第四类Caftan-Hartogs域上Bergman度量与Einstein-Kahler度量等价

In this paper,we discuss the invariaut complete metric on the Cartan-Hartogs domain of the fourth type.Firstly,we find a new invariant complete metric,and prove the equivalence between Bergman metric and the new metric;Secondly,the Ricci curvature of the new metric has the super bound and lower bound;Thirdly,we prove that the holomorphic sectional curvature of the new metric has the negative supper bound;Finally,we obtain the equivalence between Bergman metric and Einstein-Kahler metric on the Cartan-Hartogs domain of the fourth type.     

Caftan-Hartogs域上K(a)hler-Einstein度量与Bergman度量的等价

本文研究的是华罗庚域的特殊类型第二类Cartan-Hartogs域的不变Bergman度量与Kahler-Einstein度量的等价问题.引入一种与Bergman度量等价的新的完备的Kahler度量ωgλ,其Ricci曲率和全纯截取率具有负的上下界.然后应用丘成桐对Schwarz引理的推广证明ωgλ等价于Kahler-Einstein度量,从而得到了Bergman度量与Khhler-Einstein度量的等价,即丘成桐关于度量等价的猜想在第二类Cartan-Hartogs域上成立.     

Lévy-Prohorov Metric on the Measure Space

Under the premise of infinitely many pure strategies,by defining the new LP* metric,striking an equivalence of topology and weak* topology,we prove that the existence of the essential component.     

概率度量空间中的Ekeland变分原理与集值映象的Caristi重合定理

借助偏序方法,本文得到概率度量空间中之一推广形式的Ekeland变分原理及一集值形式的Caristi重合定理,同时证明了这两个定理之间的等价性.本文结果是[1,2,5,6,7,9]中相应结果的改进和推广.     

DFP变尺度法与FR共轭梯度法的二次等价性

研究了求解无约束极值问题的DFP变尺度法和FR共轭梯度法的关系问题.证明了在应用于求解二次函数的极值问题时,若将初始尺度矩阵取为单位矩阵,二者实际上是等价的,即两种方法求出的极小化点列是相同的.     

Approximation of Metric Spaces by Partial Metric Spaces

Partial metrics are generalised metrics with non-zero self-distances. We slightly generalise Matthews' original definition of partial metrics, yielding a notion of weak partial metric. After considering weak partial metric spaces in general, we introduce a weak partial metric on the poset of formal balls of a metric space. This weak partial metric can be used to construct the completion of classical metric spaces from the domain-theoretic rounded ideal completion.     

Sobolev-Type Classes of Functions with Values in a Metric Space. II

We prove equivalence of the definitions by the author and by Korevaar and Schoen of the Sobolev classes of mappings of a domain of an arithmetic n-dimensional space to a metric space.     

球面型空间中的度量平均

本文首先建立球面型空间中度量平均的概念，其次讨论度量平均过程中一些几何不变量之间的关系，最后举例说明度量平均在解决球面型空间中几何极值问题时的应用．     

On Fuzzy Metric Space

In this paper we prove a common fixed point theorem for three mappings in fuzzy metric space and then extend this result to fuzzy 2 and 3-metric spaces. Our theorem is an extension of result of Fisher [12], to fuzzy metric spaces.AMS Subject Classification (1990): 47H10, 54H25     

On Perturbation Stability of Metric Regularity

We introduce a measure of closeness for set-valued mappings from a metric space to a Banach space which allows to quantatively estimate the effect of perturbation of a set-valued mapping on its metric regularity and covering characteristics.     

度量投影的收敛性（英文）

讨论了赋范空间中度量投影的收敛性．得到了在局部紧集控制下，Chebyshev凸集序列的度量投影的收敛性与K－M收敛，Wijsman收敛和Kuratowski收敛都等价．本文的结论完善了M．Tsukada在[1]和[2]结果．     

The Wasserstein-Fisher-Rao Metric for Waveform Based Earthquake Location

In this paper, we apply the Wasserstein-Fisher-Rao (WFR) metric from the unbalanced optimal transport theory to the earthquake location problem. Compared with the quadratic Wasserstein ($W_2$) metric from the classical optimal transport theory, the advantage of this method is that it retains the important amplitude information as a new constraint, which avoids the problem of the degeneration of the optimization objective function near the real earthquake hypocenter and origin time. As a result, the deviation of the global minimum of the optimization objective function based on the WFR metric from the true solution can be much smaller than the results based on the $W_2$ metric when there exists strong data noise. Thus, we develop an accurate earthquake location method under strong data noise. Many numerical experiments verify our conclusions.     

Instantons and the Information Metric

The information metric arises in statistics as a natural inner product on a space of probability distributions. In general this inner product is positive semi-definite but is potentially degenerate.By associating to an instanton its energy density, we can examine the information metric g on the moduli spaces M of self-dual connections over Riemannian four-manifolds. Compared with the more widely known L² metric, the information metric better reflects the conformal invariance of the self-dual Yang–Mills equations, and seems to have better completeness properties. In the case of SU(2) instantons on S⁴ of charge one, g is known to be the hyperbolic metric on the five-ball. We show more generally that for charge-one SU(2) instantons over 1-connected, positive-definite manifolds, g is non-degenerate and complete in the collar region of M, and is asymptotically hyperbolic there; g vanishes at the cone points of M. We give explicit formulae for the metric on the space of instantons of charge one on CP².     

非欧空间中双基本图形的度量方程及其应用

本文提出了n维球面型空间和双曲空间中双基本图形的概念,建立了球面型空间与双曲空间中双基图形的度量方程,并给出度量方程的一些应用.     

度量空间和锥度量空间中的若干不动点定理

给出了度量空间和锥度量空间中的若干不动点定理.利用这些不动点定理,统一并推广了度量空间和锥度量空间中的若干经典的不动点定理.     

Isometries of the Half-Apollonian Metric

The half-Apollonian metric is a generalization of the hyperbolic metric, similar to the Apollonian metric. It can be defined in arbitrary domains in the euclidean space and has the advantages of being easy to calculate and estimate. We show that the half-Apollonian metric has many geodesics and use this fact to show that in most domains all the isometries of the metric are similarity mappings.     

Order Norm Completions of Cone Metric Spaces

In this article, a completion theorem for cone metric spaces and a completion theorem for cone normed spaces are proved. The completion spaces are constructed by means of an equivalence relation defined via an ordered cone norm on the Banach space E whose cone is strongly minihedral and ordered closed. This order norm has to satisfy the generalized absolute value property. In particular, if E is a Dedekind complete Banach lattice, then, together with its absolute value norm, satisfy the desired properties.     

Hilbert投影距离与Banach空间的范数

In this paper, we establish some relations between the Hilbert＇s projective metric and the norm on a Banach space and show that the metric and the norm induce equivalent convergences at certain set. As applications, we utilize the main results to discuss the eigenvalue problems for a class of positive homogeneous operators of degree a and the positive solutions for a class of nonlinear algebraic system.     

On Connection Between the Nonholonomic Metric on the Heisenberg Group and the Grushin Metric

The purpose of this paper is to compute geodesics on the Grushin plane and examine an assertion on connection between spheres of the Grushin plane and spheres of the Heisenberg group. The assertion turns out to require correction that the spheres of the Heisenberg group are directly obtained by rotation of the Grushin spheres. We find a modified Grushin metric for which the last assertion holds. Also, we prove several theorems about connections between the Grushin plane and Heisenberg group.     

Metric Lie algebras with maximal isotropic centre

A metric Lie algebra is a Lie algebra equipped with an invariant non-degenerate symmetric bilinear form. It is called indecomposable if it is not the direct sum of two metric Lie algebras. We are interested in describing the isomorphism classes of indecomposable metric Lie algebras. In the present paper we restrict ourselves to a certain class of solvable metric Lie algebras which includes all indecomposable metric Lie algebras with maximal isotropic centre. We will see that each metric Lie algebra belonging to this class is a twofold extension associated with an orthogonal representation of an abelian Lie algebra. We will describe equivalence classes of such extensions by a certain cohomology set. In particular we obtain a classification scheme for indecomposable metric Lie algebras with maximal isotropic centre and the classification of metric Lie algebras of index 2.