Potential surfaces for time-like geodesics in the Curzon metric

In this paper we deduce the general pattern of the potential surfaces for time-like geodesics in the Curzon metric. We find that for fairly small energies and orbital angular momenta, the time-like geodesics group into two sets; the geodesics of one set tend to thez-axis asR=(r²+z²)^1/2 0,R=0 being a directional singularity, the others tend to ther-axis. At low energies these two sets are detached but they merge together as the energy increases. Stable circular motion is confined to thez = 0-plane and an energy threshold for stationary motion exists and is equal (per unit of rest-mass energy) to 0.945, a value almost indistinguishable from that in the Schwarzschild space-time.     

Energy and mass-number dependence of the dissociation temperature in hydrodynamical models

Transverse-momentum distributions of andK have been analyzed within a framework of the hydrodynamical model to obtain the dependence of the collective transverse flow and the dissociation temperatureT _d inpp- and -induced multiparticle production reactions. The main outcomes are the steadily increasing transverse flow and a slowly decreasingT _d as the incident energy increases. This behavior is in excellent agreement with early Landau's estimate. An extension of this to nucleus-nucleus collisions correctly gives account of the very soft component which has been observed in heavyion experiments.     

Localization in the ground state of a disordered array of quantum rotators

We consider the zero-temperature behavior of a disordered array of quantum rotators given by the finite-volume Hamiltonian: $$H_\Lambda = - \mathop \Sigma \limits_{x \in \Lambda } \frac{{h(x)}}{2}\frac{{\partial ^2 }}{{\partial \varphi (x)^2 }} - J\mathop \Sigma \limits_{\left\langle {x,y} \right\rangle \in \Lambda } \cos (\varphi (x) - \varphi (y))$$ , wherex,y∈Z ^d , 〈,〉 denotes nearest neighbors inZ ^d ;J>0 andh={h(x)>0,x∈Z ^d } are independent identically distributed random variables with common distributiondμ(h), satisfying ∫h ^?δ dμ(h)<∞ for some δ>0. We prove that for anym>0 it is possible to chooseJ(m) sufficiently small such that, if 0<J<J(m), for almost every choice ofh and everyx∈Z ^d the ground state correlation function satisfies $$\left\langle {\cos (\varphi (x) - \varphi (y))} \right\rangle \leqq C_{x,h,J} e^{ - m\left| {x - y} \right|} $$ for ally∈Z ^d withC _x,h,J <∞.     

Solvation thermodynamics: theory and applications

Potential distribution and coupling parameter theories are combined to interrelate previous solvation thermodynamic results and derive several new expressions for the solvent reorganization energy at both constant volume and constant pressure. We further demonstrate that the usual decomposition of the chemical potential into noncompensating energetic and entropic contributions may be extended to obtain a Gaussian fluctuation approximation for the chemical potential plus an exact cumulant expansion for the remainder. These exact expressions are further related to approximate first-order thermodynamic perturbation theory predictions and used to obtain a coupling-parameter integral expression for the sum of all higher-order terms in the perturbation series. The results are compared with the experimental global solvation thermodynamic functions for xenon dissolved in n-hexane and water (under ambient conditions). These comparisons imply that the constant-volume solvent reorganization energy has a magnitude of at most approximately kT in both experimental solutions. The results are used to extract numerical values of the solute-solvent mean interaction energy and associated fluctuation entropy directly from experimental solvation thermodynamic measurements.     

Tentoxin as a scaffold for drug discovery. Total solid-phase synthesis of tentoxin and a library of analogues

[reaction: see text] A solid-phase method for the synthesis of tentoxin has been developed. Two key steps-dehydration and N-alkylation-are carried out while the peptide is anchored to the resin. The method, which has been validated by the preparation of a library of tentoxin analogues, should be applicable to the generation of further libraries that have the tentoxin scaffold structure, as well as other structures containing N-alkylated didehydroamino acids.     

1-Alkyl-2,4-dihydro-1H-pyrazino[2,1-b]quinazoline-3,6-diones as glycine templates. Synthesis of Fiscalin B

An excess of base allows the regio- and diastereoselective alkylation at C(4) of the glycine templates 1-methyl(isopropyl)-2,4-dihydro-1H-pyrazino[2,1-b]quinazoline-3,6-diones 9a and 9b without the need for N(2)-protecting groups. While the alkylation of 9a gave exclusively the 1,4-anti-isomers, the isopropyl derivative 9b required much longer reaction times and occurred with lower diastereoselectivity. Fiscalin B 3 was obtained by alkylation of 9b with N-Boc-3-indolylmethyl bromide followed by indole deprotection.     

Diverse motifs of mannoside clustering on a beta-cyclodextrin core

[reaction: see text] A new method for the synthesis of beta-cyclodextrin-based cluster mannosides by application of the Sonogashira cross-coupling reaction is described. The method allows for the persubstitution of the beta-cyclodextrin at either 2- and 3-positions to give two types of heptavalent clusters, at both 2- and 6-positions to give clusters with 14 mannopyranoside units and at 2-, 3-, and 6-positions to obtain clusters with 21 mannopyranoside ligands.     

Synthesis of 6,19-sulfamidate bridged pregnanes

Conformationally restrained substituted pregnane-20-one derivatives were obtained by an intramolecular nitrene addition onto a C-5/C-6 double bond involving a tethered C-19 sulfamoyl moiety. The resulting aziridine underwent regioselective nucleophilic ring opening at C-5 at room temperature with cyanide, fluoride, and acetate. In the isolated case of acetate, a reversal of regioselectivity was observed at higher temperatures, a result attributed to a rearrangement process involving aziridine ring opening at the C-5 position and subsequent migration of the acetyl moiety to C-6.     

SFE of rosemary oil: Assessment of the influence of process variables and extract characterization

The effects of temperature and solvent density on the characteristics of the extracts obtained from supercritical fluid extraction (SFE) of the volatile compounds from Brazilian rosemary (Rosamarinus officianalis L., Labiatae) using carbon dioxide (CO₂) as solvent were investigated. The experiments were performed in a semi-batch laboratory scale home-made unit at two temperatures, viz. 310.15 and 320.15 K, over the pressure range of 100-160 bar. This study allowed to determine the crossover point and the maximum solubility of the oil. The products were analyzed by HRGC-MS, and compounds grouped in three different classes according to their molecular mass distribution in order to evaluate the influence of the variables studied on the characteristics of the extracts. The model proposed by Sovová was adopted in an attempt to interpret the mass transfer phenomena in the extraction process.