On Generalized Douglas–Weyl(α, β)-Metrics

In this paper, we study generalized Douglas–Weyl(α, β)-metrics. Suppose that a regular(α, β)-metric F is not of Randers type. We prove that F is a generalized Douglas–Weyl metric with vanishing S-curvature if and only if it is a Berwald metric. Moreover, by ignoring the regularity, if F is not a Berwald metric, then we find a family of almost regular Finsler metrics which is not Douglas nor Weyl. As its application, we show that generalized Douglas–Weyl square metric or Matsumoto metric with isotropic mean Berwald curvature are Berwald metrics.     

The Szegö kernel on a class of non-compact CR manifolds of high codimension

We generalize Nagel’s formula for the Szegö kernel and use it to compute the Szegö kernel on a class of non-compact CR manifolds whose tangent space decomposes into one complex direction and several totally real directions. We also discuss the control metric on these manifolds and relate it to the size of the Szegö kernel.     

Q过程的不变分布(Ⅱ)

设E为一个可数集,Q=（qi,j;i,j∈E）为E×E上的矩阵,满足m为E上的概率分布满足何时存在Q过程,使得m是它的不变分布? 这个问题由Williams（1979）作为一个开问题提出.文[15]对全稳定情形,解决了这个问题;本文对单瞬时情形,完整地解决了该问题.     

凸域内单叶函数的导数

设函数f（w）为凸区域D内的单叶解析函数,对于2≤n≤8和所有w∈D,本文得到估计式|f（n）（w）/f＇（w）|的精确上界.这个结果推广了一些已知的结论.     

Cn中不同域的复合算子

令Ω1与Ω2与C^n中的两个有界齐性域，假设φ：1Ω→Ω2是一个全纯映射。在本中，我们研究相应的复合算子Cφ：β（Ω2）→β（Ω1）的有界性和紧性，特别地，我们讨论取B^n和U^n的情形。     

A method for calculating invariant subspaces of symmetric hyperbolic equations

An algorithm is constructed for calculating invariant subspaces of symmetric hyperbolic systems arising in electromagnetic, acoustic, and elasticity problems. Discrete approximations are calculated for subspaces that correspond to minimal eigenvalues and smooth eigenfunctions. Difficulties related to the presence of an infinite-dimensional kernel in the differential operator are successfully handled. The efficiency of the algorithm is demonstrated using acoustics equations.     

Quantization of Underdamped, Critically Damped, and Overdamped Electric Circuits with a Power Source

We have investigated the quantum mechanical effect of the underdamped, critically damped, and overdamped electric circuits with a power source. The charge of the underdamped circuit oscillates while those of the critically damped and overdamped ones don't. The wave function of the system of overdamped circuit represented parabolic cylinder function while underdamped circuit was represented by well-known Hermite polynomial. The eigenvalues of underdamped circuit is discrete while those of the critically damped and overdamped ones are given as continuously.     

Application of Hilbert＇s Projective Metric on Symmetric Cones

Let Ω be a symmetric cone. In this note, we introduce Hilbert＇s projective metric on Ω in terms of Jordan algebras and we apply it to prove that, given a linear invertible transformation g such that g（Ω） = Ω and a real number p, ｜p｜ 〉 1, there exists a unique element x ∈ Ω satisfying g（x） = x^p.     

Projective geometry and special relativity

Some concepts of real and complex projective geometry are applied to the fundamental physical notions that relate to Minkowski space and the Lorentz group. In particular, it is shown that the transition from an infinite speed of propagation for light waves to a finite one entails the replacement of a hyperplane at infinity with a light cone and the replacement of an affine hyperplane – or rest space – with a proper time hyperboloid. The transition from the metric theory of electromagnetism to the pre‐metric theory is discussed in the context of complex projective geometry, and ultimately, it is proposed that the geometrical issues are more general than electromagnetism, namely, they pertain to the transition from point mechanics to wave mechanics.