Automorphisms of Models of True Arithmetic: More on Subgroups which Extend to a Maximal One Uniquely

Continuing the earlier research in [14] we give some more information about nonmaximal open subgroups of G = Aut(ℳ) with unique maximal extension, where ℳ is a countable recursively saturated model of True Arithmetic.     

区间数的标准表示及其四则运算法则与泛灰数的内在联系

在回顾泛灰数四则运算法则基础上,给出了区间数的标准表示,论述了标准区间数的四则运算法则与泛灰数的内在联系及其应用前景.     

Automorphisms of Models of True Arithmetic: Subgroups which Extend to a Maximal Subgroup Uniquely

We show that if M is a countable recursively saturated model of True Arithmetic, then G = Aut(M) has nonmaximal open subgroups with unique extension to a maximal subgroup of Aut(M). Mathematics Subject Classification: 03C62, 03C50.     

泛灰线性方程组的泛灰矩阵求解方法

在概述泛灰数的概念与泛灰行列式运算的基础上 ,介绍了泛灰线性方法程组的泛灰解法 .根据泛灰数的性质 ,定义了泛灰矩阵 ,提出了泛灰线性方程组的泛灰矩阵解法 ,并给出了算例 .     

Arithmetic Processes in Semigroups

We consider the asymptotic behavior of the distributions of stochastic processes defined by multiplicative functions in an arithmetic semigroup.     

解读“微积分算术”

2011年在科学网博客上出现的微积分算术,把抽象而高深的微积分看作函数的算术,只用几步高中代数,就能避开极限而又不失严格讲解微积分.首先,用等式讲解多项式的微积分;然后用不等式讲解显式初等函数的微积分.但是,某些读者可能会存在疑问:真的能让微积分的门槛降低,而又不失严格?它到底具备什么样的特点?对学生群体的定位如何?需要进一步的解读,这就是本文的目的.     

组合算法及其应用

提出了在组合算法设计和组合算法选择方面所应当遵循的三个原则,即通用性、可计算性和较少的信息冗余量,并初步分析了它们之间的相互关系.通过分析,提示了组合算法的设计方法,改进方向和优化技术.     

普遍服务、市场竞争与消费者福利

通过构建一个简单的模型分析了普遍服务约束下的垄断产业在引入竞争后的市场竞争,模型很好地展现了垄断产业引入竞争后所出现的“撇脂现象”.通过分析得出:引入竞争后,在位者的盈利和亏损同时减少,但盈利减少得更多;竞争对消费者总体上是有利的,但竞争的好处更多地被低成本的城市消费者所获得,高成本的农村消费者则没有分享到改革的成果;...     

强算术图

一个（p,q)-图G被为是强（k,d)-算术图,如果存在一个由G的顶点集到模q的整数群Zq的单射,使得相邻两顶点标号的和导出的边值为算术级数,k,k d,……,k (q-1)d,本文讨论了这类标号图的结构和一些性质。     

Mean-Value Theorems in Arithmetic Semigroups

This paper reports on recent progress in the theory of multiplicative arithmetic semigroups, which has been initiated by John Knopfmacher's work on abstract analytic number theory. In particular, it deals with abstract versions of the mean-value theorems of Delange, of Wirsing, and of Halász for multiplicative functions on arithmetic semigroups G with Axiom A . The Turán Kubilius inequality is transferred to G , and methods developed by Rényi, Daboussi and Indlekofer, Lucht and Reifenrath are utilized. As byproduct a new proof of the abstract prime number theorem is obtained. This revised version was published online in June 2006 with corrections to the Cover Date.     

Finite Paths are Universal

We prove that any countable (finite or infinite) partially ordered set may be represented by finite oriented paths ordered by the existence of homomorphism between them. This (what we believe a surprising result) solves several open problems. Such path-representations were previously known only for finite and infinite partial orders of dimension 2. Path-representation implies the universality of other classes of graphs (such as connected cubic planar graphs). It also implies that finite partially ordered sets are on-line representable by paths and their homomorphisms. This leads to new on-line dimensions. Mathematics Subject Classifications (2000) 06A06, 06A07, 05E99, 05C99.J. Nešetřil: Supported by a Grant LN00A56 of the Czech Ministry of Education. The first author was partially supported by EU network COMBSTRU at UPC Barcelona.     

Strengths and Weaknesses of LH Arithmetic

In this paper we provide a new arithmetic characterization of the levels of the og‐time hierarchy (LH). We define arithmetic classes and that correspond to ‐LOGTIME and ‐LOGTIME, respectively. We break and into natural hierarchies of subclasses and . We then define bounded arithmetic deduction systems ′ whose ‐definable functions are precisely B( ‐LOGTIME). We show these theories are quite strong in that (1) LIOpen proves for any fixed m that , (2) TAC, a theory that is slightly stronger than ′ whose (LH)‐definable functions are LH, proves LH is not equal to ‐TIME(s) for any m> 0, where 2^s ∈L, s(n) ∈ ω(log n), and (3) TAC proves LH ≠ for all k and m. We then show that the theory TAC cannot prove the collapse of the polynomial hierarchy. Thus any such proof, if it exists, must be argued in a stronger systems than ours.     

关于奇算术图

本文讨论了$n$个$m$长圈有一个公共结点图$C^n_m$, $n$个$m$长圈与$t$长路有一个公共结点图$C^n_m\cdot P_t$, $n$个$m$阶完全图有一个公共结点图$K^n_m$和星形图的同胚图的奇算术性问题.给出了完全图,完全二部图和圈是奇算术的充要条件.     

算术图的若干性质

本文得到了算术图的一些新性质，并解决了文[1]提出的两个猜想.     

Fast and Parallel Interval Arithmetic

Infimum-supremum interval arithmetic is widely used because of ease of implementation and narrow results. In this note we show that the overestimation of midpoint-radius interval arithmetic compared to power set operations is uniformly bounded by a factor 1.5 in radius. This is true for the four basic operations as well as for vector and matrix operations, over real and over complex numbers. Moreover, we describe an implementation of midpoint-radius interval arithmetic entirely using BLAS. Therefore, in particular, matrix operations are very fast on almost any computer, with minimal effort for the implementation. Especially, with the new definition it is seemingly the first time that full advantage can be taken of the speed of vector and parallel architectures. The algorithms have been implemented in the Matlab interval toolbox INTLAB.     

Universal cycles for permutations

A universal cycle for permutations is a word of length n! such that each of the n! possible relative orders of n distinct integers occurs as a cyclic interval of the word. We show how to construct such a universal cycle in which only n+1 distinct integers are used. This is best possible and proves a conjecture of Chung, Diaconis and Graham.     

Generations for Arithmetic Groups

We prove that any noncocompact irreducible lattice in a higher rank real semi-simple Lie group contains a subgroup of finite index which is generated by three elements.A sizeable part of this paper forms the thesis of R. Sharma, submitted in April 2004 to the Tata Institute of Fundamental Research, Mumbai for the award of a PhD degree.     

泛灰线性方程组的白化求解方法与应用

在概述泛灰数的概念与泛灰行列式运算的基础上 ,介绍了泛灰线性方法程组的泛灰解法 .由于泛灰行列式运算复杂 ,根据泛灰的性质 ,提出了泛灰线性方程组的白化解法 .理论证明这种求解方法的正确性 .并给出了算例 .     

泛逻辑的零级泛运算模型的代数性质

讨论泛逻辑的零级泛运算模型的基本代数性质。证明T（x,y,^）是阿基米德型三角范数;泛与运算模型与泛蕴涵运算模型形成一个伴随对;当h∈（0,0．75）时,有界格（[0,1],∨,∧,,＊,→0,1）做成一个MV-代数;当h∈（0．75,1）时,有界格（[0,1],∨,∧,＊,→0,1）做成一个乘积代数。进一步,给出了零级泛与运算模型与泛或运算模型的加性生成元与乘性生成元。     

Universal arcs in local tournaments

An arc $uv$ of a digraph $D$ is called universal if $uv$ and $w$ are in a common cycle for any vertex $w$ of $D$. In this paper we characterize local tournaments whose every arc is universal.