Solid codes and the uniform density of fd-domains

By means of further investigation of solid codes,the problem“Is every fd-domain uni- formly dense”proposed by Yuqi Guo,C.M.Reis and G.Thierrin in 1988 is solved in this paper.     

PURE STATE APPROACH TO $C(X)×_\alpha Z_n$

ＰＵＲＥ ＳＴＡＴＥ ＡＰＰＲＯＡＣＨ ＴＯ Ｃ（ｘ）_αＺ_nＬＩＢＩＮＧＲＥＮ；ＬＩＮＱＩＮＧ（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈｉｎａ．Ｐｒｏｊｅｃｔｓｕｐｐｏｒｔｅｄｂｙｔｈ?..     

Separable anisotropic differential operators and applications

The nonlocal boundary value problems for anisotropic partial differential-operator equations with a dependent coefficients are studied. The principal parts of the appropriate generated differential operators are nonself-adjoint. Several conditions for the maximal regularity and the fredholmness in Banach-valued Lp-spaces of these problems are given. These results permit us to establish that the inverse of corresponding differential operators belongs to Schatten q-class. Some spectral properties of the operators are investigated. In applications, the nonlocal BVP's for quasielliptic partial differential equations and for systems of quasielliptic equations on cylindrical domain are studied.     

On the Patterson–Sullivan Measure for Geometrically Finite Groups Acting on Complex or Quaternionic Hyperbolic Space

The goal of this paper is to provide a tool, the Global Measure Formula, that will facilitate the study of the limit set of discrete geometrically finite groups of isometries of the rank one symmetric spaces. We consider the shadow of a ball from a fixed reference point onto the boundary, and prove a formula that describes the measure of the shadow in terms of the center of the shadowed ball, generalizing a result from real hyperbolic geometry.     

Sobolev空间H~s(R~n)上矩阵伸缩的多尺度分析特征刻画

本文对高维Sobolev空间Hs(Rn)上具有矩阵伸缩的多尺度分析特征进行了 刻划,特别给出了稠密性特征的一个充分必要条件,从而解决了文献[4]中提出的一个 问题.所得结果覆盖了这方面的已知结论.     

Geometrical study of paraxial light beam transmission in free space

By introducing an imaginary space transform curvature ρ_s, a complex space called Riemannian space is constructed, in which the light propagating in free space has the trajectory of straight line while propagating. Moreover, this curvature couples with that of the wave front of the paraxial beam ρ_w, and therefore a complex curvature ρ_c is constructed, which can be employed to investigate the behavior of the light transmission and to generalize the ABCD law. Project supported by the National Hi-Tech Inertial Confinement Fusion Committee, the Guangdong Natural Science Foundation the Postdoctoral Foundation of Guangdong and National Postdoctoral Foundation of China.     

Banach空间上算子张量积的联合谱

本文主要研究了 Banach 空间上交换算子组的张量积以及 Banach 代数的张量积中交换元组的 Taylor 联合谱,推广了 Vasilescu,F.H.及 Wrobel,V.等人结果。     

On the phase space approach to complexity

We elaborate in some detail on a new phase space approach to complexity, due to Y.-C. Zhang. We show in particular that the connection between maximal complexity and power law noise or correlations can be derived from a simple variational principle. For a 1D signal we find 1/f noise, in accordance with Zhang.     

On the Solvability of the Multidimensional Version of the First Darboux Problem for a Model Second-Order Degenerating Hyperbolic Equation

A multidimensional version of the first Darboux problem is considered for a model second-order degenerating hyperbolic equation. Using the technique of functional spaces with a negative norm, the correct formulation of this problem in the Sobolev weighted space is proved.     

A Class of Cauchy Problem for Quasilinear Hyperbolic Systems with the Weakly Dissipative Terms

ＡＣｌａｓｓｏｆＣａｕｃｈｙＰｒｏｂｌｅｍｆｏｒＱｕａｓｉｌｉｎｅａｒＨｙｐｅｒｂｏｌｉｃＳｙｓｔｅｍｓｗｉｔｈｔｈｅＷｅａｋｌｙＤｉｓｓｉｐａｔｉｖｅＴｅｒｍｓ￥ＬｉｕＦａｇｕｉ；ＹａｎｇＱｉａｏ（ＮｏｒｔｈＣｈｉｎａＩｎｓｔｉｔｕｔｅｏｆＷａｔｅ...