映射的Munkholm型定理

本文应用 Smith周期变换理论 ,根据球面在周期变换下的指数 ,对球面到光滑流形的连续映射做了进一步探讨 ,从而得到了 Munkholm型定理 .     

均匀磁场中的转动导体和麦克斯韦方程组的协变性

对某文献中"形如E=±v×B的电场的非零散度与真实的电荷密度无本质关联"的观点提出商榷,指出它违反麦克斯韦方程组的协变性,而实际情形是电场的散度仍然为0.然后就原文举出的匀强磁场的例子,在匀速转动系中利用曲线坐标系和嘉当(Cartan)随动标架进行了相应的计算,结果表明麦克斯韦方程组的协变性并未被破坏.