关于一阶理论的型与可数模型的关系

引入了一类特殊的型的概念，较集中地论述了一阶理论的型与可数模型的关系．     

On Interstices of Countable Arithmetically Saturated Models of Peano Arithmetic

We give some information about the action of Aut(M) on M(0), where M is a countable arithmetically saturated model of Peano Arithmetic. We concentrate on analogues of moving gaps and covering gaps inside M(0).     

On a Connection of Number Theory with Graph Theory

We assign to each positive integer n a digraph whose set of vertices is H = {0, 1, ..., n – 1} and for which there is a directed edge from a H to b H if a ² b (mod n). We establish necessary and sufficient conditions for the existence of isolated fixed points. We also examine when the digraph is semiregular. Moreover, we present simple conditions for the number of components and length of cycles. Two new necessary and sufficient conditions for the compositeness of Fermat numbers are also introduced.     

On Distributions of Countable Models of Disjoint Unions of Ehrenfeucht Theories

We describe Rudin–Keisler preorders and distribution functions of numbers of limit models for disjoint unions of Ehrenfeucht theories. We also find decomposition formulas for these distributions.     

Model Companions with Finitely Many Countable Models

We present two conditions which are equivalent to having an almost χ₀-categorical model companion. Mathematics Subject Classification: 03C35.     

On the Equality Relation Modulo a Countable Set

Mathematical Notes -     

关于具有局部可数sn-网的空间

In this paper,spaces with a locally countable sn-network are discussed.It is shown that a space with a locally countable sn-network iff it is an snf-countable space with a locally countable k-network.As its application,almost-open and closed mappings(or finite-to-one and closed mapping) preserve locally countable sn-networks,and a perfect preimage theorem on spaces with a locally countable sn-network is established.     

关于一个数论函数的导数及应用

Kanemitsu教授给出了欧拉求和函数的推广公式Lu(x,a)=0n相似文献   

On the Countable Tightness of Product Spaces

In this paper, we discuss the countable tightness of products of spaces which are quotient simages of locally separable metric spaces, or k-spaces with a star-countable k-network. The main result is that the following conditions are equivalent： （1） b = ω1; （2） t（Sω×Sω1） 〉 ω; （3） For any pair （X, Y）, which are k-spaces with a point-countable k-network consisting of cosmic subspaces, t（X×Y）≤ω if and only if one of X, Y is first countable or both X, Y are locally cosmic spaces. Many results on the k-space property of products of spaces with certain k-networks could be deduced from the above theorem.     

Complete Theories with Finitely Many Countable Models. I

A syntactic characterization is furnished for the class of elementary complete theories with finitely many countable models, which is the analog of a known theorem by Ryll-Nardzewski on countably categorical theories, and is based on classifying the theories by Rudin-Keisler quasiorders and distribution functions of a number of models limit over types.     

关于矩形和斜带模型的反强迫数和反凯库勒数

在苯类化合物的凯库勒结构的研究中引入了反强迫数和反凯库勒数.通过分析矩形和斜带模型苯类化合物的分子图的结构,证明了具有k行l列的矩形R[k,l]和斜带模型Z[k,l]的反凯库勒数是2,R[k,l]的反强迫数是l,Z[k,l]的反强迫数不超过[(l+1)/2],其中[x]表示不超过x的最大整数.     

On Some Results in Probabilistic Number Theory

The paper presents an overview of main methods and results of the value distribution problem of additive arithmetical functions.     

On Quasistatic Models in the Theory of Inelastic Deformations

Systems of equations describing an inelastic response of metals, with the fundamental assumption of small deformations, consist of linear partial differential equations coupled with nonlinear differential inclusions (or ordinary differential equations) for the vector of internal variables. We study here the quasistatic case, this means that in the balance of momentum the acceleration term is neglected.     

图的分散数

The decay number of a connected graph is defined to be the minimum number of the components of the cotree of the graph. Upper bounds of the decay numbers of graphs are obtained according to their edge connectivities. All the bounds in this paper are tight. Moreover, for each integer k between one and the upper bound, there are infinitely many graphs with the decay number k.     

On the Cop Number of a Graph

The cop number c(G) of a graph G is an invariant connected with the genus and the girth. We prove that for a fixed k there is a polynomial-time algorithm which decides whether c(G) ≤ k. This settles a question of T. Andreae. Moreover, we show that every graph is topologically equivalent to a graph with c ≤ 2. Finally we consider a pursuit-evasion problem in Littlewood′s miscellany. We prove that two lions are not always sufficient to catch a man on a plane graph, provided the lions and the man have equal maximum speed. We deal both with a discrete motion (from vertex to vertex) and with a continuous motion. The discrete case is solved by showing that there are plane graphs of cop number 3 such that all the edges can be represented by straight segments of the same length.     

On the Decomposition of Order-Separable Posets of Countable Width into Chains

Order - A partially ordered set X has countable width if and only if every collection of pairwise incomparable elements of X is countable. It is order-separable if and only if there is a countable...     

Ponomarev系与可数型的（P）映射

本文讨论了3类Ponomarev系中（P）映射与子集族的精确关系,获得了下列的结论：（1）在Ponomarev系（f,M,X,P）中f是点有限（点可数）映射当且仅当P是X的点有限（点可数）网络;（2）在Ponomarev系（f,M,X,P）中f是紧有限（紧可数）映射当且仅当P是X的紧有限（紧可数）网络;（3）在Ponomarev系（f,M,X,P）中f是局部有限（局部可数）映射当且仅当P是X的局部有限（局部可数）网络．     

On the Smoothness of the Invariant Torus of a Countable System of Difference Equations with Parameters

We establish sufficient conditions for the differentiability of the invariant torus of a countable system of linear difference equations defined on a finite-dimensional torus with respect to an angular variable and the parameter of the original system of equations.     

On the Fractional Intersection Number of a Graph

 An intersection representation of a graph G is a function f:V(G)→2^S (where S is any set) with the property that uv∈E(G) if and only if f(u)∩f(v)≠∅. The size of the representation is |S|. The intersection number of G is the smallest size of an intersection representation of G. The intersection number can be expressed as an integer program, and the value of the linear relaxation of that program gives the fractional intersection number. This is in consonance with fractional versions of other graph invariants such as matching number, chromatic number, edge chromatic number, etc.  We examine cases where the fractional and ordinary intersection numbers are the same (interval and chordal graphs), as well as cases where they are wildly different (complete multipartite graphs). We find the fractional intersection number of almost all graphs by considering random graphs. Received: July 1, 1996 Revised: August 11, 1997