Synthesis and reactions of optically pure cyclohexyl(o-methoxyphenyl)phosphine-borane and t-butyl-(o-methoxyphenyl)phosphine-borane

Cyclohexyl(o-methoxyphenyl)menthyloxyphosphineborane and t-butyl(o-methoxyphenyl)menthyloxyphosphine-borane were prepared from dichlorocyclohexylphosphine and t-butyldichlorophosphine by successive treatments with (−)-menthol, o-methoxyphenylmagnesium bromide, and borane-THF complex. The separated pure diastereomers of each of the compounds underwent reaction with lithium naphthalenide to afford optically pure cyclohexyl(o-methoxyphenyl)phosphine-borane and t-butyl(o-methoxyphenyl)phosphine-borane, respectively. These secondary phosphine-boranes reacted readily with various electrophiles in the presence of bases with virtually net retention of configuration. A new chiral phosphine ligand, (S,S)-1,2-bis[cyclohexyl(o-methoxyphenyl)phosphino]ethane was synthesized via the optically pure phosphine-boranes.     

The static deformation of the asymmetric Japanese bow: modelling bow asymmetries with the elastica theory

Meccanica - The static deformation of symmetric bow limbs has been widely studied in the last century. However, asymmetries in shape and length which correspond to a more realistic situation, have...     

Calorimetric study ofβ-cyclodextrin undecahydrate

Heat capacities of crystalline-cyclodextrin undecahydrate have been measured in the temperature range between 13 and 300K by use of a miniaturized adiabatic low-temperature calorimeter. A first-order phase transition occurred at 226K with a discontinuous entropy change of 45.0 ± 1.0J K ^–1 mol^–1. The highly disordered nature of the high temperature phase was considered in relation to the entropy contribution. A glass transition phenomenon observed around 150K was ascribed to the freezing of a configurational change of the protons engaged in the four-membered hydrogen-bonded ring which appeared only in the low temperature phase.     

Superstring thermodynamics and its application to cosmology

The thermodynamics of superstring theories (SST-I, SST-II and heterotic string theory) and its application to the cosmology are studied. The free energy of superstring gas is calculated in the one-loop approximation and the stability of the extra torus dimensions is discussed. Assuming that the Einstein equation dictates the evolution of the universe, we show that matter dominated universe filled with massive particles would never be realized at the beginning of the universe, contrary to the naive expectation in the superstring cosmology.     

Electronic structure of the organic conductors based on BMDT-TTF (BIS(methylenedithio)tetrathiafulvalene)

In the crystals of the cation radical salts based on the organic donor BMDT-TTF, the charge separation is observed. This comes from (1) nonequivalency of the site potential and (2) the long range electron-electron interaction, which are related to the two-dimensional nature of the molecular arrangement. The effects of the charge separation on the elctronic structure are discussed.     

Conservative numerical schemes for the Ostrovsky equation

The Ostrovsky equation describes gravity waves under the influence of Coriolis force. It is known that solutions of this equation conserve the L² norm and an energy function that is determined non-locally. In this paper we propose four conservative numerical schemes for this equation: a finite difference scheme and a pseudospectral scheme that conserve the norm, and the same types of schemes that conserve the energy. A numerical comparison of these schemes is also provided, which indicates that the energy conservative schemes perform better than the norm conservative schemes.     

Superquadratic convergence of DLASQ for computing matrix singular values

DLASQ is a routine in LAPACK for computing the singular values of a real upper bidiagonal matrix with high accuracy. The basic algorithm, the so-called dqds algorithm, was first presented by Fernando-Parlett, and implemented as the DLASQ routine by Parlett-Marques. DLASQ is now recognized as one of the most efficient routines for computing singular values. In this paper, we prove the asymptotic superquadratic convergence of DLASQ in exact arithmetic.     

Calorimetric and dielectric studies of a phase transition in thallium dihydrogen phosphate: A nearly critical case

The heat capacity of thallium dihydrogen phosphate was measured from 12 to 300 K. A lambda anomaly with a small first order discontinuity was found at 229.76 K with the integrated enthalpy and entropy changes equal to 370 J mol^-1 and 1.8 J K^-1 mol^-1, respectively. The entropy discontinuity at the first order transition is 0.25 J K^-1 mol^-1. The Landau theory of phase transitions of the second kind reproduces closely the temperature dependence of the anomalous heat capacity. This, together with the small discontinuity in the entropy, implies that the phase transition is close to a classical critical point of higher order. The relative dielectric permittivity ?_r(b) along the b-axis at 1 kHz is anomalously large and strongly temperature dependent, while the ?_r(a¹) and ?_r(c) are not. A broad absorption centered at 1700 cm^-1 was observed in the infrared absorption spectrum, indicating presence of hydrogen bonding of the length ～ 0.25 nm. Occurrence of a phase transition at 127 ± 2 K was suggested by differential thermal analysis of thallium dideuterium phosphate.     

Front shock behavior of stable curved detonation waves in rectangular-cross-section curved channels

The propagation of curved detonation waves of gaseous explosives stabilized in rectangular-cross-section curved channels is investigated. Three types of stoichiometric test gases, C₂H₄ + 3O₂, 2H₂ + O₂, and 2C₂H₂ + 5O₂ + 7Ar, are evaluated. The ratio of the inner radius of the curved channel (r_i) to the normal detonation cell width (λ) is an important factor in stabilizing curved detonation waves. The lower boundary of stabilization is around r_i/λ = 23, regardless of the test gas. The stabilized curved detonation waves eventually attain a specific curved shape as they propagate through the curved channels. The specific curved shapes of stabilized curved detonation waves are approximately formulated, and the normal detonation velocity (D_n)?curvature (κ) relations are evaluated. The D_n nondimensionalized by the Chapman–Jouguet (CJ) detonation velocity (D_CJ) is a function of the κ nondimensionalized by λ. The D_n/D_CJ?λκ relation does not depend on the type of test gas. The propagation behavior of the stabilized curved detonation waves is controlled by the D_n/D_CJ?λκ relation. Due to this propagation characteristic, the fully-developed, stabilized curved detonation waves propagate through the curved channels while maintaining a specific curved shape with a constant angular velocity. Self-similarity is seen in the front shock shapes of the stabilized curved detonation waves with the same r_i/λ, regardless of the curved channel and test gas.     

Sound modes in holographic hydrodynamics for charged AdS black hole

In the previous paper we studied the transport coefficients of quark–gluon plasma in finite temperature and finite density in vector and tensor modes. In this paper, we extend it to the scalar modes. We work out the decoupling problem and hydrodynamic analysis for the sound mode in charged AdS black hole and calculate the sound velocity, the charge susceptibility and the electrical conductivity. We find that Einstein relation among the conductivity, the diffusion constant and the susceptibility holds exactly.