Class two analogue of T. Y. Thomas's theorem and different types of embeddings of static spherically symmetric space-times

A Riemannian space of embedding class two is characterised by two symmetric tensors a _ij , b _ij and a vector s_i, satisfying the equations of Gauss, Codazzi and Ricci. It is proved that the Gauss equations together with one set of Codazzi equations imply the other set of Codazzi equations and the Ricci equations, provided that the matrix of the tensor b _ij (or a _ij ) is nonsingular. (The class m generalisation of the result has also been suggested). The result so proved has further been utilized in finding explicitly the a _ij 's and b _ij 's in the case of the static spherically symmetric line element. It is further indicated that the a _ij 's and b _ij 's so obtained are responsible for the different types of embeddings of the spacetime considered.     

Programming with a special class of nonlinear functionals

Summary In this paper we consider programming problems in which the constraints are linear and the objective function is the product or the quotient of two functions, each function being a homogeneous form of first degree with a constant added to it.With the proper assumptions of concavity or convexity of the homogeneous forms, this nonlinear programming problem is reduced to that of maximization of a concave function over a convex constraint set.

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Zusammenfassung In der vorliegenden Arbeit werden Programme untersucht, bei denen die Nebenbedingungen linear sind und die Zielfunktion als Produkt bzw. Quotient zweier Funktionen darstellbar ist, die bis auf additive Konstanten homogen von 1. Grad sind. Bei geeigneten Konvexitäts- oder Konkavitätsannahmen für diese Funktionen lassen sich solche Programme auf die Maximierung einer konkaven Funktion in einem konvexen Gebiet zurückführen.

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Prepared with the partial support of the C.S.I.R., India.

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Vorgel. v.:J. Nitsche.     

Pyridinium dichlorophosphinomethylides

Seven new pyridinium dichlorophosphinomethylides 2 have been obtained from dichlorophosphinylation of the pyridinium methylides generated in situ. 2 give 1,3‐bis(alkoxycarbonyl)‐2‐phosphaindolizines 4 through 1,5‐electrocyclization of the intermediate, bis(pyridinium ylidyl)phosphenium chloride 3 which is generated either from disproportionation of 2 or from the reaction of 2 with pyridinium methylide. Formation of 3 has been confirmed by carrying out a crossed reaction. 3‐Substituted 2 forms 4 regiospecifically. Intramolecular 1,5‐cyclocondensation of 2‐methylpyridinium dichlorophosphinomethylide is preferred over its disproportionation. © 2001 John Wiley & Sons, Inc. Heteroatom Chem 12:602–609, 2001     

Electronic and structural effects on the nonlinear optical behavior in π‐conjugated structure bis(4‐nitrophenyl) carbonate: a vibrational spectroscopic approach

Fourier transform (FT)‐Raman and infrared (IR) spectra of the nonlinear optical (NLO) material bis(4‐nitrophenyl) carbonate were recorded and analyzed. The geometry, first hyperpolarizability and harmonic vibrational wavenumbers were calculated with the help of Becke3–Lee–Yang–Parr density functional theory method. The detailed interpretation of the vibrational spectra was carried out with the aid of normal coordinate analysis following the scaled quantum mechanical force field methodology. The second‐order NLO properties of the molecule were studied by the Kurtz and Perry powder reflection technique. Stability of the molecule arising from hyperconjugative interactions leading to its NLO activity and charge delocalization were analyzed using natural bond orbital analysis. Copyright © 2010 John Wiley & Sons, Ltd.     

Condensation of α-Cyanothioacetamide with Aldehydes Catalyzed by Envirocat EPZG1

Condensation of α-cyanothioacetamide with aldehydes has been carried out in excellent yield under mild conditions by using Envirocat EPZG as a heterogenous reusable catalyst.     

Quantification of hepcidin using matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry

Hepcidin is known to be a key systemic iron‐regulatory hormone which has been demonstrated to be associated with a number of iron disorders. Hepcidin concentrations are increased in inflammation and suppressed in hemochromatosis. In view of the role of hepcidin in disease, its potential as a diagnostic tool in a clinical setting is evident. This study describes the development of a matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry (MALDI‐TOF MS) assay for the quantitative determination of hepcidin concentrations in clinical samples. A stable isotope labeled hepcidin was prepared as an internal standard and a standard quantity was added to urine samples. Extraction was performed with weak cation‐exchange magnetic nanoparticles. The basic peptides were eluted from the magnetic nanoparticles using a matrix solution directly onto a target plate and analyzed by MALDI‐TOF MS to determine the concentration of hepcidin. The assay was validated in charcoal stripped urine, and good recovery (70–80%) was obtained, as were limit of quantitation data (5 nmol/L), accuracy (RE <10%), precision (CV <21%), within ‐day repeatability (CV <13%) and between‐day repeatability (CV <21%). Urine hepcidin levels were 10 nmol/mmol creatinine in healthy controls, with reduced levels in hereditary hemochromatosis (P < 0.000005) and elevated levels in inflammation (P < 0.0007). In summary a validated method has been developed for the determination of hepcidin concentrations in clinical samples. Copyright © 2009 John Wiley & Sons, Ltd.