Abel群在数论函数中的一个应用

<正> 数论函数是研究数论的极其重要的工具。用群的观点研究一类数论函数,能使一类数论函数的证明简易,能对一类数论函数的认识更加清晰,下面仅就一类数论函数形成Abel群作一介绍,并通过化简证明标准的 Mobius变换定理(下面简称标准定理),说明其应用.     

巧用一条定理 妙解一串赛题

数学竟赛中的初等数论所涉及的一些问题都是数论理论的具体运用。而有些数论理论虽然十分简单,却显示出神通广大的功能。本文提出的“弃九法”定理正是如此。定理十进整数     

欧拉定理、费马定理的另证

欧拉定理和费马定理是数论中两个非常著名而重要的定理．     

符号动力系统与费马小定理

费马小定理是数论中的一个重要定理.利用符号动力系统计算周期轨的方法给出了费马小定理一个新的证明,讨论了数的整除性,并解释了费马小定理的几何意义.     

Wolstenholme定理的另一个等价形式及其推广

本文提出数论中Wolstenholme定理的又一个等价形式并作了推广     

一个整数与其关于模N的逆之差

利用Dirichlet L-函数的均值定理来研究一类数论函数的渐近性质, 并给出一个有趣的均值公式.     

一种Goldbach可换环R上的Dirichlet定理

[1]—[3]用模型论及数论方法讨论了整数环的某些扩环的数论性质,以说明一些数论命题之间的和谐性和相对独立性.[4]进一步作出了一种新可换环R,分析了R与整数环I的异同,证明了在R中Goldbaeh性质成立,而Dirichlet定理不成立,只成立了一些较弱形式的Diriehlet定理.如R中α≠0,(α,β)=1,α的互不相件素因子只有有限多种,则存在无限多个形状为αχ β(χ∈R)的素元.但这只是一个充分条件而不是必要条件.那么,确定R中存在无限多个形如αχ β的秦元的充要条件就是一个有趣的问题了,本文利用R上正则素元的概念,给出一个达样的充分必要条件,从而解决了达一问题.     

L-函数的一种新型的均值公式

本文利用特征和的估计以及数论中著名的Bombieri-Vinogradov定理给出L-函数的一种新型的高次均值公式.     

一个代数无关性定理及其应用

代数无关性是超越数论的重要课题。本文在§1中给出一个代数无关性的判别定理,在§2中,作为定理的应用研究了Mahler小数的代数无关性。     

毕达哥拉斯之谜

1 提尔--数论的诞生地 斜边的平方, 如果我没有弄错, 等于其它两边的平方之和. 2500多年前,希腊人毕达哥拉斯用诗歌描述了他发现并证明的第一个数学定理,史称毕达哥拉斯定理,它在中国又被叫作勾股定理.可以说,这个定理为全世界每一个中学生所熟知.     

The Generalization of the Chinese Remainder Theorem

We generalize the Chinese Remainder Theorem, use it to study number theory models, compare and analyse several number theory theorems in non-standard number theory models. Received August 18, 1999, Accepted February 5, 2001     

An undecidable extension of Morley's theorem on the number of countable models

We show that Morley's theorem on the number of countable models of a countable first-order theory becomes an undecidable statement when extended to second-order logic. More generally, we calculate the number of equivalence classes of equivalence relations obtained by countable intersections of projective sets in several models of set theory. Our methods include random and Cohen forcing, Woodin cardinals and Inner Model Theory.     

拓扑学在模型论中的一个应用

本文利用拓扑学方法研究了ω-范畴理论的性质，并对模型个数问题进行了讨论，获得了ω-范畴的新结果，并得到了关于模型个数的几个结果．     

Generalizing realizability and Heyting models for constructive set theory

This article presents a common generalization of the two main methods for obtaining class models of constructive set theory. Heyting models are a generalization of the Boolean models for classical set theory which are a variant of forcing, while realizability is a decidedly constructive method that has first been developed for number theory by Kleene and was later very fruitfully adapted to constructive set theory. In order to achieve the generalization, a new kind of structure (applicative topologies) is introduced, which contains both elements of formal topology and applicative structures. This approach not only deepens the understanding of class models and leads to more efficiency in proofs about these kinds of models, but also makes it possible to prove new results about the two special cases that were not known before and to construct new models.     

On the Number of Countable Models of a Countable Supersimple Theory

It is proved that the number of countable models of a countablesupersimple theory is either 1 or infinite. This result is anextension of Lachlan's theorem on a superstable theory.     

Conformity and independence with coherent lower previsions

We define the conformity of marginal and conditional models with a joint model within Walley's theory of coherent lower previsions. Loosely speaking, conformity means that the joint can reproduce the marginal and conditional models we started from. By studying conformity with and without additional assumptions of epistemic irrelevance and independence, we establish connections with a number of prominent models in Walley's theory: the marginal extension, the irrelevant natural extension, the independent natural extension and the strong product.     

Theory and classification of the reversible structures of discontinuities in hydrodynamic-type models

The results of an analysis of the numerical and analytical solutions of the partial differential equations for different models of continuum mechanics and also the solutions of the ordinary differential equations of the travelling waves for these models are presented. Typical models, the basic theses of the theory of discontinuities in models of the reversible and weakly dissipative type, the classification of time-invariant structures and time-varying ordered structures are considered. The theory includes elements such as the use of averaged equations, evolutionary conditions, conditions for the complete and partial reversibility of a discontinuity, conditions for the existence of a solution in the typical case obtained using dimensional analysis of the invariant manifolds and the number of additional parameters varied and the classification of the periodic waves, solitary waves and kinks with respect to the number of free parameters.     

Constructing quasiminimal structures

Quasiminimal structures play an important role in non‐elementary categoricity. In this paper we explore possibilities of constructing quasiminimal models of a given first‐order theory. We present several constructions with increasing control of the properties of the outcome using increasingly stronger assumptions on the theory. We also establish an upper bound on the Hanf number of the existence of arbitrarily large quasiminimal models.     

Local computations in Dempster–Shafer theory of evidence

When applying any technique of multidimensional models to problems of practice, one always has to cope with two problems: the necessity to represent the models with a ”reasonable” number of parameters and to have sufficiently efficient computational procedures at one’s disposal. When considering graphical Markov models in probability theory, both of these conditions are fulfilled; various computational procedures for decomposable models are based on the ideas of local computations, whose theoretical foundations were laid by Lauritzen and Spiegelhalter.The presented contribution studies a possibility of transferring these ideas from probability theory into Dempster-Shafer theory of evidence. The paper recalls decomposable models, discusses connection of the model structure with the corresponding system of conditional independence relations, and shows that under special additional conditions, one can locally compute specific basic assignments which can be considered to be conditional.     

An Empirical Evaluation of Investigating Transportation Mode Attributes for Commodities

A number of transportation demand models have been formulated using the abstract mode concept. Unfortunately, most of these models use a priori economic theory to derive the variables used in the analysis. This study describes an empirical approach for the specification of mode attributes used by purchasers of transportation modes for the movement of commodities. Results reported from a study conducted on the Montreal-Toronto corridor in Canada suggest that a number of important variables have been neglected in models of carrier selection for freight.