Induced trees in sparse random graphs

The random graphG(n, p) onn vertices with edge probabilityp = c/n contains an induced tree of order _c n where _c > 0 forc > 1. This proves a conjecture of Erdös and Palka.     

Synthetic oligorhamnans related to the most common O-chain backbone from phytopathogenic bacteria

The synthesis of the tetrasaccharide rhamnanic motif α-l-Rha-(1→3)-α-l-Rha-(1→2)-α-l-Rha-(1→2)-α-l-Rha and its dimerization to octasaccharide have been developed. Three different pathways toward the dimerization have been investigated; the best one was based on a [4+2]+2 stepwise condensation of a rhamnose tetrasaccharide with two rhamnosyl N-phenyl trifluoroacetimidates as glycosyl donors and on an orthogonal set of protecting groups consisting of benzoyl, levulinoyl, and allyl groups.     

Non-Markovian stochastic Schrödinger equations in different temperature regimes: a study of the spin-boson model

Stochastic Schrodinger equations are used to describe the dynamics of a quantum open system in contact with a large environment, as an alternative to the commonly used master equations. We present a study of the two main types of non-Markovian stochastic Schrodinger equations, linear and nonlinear ones. We compare them both analytically and numerically, the latter for the case of a spin-boson model. We show in this paper that two linear stochastic Schrodinger equations, derived from different perspectives by Diosi, Gisin, and Strunz [Phys. Rev. A 58, 1699 (1998)], and Gaspard and Nagaoka [J. Chem. Phys. 13, 5676 (1999)], respectively, are equivalent in the relevant order of perturbation theory. Nonlinear stochastic Schrodinger equations are in principle more efficient than linear ones, as they determine solutions with a higher weight in the ensemble average which recovers the reduced density matrix of the quantum open system. However, it will be shown in this paper that for the case of a spin-boson system and weak coupling, this improvement does only occur in the case of a bath at high temperature. For low temperatures, the sampling of realizations of the nonlinear equation is practically equivalent to the sampling of the linear ones. We study further this result by analyzing, for both temperature regimes, the driving noise of the linear equations in comparison to that of the nonlinear equations.     

Studies on quinones. VII. Synthesis of some benzo[b]thiophene-4,7-diones

The synthesis of methyl 4,7-dihydro-4,7-dioxobenzo[b]thiophene-2-carboxylate ( 20 ) based on the reaction of methyl mercaptoacetate with activated 1,4-benzoquinones is described. Methyl 4,7-dihydro-4,7-dioxo-5-hydroxybenzo[b]thiophene-2-carboxylate ( 24 ) and its corresponding methyl ether 26 were obtained through a Thiele-Winter acetoxylation on 20 . On the basis of the properties of methyl 4,7-dihydro-4,7-dioxo-6-methoxy-benzo[b]thiophene-2-carboxylate ( 21 ) obtained from 2,4,5-trimethoxybenzaldehyde ( 32 ), the structures of the products 24 and 26 are proposed.     

Double quantum modulation NMR spectroscopy on spins with I = 1 in solids

NMR experiments with amplitude modulated rf pulses are introduced for the detection of double quantum coherences from spin I = 1 nuclei with large quadrupolar frequencies v_Q in solids. rf pulses of intensity v₁ and with modulation frequency v_m create effective irradiation fields of intensity $\text{1}\text{4}$v²₁/(v_Q-v_m) on the double quantum transition when v₁<¦v_Q-v_m¦?v_Q+v_m. ²D-NMR measurements on an oriented single crystal of deuterated malonic acid are presented.     

Application of HPTLC to the Analysis of Horminone in Sphacele chamaedryoides (Balbis) Briq.

JPC – Journal of Planar Chromatography – Modern TLC - Royleanones are diterpene quinones ubiquitous in plants belonging to the Lamiaceae family. Sphacele chamaedryoides is a plant used...