连续自映射拓扑压的两个注记

令T:X→ X是紧度量空间(X,d)上的连续映射.该文给出了T的拓扑压和T在非游荡集上的限制的拓扑压相等的不依赖于变分原理的一个直接证明.同时,还讨论了半共轭的两个系统的拓扑压之间的关系,证明了拓扑压在一致有限对一条件下是半共轭不变量.     

Optimal shape design for fluid flow using topological perturbation technique

This paper is concerned with an optimal shape design problem in fluid mechanics. The fluid flow is governed by the Stokes equations. The theoretical analysis and the numerical simulation are discussed in two and three-dimensional cases. The proposed approach is based on a sensitivity analysis of a design function with respect to the insertion of a small obstacle in the fluid flow domain. An asymptotic expansion is derived for a large class of cost functions using small topological perturbation technique. A fast and accurate numerical algorithm is proposed. The efficiency of the method is illustrated by some numerical examples.     

Horseshoe chaos and topological entropy estimate in a simple power system

This paper presents rigorous arguments on existence of chaos and an estimate of topological entropy in a simple power system by means of topological horseshoe theory and computer computations.     

Weak Form of Fuzzy Open Sets and Their Related Continuity

The aim of this paper is to give a new class of fuzzy open sets called fuzzy pre-γ-open sets in fuzzy topological spaces. Also,a new type of fuzzy continuous functions called,fuzzy pre-γ-continuous functions is introduced and studied.     

Topological Hypergroups in the Sense of Marty

In this paper, we introduce the concept of topological hypergroups as a generalization of topological groups. A topological hypergroup is a nonempty set endowed with two structures, that of a topological space and that of a hypergroup. Let (H, ○) be a hypergroup and (H, τ) be a topological space such that the mappings (x, y) → x ○ y and (x, y) → x/y from H × H to 𝒫*(H) are continuous. The main tool to obtain basic properties of hypergroups is the fundamental relation β*. So, by considering the quotient topology induced by the fundamental relation on a hypergroup (H, ○) we show that if every open subset of H is a complete part, then the fundamental group of H is a topological group.

It is important to mention that in this paper the topological hypergroups are different from topological hypergroups which was initiated by Dunkl and Jewett.     

The topological dynamics of semigroup actions

In these notes we explore the fine structure of recurrence for semigroup actions, using the algebraic structure of compactifications of the acting semigroup.

     

Region merging with topological control

This paper presents a region merging process controlled by topological features on regions in three-dimensional (3D) images. Betti numbers, a well-known topological invariant, are used as criteria. Classical and incremental algorithms to compute the Betti numbers using information represented by the topological map of an image are provided. The region merging algorithm, which merges any number of connected components of regions together, is explained. A topological control of the merging process is implemented using Betti numbers to control the topology of an evolving 3D image partition. The interest in incremental approaches of the computation of Betti numbers is established by providing a processing time comparison. A visual example showing the result of the algorithm and the impact of topological control is also given.     

Invariance properties of coHochschild homology

The notion of Hochschild homology of a dg algebra admits a natural dualization, the coHochschild homology of a dg coalgebra, introduced in [23] as a tool to study free loop spaces. In this article we prove “agreement” for coHochschild homology, i.e., that the coHochschild homology of a dg coalgebra C is isomorphic to the Hochschild homology of the dg category of appropriately compact C-comodules, from which Morita invariance of coHochschild homology follows. Generalizing the dg case, we define the topological coHochschild homology (coTHH) of coalgebra spectra, of which suspension spectra are the canonical examples, and show that coTHH of the suspension spectrum of a space X is equivalent to the suspension spectrum of the free loop space on X, as long as X is a nice enough space (for example, simply connected.) Based on this result and on a Quillen equivalence established in [24], we prove that “agreement” holds for coTHH as well.     

关于S~1上扩张映射的拓扑熵的改进

对文献 [1 ]中圆周上扩张映射的拓扑熵的结论给予了改进 ,得到了结论 :设 f∈ Cr(S1 ,S1 )是扩张映射 ,则 ent(f) =log|deg(f) |.     

Hyper-Kähler geometry and invariants of three-manifolds

We study a 3-dimensional topological sigma-model, whose target space is a hyper-Kähler manifold X. A Feynman diagram calculation of its partition function demonstrates that it is a finite type invariant of 3-manifolds which is similar in structure to those appearing in the perturbative calculation of the Chern-Simons partition function. The sigma-model suggests a new system of weights for finite type invariants of 3-manifolds, described by trivalent graphs. The Riemann curvature of X plays the role of Lie algebra structure constants in Chern-Simons theory, and the Bianchi identity plays the role of the Jacobi identity in guaranteeing the so-called IHX relation among the weights. We argue that, for special choices of X, the partition function of the sigma-model yields the Casson-Walker invariant and its generalizations. We also derive Walker's surgery formula from the SL(2, Z) action on the finite-dimensional Hilbert space obtained by quantizing the sigma-model on a two-dimensional torus.     

On a lower bound for the connectivity of the independence complex of a graph

Aharoni, Berger and Ziv proposed a function which is a lower bound for the connectivity of the independence complex of a graph. They conjectured that this bound is optimal for every graph. We give two different arguments which show that the conjecture is false.     

Topological Graphs with No Large Grids

Let G be a topological graph with n vertices, i.e., a graph drawn in the plane with edges drawn as simple Jordan curves. It is shown that, for any constants k,l, there exists another constant C(k,l), such that if G has at least C(k,l)n edges, then it contains a k×l-gridlike configuration, that is, it contains k+l edges such that each of the first k edges crosses each of the last l edges. Moreover, one can require the first k edges to be incident to the same vertex. Received: April, 2003 Janos Pach and Micha Sharir has been supported by NSF Grants CCR-97-32101 and CCR-00-98246, and by a joint grant from the U.S.–Israel Binational Science Foundation. János Pach has also been supported by PSC-CUNY Research Award 63382-0032 and by OTKA T-032452. Micha Sharir has also been supported by a grant from the Israeli Academy of Sciences for a Center of Excellence in Geometric Computing at Tel Aviv University, and by the Hermann Minkowski–MINERVA Center for Geometry at Tel Aviv University. Géza Tóth has been supported by OTKA-T-038397 and by an award from the New York University Research Challenge Fund.     

A countable nondiscrete topological field without nontrivial convergent sequences

A construction of a space in the title is presented, answering a question asked by A. Arkhangelskii and D. Shakhmatov.

     

A Survey on the Relation Between Transitivity and Dense Periodicity for Graph Maps

This paper is an outline of the relation between the transitivity, the dense periodicity and the topological entropy of graph maps.     

拓扑群在连续统上的膨胀作用

本文把一个同胚的膨胀作用推广到拓扑群的情形,并研究了有限生成离散群 的膨胀作用,得到了如下结果:Z×Z不能膨胀地作用在单位闭区间I上,而自由积 Z★Z可以膨胀地作用在I上.     

Topological degree and the Sperner lemma

In this paper, we give a new proof of Sperner's lemma, in its superstrong from, using the topological degree. Thus, we point out a relation between several methods for fixed-point theorems using either the topological degree, or the KKM lemma, or the Sperner lemma.The author would like to thank Dr. G. Leitmann for his remarks and suggestions.     

Topological sensitivity analysis for elliptic differential operators of order 2m

The topological derivative is defined as the first term of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of a singular domain perturbation. It has applications in many different fields such as shape and topology optimization, inverse problems, image processing and mechanical modeling including synthesis and/or optimal design of microstructures, fracture mechanics sensitivity analysis and damage evolution modeling. The topological derivative has been fully developed for a wide range of second order differential operators. In this paper we deal with the topological asymptotic expansion of a class of shape functionals associated with elliptic differential operators of order 2m  , m?1$m?1$. The general structure of the polarization tensor is derived and the concept of degenerate polarization tensor is introduced. We provide full mathematical justifications for the derived formulas, including precise estimates of remainders.     

Geometrical properties of nonlinear maps and their application, Part I: The topological degree of quasiruled Fredholm maps on quasicylindrical domains

In this paper we introduce the notion of quasicylindrical domains in Banach spaces and develop a concept of a degree for quasiruled Fredholm mappings on quasicylindrical domains. Note that this quasicylindrical structure appears in a rather natural way, whenever “analytically” given nonlinear pseudodifferential operators are investigated in spaces of sufficiently smooth functions. Moreover, the class of quasiruled Fredholm mappings on quasicylindrical domains is sufficiently large, so that within this framework one can study a quite large class of nonlinear boundary value problems which are related to pseudodifferential operators.