On the Parametric Cubic Spline Approach for Solving Second Order Boundary Value Problems

In this article some comments on the paper “parametric cubic spline approach to the solution of a system of second order boundary value problems” in (Khan and Aziz, J. Optim. Theory Appl. 118:45–54, 2003) are given. This paper concerns with a numerical method for solving a second order boundary value problem associated with obstacle, unilateral and contact problems. Corrections are given for the convergence analysis of the numerical method and the computational experiments.     

Coulomb blockade anisotropic magnetoresistance effect in a (Ga,Mn)As single-electron transistor

We observe low-field hysteretic magnetoresistance in a (Ga,Mn)As single-electron transistor which can exceed 3 orders of magnitude. The sign and size of the magnetoresistance signal are controlled by the gate voltage. Experimental data are interpreted in terms of electrochemical shifts associated with magnetization rotations. This Coulomb blockade anisotropic magnetoresistance is distinct from previously observed anisotropic magnetoresistance effects as it occurs when the anisotropy in a band structure derived parameter is comparable to an independent scale, the single-electron charging energy. Effective kinetic-exchange model calculations in (Ga,Mn)As show chemical potential anisotropies consistent with experiment and ab initio calculations in transition metal systems suggest that this generic effect persists to high temperatures in metal ferromagnets with strong spin-orbit coupling.     

Projection iterative methods for extended general variational inequalities

In this paper, we introduce and study a new class of variational inequalities involving three operators, which is called the extended general variational inequality. Using the projection technique, we show that the extended general variational inequalities are equivalent to the fixed point and the extended general Wiener-Hopf equations. This equivalent formulation is used to suggest and analyze a number of projection iterative methods for solving the extended general variational inequalities. We also consider the convergence of these new methods under some suitable conditions. Since the extended general variational inequalities include general variational inequalities and related optimization problems as special cases, results proved in this paper continue to hold for these problems.     

Falkner-Skan equation for flow past a stretching surface with suction or blowing: Analytical solutions

The simultaneous effects of suction and injection on tangential movement of a nonlinear power-law stretching surface governed by laminar boundary layer flow of a viscous and incompressible fluid beneath a non-uniform free with stream pressure gradient is considered. The self-similar flow is governed by Falkner-Skan equation, with transpiration parameter γ, wall slip velocity λ and stretching sheet (or pressure gradient) parameter β. The exact solution for β = −1 and three closed form asymptotic solutions for β large, large suction γ, and λ → 1 have also been presented. Dual solutions are found for β = −1 for each value of the transpiration parameter, including the non-permeable surface, for each prescribed value of the wall slip velocity λ. The large β asymptotic solution also dual with respect to wall slip velocity λ, but do not depend on suction and blowing. The critical values of γ, β and λ are obtained and their significance on the skin friction and velocity profiles is discussed. An approximate solution by integral method for a trial velocity profile is presented and results are compared with the exact solutions.     

Simplified SCF calculations on the diatomic alkali metal molecules

An account is given of a new formalism for calculating energy levels in molecules using techniques that derive from the band theory of metals. After showing how the molecular potential may be transformed into a cellular potential we define the basis set of muffin-tin orbitals and discuss some of their properties. The relationship between the scattered wave formulation of Johnson, which is restricted to muffin-tin potentials, and our more general approach based on the use of a linear combination of muffin-tin orbitals (L.C.M.T.O.) is explicitly indicated. We then show how the properties of the muffin-tin orbitals, together with the technique of cellular integration, give rise to a hamiltonian matrix. This matrix is as general as, but simpler than that obtained by the use of atomic orbitals, and it is linear in energy and therefore computationally faster than the secular matrix of the scattered wave method.     

Spectral,electron microscopic and chemical investigations of gamma-induced purple color zonings in amethyst crystals from the Dursunbey-Balıkesir region of Turkey

Amethyst crystals on matrix specimens from the Dursunbey-Bal?kesir region in Turkey have five representative purple color zonings: dark purple, light purple, lilac, orchid, and violet. The purple color zonings have been analyzed with optical absorption spectra in the visible wavelength region, chemical full trace element analyses (inductively coupled plasma-atomic emission spectroscopy and inductively coupled plasma-mass spectroscopy), and scanning electron microscopic images with high magnification. It can be proposed that the production of the purple color in amethyst crystals is due to three dominant absorption bands centered at 375, 530, and 675 nm, respectively. In addition, the purple color zonings are also due to four minor absorption bands centered at 435, 480, 620, and 760 nm. X-ray diffraction graphics of the investigated amethyst crystals indicate that these crystals are composed of a nearly pure alpha-quartz phase and do not include any moganite silica phase and/or other mineral implications. Trace element analyses of the amethyst crystals show five representative purple color zonings, suggesting that the absorption bands can be mainly attributed to extrinsic defects (chemical impurities). However, another important factor that influences all structural defects in amethyst is likely to be the gamma irradiation that exists during amethyst crystallization and its inclusion in host materials. This gamma irradiation originates from the large underlying intrusive granitoid body in the region of amethyst formation. Irradiation modifies the valence values of the impurity elements in the amethyst crystals. It is observed that the violet-colored amethyst crystals have the most stable and the least reversible coloration when exposed to strong light sources. This situation can be related to the higher impurity content of Fe (2.50 ppm), Co (3.1 ppm), Ni (38 ppm), Cu (17.9 ppm), Zn (10 ppm), Zr (3.9 ppm), and Mo (21.8 ppm).     

Free convection effects on the oscillatory flow past a vertical porous plate in the presence of radiation for an optically thin fluid

The purpose of this work is to study the effect of transverse sinusoidal suction velocity on the flow and mass transfer on free convective oscillatory viscous and optically thin grey fluid over a porous vertical plate in the presence of radiation. The flow becomes three-dimensional due to the variation of suction velocity in the transverse direction. Analytical expressions for velocity and temperature fields are obtained using the perturbation technique. The governing equations has been transformed to ordinary differential equations. Numerical solutions are obtained for different values of radiation parameter, Grashof number and Schmidt number. It is found that non-dimensional velocity decreases with increase of radiation parameter, increases with increase of Grashof number, decreases with increase of Schmidt number and non-dimensional temperature decreases with the increase of radiation parameter.     

An efficient and highly diastereoselective synthesis of carbocyclic spiropyrazolones via one-pot sequential dual organo-silver catalyzed Michael-hydroalkylation reactions

An economical approach for the diastereoselective synthesis of highly functionalized carbocyclic spiropyrazolone derivatives having one quaternary and two tertiary stereocenters along with one exocyclic double bond exploiting dual organo-silver sequential catalysis has been developed. The unified method to both cyclohexyl and cyclopentyl spirocompounds involves the reaction of γ- and β-nitroalkynes with alkylidene pyrazolones catalyzed by Hünig’s base followed by carbophilic activation of the triple bond with a Ag(I) salt leading to cyclization via hydroalkylation.     

Energy limits imposed by two-photon absorption for pulse amplification in high-power semiconductor optical amplifiers

We study the combined effects of dynamic gain saturation and two-photon absorption on the amplification of short pulses in semiconductor optical amplifiers and show that two-photon absorption can saturate the amplifier gain and limit the output pulse energies even for amplifiers with large gain saturation energies. We discuss the upper limits for the pulse energies obtainable from semiconductor optical amplifiers in the presence of two-photon absorption and show that for single transverse mode waveguide amplifiers these upper limits can range from values as small as a few picojoules to several hundred picojoules for pulse widths in the 0.5 ps to 20 ps range, respectively.     

Total Fragmentation Cross Section of 158A GeV Lead Projectiles in Cu Target

Total fragmentation cross section for the reaction 158A Pb ions ＋ Cu target is measured using the most sensitive track detector CR-39. Measured values are compared with calculations. Exposures of target-detector stack with 158A P5 projectiles are made at CERN-SPS beam facility. Results of calibration of CR-39 detector in a charge region （63 ≤ Z ≤ 83） are also reported, which can be used for high energy particle identification using CR-39 and in determination of partial charge changing cross sections. The charge resolution δz achieved by this technique is about 0.2e. A systematic dependence of total fragmentation cross section on target properties is revealed and the corresponding results are presented.