The Coarse ℓ p -Novikov Conjecture and Banach Spaces with Property (H)∗

In this paper, for 1 < p < ∞, the authors show that the coarse ? p -Novikov conjecture holds for metric spaces with bounded geometry which are coarsely embeddable into a Banach space with Kasparov-Yu’s Property (H).     

Persistence Approximation Property for Maximal Roe Algebras

Persistence approximation property was introduced by Hervé Oyono-Oyono and Guoliang Yu. This property provides a geometric obstruction to Baum-Connes conjecture. In this paper, the authors mainly discuss the persistence approximation property for maximal Roe algebras. They show that persistence approximation property of maximal Roe algebras follows from maximal coarse Baum-Connes conjecture. In particular, let X be a discrete metric space with bounded geometry, assume that X admits a fibred coar...     

Ideals in the Roe Algebras of Discrete Metric Spaces with Coefficients in B（H）

The notion of an ideal family of weighted subspaces of a discrete metric space X with bounded geometry is introduced. It is shown that, if X has Yu＇s property A, the ideal structure of the Roe algebra of X with coefficients in B（H） is completely characterized by the ideal families of weighted subspaces of X, where B（H） denotes the C＊-algebra of bounded linear operators on a separable Hilbert space H.     

一些超空间的非双Lipschitz 齐次性

A metric space(X, d) is called bi-Lipschitz homogeneous if for any points x, y ∈ X,there exists a self-homeomorphism h of X such that both h and h-1are Lipschitz and h(x) = y.Let 2(X,d)denote the family of all non-empty compact subsets of metric space(X, d) with the Hausdorff metric. In 1985, Hohti proved that 2([0,1],d)is not bi-Lipschitz homogeneous, where d is the standard metric on [0, 1]. We extend this result in two aspects. One is that 2([0,1],e)is not bi-Lipschitz homogeneous for an admissible metric e satisfying some conditions. Another is that 2(X,d)is not bi-Lipschitz homogeneous if(X, d) has a nonempty open subspace which is isometric to an open subspace of m-dimensional Euclidean space Rm.     

具有性质$b_1$空间的乘积性

In this note,we present that:(1)Let X=σ{Xα:α∈A} be|A|-paracompact (resp.,hereditarily |A|-paracompact).If every finite subproduct of {Xα:α∈A} has property b1 (resp.,hereditarily property b1),then so is X.(2) Let X be a P-space and Y a metric space.Then,X×Y has property b1 iff X has property b1.(3) Let X be a strongly zero-dimensional and compact space.Then,X×Y has property b1 iff Y has property b1.     

A General Existence Principle for Fixed Point Theorems in One Parameter Case of Soft $D_{a}$-Metric Space

In this paper, we take the case of soft points into consideration and propose a new metric structure called soft D_a-metric space for a specific orbit defined with soft points. In order to establish fixed point results in the modified metric space, we modify a few existing definitions in the sense of soft points.     

On Products of Property b1

In this note,we present that:(1)Let X=σ{Xα:α∈A} be|A|-paracompact (resp.,hereditarily |A|-paracompact).If every finite subproduct of {Xα:α∈A} has property b1 (resp.,hereditarily property b1),then so is X.(2) Let X be a P-space and Y a metric space.Then,X×Y has property b1 iff X has property b1.(3) Let X be a strongly zero-dimensional and compact space.Then,X×Y has property b1 iff Y has property b1.     

Slowly Increasing Cohomology for Discrete Metric Spaces with Polynomial Growth

The authors introduce a kind of slowly increasing cohomology HS*(X) for a discrete metric space X with polynomial growth,and construct a character map from the slowly increasing cohomology HS*(X) into HC*cont(S(X)),the continuous cyclic cohomology of the smooth subalgebra S(X) of the uniform Roe algebra B*(X).As an application,it is shown that the fundamental cocycle,associated with a uniformly contractible complete Riemannian manifold M with polynomial volume growth and polynomial contractibility radius growth,is slowly increasing.     

具有半对称度量联络的复空间型中全实子流形的Chen型不等式

In this paper, we obtain Chen＇s inequalities for totally real submanifolds in complex space forms with a semi-symmetric metric connection. Also, some results of A. Mihai and C. Ozgiir＇s paper have been modified.     

集值离散系统的某些动力性质

A discrete dynamical system can be expressed as xn 1 =f(xn), n=0,1, 2,... where X isa metric space and f : X→X is a continuous map. The study of it tells us how the points in the base space X moved. Nevertheless, this is not enough for the researches of biological species, demography, numerical simulation and attractors (see [1], [2]).     

Coarsely embeddable metric spaces without Property A

We study Guoliang Yu's Property A and construct metric spaces which do not satisfy Property A but embed coarsely into the Hilbert space.     

Fixed Point Theorems for (p,q)-Quasi-Contraction Mappings in Cone Metric Spaces

In this work, the authors introduce the concept of $(p,q)$-quasi-contraction mapping in a cone metric space. We prove the existence and uniqueness of a fixed point for a $(p,q)$-quasi-contraction mapping in a complete cone metric space. The results of this paper generalize and unify further fixed point theorems for quasi-contraction, convex contraction mappings and two-sided convex contraction of order $2$.     

函数空间SUF的RNP与模糊上鞅

本文证明取值于度量空间的函数的Ｂｏｃｈｎｅｒ积分与Ａｕｍａｎｎ积分是等价的，且积分值相等。空间的Ｒａｄｏｎ－Ｎｉｋｏｄｙｍ性质（简称ＲＮＰ）在正线性等距映射下保持不变。在此基础上得到空间ＳＵＦ具有ＲＮＰ，且把诸结果应用于模糊上秧的研究，得到了模糊上鞅的几个收敛定理。     

Homotopy Method for a General Multiobjective Programming Problem

In this paper, we study a class of vector minimization problems on a complete metric space X which is identified with the corresponding complete metric space of objective functions . We do not impose any compactness assumption on X. We show that, for most (in the sense of Baire category) functions , the corresponding vector optimization problem has a solution.     

The Non-Archimedean Theory of Discrete Systems

In the paper, we study behaviour of discrete dynamical systems (automata) w.r.t. transitivity; that is, speaking loosely, we consider how diverse may be behaviour of the system w.r.t. variety of word transformations performed by the system: we call a system completely transitive if, given arbitrary pair a, b of finite words that have equal lengths, the system ${\mathfrak{A}}$ , while evolution during (discrete) time, at a certain moment transforms a into b. To every system ${\mathfrak{A}}$ , we put into a correspondence a family ${\mathcal{F}_{\mathfrak{A}}}$ of continuous mappings of a suitable non-Archimedean metric space and show that the system is completely transitive if and only if the family ${\mathcal{F}_{\mathfrak{A}}}$ is ergodic w.r.t. the Haar measure; then we find easy-to-verify conditions the system must satisfy to be completely transitive. The theory can be applied to analyse behaviour of straight-line computer programs (in particular, pseudo-random number generators that are used in cryptography and simulations) since basic CPU instructions (both numerical and logical) can be considered as continuous mappings of a (non-Archimedean) metric space ${\mathbb{Z}_{2}}$ of 2-adic integers.     

Some Low Distortion Metric Ramsey Problems

In this note we consider the metric Ramsey problem for the normed spaces $\ell_p$. Namely, given some $1\le p \le \infty$ and $\alpha \ge 1$, and an integer $n$, we ask for the largest $m$ such that every $n$-point metric space contains an $m$-point subspace which embeds into $\ell_p$ with distortion at most $ \alpha$. In [1] it is shown that in the case of $\ell_2$, the dependence of $m$ on $\alpha$ undergoes a phase transition at $\alpha =2$. Here we consider this problem for other $\ell_p$, and specifically the occurrence of a phase transition for $p\neq 2$. It is shown that a phase transition does occur at $\alpha=2$ for every $p\in [1,2]$. For $p > 2$ we are unable to determine the answer, but estimates are provided for the possible location of such a phase transition. We also study the analogous problem for isometric embedding and show that for every $1 < p < \infty$ there are arbitrarily large metric spaces, no four points of which embed isometrically in $\ell_p$.     

强零维度量空间的刻画

本文研究了强零维度量空间,借助点星弱邻域网刻画了强零维度量空间,获得了强零维度量空间等价于具有离散覆盖列的点星弱邻域网的非空正则空间,回答了葛英提出的一个问题.