Existence of multiple positive solutions for N-laplacian in a bounded domain in R-N

Let Ohm be a bounded domain in IRN, N greater than or equal to 2, lambda > 0, q is an element of (0, N - 1) and alpha is an element of (1, N/N-1 In this article we show the existence of at least two positive solutions for the following quasilinear elliptic problem with an exponential type nonlinearity:

Creep behaviour of nimonic and R.R. 59 alloys

The Ramberg-Osgood relation which adequately describes the stress-strain curve of a strain-hardening material is extended to formulate the constitutive laws for creep. The constitutive laws which describe primary creep adequately are extended to secondary creep. The results are verified for the case of R.R. 59 at 200°C, Nimonic 80A and Nimonic 90 alloys at 750°C.

Hydrogen bonding in thiolbenzoic acid. Infra-red, ultra-violet, n.m.r. and cryoscopic studies

Dimerization of thiolbenzoic acid has been studied by infra-red, ultra-violet and n.m.r. spectroscopy and cryoscopy. The results indicate that the tendency to form S - H. O hydrogen bonds is not appreciable.

An optimum criterion for eccentrically loaded R. C. columns

An analysis of eccentrically loaded short reinforced concrete columns using a variable failure strain criterion is presented. The method dispenses with the usual procedure of assuming a fixed value for the ultimate strain in concrete. The analysis is based on the use of a simple, single equation for the complete stress-strain curve of concrete and the adoption of a process of maximisation of moment with respect to extreme fibre concrete compressive strain. Columns of rectangular section and loaded eccentrically along one axis only are considered in this paper. A good agreement is observed between the theoretical and experimental values of some test results.

Confined concrete—Its application in R.C. beams and frames

Stress-strain characteristics of concrete confined in steel binders have been determined. A new factor “confinement index” has been introduced for a quantitative measure of the confinement and using these results a “stress-block” has been developed. Tests have been made on simply supported reinforced concrete beams with spiral binder confinement and analysed on the basis of the proposed stress-block. Tests have also been made oon reinforced concrete portal frames and continuous beams with spiral binder confinement at sections of possible plastic hinge formation. An analysis of these tests indicates that a full redistribution of moments has taken place at ultimate.

Limit analysis of rectangular R.C. slabs on ground

A method is presented for obtaining lower bound on the carrying capacity of reinforced concrete foundation slab-structures subject to non-uniform contact pressure distributions. Functional approach suggested by Vallance for simply supported square slabs subject to uniform pressure distribution has been extended to simply supported rectangular slabs subject to symmetrical non-uniform pressure distributions. Radial solutions, ideally suited for rotationally symmetric problems, are shown to be adoptable for regular polygonal slabs subject to contact pressure paraboloids with constant edge pressures. The functional approach has been shown to be well suited even when the pressure is varying along the edges.

Certain novel features of the R.F. response of the YBa2Cu3O7−x superconductors

The r.f. absorption experiment performed on YBa2Cu3O7-x ceramic pellets using a CW NMR spectrometer shows some novel observed in the microwave range.

Am unexpected entry into the silver(I) chemistry of diphosphazane ligands: Crystal and molecular structures of [Ag{Ph2PN(Pr-i)PPh2}(CF3SO3)](2), [Ag{Ph2PN(Pr-i)PPh(OC6H3Me2-2,6)}(2)]PF6, and [Ag-3(mu-Cl)(2){Ph2PN(R)PPh2}(3)]PF6 (R = H, Pr-i)

Mononuclear, binuclear and trinuclear silver(l) complexes were obtained unexpectedly while probing the reactivity of diphosphazane ligands of the type X2PN(Pr-i)PXY towards the ruthenium-based precursor Ru(bipy)(2)Cl-2 center dot 2H(2)O, in the presence of a silver salt as a chloride scavenger. Subsequently, the reactions of AgX [X = Cl, NO3 or CF3SO3] with Ph2PN(R)PPh(Y) [R = H, Y = Ph; R = Pr-i, Y = Ph or OC6H3Me2-2,6] in a 1: 1 or 1:2 molar ratio have been investigated. Mononuclear or binuclear Ag(I) complexes containing either chelating or bridging diphosphazane ligands are obtained. Trinuclear silver(l) complexes are accessible by the treatment of diphosphazane ligands, Ph2PN(R)PPh2 [R = H, Pr-i] with AgCl using piperidine as the solvent. In the presence of a suitable chloride donor species, the mononuclear and binuclear complexes of Ph2PN(Pr-i)PPh2 are transformed slowly to the trinuclear complex [Ag-3(mu-Cl)(2){Ph2PN(Pr-i)PPh2}(3)]X, over a period 20 h. The structures of representative complexes have been confirmed by X-ray crystallography and the salient structural features are discussed

Open manifolds, Ozsvath-Szabo invariants and exotic R-4 ` S

We construct an invariant of certain open four-manifolds using the Heegaard Floer theory of Ozsvath and Szabo. We show that there is a manifold X homeomorphic to R-4 for which the invariant is non-trivial,showing that X is an exotic R-4. This is the first invariant that detects exotic R-4' s. (C) 2009 Published by Elsevier GmbH.

An enantiospecific approach to thapsanes from R-carvone: synthesis of (−)-thaps-8-en-5-ol†

The first enantiospecific synthesis of a thapsane, containing three contiguous quaternary carbon atoms, is accomplished starting from R-carvone. An intramolecular alkylation and an intramolecular diazoketone cyclopropanation reaction were employed for the stereo- and regiospecific generation of three contiguous quaternary carbon atoms present in the thapsane framework.

A new chiral oxazoline derived from camphor and its conversion to (R)-2-methylalkanoic acids

1S,5R,7R)-(-)-10, 10-Dimethyl-3-ethyl-4-oxa--atricyclo[5.2.1.0(1,5)]dec-2-ene 2 was prepared in 95% yield from (1S)-1-amino-2-exo-hydroxyapocamphane 1. The chiral oxazoline could be alkylated (Lhttp://eprints.iisc.ernet.in/cgi/users/home?screen=EPrint::Edit&eprintid=31175&stage=core#tDA/THF/-78 degrees C/RX, RX = ethyl, n-propyl, n-butyl iodides or benzyl bromide) to 3 in 95% yield and > 95% diastereoselectivity, and the products hydrolysed to (R)-2-methylalkanoic acids 4 (43-47% yield, 93-98% e.e.). (C) 2000 Elsevier Science Ltd. All rights reserved.

Chiral synthons from carvone, Part 40. A simple, enantiospecific approach to both enantiomers of 1 alpha,25-dihydroxyvitamin D-3 A-ring precursors from R-carvone

A simple and direct approach to both enantiomeric series of A-ring derivatives of 1 alpha,25-dihydroxyvitamin D-3 and the corresponding 1 alpha,3 alpha-derivatives, starting from the abundantly available R-carvone, is described. (C) 2000 Elsevier Science Ltd. All rights reserved.

An enantiospecific approach to pinguisanes from (R)-carvone. Total synthesis of (+)-pinguisenol

Enantiospecific total synthesis of (+)-pinguisenol 1, a sesquiterpene containing a cis-1,2,6,7-tetramethylbicyclo[4.3.0]nonane carbon framework incorporating two vicinal quaternary carbon atoms and four cis-oriented methyl groups on four contiguous carbon atoms, isolated from a liverwort, is described. The orthoester Claisen rearrangement of the allyl alcohol 9, obtained from (R)-carvone, generates the ester 12. Intramolecular cyclopropanation of the diazo ketone 13, derived from the ester 12, furnishes the tricyclic ketone 7. Degradation of the isopropenyl group followed by regioselective reductive cyclopropane ring cleavage transforms compound 7 into the hydroxy ketone 21. Wolff–Kishner reduction of the hydroxy ketone 21 followed by oxidation and Grignard reaction furnishes pinguisenol (+)- 1.

Metabolism of a monoterpene ketone, R-(+)-pulegone—a hepatotoxin in rat

R-(+)-Pulegone was administered orally to rats and the urinary metabolites were investigated. Six metabolites were isolated and purified using column and thin layer chromatographic techniques. Metabolites were identified by i.r., n.m.r. and mass spectral analyses.The neutral metabolites isolated from urine of rats treated with pulegone (I) were: pulegol (II), 2-hydroxy-2(1'-hydroxy-1'-methylethyl)-5-methylcyclohexanone (III), 3,6-dimethyl-7a-hydroxy-5,6,7,7a-tetrahydro-2(4H)-benzofuranone (V) and menthofuran (VII). Metabolites II and III were also excreted in conjugated form.Acidic metabolites isolated from urine of rats treated with pulegone (I) were: 5-methyl-2(1'-methyl-1'-carboxyethylidene)cyclohexanone (IV) and 5-methyl-5-hydroxy-2(1'hydroxy-'-carboxyethyl)cyclohexanone (VI).