La reduction minimale d'un graphe a une reunion de cliques

On obtient la valeur maximale de l'indice de réduction minimale d'un graphe á une réunion de k cliques.     

Class A spacetimes

We introduce class A spacetimes, i.e. compact vicious spacetimes (M, g) such that the Abelian cover ${(\overline{M}, \overline{g})}$ is globally hyperbolic. We study the main properties of class A spacetimes using methods similar to those introduced in Sullivan (Invent Math 36:225?C255, 1976) and Burago (Adv Sov Math 9:205?C210, 1992). As a consequence we are able to characterize manifolds admitting class A metrics completely as mapping tori. Further we show that the notion of class A spacetime is equivalent to that of SCTP (spacially compact time-periodic) spacetimes as introduced in Galloway (Comm Math Phys 96:423?C429, 1984). The set of class A spacetimes is shown to be open in the C ⁰-topology on the set of Lorentzian metrics. As an application we prove a coarse Lipschitz property for the time separation of the Abelian cover. This coarse Lipschitz property is an essential part in the study of Aubry-Mather theory in Lorentzian geometry.     

Class of equivalent equations

It is shown that, for certain second-order linear homogeneous partial differential equations, there exists a set of equivalence transformations to the form Δ₂u+c′(x)u = 0 in the metric of spaces conformal to the space V_n related to the equation. An element of this space is a transformation of the equation to the canonical form

$$\Delta _2 u + \frac{{n - 2}}{{4(n - 1)}}Ru = \pm u$$     

A Class of Groupoids

A new class of left distributive groupoids and their relationship with homogeneous spaces are studied. Bibliography: 5 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 305, 2003, pp. 136–143.     

The Hermitian Class Group

In this note, we study the Hermitian class group of orders over a Krulldomain and derive some exact sequences, permitting to calculate it inconcrete situations.In particular, we will show the Hermitian class group of a divisorialAzumaya algebra to be independent of its involution.     

Almost all quartic half-arc-transitive weak metacirculants of Class II are of Class IV

A half-arc-transitive graph is a vertex- and edge- but not arc-transitive graph. A weak metacirculant is a graph admitting a transitive metacyclic group that is a group generated by two automorphisms ρ and σ, where ρ is (m,n)-semiregular for some integers m≥1 and n≥2, and where σ normalizes ρ. It was shown in [D. Maruši?, P. Šparl, On quartic half-arc-transitive metacirculants, J. Algebr. Comb. 28 (2008) 365-395] that each connected quartic half-arc-transitive weak metacirculant X belongs to one (or possibly more) of four classes of such graphs, reflecting the structure of the quotient graph X_ρ relative to the semiregular automorphism ρ. The first of these classes, called Class I, coincides with the class of so-called tightly attached graphs. Class II consists of the quartic half-arc-transitive weak metacirculants for which the quotient graph X_ρ is a cycle with a loop at each vertex. Class III consists of those graphs for which each vertex of the quotient graph X_ρ is connected to three other vertices, to one with a double edge. Finally, Class IV consists of those graphs for which X_ρ is a simple quartic graph.This paper consists of two results concerning graphs of Class II. It is shown that, with the exception of the Doyle-Holt graph and its canonical double cover, each quartic half-arc-transitive weak metacirculant of Class II is also of Class IV. It is also shown that although quartic half-arc-transitive weak metacirculants of Class II which are not tightly attached exist they are “almost tightly attached”. More precisely, their radius is at most four times their attachment number.     

复杂设计下类均值复制与类加权均值复制的比较（英文）

复制数据是处理抽样调查中数据项目缺失的一种常用方法。在两种常见模型及复杂抽样设计下，本文对处理数据项目缺失的类均值复制和类加权均值复制方法进行了对比。     

Two Hypotheses on the Exponential Class in the Class Of O-subexponential Infinitely Divisible Distributions

Journal of Theoretical Probability - Two hypotheses on the class $${mathcal {L}}(gamma )$$ in the class $$mathcal {OS}cap mathcal {ID}$$ are discussed. Two weak hypotheses on the class...     

不要把问题解决教学课上成问题解答介绍课——兼评分部积分法的两种不同的教学方法

结合数学分析中分部积分法这一内容的两种不同的教学方法,论述了在问题解决教学中切忌把问题解决教学课上成问题解答介绍课.     

Elementary Definability of the Class of Universal Planar Automata in the Class of Semigroups

Siberian Mathematical Journal - Universal planar automata are universal attracting objects in the category of semigroup automata whose set of states and set of output signals are equipped with...     

Class of singular integral operators

A class of singular integral operators is studied from the point of view of the boundedness of their action from some symmetric spaces into other spaces.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 1, pp. 105–110, January, 1991.     

一类特定的AF-代数

讨论了一类特定的AF-代数,其上的恒等同态可以用一列有限维值域的自同态逐点逼近.给出了这类AF-代数的K-理论刻画,并给出了一个不在这一类中的RFD AF-代数的例子.     

一类优美图

设u、ν是两个固定顶点.用b条内部互不相交且长度皆为a的道路连接u、ν所得的图用P_a,b表示.KM.Kathiresan证实P_2,2m-1(r,m皆为任意正整数)是优美的,且猜想:除了(a,b)=(2r+1,4s+2)外,所有的P_a,b都是优美的.杨元生已证实P_2r+1,2m-1是优美的,并且证实了当r=1,2,3,4时的P_2r,2m也是优美的.本文证实r=5,6,7时P_{2r,2m相似文献}   

一类可补子群

本文在有限群的半正规子群的研究基础上对可补子群进行研究．用半正规代替正则，推广了已有的一些结果．     

Class groups and Brauer groups

LetF be a global field,n a positive integer not divisible by the characteristic ofF. Then there exists a finite extensionE ofF whose class group has a cyclic direct summand of ordern. This theorem, in a slightly stronger form, is applied to determine completely, on the basis of the work of Fein and Schacher, the structure of the Brauer group Br(F()) of the rational function fieldF(t). As a consequence of this, an additional theorem of the above authors, together with a note at the end of the paper, imply that Br(F(t)) ≊ Br(F(t ₁, ···,t _n)), wheret ₁, ···,t _n are algebraically independent overF.     

使无穷小等价成为一个等价关系

修订等价无穷小的定义,可使无穷小量的等价真正成为一种等价关系,即满足自反性,对称性和传递性。     

A Remarkable Class of Rings

We consider a remarkable class of rings, which we call corpids, that is the rings (K, +, ·), such that (K, ·) is an inverse semigroup (or groupid, which is the name used by Tallini (Ann Math 71:295–322, 1966). We prove several theorems concerning this structure, an order relation which allows us to formulate characterization theorems. We define the notion of simple idempotent and prove theorems about zero-divisors, idempotents, subcorpids, ideals and characteristic in a corpid.