On the Global Well-Posedness of 3-D Boussinesq System with Variable Viscosity

In this paper, the authors first consider the global well-posedness of 3-D Boussinesq system, which has variable kinematic viscosity yet without thermal conductivity and buoyancy force, provided that the viscosity coefficient is sufficiently close to some positive constant in L∞and the initial velocity is small enough in B_(3,1)~0(R~3). With some thermal conductivity in the temperature equation and with linear buoyancy force θe3 on the velocity equation in the Boussinesq system, the authors also prove the global well-posedness of such system with initial temperature and initial velocity being sufficiently small in L~1(R~3)and B_(3,1)~0(R~3) respectively.     

Modeling the plasma kinetics mechanisms of CuBr laser with neon–hydrogen additives

A mathematical model describing the discharge kinetics and lasing characteristics of copper bromide vapor laser with neon and hydrogen additives has been developed. The suggested model is based on a “zero-dimensional” model and offers simple mechanisms to explain discharge kinetics mechanisms, different physical processes and hydrogen additive effects on the copper bromide vapor laser.The model estimates the temporal evolution of discharge voltage and current, population densities, laser beam density, electron temperature and radial distribution of pressure and buffer gas temperature. The suggested mechanism assumes that the electron detachment from negative hydrogen ions does not contribute to the copper ionization process.Numerical solutions of a nonlinear rate equation system predict the generation of nanosecond pulses. The calculated maximum values of discharge voltage, current, average output laser power, electron temperature, etc. are in good agreement with other reported calculated and experimental data.     

Ionic Mobility and Dielectric Relaxation in Glass-Forming Mixtures of Sodium Chloride and Glycerol

Measurements of electrical conductivities of liquid and supercooled liquid NaCl–glycerol solutions were carried out between +42° and ?87°C. Time-domain measurements of dielectric relaxation in pure glycerol and in NaCl–glycerol solutions between ?78 and ?89.9°C are described. The transient response data were fitted to the empirical Davidson–Cole response model. The specific conductivity data show a non-Arrhenius behavior near the glass-transition temperature and is well described by the Vogel–Tammann–Fulcher (VTF) law, which also fits the dielectric relaxation time data. The Vogel–Fulcher divergence temperature is consistent with the Kauzmann temperature. The dielectric relaxation time is increased significantly by the addition of sodium chloride, whereas the static relative permittivity decreases linearly with concentration, indicating that NaCl has a “structure-making” effect on the structure of glycerol.     

Reflection coefficient determination of the complex resonator mirrors in solid state laser

On the basis of pulse-energy measurement of Nd–YAG laser emission, the reflection coefficient of complex mirror is determined as a function of pumping energy and resonator parameters. It is shown that the reflection coefficient of complex mirror has the tendency to stabilize with increasing pumping energy above the threshold energy. The practical interest of this work is to determine the reflection coefficient of resonant mirror without using calibrated mirrors.     

Synthesis and binding properties of calix[4]arenes with [2 + 2'] mixed ligating functional groups

A series of mixed [2 + 2'] p-tert-butylcalix[4]arene have been synthesised by selective 1,3-dialkylation of phenolic groups using various alkylating agents such as benzyl bromide, methyl iodide, ethyl bromoacetate, and 2-methoxyethyl tosylate. The extraction and complexation properties of the synthesized calixarenes towards alkali and alkaline earth metal cations have been investigated in acetonitrile by means of UV spectrophotometry and 1H NMR spectroscopy. The results show the formation of ML and/or ML2 species depending on the ligand and the cation. The enthalpies and entropies of complexation of alkali metal cations by a tetraglycol, diglycol-dibenzyl and diglycol-diester derivatives have been obtained from calorimetric measurements. The results revealed that the formation of ML species is controlled by enthalpy while the formation of ML2 from ML is entropy driven.     

Sur quelques problèmes concernant les fonctions holomorphes et plurisousharmoniques

Résumé  On établira dans ce papier le lien biunivoque entre fonctios plurisousharmoniques et fonctions holomorphes.

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We prove in this paper the connection between plurisubharmonic and holomorphic functions.

     

Et3B-mediated palladium-catalyzed direct allylic substitution reactions of Morita–Baylis–Hillman alcohols with aromatic amines

An efficient, direct allylic amination of both cyclic and acyclic Morita–Baylis–Hillman alcohols with aromatic amines, in tetrahydrofuran (THF) at room temperature, catalyzed by Pd(0)/Et₃B, is reported herein. The corresponding amines are obtained with a high α -regioselectivity in 65–87% yields.     

Anomalous behaviour of uranium isotopes in backwater sediments of Zuari river

The surface leaching of the labile component of uranium has been carried out in estuarine sediments of Zuari river in Goa. The measurements of alpha activities of²³⁸U,²³⁵U and²³⁴U in the leachates indicated a remarkable anomaly between the activities of²³⁸U and²³⁴U. The activity ratios of²³⁴U/²³⁸U in these leachates have been found to be in the range of 1.10 to 1.14. However, the activity ratios of²³⁵U/²³⁸U have been found to be 0.045 which is close to that in natural uranium. It has also been observed that the anomaly between²³⁸U and²³⁴U exists only on the surface organic layers of the backwater sediments of the Zuari river.