Energy levels of λx 2k anharmonic oscillators using the quantum normal form

The ground state and first few excited energy levels of the generalized anharmonic oscillator defined by the HamiltonianH=–d ²/dx ²+x ²+x ^2k (k=3, 4,...) have been calculated by employing the method of quantum normal form, which is the quantum mechanical analogue of the classical Birkhoff-Gustavson normal form. The present energy eigenvalues are consistent with other tabulations of the energy levels.     

Photodetachment dynamics from closed‐shell anions in the presence of a bichromatic field

I have studied the dynamics of photodetachment from closed‐shell anions in the presence of a two‐color (bichromatic) laser field. The electronic states of halide ions are modeled by a 1‐D Hamiltonian with a potential V(x) = ?V₀e. The two parameters V₀ and σ are fixed by requiring V(x) to reproduce the experimentally observed ground‐state ionization energy of the halide ions concerned. The potentials so generated are shown to support only one bound state in each case. The time‐dependent Fourier grid Hamiltonian method is used to follow the detachment dynamics with fairly high intensities of light. The environmental effects on the dynamics are sought to be modeled by allowing the well depth (V₀) to fluctuate randomly (V₀(t) = V₀[1 + ΔVR(t)]; R(t) randomly fluctuates between +1 and ?1 with time, when ΔV is fixed). The average detachment rate constants k_av are seen to increase with increase in the intensities of used bichromatic field. An alternative model potential, V(x) = ?V₀e^?σx, is also shown to yield similar results. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Oxidation reactions in triterpenes under chemical ionization conditions

From a collisional activation spectral study it has been found that certain triterpene alcohols with an ursane or oleanane skeleton undergo oxidation to the corresponding ketones under chemical ionization (NH₃) conditions giving rise to abundant [M + NH₄ ? 2]⁺ ions. Mass-analysed ion kinetic energy and B²/E scan results indicate that both [M + NH₄]⁺ and [M + N₂H₇ ? 2]⁺ ions contribute to the formation of the [M + NH₄ ? 2]⁺ ion.     

Ultra fast magic angle spinning solid – state NMR spectroscopy of intact bone

Ultra fast magic angle spinning (MAS) has been a potent method to significantly average out homogeneous/inhomogeneous line broadening in solid‐state nuclear magnetic resonance (ssNMR) spectroscopy. It has given a new direction to ssNMR spectroscopy with its different applications. We present here the first and foremost application of ultra fast MAS (~60 kHz) for ssNMR spectroscopy of intact bone. This methodology helps to comprehend and elucidate the organic content in the intact bone matrix with resolution and sensitivity enhancement. At this MAS speed, amino protons from organic part of intact bone start to appear in ¹H NMR spectra. The experimental protocol of ultra‐high speed MAS for intact bone has been entailed with an additional insight achieved at 60 kHz. Copyright © 2015 John Wiley & Sons, Ltd.     

Biogenic synthesis of Fe2O3@SiO2 nanoparticles for ipso-hydroxylation of boronic acid in water

Here, biogenic synthesis of Fe₂O₃@SiO₂ nanoparticles using fruit extract of Zanthoxylum rhetsa is reported. The SiO₂ nanoparticles was synthesized using paddy straw which is a byproduct obtained in cultivation of rice. The composite was characterised by spectroscopic method like XRD, SEM, TEM and EDX analysis. The ipso-hydroxylation reactions were carried out with excellent yield within a moderate time period with mild reaction condition in all cases. Therefore, this approach may be considered as simple, easy, cheap and greener, environment friendly protocol for ipso-hydroxylation of arylboronic acids at 50 °C temperature.     

Study of a fractional-order model of chronic wasting disease

This paper studies a fractional-order modelling chronic wasting disease (CWD). The basic results on existence, uniqueness, non-negativity, and boundedness of the solutions are investigated for the considered model. The criterion for local as well as global stability of the equilibrium points is derived. A numerical analysis for Hopf-type bifurcation is presented. Finally, numerical simulations are provided to justify the results obtained.     

Azido derivatives of dinuclear copper(II) and 1D polynuclear nickel(II) complexes containing an unsymmetrical bidentate amine: synthesis,crystalline architecture,and magnetic behavior

Transition Metal Chemistry - Dinuclear copper(II) complex [Cu2(L)2(μ2-1,1-N3)2(N3)2] (1) with double μ1,1-azido bridges and polynuclear nickel(II) complex...     

Existence of Extremizers for a Model Convolution Operator

The operator T, defined by convolution with the affine arc length measure on the moment curve parametrized by \(h(t)=(t,t^{2},\ldots ,t^{d})\) is a bounded operator from \(L^{p}\) to \(L^{q}\) if \((\frac{1}{p}, \frac{1}{q})\) lies on a line segment. In this article we prove that at non-end points there exist functions which extremize the associated inequality and any extremizing sequence is pre compact modulo the action of the symmetry of T. We also establish a relation between extremizers for T at the end points and the extremizers of an X-ray transform restricted to directions along the moment curve. Our proof is based on the ideas of Michael Christ on convolution with the surface measure on the paraboloid.