无限大平面磁通量的规律性及其应用

对于球解高对称性静磁场，如果仅应用安培环路定理和高斯定理，在解答中会存在一些不能唯一确定的常量，为了研究确定这些常量的规律，本讨论了穿过一个无限大平面的磁通量并用得到了一个有意义的结论。     

Validity of the quantum regression theorem for resonance fluorescence in a photonic crystal

Correlation functions of a driven two‐level system embedded in a photonic crystal are analyzed. The spectral density of the photonic bands near a gap makes this system non‐Markovian. The equations of motion for two‐time correlations are derived by two different methods, the quantum regression theorem and the fluctuation dissipation theorem, and found to be the same.     

A Kochen-Specker inequality from a SIC

Yu and Oh (eprint) [1] have given a state-independent proof of the Kochen-Specker theorem in three dimensions using only 13 rays. The proof consists of showing that a non-contextual hidden variable theory necessarily leads to an inequality that is violated by quantum mechanics. We give a similar proof making use of 21 rays that constitute a SIC (symmetric informationally-complete positive operator-valued measure) and a complete set of MUB (mutually unbiased bases). A theory-independent inequality is also presented using the same 21 rays, as required for experimental tests of contextuality.     

Birkhoff系统的Hojman定理的几何基础

研究了Birkhoff系统的Hojman定理的几何基础.建立了系统的运动微分方程和Hojman守恒 定理，利用现代微分几何给出了Birkhoff系统的Hojman定理的一个证明. 关键词： Birkhoff系统 Hojman定理 对称性 微分几何     

平面运动刚体加速度瞬心的确定及应用

给出在特殊情况下,确定刚体平面运动加速度瞬心的方法以实例说明加速度瞬心在运动学以及动力学中的应用,可使一些问题求解大为简化．     

HYPERFINITE TRANSVERSAL THEORY. II

We continue the investigation of validity of Hall's theorem in the case of the Loeb space of an internal, uniformly distributed, hyperfinite measure space initiated in1992 by the author. Some new classes of graphs are introduced for which the measure theoretic version of Hall's theorem still holds.

     

Strictly pseudoconvex domains and algebraic varieties

In the paper, we consider applications of strictly pseudoconvex domains to the problems of algebraicity and rationality. We give a new proof of the Kodaira theorem on the algebraicity of a surface and we also prove a multidimensional version of this theorem. Theorems analogous to the Hodge index theorem and the Lefschetz theorem about (1, 1)-classes are obtained for strictly pseudoconvex domains. Conjectures on the geometry of strictly pseudoconvex domains on algebraic surfaces are formulated. Translated fromMatematicheskie Zametki, Vol. 60, No. 3, pp. 414–422, September, 1996. This research was supported by the Russian Foundation for Basic Research under grant No. 93-01-00225 and by the International Science Foundation under grant No. 508.     

Asymptotic Behavior of Heat Kernels on Spheres of Large Dimensions

Forn2, let (μ^x_τ, n)_τ0be the distributions of the Brownian motion on the unit sphereS^{n n+1}starting in some pointxSⁿ. This paper supplements results of Saloff-Coste concerning the rate of convergence ofμ^x_τ, nto the uniform distributionU_nonSⁿforτ→∞ depending on the dimensionn. We show that,[formula]forτ_n:=(ln n+2s)/(2n), where erf denotes the error function. Our proof depends on approximations of the measuresμ^x_τ, nby measures which are known explicitly via Poisson kernels onSⁿ, and which tend, after suitable projections and dilatations, to normal distributions on forn→∞. The above result as well as some further related limit results will be derived in this paper in the slightly more general context of Jacobi-type hypergroups.     

一个新的极大极小定理及应用

本文得到一个新的极大极小定理及其几个等价形式．作为这一结果的应用，我们得到区间空间上的Ｋｙ Ｆａｎ型截口定理，匹配定理和几个集值映象的不动点定理．     

A Note on Orthogonal Multiplication

Hurewicz-Radon theorem [1] gives a sufficient and necessary condition about the existence of an orthogonal multiplication f:Rk×Rn→Rn. In this paper,we shall discuss two extensions of the theorem.that is,the sufficient and necessary conditions about the existence of an orthogonal multiplication f:Rk×Rn→Rn 1or f:Rk×Rn→Rn 2