Letter: On the Global Hyperbolicity of Lorentz 2-Step Nilpotent Lie Groups

This work is concerned with the existence of Lorentz 2-step nilpotent Lie groups having a timelike center and which are not globally hyperbolic. Namely, we prove that any left invariant Lorentz metric with a timelike center on the Heisenberg group H ²ⁿ⁺¹ is not globally hyperbolic.     

A Hurewicz-type theorem for asymptotic dimension and applications to geometric group theory

We prove an asymptotic analog of the classical Hurewicz theorem on mappings that lower dimension. This theorem allows us to find sharp upper bound estimates for the asymptotic dimension of groups acting on finite-dimensional metric spaces and allows us to prove a useful extension theorem for asymptotic dimension. As applications we find upper bound estimates for the asymptotic dimension of nilpotent and polycyclic groups in terms of their Hirsch length. We are also able to improve the known upper bounds on the asymptotic dimension of fundamental groups of complexes of groups, amalgamated free products and the hyperbolization of metric spaces possessing the Higson property.

     

On the fundamental group of manifolds with almost nonnegative Ricci curvature

Gromov conjectured that the fundamental group of a manifold with almost nonnegative Ricci curvature is almost nilpotent. This conjecture is proved under the additional assumption on the conjugate radius. We show that there exists a nilpotent subgroup of finite index depending on a lower bound of the conjugate radius.

     

Nonanticommutative deformations of <Emphasis Type="Italic">N</Emphasis>=(1, 1) supersymmetric theories

We discuss chirality-preserving nilpotent deformations of the four-dimensional N=(1, 1) Euclidean harmonic superspace and their implications in N=(1, 1) supersymmetric gauge and hypermultiplet theories. For the SO(4) × SU(2)-invariant deformation, we present nonanticommutative Euclidean analogues of the N=2 gauge multiplet and hypermultiplet off-shell actions.As a new result, we consider a specific nonanticommutative hypermultiplet model with the N=(1, 0) supersymmetry. It involves free scalar fields and interacting right-handed spinor fields.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 2, pp. 235–251, February, 2005.     

Frattini子群是无限循环群的有限生成幂零群

完整地确定了Frattini子群是无限循环群的有限生成幂零群的结构,证明了下面的定理.设G是有限生成幂零群,则G的Frattini子群是无限循环群当且仅当G可以分解为G=S×F×T,其中F是秩为s的自由Abel群,T=Z_m_1⊕Zm_2⊕…⊕Z_m_u,m_1,m_2,…,m_u都是大于1的没有平方因子的自然数,m_1|m_2|…|m_u,■式中d_1,d_2,…,d_r都是正整数,d_1|d_2|…|d_r.进一步,(d_1,d2,…,d_r;s;m_1…,m_2,…,m_u)是群G的同构不变量,即若群H也是Frattini子群是无限循环群的有限生成幂零群,那么G同构于H的充要条件是它们有相同的不变量.     

Breadth and characteristic sequence of nilpotent Lie algebras

The notion of breadth of a nilpotent Lie algebra was introduced and used to approach problems of classification up to isomorphism in [5 Khuhirun, B., Misra, K. C., Stitzinger, E. (2015). On nilpotent Lie algebras of small breadth. J. Algebra 444:328–338.[Crossref], [Web of Science ®] , [Google Scholar]]. In the present paper, we study this invariant in terms of characteristic sequence, another invariant, introduced by Goze and Ancochea in [1 Ancochea-Bermúdez, J. M., Goze, M. (1986). Sur la classification des algèbres de Lie nilpotentes de dimension 7. C. R. Acad. Sci. Paris 302:611–613. [Google Scholar]]. This permits to complete the determination of Lie algebras of breadth 2 studied in [5 Khuhirun, B., Misra, K. C., Stitzinger, E. (2015). On nilpotent Lie algebras of small breadth. J. Algebra 444:328–338.[Crossref], [Web of Science ®] , [Google Scholar]] and to begin the work for Lie algebras with breadth greater than 2.     

Estimation based on one step ahead prediction versus estimation based on multi-step ahead prediction

In this paper we consider a strictly stationary time series generated by a nonlinear autoregression. We are concerned with the estimation of the parameter θ₀ which specifies the autoregression Two estimators are considered, namely. θ _n obtained by minimising the sum of squarcs of the sample prediction emets of a one step ahead predictor and θ _n obtained by minimising the sum of squares of the sample prediction errors of a multi-step ahead predictor. It is shown that θ_n is a better estimator of θ₀ than θ _n .