On null isotropy in spacetimes

Null isotropy in a spacetime is defined. The relation of null isotropy to the constant curvature and infinitesimal spatial isotropy is investigated. The influence of null isotropy on conjugate points along null geodesics and curvature singularities is investigated.     

拓扑近藤半金属

拓扑物态是凝聚态物理近年来最重要的研究领域之一。随着研究的不断深入,对拓扑物态的研究逐渐从弱关联材料体系拓展到了强关联材料体系。文章梳理了近年来对拓扑近藤半金属的相关研究,介绍了其中的理论模型、计算方法和一些候选材料及实验研究,并对该方向未来的发展做了展望。     

Refinements of the Weyl Pure Geometrical Thick Branes From Information‐Entropic Measure

This work aims to analyse the so‐called configurational entropy in the Weyl pure geometrical thick brane model. The Weyl structure plays a prominent role in the brane thickness of this model. We find a set of parameters associated to the brane width where the configurational entropy exhibits critical points. The information‐theoretical measure sets bounds into parameter of Weyl pure geometrical brane model. In addition, we also argue that a similar approach can be useful to analyze the corrections to Newtonian and Coulombian potentials in Weyl scenarios.     

Nontangential Limit of the Weyl m-Functions for the Ergodic Schrödinger Equation

This paper deals with the spectral and qualitative problems associated with the one-dimensional ergodic Schrödinger equation. Let A ₂ be the set of those energies for which the real projective flow admits an invariant linear measure with square integrable density function. On this set we calculate the directional derivative of the Floquet coefficient and prove the existence of a nontangential limit of the Weyl m-functions in the L ¹-topology. In particular, we verify that the known Dieft–Simon inequality for the derivative of the rotation number obtained from Kotani's theory is in fact an equality. In the bounded orbit case we deduce the uniform boundedness of the Weyl m-functions and obtain necessary and sufficient conditions to assure their uniform convergence.     

Similarity of $$sgn x( - \tfrac{{d^2 }}{{dx^2 }} + c\delta )$$ Type Operators to Normal and Self-adjoint Operators

Mathematical Notes -     

The evaluation of matrix elements for non-canonical Weyl tableau basis states adapted toU(n 1+n 2)⊃U(n 1)×U(n 2)

Summary This is the first paper of a series of two, which enables the evaluation ofU(n) generator matrix elements in the non-canonical Weyl tableau basis adapted to subgroupU(n ₁)×U(n ₂). In this paper the explicit closed formulae for subduction coefficients are presented. These formulae will become useful through an inductive method to be presented in the second paper.     

Quadrature formulas for the generalized Riemann-Stieltjes integral

In this paper we propose a technique of approximation for the generalized Riemann-Stieltjes integral and we found an analogue for Newton-Cotes formulas in the case n = 2 and n = 3. *Beneficiary of a Socrates fellowship at the Department of Mathematics, University of Study of Cagliari, Via Ospedale, n. 72, Cagliari, 09124, Italy, in the period February – July 2002.     

Bruhat intervals as rooks on skew Ferrers boards

We characterise the permutations π such that the elements in the closed lower Bruhat interval [id,π] of the symmetric group correspond to non-taking rook configurations on a skew Ferrers board. It turns out that these are exactly the permutations π such that [id,π] corresponds to a flag manifold defined by inclusions, studied by Gasharov and Reiner.Our characterisation connects the Poincaré polynomials (rank-generating function) of Bruhat intervals with q-rook polynomials, and we are able to compute the Poincaré polynomial of some particularly interesting intervals in the finite Weyl groups An and Bn. The expressions involve q-Stirling numbers of the second kind, and for the group An putting q=1 yields the poly-Bernoulli numbers defined by Kaneko.     

Conformally flat tilted Bianchi Type-V cosmological models in general relativity

We have investigated two conformally flat tilted Bianchi Type-V cosmological models in general relativity. To get a determinate solution, we have assumed a supplementary conditionA =B ⁿ between metric potentials wheren is a constant. The behaviour of the model forn = 2 is discussed in detail. Various physical and geometrical aspects of the models are also discussed.