Generalization of Dynkin's Identity and Some Applications

Let X(t) be a right continuous temporally homogeneous Markov pro- cess, Tt the corresponding semigroup and A the weak infinitesimal genera- tor. Let g(t) be absolutely continuous and r a stopping time satisfying E.( S f I g(t) I dt) < oo and E.( f " I g'(t) I dt) < oo Then for f e 9iJ(A) with f(X(t)) right continuous the identity Exg(r)f(X(z)) - g(O)f(x) = E( 5 " g'(s)f(X(s)) ds) + E.( 5 " g(s)Af(X(s)) ds) is a simple generalization of Dynkin's identity (g(t) 1). With further restrictions on f and r the following identity is obtained as a corollary: Ex(f(X(z))) = f(x) + k! Ex~rkAkf(X(z))) + n-1E + (n ) )!.E,(so un-1Anf(X(u)) du). These identities are applied to processes with stationary independent increments to obtain a number of new and known results relating the moments of stopping times to the moments of the stopped processes.

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).

Crystal structure and conformation study of N-methyl-t-3-methyl-r-2, c-6-diphenylpiperidin-4-one thiosemicarbazone

Thiosemicarbazones are having the ability to bind with metal and inhibit the enzyme ribonucleoside diphosphate reductase(RDR),an enzyme which is involved in the synthesis of DNA precursors in the mammalian cells.The title compound N-methyl-t-3-methyl-r-2, c-6-diphenylpiperidin-4-one thiosemicarbazone (NMMDPT), CCDC 218052, was prepared using Mannich reaction and characterized by X-ray diffraction methods.The crystal data are:C20H24N4S; M.W= 352.49, triclinic,space group P (1) over bar, a = 8.467(2)angstrom, b = 10.228(2)angstrom, c = 12.249(2)angstrom; lpha=92.595(3)degrees, beta=104.173(3)degrees, gamma=13.628(3)degrees; V=930.0(3)angstrom(3), Z=2, D-cal=1.259Mgm(-3),mu=0.184mm(-1),lambda (MoKalpha)=0.71073 angstrom, final R1 and wR2 are 0.0470 and 0.1052, respectively. The piperidine rings adopt chair conformation. The planar phenyl rings are oriented equatorially at 2,6-positions of the piperidine ring. The molecular packing can be viewed as dimers held together by two N-H...S types of intermolecular hydrogen bonds. Weak C-H...pi interactions also support the stability of the molecules in the crystal in addition to van der Waals forces. (c) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

13C-N.M.R. studies of discotics

13C-N.M.R. spectra of benzene-hexa-n-octanoate (a discotic liquid-crystalline material) show significant differences in the isotropic, mesomorphic and solid states. The presence of four molecules per asymmetric unit is required to explain the results in the solid state.

Support theorems on R-n and non-compact symmetric spaces

We consider convolution equations of the type f * T = g, where f, g is an element of L-P (R-n) and T is a compactly supported distribution. Under natural assumptions on the zero set of the Fourier transform of T, we show that f is compactly supported, provided g is. Similar results are proved for non-compact symmetric spaces as well. (C) 2010 Elsevier Inc. All rights reserved.

Molecular conformation of alamethicin in dimethylsulfoxide solution A two-dimensional n.m.r. study

The solution conformation of alamethicin, a 20-residue antibiotic peptide, has been investigated using two-dimensional n.m.r. spectroscopy. Complete proton resonance assignments of this peptide have been carried out using COSY, SUPERCOSY, RELAY COSY and NOESY two-dimensional spectroscopies. Observation of a large number of nuclear Overhauser effects between sequential backbone amide protons, between backbone amide protons and CβH protons of preceding residues and extensive intramolecular hydrogen bonding patterns of NH protons has established that this polypeptide is in a largely helical conformation. This result is in conformity with earlier reported solid state X-ray results and a recent n.m.r. study in methanol solution (Esposito et al. (1987) Biochemistry26, 1043-1050) but is at variance with an earlier study which favored an extended conformation for the C-terminal half of alamethicin (Bannerjee et al.

Spectral Invariance of SG Pseudo-Differential Operators on L-P(R-n)

We prove the spectral invariance of SG pseudo-differential operators on L-P(R-n), 1 < p < infinity, by using the equivalence of ellipticity and Fredholmness of SG pseudo-differential operators on L-p(R-n), 1 < p < infinity. A key ingredient in the proof is the spectral invariance of SC pseudo-differential operators on L-2(R-n).