Uniqueness and set sharing of derivatives of meromorphic functions

We prove some uniqueness theorems concerning the derivatives of meromorphic functions when they share two or three sets which will improve some existing results.     

Diastereoselective scalable synthesis of 2,6-trans-Piperidines using an aza-Michael reaction

Highly efficient substrate and reagent controlled stereoselective synthesis of 2,6-trans-piperidine derivative (1) using an aza-Michael reaction is reported. This method was utilized to synthesize a variety of trans-piperidines on hundred-gram scales.     

Fluorescence Resonance Energy Transfer between organic dyes adsorbed onto nano-clay and Langmuir–Blodgett (LB) films

In this communication we investigate two dyes N,N′-dioctadecyl thiacyanine perchlorate (NK) and octadecyl rhodamine B chloride (RhB) in Langmuir and Langmuir–Blodgett (LB) films with or with out a synthetic clay laponite. Observed changes in isotherms of RhB in absence and presence of nano-clay platelets indicate the incorporation of clay platelets onto RhB-clay hybrid films. AFM images confirm the incorporation of clay into hybrid films. FRET is observed in clay dispersion and LB films with and without clay. Efficiency of energy transfer is maximum in LB films with clay.     

Vibrational spectrum of CF<Subscript>4</Subscript> isotopes in an algebraic model

In this paper the stretching vibrational modes of CF₄ isotopes are calculated up to first overtone using the one-dimensional vibron model for the first time. The model Hamiltonian so constructed seems to describe the C-F stretching modes accurately using a relatively small set of well-defined parameters.     

Evidence of phase transition in the break up of Kr-projectile nuclei at 0.95A GeV

Projectile fragmentation mechanism and the possible liquid gas phase transition have been studied by extracting the critical exponents using cluster approximation technique. A ‘toy model’, schematically accounting for pre-equilibrium, has been developed and various moments as well as conditional moments have been evaluated with the data obtained from the toy model to see the effect of mass conservation constraint. An exponent δ, related to third order moment, has been evaluated to obtain a set of values of γ, β and τ that follow the corresponding scaling relation. The values of γ, β and τ so obtained are found to be 1.34±0.19, 0.54±0.15 and 2.31±0.06 respectively.     

Electrical properties of thin films of Eu2O3 substituted compounds

Europium oxide (Eu₂O₃) substituted compound has been prepared by solid-solid reaction of the powders of Eu₂O₃, BaCO₃ and CuO at 950°C for 16 hours. The thin films have been deposited by high vacuum evaporation technique (vacuum ≈ 10⁻⁶ torr). The variation of current (I) with voltage (V) at room temperature (RT) i.e. 294 K and in ice (273 K) are found to be linear. The variation of electrical resistivity (ρ) with temperature (T) by heating the sample above RT has been determined. Resistivity is found to decrease with increase in temperature. Further the variation of electrical resistivity (ρ) with temperature (T) from 77 K, liquid nitrogen temperature (LNT), to 270 K has also been determined. It is observed that resistivity suddenly becomes zero at around 87 K. Thus the prepared material has superconducting properties with superconducting transition temperature, T _c at 87 K.      

A comparative study of the vibrational spectra of OCS and HCP using the Lie algebraic method

Using the Lie algebraic method the vibrational energy levels of OCS and HCP are calculated for 58 vibrational bands each using the local Hamiltonian. A comparative study is made between the two.     

Atomistic spin dynamic method with both damping and moment of inertia effects included from first principles

We consider spin dynamics for implementation in an atomistic framework and we address the feasibility of capturing processes in the femtosecond regime by inclusion of moment of inertia. In the spirit of an s-d-like interaction between the magnetization and electron spin, we derive a generalized equation of motion for the magnetization dynamics in the semiclassical limit, which is nonlocal in both space and time. Using this result we retain a generalized Landau-Lifshitz-Gilbert equation, also including the moment of inertia, and demonstrate how the exchange interaction, damping, and moment of inertia, all can be calculated from first principles.     

Competing order parameters and a tricritical point with a difference

We propose a mean-field, phenomenological Ginzburg–Landau free energy functional with two competing order parameters for a two-component, spin-polarized Fermi gas. This free energy supports a tricritical point which is different from the conventional one and this change offers a correct understanding of the experimental phase diagram of imbalanced Fermi systems (Shin et al. (2008) [17]). The specific heat also happens to be different than in standard theory.