One Pot Reduction of Imines Generated in-situ from Aldehydes and Amines by the NaBH4-InCl3 System

A combination of sodium borohydride and a catalytic amount of indium（Ⅲ） chloride in acetonitrile reduces imines formed in-situ from aldehydes and amines to the corresponding functionalised secondary and tertiary amines in moderate to good yields. Noteworthy is that highly chemoselective reactions were achieved in the presence of other functional groups such as halogens, carbon-carbon double bonds and hydroxyl groups.     

Superconvergence of a Collocation-type Method for Hummerstein Equations

This paper considers the numerical solution of Hammerstein equationsof the form by a collocation method applied not to this equation, but ratherto an equivalent equation for z(t) :=g(t, y(t)). The desiredapproximation to y is then obtained by use of the (exact) equation In an earlier paper, questions of existence and optimal convergenceof the respective approximations to z and y were examined. Inthis sequel, collocation approximations to z are sought in certainpiecewise polynomial function spaces, and analogous of knownsuperconvergence results for the iterated collocation solutionof (linear) second-kind Fredhoim integral equations are statedand proved for the approximation to y.     

Optimal control of vibrational transitions of HCl

Control of fundamental and overtone transitions of a vibration are studied for the diatomic molecule, HCl. Specifically, the results of the effect of variation of the penalty factor on the physical attributes of the system (i.e., probabilities) and pulse (i.e., amplitudes) considering three different pulse durations for each value of the penalty factor are shown and discussed. We have employed the optimal control theory to obtain infrared pulses for selective vibrational transitions. The optimization of initial guess field with Gaussian envelope, phrased as maximization of cost functional, is done using the conjugate gradient method. The interaction of the field with the molecule is treated within the semiclassical dipole approximation. The potential and the dipole moment functions used in the calculations of control dynamics are obtained from high level ab-initio calculations.     

Two-soliton and three-soliton interactions of electron acoustic waves in quantum plasma

The overtaking collision between electron acoustic multisolitons in an unmagnetized quantum plasma consisting of ions, and both hot and cold electrons has been investigated. The Hirota bilinear method is employed to study phase shifts and trajectories during the overtaking collision of multisolitons. It is observed that phase shifts are significantly affected by the quantum parameter H. The phase shifts are proportional to B^1/3 (dispersion coefficient) and are functions of their respective amplitudes. It is also seen that the soliton structure occurs only if H < 2.     

A new temperature-dependent equation of state of solids

In the present paper, a temperature-dependent equation of state (EOS) of solids is discussed which is found to be applicable in high-pressure and high-temperature range. Present equation of state has been applied in 18 solids. The calculated data are found in very good agreement with the data available from other sources.     

A class of degenerate stochastic differential equations with non-Lipschitz coefficients

We obtain sufficient condition for SDEs to evolve in the positive orthant. We use arguments based on comparison theorems for SDEs to achieve this. As an application we prove the existence of a unique strong solution for a class of multidimensional degenerate SDEs with non-Lipschitz diffusion coefficients.     

Presence of Jahn-Teller distortions in a novel six-coordinate Ag(II) complex: temperature dependent EPR,optical and magnetic susceptibility measurements

Single-crystal variable temperature EPR, optical and polycrystalline magnetic susceptibility studies have been made on a novel six-coordinate Ag(II) complex. Temperature dependent EPR studies on pure single crystals of this compound reveal that dynamic Jahn-Teller distortion operates above 230 K, between 230 K and 120K static Jahn-Teller distortion sets in and below 110 K there is evidence of exchange interaction. Crystal g values were obtained by least-squares fitting with the data obtained from the orientation dependent EPR spectra of the undiluted single crystal of this complex at 300 K and 77 K. From an optical study the Jahn-Teller stabilization energy is found to be ～2250cm^?1. Comparison of Abs_max values for other silver(II) compounds enables us to conclude that the formal geometry of this complex is a tetragonally distorted octahedral. Infrared spectra of this complex were also recorded over a wide range of temperature. Magnetic susceptibility measurements over a wide range of temperature on the powder sample of this compound reveal that the complex is antiferromagnetically coupled in the temperature range 5–40 K with 2J = 0.906cm^?1, and above 40K it is ferromagnetically coupled with 2J = +7.4cm^?1. The effective magnetic moment (μ_eff) of this complex has been compared with that of a series of other silver(II) complexes available in the literature. Finally, the spectral and magnetic data of this complex have been compared with those of a corresponding isostructural and isomorphous copper(II) complex.