Almost arcwise connectivity in unicoherent continua

K.R. Kellum has proved that a continuum is an almost continuous image of the interval [0, 1] if and only if it is an almost Peano continuum. Hence, a continuum is an almost continuous image of [0, 1] if it has a dense arc component.Our principal result is that any almost arcwise connected, semi-hereditarily unicoherent, metric continuum with only countably many arc components has a dense arc component. An example is given to show that this is not true for unicoherent continua in general. It is also shown that any semi-hereditarily unicoherent continuum with only countably many arc components has at most one dense arc component, and if it has a dense arc component, then every other arc component is nowhere dense. This generalizes results of Fugate and Mohler for λ-dendroids.     

Sensitive open maps on Peano continua having a free arc

Let X be a Peano continuum having a free arc. If X admits a sensitive open map, then X either is homeomorphic to the closed interval [0, 1], or is homeomorphic to the unit circle S¹.     

A short proof that hyperspaces of Peano continua are absolute retracts

We give a short proof of Wojdyslawski's famous theorem.

     

Controlled Hahn-Mazurkiewicz Theorem and some new dimension functions of Peano continua

Given a metric Peano continuum X we introduce and study the Hölder Dimension there is a -Hölder onto map of X as well as its topological counterpart is an admissible metric for X}. We show that for each convex metric continuum X the dimension Hö-dim(X) equals the fractal dimension of X. The topological Hölder dimension Hö-dim(Mn) of the n-dimensional universal Menger cube Mn equals n. On the other hand, there are 1-dimensional rim-finite Peano continua X with arbitrary prescribed Hö-dim(X)?1.     

Substructure lattices and almost minimal end extensions of models of Peano arithmetic

This paper concerns intermediate structure lattices Lt(??/??), where ?? is an almost minimal elementary end extension of the model ?? of Peano Arithmetic. For the purposes of this abstract only, let us say that ?? attains L if L ? Lt(??/??) for some almost minimal elementary end extension of ??. If T is a completion of PA and L is a finite lattice, then: (A) If some model of T attains L, then every countable model of T does. (B) If some rather classless, ?₁‐saturated model of T attains L, then every model of T does. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The shortest definition of a number in Peano arithmetic

The shortest definition of a number by a first order formula with one free variable, where the notion of a formula defining a number extends a notion used by Boolos in a proof of the Incompleteness Theorem, is shown to be non computable. This is followed by an examination of the complexity of sets associated with this function.     

Almost compactness in fuzzy topological spaces

We introduce and study almost compactness for fuzzy topological spaces. We show that the almost continuous image of an almost compact fuzzy topological space is almost compact. Moreover, we show that generally almost compactness for fuzzy topological spaces is not product-invariant, but if X and Y are almost fuzzy topological spaces and X is product related to Y, then their fuzzy topological product is almost compact.     

Singularities of o‐minimal Peano derivatives

The notion of Peano differentiability generalizes the differentiability in the usual sense to higher order. Peano differentiable functions have derivatives which are sometimes differentiable or continuous or not even locally bounded. We give a complete characterisation of the sets in which Peano differentiable functions which are definable in an o‐minimal expansion of a real closed field are continuously differentiable. Thereby, we also distinguish between several kinds of discontinuities (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Induced path transit function, monotone and Peano axioms

The induced path transit function J(u,v) in a graph consists of the set of all vertices lying on any induced path between the vertices u and v. A transit function J satisfies monotone axiom if x,y∈J(u,v) implies J(x,y)⊆J(u,v). A transit function J is said to satisfy the Peano axiom if, for any u,v,w∈V,x∈J(v,w), y∈J(u,x), there is a z∈J(u,v) such that y∈J(w,z). These two axioms are equivalent for the induced path transit function of a graph. Planar graphs for which the induced path transit function satisfies the monotone axiom are characterized by forbidden induced subgraphs.     

概周期系统概周期解的存在唯一性

应用构造Ляпунов函数的方法，讨论了非线性微分方程系概周期解的存在唯一性.同时给出了Liénard方程存在唯一概周期解的一组充分条件.     

一致概周期矩阵函数的一些性质

利用纯量概周期函数性质讨论了一致概周期矩阵函数的一些性质.     

概周期系统的一个重要性质

将概周期序列与系统相联系,给出了概周期系统这一特殊的时变系统的一个重要性质,并说明了此性质住一般的时变系统中是不成立的．     

Expanding the additive reduct of a model of Peano arithmetic

Let M be a model of first order Peano arithmetic ( PA ) and I an initial segment of M that is closed under multiplication. LetM₀ be the {0, 1,+}‐reduct ofM. We show that there is another model N of PA that is also an expansion of M₀ such that a · ^M a = a · ^N a if and only if a ∈ I for all a ∈ M.     

An injective characterization of Peano spaces

It is shown that a continuous map defined on a closed zero-dimensional subspace S of a compact space T into a Peano space X can be continuously extended over T or, equivalently, X is an AE(0, ∞),and this property precisely characterizes Peano spaces within the class of compact metric spaces. Surjectively, a compact AE(0, ∞) of arbitrary weight is proved to be the continuous image of a Tychonoff cube by a map satisfying the zero-dimensional lifting property.     

带逐段常变量的非线性双曲微分方程的伪概周期解

In this paper,we investigate the pseudo almost periodicity of the unique bounded solution for a nonlinear hyperbolic equation with piecewise constant argument.The equation under consideration is a mathematical model for the dynamics of gas absorption.     

Interstitial and pseudo gaps in models of Peano Arithmetic

In this paper we study the automorphism groups of models of Peano Arithmetic. Kossak, Kotlarski, and Schmerl [9] shows that the stabilizer of an unbounded element a of a countable recursively saturated model of Peano Arithmetic M is a maximal subgroup of Aut(M) if and only if the type of a is selective. We extend this result by showing that if M is a countable arithmetically saturated model of Peano Arithmetic, Ω ? M is a very good interstice, and a ∈ Ω, then the stabilizer of a is a maximal subgroup of Aut(M) if and only if the type of a is selective and rational (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

∑上的非弱几乎周期的回复点集和SS混沌集

该文对单边符号空间上的转移自映射进行了讨论,证明了在非弱几乎周期的回复点集上存在不可数的SS混沌集.     

Characterizing indecomposable plane continua from their complements

We show that a plane continuum is indecomposable iff has a sequence of not necessarily distinct complementary domains satisfying the double-pass condition: for any sequence of open arcs, with and , there is a sequence of shadows , where each is a shadow of , such that . Such an open arc divides into disjoint subdomains and , and a shadow (of ) is one of the sets .

     

浅谈二元函数的带Peano型余项的Taylor公式

本文讨论了二元函数带Peano型余项的泰勒公式及唯一性,例说其应用.     

Nonstandard models that are definable in models of Peano Arithmetic

In this paper, we investigate definable models of Peano Arithmetic PA in a model of PA. For any definable model N without parameters in a model M, we show that N is isomorphic to M if M is elementary extension of the standard model and N is elementarily equivalent to M. On the other hand, we show that there is a model M and a definable model N with parameters in M such that N is elementarily equivalent to M but N is not isomorphic to M. We also show that there is a model M and a definable model N with parameters in M such that N is elementarily equivalent to M, and N is isomorphic to M, but N is not definably isomorphic to M. And also, we give a generalization of Tennenbaum's theorem. At the end, we give a new method to construct a definable model by a refinement of Kotlarski's method. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)