Vortices and Jacobian varieties

We investigate the geometry of the moduli space of N$N$ vortices on line bundles over a closed Riemann surface Σ$\Sigma$ of genus g>1$g>1$, in the little explored situation where 1≤N<g$1\le N<g$. In the regime where the area of the surface is just large enough to accommodate N$N$ vortices (which we call the dissolving limit), we describe the relation between the geometry of the moduli space and the complex geometry of the Jacobian variety of Σ$\Sigma$. For N=1$N=1$, we show that the metric on the moduli space converges to a natural Bergman metric on Σ$\Sigma$. When N>1$N>1$, the vortex metric typically degenerates as the dissolving limit is approached, the degeneration occurring precisely on the critical locus of the Abel–Jacobi map of Σ$\Sigma$ at degree N$N$. We describe consequences of this phenomenon from the point of view of multivortex dynamics.     

基于视觉感知的光谱评估尺度

光谱颜色复现和色度精度是评价光谱重建算法准确的基础。简单而直观的评价指标对颜色复现控制是必不可少。该指标需要同时表征复现颜色的光谱差和色度差。在研究光谱匹配评估的方法基础上,提出基于颜色视觉感知的三种光谱评估指标,通过加权人眼视觉匹配函数,实现颜色光谱差与色度的评估。通过孟塞尔颜色系统的光谱数据,该论文分析与验证三种视觉加权的评估指标的有效性。通过孟塞尔颜色系统数据,这些指标在CIELab均匀色空间中分布均匀而稳定,从而证明加权算法的评估指标是既表征到颜色感知又反映出颜色的光谱相似度。实证结果表明,加权的指标可以实现同时表征实际人眼的颜色感知和颜色光谱差异。基于人眼视觉感知的评估指标解决了颜色的原始光谱和重建光谱的光谱匹配精度的定量评价问题。所提出评价指标通过一个简单而直观的数值实现对复现颜色光谱与色度评估。     

Submanifolds in Cauchy Riemann Geometry

In this paper I would like to make a report on the results about hypersurfaces in the Heisenberg group and invariant curves and surfaces in CR geometry. The results are contained in the papers [8, 9, 16] and [14]. Besides, I would also report on the results about the strong maximum principle for a class of mean curvature type operators in [10].     

On some classes of projectively flat Finsler metrics with constant flag curvature

In this paper, we give the equivalent PDEs for projectively flat Finsler metrics with constant flag curvature defined by a Euclidean metric and two 1-forms. Furthermore, we construct some classes of new projectively flat Finsler metrics with constant flag curvature by solving these equivalent PDEs.     

Canonical measures on the moduli spaces of compact Riemann surfaces

We study some explicit relations between the canonical line bundle and the Hodge bundle over moduli spaces for low genus. This leads to a natural measure on the moduli space of every genus which is related to the Siegel symplectic metric on Siegel upper half-space as well as to the Hodge metric on the Hodge bundle.     

一类拟凸域的Bergman度量与Kobayashi度量的比较定理

本文对一类拟凸域Ｅ（ｍ，ｎ，Ｋ）给出其不变Ｋａｈｌｅｒ度量下的全纯截曲率的显表达式，并构造了Ｅ（ｍ，ｎ，Ｋ）的一个不变的完备的Ｋａｈｌｅｒ度量，使得它大于或等于Ｂｅｒｇｍａｎ度量，而且其全纯截曲率的上界是一个负常数，从而得到Ｅ（ｍ，ｎ，Ｋ）的Ｂｅｒｇｍａｎ度量和Ｋｏｂａｙａｓｈｉ度量的比较定理。     

Almost Complex Structures Which Are Compatible with Kähler or Symplectic Structures

In this note we prove that half of all homotopy classes of almost complex structures on M is not compatible with any symplectic structure for a certain class of oriented compact 4-manifolds M. In particular, half of all homotopy classes of almost complex structures on an oriented 4-manifold is not compatible to any Kähler structure.     

近严格凸与最佳逼近

本文研究近严格凸与最佳逼近的关系．证明了Ｂａｎａｃｈ空间Ｘ是近严格凸的当且仅当Ｘ的每个子空间是紧－半－切比晓夫空间．     

Lip_J-扩张域和一致域(英文)

本文证明了如下两个结果:(1)域D(?)R~n是一致域当且仅当D是Lip_J-扩张域;(2)Jordan域D(?)R~2是拟圆当且仅当对在D上满足|f′(z)|≤d(z,(?)D)~(-1)的任意的解析函数f恒有f∈Lip_J(D),其中J(x_1,x_2)=1/2 log(1+|x_1-x_2|/d(x_1,(?)D))(1+|x_1-x_2|/d(x_2,(?)D)),x_1,x_2∈D.     

Metric of States

Metric of quantum states plays an important role in quantum information theory. In this letter, we find the deep connection between quantum logic theory and quantum information theory. Using the method of quantum logic, we can get a famous inequality in quantum information theory, and we answer a question raised by S. Gudder.