Approximation of solutions to fractional integral equation

In this paper we shall study a fractional integral equation in an arbitrary Banach space X. We used the analytic semigroups theory of linear operators and the fixed point method to establish the existence and uniqueness of solutions of the given problem. We also prove the existence of global solution. The existence and convergence of the Faedo–Galerkin solution to the given problem is also proved in a separable Hilbert space with some additional assumptions on the operator A. Finally we give an example to illustrate the applications of the abstract results.

Asymtotic solution of the Frieman and Book equation for the pair-correlation function

Using Thomé's procedure, the asymptotic solutions of the Frieman and Book equation for the two-particle correlation in a plasma have been obtained in a complete form. The solution is interpreted in terms of the Lorentz distance. The exact expressions for the internal energy and pressure are evaluated and they are found to be a generalization of the result obtained earlier by others.

Computationally efficient optical tomographic reconstructions through waveletizing the normalized quadratic perturbation equation - art. no.61640R

In this paper, we present a wavelet - based approach to solve the non-linear perturbation equation encountered in optical tomography. A particularly suitable data gathering geometry is used to gather a data set consisting of differential changes in intensity owing to the presence of the inhomogeneous regions. With this scheme, the unknown image, the data, as well as the weight matrix are all represented by wavelet expansions, thus yielding the representation of the original non - linear perturbation equation in the wavelet domain. The advantage in use of the non-linear perturbation equation is that there is no need to recompute the derivatives during the entire reconstruction process. Once the derivatives are computed, they are transformed into the wavelet domain. The purpose of going to the wavelet domain, is that, it has an inherent localization and de-noising property. The use of approximation coefficients, without the detail coefficients, is ideally suited for diffuse optical tomographic reconstructions, as the diffusion equation removes most of the high frequency information and the reconstruction appears low-pass filtered. We demonstrate through numerical simulations, that through solving merely the approximation coefficients one can reconstruct an image which has the same information content as the reconstruction from a non-waveletized procedure. In addition we demonstrate a better noise tolerance and much reduced computation time for reconstructions from this approach.

Temperature- and pressure-dependent study of Cl-35 NQR frequency and spin lattice relaxation time in 2,3-dichloroanisole

The temperature and pressure dependence of Cl-35 NQR frequency and spin lattice relaxation time (T-1) were investigated in 2,3-dichloroanisole. Two NQR signals were observed throughout the temperature and pressure range studied. T-1 were measured in the temperature range from 77 to 300 K and from atmospheric pressure to 5 kbar. Relaxation was found to be due to the torsional motion of the molecule and also reorientation f motion of the CH3 group. T-1 versus temperature data were analyzed on the basis of Woessner and Gutowsky model, and the activation energy for the reorientation of the CH3 group was estimated. The temperature dependence of the average torsional lifetimes of the molecules and the transition probabilities were also obtained. NQR frequency shows a nonlinear behavior with pressure, indicating both dynamic and static effects of pressure. The pressure coefficients were observed to be positive for both the lines. A thermodynamic analysis of the data was carried out to determine the constant volume temperature coefficients of the NQR frequency. The variation of spin lattice time with pressure was very small, showing that the relaxation is mainly due to the torsional motions of the molecules. Copyright (C) 2010 John Wiley & Sons, Ltd.

Critical micelle concentration from a lattice gas model

The temperature dependence of the critical micelle concentration (CMC) and a closed-loop coexistence curve are obtained, via Monte Carlo simulations, in the water surfactant limit of a two-dimensional version of a statistical mechanical model for micro-emulsions, The CMC and the coexistence curve reproduce various experimental trends as functions of the couplings. In the oil-surfactant limit, there is a conventional coexistence cure with an upper consolute point that allows for a region of three-phase coexistence between oil-rich, water-rich and microemulsion phases.

Determination of distances of sugar protons from Mn2+ in concanavalin A

1H NMR spin-lattice relaxation time (T1) measurements have been carried out with various sugars, viz. methyl alpha-D-glucopyranoside (alpha-MeGluP), methyl beta-D-lucopyranoside (beta-MeGluP), methyl alpha--annopyranoside (alpha-MeManP), maltose (4-O-alpha-D-glucopyranosyl--glucose), nigerose (3-O-alpha-D-glucopyranosyl-D-glucose), p-nitrophenyl alpha-maltoside (PNP-alpha-maltoside) and p-nitrophenyl beta-maltoside (PNP-beta-maltoside) to determine the distances of sugar protons from Mn2+ in concanavalin A (Con A). With a rotational correlation time of 1.58 x 10(-10) s determined, distances were calculated using Solomon-Bloembergen equation. The data obtained indicated differences in disposition of different groups in the binding site of Con A. An average value of about 10 A was obtained for the distances of sugar protons from Mn2+ in Con A. In the case of mono and disaccharides, the non-reducing end sugar unit was found to be closer to Mn2+ than the reducing end one.

A simple technique for approximate solutions of the Falkner-Skan equation

A simple, sufficiently accurate and efficient method for approximate solutions of the Falkner-Skan equation is proposed here for a wide range of the pressure gradient parameter. The proposed approximate solutions are obtained utilising a known solution of another differential equation.

Correlations and the Ring-Kinetic Equation in Dense Sheared Granular Flows

A formal way of deriving fluctuation-correlation relations in dense sheared granular media, starting with the Enskog approximation for the collision integral in the Chapman-Enskog theory, is discussed. The correlation correction to the viscosity is obtained using the ring-kinetic equation, in terms of the correlations in the hydrodynamic modes of the linearised Enskog equation. It is shown that the Green-Kubo formula for the shear viscosity emerges from the two-body correlation function obtained from the ring-kinetic equation.

Nature of hydrogen atom trapped inside palladium lattice

Colloid of palladium nanoparticles has been prepared by the Solvated Metal Atom Dispersion (SMAD) method. Reaction of Pd(0) nanopowder obtained upon precipitation from the colloid, with ammonia borane (H3N center dot BH3, AB) in aqueous solutions at room temperature results in the generation of active hydrogen atoms. The active hydrogen atoms either combine with one another resulting in H-2 evolution or diffuse into the Pd lattice to afford PdHx. Diffusion of hydrogen atoms leads to an expansion of the Pd lattice. The diffused hydrogen atoms are distributed uniformly over the entire particle. These features were established using powder XRD and electron microscopy studies. The H-1 NMR spectral studies of PdHx before and after desorption of H-2 revealed that the hydrogen atoms trapped inside Pd lattice are hydridic in nature. Desorption of hydrogen from PdHx did not result in complete reversibility suggesting that some hydrogen atoms are strongly trapped inside the Pd lattice. (C) 2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.

Influence of lattice distortion on the Curie temperature and spin-phonon coupling in LaMn0.5Co0.5O3

Two distinct ferromagnetic phases of LaMn0.5Co0.5O3 having monoclinic structure with distinct physical properties have been studied. The ferromagnetic ordering temperature T-c is found to be different for both the phases. The origin of such contrasting characteristics is assigned to the changes in the distance(s) and angle(s) between Mn-O-Co resulting from distortions observed from neutron diffraction studies. Investigations on the temperature dependent Raman spectroscopy provide evidence for such structural characteristics, which affects the exchange interaction. The difference in B-site ordering which is evident from the neutron diffraction is also responsible for the difference in T-c. Raman scattering suggests the presence of spin-phonon coupling for both the phases around the T-c. Electrical transport properties of both the phases have been investigated based on the lattice distortion.

Generalized Equation for Compression Ratio

For highly compressible normally consolidated saturated soil the compression index, Cc, is not constant over the entire pressure range. However, the ratio of the compression index and the initial specific volume, generally known as the compression ratio, appears to be constant. Thus settlement seems to depend on Cc/(1 + e) rather than Cc alone. Using the theoretical zero air voids line and the generalized compressibility equation for normally consolidated saturated soils, a generalized and simple equation for compression has been derived in the form: C'c = 0.003wL.

The physical properties of SnS films grown on lattice-matched and amorphous substrates

The development of high-quality tin monosulphide (SnS) layers is one of the crucial tasks in the fabrication of efficient SnS-based optoelectronic devices. Reduction of strain between film and the substrate by using an appropriate lattice-matched (LM) substrate is a new attempt for the growth of high-quality layers. In this view, the SnS films were deposited on LM Al substrate using the thermal evaporation technique with a low rate of evaporation. The as-grown SnS films were characterized using appropriate techniques and the obtained results are discussed by comparing them with the properties of SnS films grown on amorphous substrate under the same conditions. From structural analysis of the films, it is noticed that the SnS films deposited on amorphous substrate have crystallites that were oriented along different directions. However, the SnS crystallites grown on Al substrate exhibited epitaxial growth along the 101] direction. Photoluminescence (PL) and Raman studies reveal that the films grown on Al substrate have better optical properties than those of the films grown on amorphous substrates. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

The Alfvén Wave Equation for Magnetospheric Plasmas

It is shown that besides the continuous spectrum which damps away as inverse power of time, the coupled Alfvén wave equation, which gives coupling between a shear Alfvén wave and a surface wave, can also admit a well behaved harmonic solution in the closed form for a set of initial conditions. This solution, though valid for finite time intervals, points out that the Alfvén surface waves can have a band of frequency (instead of a monochromatic frequency for a nonsheared magnetic field) within which the local field line resonance frequency can lie, and thus can excite magnetic pulsations with latitude-dependent frequency. By considering magnetic fields not only varying in magnitude but also in direction, it is shown that the time interval for the validity of the harmonic solution depend upon the angle between the magnetic field directions on either side of the magnetopause. For small values of the angle the time interval can become appreciably large.

Probability Distribution of the Eigenvalues of the Random String Equation

The probability distribution of the eigenvalues of a second-order stochastic boundary value problem is considered. The solution is characterized in terms of the zeros of an associated initial value problem. It is further shown that the probability distribution is related to the solution of a first-order nonlinear stochastic differential equation. Solutions of this equation based on the theory of Markov processes and also on the closure approximation are presented. A string with stochastic mass distribution is considered as an example for numerical work. The theoretical probability distribution functions are compared with digital simulation results. The comparison is found to be reasonably good.