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.     

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.     

Mixed-State Localization Operators: Cohen’s Class and Trace Class Operators

Journal of Fourier Analysis and Applications - We study mixed-state localization operators from the perspective of Werner’s operator convolutions which allows us to extend known results from...     

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

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

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.     

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...     

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。     

A Class of Multiplicative Lattices

Czechoslovak Mathematical Journal - We study the multiplicative lattices L which satisfy the condition a = (a : (a : b))(a : b) for all a, b ∈ L. Call them sharp lattices. We prove that every...     

Class groups of dihedral extensions

Let L/F be a dihedral extension of degree 2p, where p is an odd prime. Let K/F and k/F be subextensions of L/F with degrees p and 2, respectively. Then we will study relations between the p‐ranks of the class groups Cl(K) and Cl(k). (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Class of Non-Ordinary Half-Planes

All half-planes that are known in the literature are ordinary [3]. In this note we construct a class of non-ordinary half-planes.     

一类无限维半单李代数

研究了秩为2的Witt型的李代数W2的子代数g1,讨论其同态,同构,核的性质.证明了g1为无限维半单李代数.     

A Class of FBI Transforms

We introduce a class of FBI transforms whose phase functions may have a degenerate Hessian and present an application of these transforms to the microlocal analytic hypoellipticity of certain systems of vector fields.     

A Class Matrix Evolution Equations

在文献[5]中，考虑了如下特征值问题 $\[{\varphi _x} = M\varphi ,{\varphi _x} = \frac{{\partial \varphi }}{{\partial x}}\]$ 其中 $\[\varphi = \left( {\begin{array}{*{20}{c}} {{\varphi _1}}\{{\varphi _2}} \end{array}} \right)\]$ (1) $\[M = \left( {\begin{array}{*{20}{c}} { - i\xi }&{q(x,t)}\{r(x,t)}&{i\xi } \end{array}} \right)\]$ (2) 这里假定特征值$\xi$以某种规律随着时间变化而变化。文章中得出了一类发展方程，其中两个特殊情形：r=1,q=u(x,t)分别可以当做推广的KDV方程和推广的MKDV方程，并证明了不仅在KDV方程和MKDV方程之间存在Miura变换，而且在推广的KDV方程和推广的MKDV方程之间也存在Miura变换，又证明了对推广的KDV方程存在Backlund变换。 本文将[5]的结果推广至矩阵情形： 设 $\[M = \left( {\begin{array}{*{20}{c}} { - i\xi }&{Q(x,t)}\{R(x,t)}&{i\xi I} \end{array}} \right)\]$ (3) 这里Q,R为N*N矩阵，I是N*N单位阵，相应的在(1)式中的向量$\varphi$是2N维向量。我们引进矩阵型的Miura变换，并得到了与[5]相平行的结果。