Anisotropic spheres with uniform energy density in general relativity

An ansatz is developed to obtain interior solutions of the Einstein field equations for anisotropic spheres. This procedure necessitates a choice for the energy-density and the radial pressure. A class of solutions for a uniform energy-density source is presented. These anisotropic spheres match smoothly to the Schwarzschild exterior and are well-behaved in the interior of the sphere.     

Conformal symmetries in static spherically symmetric spacetimes

We obtain the conformal symmetry vector in static, spherically symmetric spacetimes, in terms of functions subject to a number of integrability conditions that also place restrictions on the metric. Some conformal symmetries found previously are regained as special cases.     

Stationary rotating string world models with a magnetic field

Following the techniques used by Letelier and Stachel some new physically relevant stationary solutions of string cosmology with magnetic field are presented. In these solutions, the flow vector of matter has non-zero rotation and the cosmological constant is taken to be non-zero. Previously known solutions are derived as particular cases from our class of solutions. Some string models with vanishing cosmological constant are also discussed.     

Expanding spherically symmetric models without shear

The integrability properties of the field equationL _xx =F(x)L ² of a spherically symmetric shear-free fluid are investigated. A first integral, subject to an integrability condition onF(x), is found, giving a new class of solutions which contains the solutions of Stephani and Srivastava as special cases. The integrability condition onF(x) is reduced to a quadrature which is expressible in terms of elliptic integrals in general. There are three classes of solution and in general the solution ofL _xx =F(x)L ² can only be written in parametric form. The case for whichF=F(x) can be explicitly given corresponds to the solution of Stephani. A Lie analysis ofL _xx =F(x)L ² is also performed. If a constant vanishes, then the solutions of Kustaanheimo and Qvist and of this paper are regained. For 0 we reduce the problem to a simpler, autonomous equation. The applicability of the Painlevé analysis is also briefly considered.     

On the qth power algorithm

Leonard and Pellikaan developed the qth power algorithm to compute module bases for the integral closure of the polynomial ring in a class of function fields. In this paper, their algorithm is adapted to efficiently obtain an -basis for a class of Riemann–Roch spaces without having to compute the entire integral closure. This reformulation allows one to determine the complexity of the algorithm. Further, we obtain a simple characterization of the integral closure.     

A facial microwave-assisted synthesis, spectroscopic characterization and preliminary complexation studies of calix[4]pyrroles containing the hydroxamic-acid moiety

The synthesis, spectroscopic characterization and preliminary complexation properties of functionalized calix[4]pyrroles are described. To date, two generalized preparative approaches have been pursued (i) modifying the basic pyrrole-plus-ketone synthesis of calix[4]pyrrole by using microwave irradiation protocol, (ii) the basic meso-tetra(methyl) meso-tetra(p-nitrophenyl) calix[4]pyrrole skeleton was functionalized to give hydroxamic acids, especially in the meso-position of the macrocycles. The structures of novel calix[4]pyrrole hydroxamic acid derivatives were confirmed on the basis of various physico-chemical techniques such as elemental analysis, FT-IR, ¹H NMR and FAB-Mass. The results of preliminary studies on the extraction of vanadium (V) with the host calix[4]pyrrole hydroxamic acids were elucidated by significant examination of UV–Vis spectroscopy and ICP-AES. Single crystal structure of basic meso-tetra(methyl) meso-tetra (p-nitro phenyl) calix[4]pyrrole moiety has also been reported.     

Quenching of aromatic ketone phosphorescence by sterically hindered alkenes

The deactivation of the excited states of triplet ketones by sterically hindered alkenes results in lower rate constants (usually due to increased activation energies) than by relatively unhindered alkenes.     

Generalized Euclidean stars with equation of state

This article has a dual purpose: i) to provide a flavor of the scientific highlights of the landmark conference, GR3, held in July 1962 at Jablonna, near Warsaw; and, ii) to present a bird’s eye view of the tremendous advances that have occurred over the half century that separates GR3 and GR20, which was again held in Warsaw in July 2013.