Quantification of appetite suppressing steroid glycosides from Hoodia gordonii in dried plant material, purified extracts and food products using HPLC-UV and HPLC-MS methods

High-performance liquid chromatography (HPLC)-UV and HPLC-Mass Spectrometry (MS) methods were developed for the quantitative analysis of the family of Hoodia gordonii steroid glycosides with appetite suppressing properties in dried plant material, in purified and enriched extracts and in various prototype food-products fortified with H. gordonii extracts. For solid materials, e.g. dried plants or for non-fatty foods, extraction of the steroid glycosides is performed using methanol. For products where the steroid glycosides are present in an oil matrix, direct injection of the oil after dilution in tetrahydrofuran is applied. The HPLC separation is performed on an octyl-modified reversed-phase column in the gradient mode with UV detection at lambda = 220 nm. Quantification is performed against an external calibration line prepared using either one of the pure steroid glycosides or geranyl-tiglate. Short- and long-term repeatabilities of the methods are better than 3 and 6%, respectively. Recoveries are better than 85%, even in the analysis of the least abundant steroid glycosides in a complex yoghurt drink. Linearity is better than 3-4 orders of magnitude and the detection limits are below approximately 2 microg g(-1) for the individual steroid glycosides in dried plant material and food products. HPLC-MS is used to confirm that the steroid glycosides contain the characteristic steroid core, the carbohydrate chain and the tigloyl group.     

Generalized isothermal models with strange equation of state

We consider the linear equation of state for matter distributions that may be applied to strange stars with quark matter. In our general approach the compact relativistic body allows for anisotropic pressures in the presence of the electromagnetic field. New exact solutions are found to the Einstein-Maxwell system. A particular case is shown to be regular at the stellar centre. In the isotropic limit we regain the general relativistic isothermal Universe. We show that the mass corresponds to the values obtained previously for quark stars when anisotropy and charge are present.      

Conformally flat collapsing stars in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

The present work includes an analytical investigation of a collapsing spherical star in f(R) gravity. The interior of the collapsing star admits a conformal flatness. Information regarding the fate of the collapse is extracted from the matching conditions of the extrinsic curvature and the Ricci curvature scalar across the boundary hypersurface of the star. The radial distribution of the physical quantities such as density, anisotropic pressure and radial heat flux are studied. The inhomogeneity of the collapsing interior leads to a non-zero acceleration. The divergence of this acceleration and the loss of energy through a heat conduction forces the rate of the collapse to die down and the formation of a zero proper volume singularity is realized only asymptotically.     

Geodesic models generated by Lie symmetries

New theorems about the existence of solution for a system of infinite linear equations with a Vandermonde type matrix of coefficients are proved. Some examples and applications of these results are shown. In particular, a kind of these systems is solved and applied in the field of the General Relativity Theory of Gravitation. The solution of the system is used to construct a relevant physical representation of certain static and axisymmetric solution of the Einstein vacuum equations. In addition, a newtonian representation of these relativistic solutions is recovered. It is shown as well that there exists a relation between this application and the classical Haussdorff moment problem.     

Inheriting geodesic flows

We investigate the propagation equations for the expansion, vorticity and shear for perfect fluid space-times which are geodesic. It is assumed that space-time admits a conformal Killing vector which is inheriting so that fluid flow lines are mapped conformally. Simple constraints on the electric and magnetic parts of the Weyl tensor are found for conformal symmetry. For homothetic vectors the vorticity and shear are free; they vanish for nonhomothetic vectors. We prove a conjecture for conformal symmetries in the special case of inheriting geodesic flows: there exist no proper conformal Killing vectors (ψ _;ab ≠ 0) for perfect fluids except for Robertson-Walker space-times. For a nonhomothetic vector field the propagation of the quantity ln (R _ab u ^a u ^b ) along the integral curves of the symmetry vector is homogeneous.     

Cosmic strings in Bianchi II,VIII and IX spacetimes: Integrable cases

We investigate the integrability of cosmic strings in Bianchi II, VIII and IX space-times using a Lie symmetry analysis. The behaviour of the gravitational field is governed by solutions of a single second order nonlinear differential equation. We demonstrate that this equation is integrable and admits an infinite family of physically reasonable solutions. Particular solutions obtained by other authors are shown to be special cases of our class of solutions.     

New anisotropic models from isotropic solutions

We establish an algorithm that produces a new solution to the Einstein field equations, with an anisotropic matter distribution, from a given seed isotropic solution. The new solution is expressed in terms of integrals of known functions, and the integration can be completed in principle. The applicability of this technique is demonstrated by generating anisotropic isothermal spheres and anisotropic constant density Schwarzschild spheres. Both of these solutions are expressed in closed form in terms of elementary functions, and this facilitates physical analysis. Copyright © 2005 John Wiley & Sons, Ltd.     

Inhomogeneous and Radiating Composite Fluids

We consider the energy conditions for a dissipative matter distribution. The conditions can be expressed as a system of equations for the matter variables. The energy conditions are then generalised for a composite matter distribution; a combination of viscous barotropic fluid, null dust and a null string fluid is also found in a spherically symmetric spacetime. This new system of equations comprises the energy conditions that are satisfied by a Type I fluid. The energy conditions for a Type II fluid are also presented, which are reducible to the Type I fluid only for a particular function. This treatment will assist in studying the complexity of composite relativistic fluids in particular self-gravitating systems.     

Generating potentials via difference equations

The condition for pressure isotropy, for spherically symmetric gravitational fields with charged and uncharged matter, is reduced to a recurrence equation with variable, rational coefficients. This difference equation is solved, in general, using mathematical induction leading to an exact solution to the Einstein field equations which extends the isotropic model of John and Maharaj. The metric functions, energy density and pressure are well behaved, which suggests that this model could be used to describe a relativistic sphere. The model admits a barotropic equation of state, which approximates a polytrope close to the stellar centre. Copyright © 2006 John Wiley & Sons, Ltd.     

Nonlinear shear‐free radiative collapse

We study realistic models of relativistic radiating stars undergoing gravitational collapse which have vanishing Weyl tensor components. Previous investigations are generalized by retaining the inherent nonlinearity at the boundary. We transform the boundary condition to an Abel equation of the first kind. A variety of nonlinear solutions is generated all of which can be written explicitly. Several classes of infinite solutions exist. Copyright © 2007 John Wiley & Sons, Ltd.