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.     

Information,Quantum Mechanics,and Gravity

This is a basically expository article, with some new observations, tracing connections of the quantum potential to Fisher information, to Kähler geometry of the projective Hilbert space of a quantum system, and to the Weyl-Ricci scalar curvature of a Riemannian flat spacetime with quantum matter.Á Denise     

An improved method for the analysis of major antioxidants of Hibiscus esculentus Linn

Major antioxidants of aqueous ethanol extract from Lady's Finger (Hibiscus esculentus Linn) were systematically investigated in this study. Firstly, high-performance liquid chromatography (HPLC) was applied to identify antioxidant peaks in a sample by spiking the sample extract with 2,2'-azino-bis-(3-ethylbenzothiazoline-6-sulfonic acid) (ABTS) free radical, which was prepared from manganese dioxide and ABTS. Secondly, in order to identify the elution period of major antioxidant peaks, the antioxidant capacities of different fractions from solid-phase extraction (SPE) were measured, and the chromatograms of fractions were also recorded. Lastly, multiple mass spectrometry (MS(n)) was used to elucidate the possible chemical structures of antioxidants, and nuclear magnetic resonance (NMR) was further applied for structure confirmation. The major antioxidant compounds in lady's finger were identified to be quercetin derivatives and (-)-epigallocatechin using HPLC-MS and HPLC-MS(n) (n = 2-4) techniques. It was found that about 70% of total antioxidant activity was contributed by four quercetin derivatives. The structures of major antioxidants, which were isolated by semi-preparative RP-HPLC with two tandem C18 columns, were further confirmed using UV-vis absorption spectroscopy and 13C NMR spectra. Quercetin 3-O-xylosyl (1' --> 2') glucoside, quercetin 3-O-glucosyl (1' --> 6') glucoside, quercetin 3-O-glucoside and quercetin 3-O-(6'-O-malonyl)-glucoside were first identified and characterized as major antioxidants in lady's finger.     

Compact Almost Kähler Manifolds with Divergence-Free Weyl Conformal Tensor

We prove that a compact almost Kähler manifold satisfying that a certain part of thedivergence W of the Weyl conformal tensor W vanishes isKähler.     

Transverse Frames for Petrov Type I Spacetimes: A General Algebraic Procedure

We develop an algebraic procedure to rotate a general Newman-Penrose tetrad in a Petrov type I spacetime into a frame with Weyl scalars ₁ and ₃ equal to zero, assuming that initially all the Weyl scalars are non vanishing. The new frame highlights the physical properties of the spacetime. In particular, in a Petrov type I spacetime, setting ₁ and ₃ to zero makes apparent the superposition of a Coulomb-type effect ₂ with transverse degrees of freedom ₀ and ₄.     

On Norden Metrics which Are Locally Conformal to Anti-Kählerian Metrics

We build examples of Norden metrics on × S ¹, where R ^{2 n} _n is either a pseudosphere or a pseudohyperbolic space. These turn out to be locally conformal to flat anti-Kählerian metrics, strongly non anti-Kählerian, and with a parallel Lee form. Conversely, any connected complete anti-Hermitian manifold possessing these properties is shown to be locally analytically homothetic to × S ¹.     

On the Gelfand-Kirillov conjecture for quantum algebras

Let be a complex not a root of unity and be a semi-simple Lie -algebra. Let be the quantized enveloping algebra of Drinfeld and Jimbo, be its triangular decomposition, and the associated quantum group. We describe explicitly and as a quantum Weyl field. We use for this a quantum analogue of the Taylor lemma.

     

A Quantization on Riemann Surfaces with Projective Structure

Let X be a Riemann surface equipped with a projective structure. Let be a square-root of the holomorphic cotangent bundle K _X . Consider the symplectic form on the complement of the zero section of obtained by pulling back the symplectic form on K _X using the map ². We show that this symplectic form admits a natural quantization. This quantization also gives a quantization of the complement of the zero section in K _X equipped with the natural symplectic form.     

On intensities of perturbed random measures on Hausdorff spaces

Abstract

This article studies classes of random measures on topological spaces perturbed by stochastic processes (a.k.a. modulated random measures). We render a rigorous construction of the stochastic integral of functions of two variables and showed that such an integral is a random measure. We establish a new Campbell-type formula that, along with a rigorous construction of modulation, leads to the intensity of a modulated random measure. Mathematical formalism of integral-driven random measures and their stochastic intensities find numerous applications in stochastic models, physics, astrophysics, and finance that we discuss throughout the article.     

Weyl-Titchmarsh theory for symplectic difference systems

In this work, we establish Weyl-Titchmarsh theory for symplectic difference systems. This paper extends classical Weyl-Titchmarsh theory and provides a foundation for studying spectral theory of symplectic difference systems.