Characterization of polynomials and divided difference

For distinct points x₁,x₂,…,x_n in ℛ (the reals), letϕ[x₁, x₂,…,x_n] denote the divided difference ofϕ. In this paper, we determine the general solutionϕ,g: ℛ → ℛ of the functional equationϕ[x₁,x₂,…,x_n] =g(x₁,+ x₂ + … + x_n) for distinct x₁,x₂,…, x_n in ℛ without any regularity assumptions on the unknown functions.     

Modified complex method for constrained design and optimization of optical multilayer thin-film devices

A new computer design program based on the modified-complex method has been developed for constrained optimization and refinement of optical thin-film multilayer devices. This program is having a provision to include both limiting constraints as well as constraint equations. Constraints are suitably accommodated to generate designs which are practicable and withstand high laser power. Various rapid convergent processes like dynamic contraction and expansion of feasible vertices are incorporated for efficient scanning of the constraint parametric space. A broad band IR antireflection coating has been designed to test its relative efficiency with respect to other available methods. A wide varieties of highly useful multilayer devices have been successfully developed using this method.     

Temperature effects on the structure of liquid D-methanol through neutron diffraction

The study of changes in the structure (H-bonded) of liquid alcohols at elevated temperatures is rare probably due to low flash points of these liquids. An indigenously devised special quartz cell is now used to carry out the structural studies of these liquids at elevated temperatures through neutron diffraction. Here, the liquid consists of deuterated methanol and neutron data was collected on the high-Q diffractometer at Dhruva, BARC. The corrected data at elevated temperatures (BP (boiling point) and double the BP) show that there is a large change in the H-bonded structure of this liquid. The pre-peak or hump, known to be signature of H-bonded clusters appears to be present at all the three temperatures studied. In the low-Q (scattering vector) data Ornstein Zernike (OZ) behaviour is also observed. It is, however, seen that the intramolecular structure does not change very much at higher temperatures. A detailed model analysis is in progress and would be reported later.     

Atomic Vibrational Dynamics of Thin Films Studied by Nuclear Resonant Inelastic X-Ray Scattering: Amorphous Tb1−x Fe x Alloys

Hyperfine Interactions - Nuclear resonant inelastic X-ray scattering (NRIXS) of 14.4125 keV synchrotron radiation was used to measure directly the partial vibrational density of states (VDOS),...     

Many-body effects in hyperfine interactions in <Superscript>205</Superscript>Pb<Superscript>+</Superscript>

Ab initio calculations have been carried out to study the magnetic dipole and electric quadrupole hyperfine structure constants of ²⁰⁵Pb⁺. Many-body effects have been considered to all orders using the relativistic coupled-cluster theory in the singles, doubles and partial triples approximation. The trends of these effects are found to be different from atomic systems that have been studied earlier.     

Palladium(II)‐Catalyzed meta‐CH Olefination: Constructing Multisubstituted Arenes through Homo‐Diolefination and Sequential Hetero‐Diolefination

Divinylbenzene derivatives represent an important class of molecular building blocks in organic chemistry and materials science. Reported herein is the palladium‐catalyzed synthesis of divinylbenzenes by meta‐C? H olefination of sulfone‐based arenes. Successful sequential olefinations in a position‐selective manner provided a novel route for the synthesis of hetero‐dialkenylated products, which are difficult to access using conventional methods. Additionally, 1,3,5‐trialkenylated compounds can be generated upon successful removal of the directing group.     

Tetrazolo[1,5‐a]quinoline‐4‐carbaldehyde and its Schiff base on mild steel as corrosion inhibitor in 1 M HCl solution: electrochemistry,theoretical and SEM surface analysis

The corrosion inhibition impact of two quinoline derivatives, viz tetrazolo [1,5‐a] quinoline‐4‐carbaldehyde ( TQC ) and (Z) ?5‐methyl‐N‐(tetrazolo [1,5‐a] quinolin‐4‐ylmethylene) thiazol‐2‐amine ( MTQT ), has been examined against mild steel in 1 M HCl solution using conventional weight loss, potentiodynamic polarization, linear polarization, electrochemical impedance spectroscopy, quantum chemical, and scanning electron microscopic studies. The experimental results have showed that TQC and MTQT revealed a good corrosion inhibition and that the inhibition efficiency increases with the increase of concentration of inhibitor to attain 94.54% for TQC and 99.25% for MTQT at 25 ppm. Polarization measurements suggest that TQC and MTQT act as a mixed‐type inhibitor. A synergism between inhibitors can be observed by polarization measurements. Electrochemical impedance spectroscopy measurements show an increase of the transfer resistance with the inhibitor concentration. Adsorption of TQC and MTQT on the mild steel surfaces in 1 N HCl solution follows the Langmuir adsorption isotherm model. Furthermore, quantum chemical calculations have been conducted using B3LYP functional and 6‐31G(d,p) basis set to complement the experimental evidences. Copyright © 2015 John Wiley & Sons, Ltd.     

On the Lipschitz continuity of certain quasiregular mappings between smooth Jordan domains

We first investigate the Lipschitz continuity of (K,K’)-quasiregular C ² mappings between two Jordan domains with smooth boundaries, satisfying certain partial differential inequalities concerning Laplacian. Then two applications of the obtained result are given: As a direct consequence, we get the Lipschitz continuity of ρ-harmonic (K,K’)-quasiregular mappings, and as the other application, we study the Lipschitz continuity of (K,K’)- quasiconformal self-mappings of the unit disk, which are the solutions of the Poisson equation Δw = g. These results generalize and extend several recently obtained results by Kalaj, Mateljevi? and Pavlovi?.     

A new method for exact solutions of variant types of time‐fractional Korteweg‐de Vries equations in shallow water waves

The current article devoted on the new method for finding the exact solutions of some time‐fractional Korteweg–de Vries (KdV) type equations appearing in shallow water waves. We employ the new method here for time‐fractional equations viz. time‐fractional KdV‐Burgers and KdV‐mKdV equations for finding the exact solutions. We use here the fractional complex transform accompanied by properties of local fractional calculus for reduction of fractional partial differential equations to ordinary differential equations. The obtained results are demonstrated by graphs for the new solutions. Copyright © 2016 John Wiley & Sons, Ltd.