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.

Generalised vortex motion of compressible fluid with and without magnetic field and suction

The laminar boundary layer over a stationary infinite disk induced by a rotating compressible fluid is considered. The free stream velocity has been taken as tangential and varies as a power of radius, i.e. v∞ ˜ r−n. The effect of the axial magnetic field and suction is also included in the analysis. An implicit finite difference scheme is employed to the governing similarity equations for numerical computations. Solutions are studied for various values of disk to fluid temperature ratio and for values of n between 1 and −1. In the absence of the magnetic field and suction, velocity profiles exhibit oscillations. It has been observed that for a hot disk in the presence of a magnetic field the boundary layer solutions decay algebraically instead of decaying exponentially. In the absence of the magnetic field and suction, the solution of the similarity equations exists only for a certain range of n.

Can biological motion be a biometric?

Biological motion has successfully been used for analysis of a person's mood and other psychological traits. Efforts are made to use human gait as a non-invasive mode of biometric. In this reported work, we try to study the effectiveness of biological gait motion of people as a cue to biometric based person recognition. The data is 3D in nature and, hence, has more information with itself than the cues obtained from video-based gait patterns. The high accuracies of person recognition using a simple linear model of data representation and simple neighborhood based classfiers, suggest that it is the nature of the data which is more important than the recognition scheme employed.

Apsidal motion in 4U 0115+63 and orbital parameters of 2S 1417-624 and V0332+53

Be/X-ray binary pulsars have wide eccentric orbits and hence the angle of periastron of the orbit is very well defined in these sources. The presence of an X-ray pulsar allows for accurate measurements of orbital elements. A Be star usually is a rapidly rotating star and hence will deviate from spherical geometry. The tidal interaction between the neutron star and the Be star will add to the distortion of the Be star and alter its mass distribution. Thus a measurable rate of apsidal motion is expected from these systems. In this paper, we present the first conclusive detection of apsidal motion of the binary 4U 0115+63. We also present new and accurate orbital parameters of the Be/X-ray binaries V0332+53 and 2S 1417-624.

Change in spectrum of Brownian fluctuations of optically trapped red blood cells due to malarial infection

We study the properties of single red blood cells (RBCs) held in an optical-tweezers trap. We observe a change in the spectrum of Brownian fluctuations between RBCs from normal and malaria-infected samples. The change, caused by infection-induced structural changes in the cell, appears as a statistical increase in the mean (by 25%) and standard deviation (by 200%) of the corner frequency measured over similar to 100 cells. The increase is observed even though the ensemble of cells being measured consists mostly of cells that do not actually host the parasite, but are from an infected pool. This bystander effect appears to vindicate other observations that infected cells can affect the biomechanical properties of uninfected cells. The change is also observed to be independent of the stage of infection and its duration, highlighting its potential for disease detection. (C) 2010 Society of Photo-Optical Instrumentation Engineers. [DOI: 10.1117/1.3427142].

Chlorine-35 nuclear quadrupole resonance study of molecular torsional motion in some chloropyridine-N-oxides and chloroquinoline-N-oxides

Chlorine has been substituted at the 2- and 4-positions in the pyridine and quinoline rings of the corresponding N-oxides and 35Cl n.q.r. spectra have been studied in the temperature range 77–300 K. The change in the n.q.r. frequencies in N-oxides as compared to their parent compounds are interpreted in terms of the conjugative effect and the inductive effect of the N+—O– group. The negative temperature coefficients of the resonance frequencies in chloropyridine-N-oxides have been analysed using the Bayer, Kushida and Brown equations. The calculated torsional frequencies, which are in the range 52–78 cm–1, are found to be only slightly temperature dependent.

Fractional quantum Hall edge: Effect of nonlinear dispersion and edge roton

According to Wen's theory, a universal behavior of the fractional quantum Hall edge is expected at sufficiently low energies, where the dispersion of the elementary edge excitation is linear. A microscopic calculation shows that the actual dispersion is indeed linear at low energies, but deviates from linearity beyond certain energy, and also exhibits an "edge roton minimum." We determine the edge exponent from a microscopic approach, and find that the nonlinearity of the dispersion makes a surprisingly small correction to the edge exponent even at energies higher than the roton energy. We explain this insensitivity as arising from the fact that the energy at maximum spectral weight continues to show an almost linear behavior up to fairly high energies. We also study, in an effective-field theory, how interactions modify the exponent for a reconstructed edge with multiple edge modes. Relevance to experiment is discussed.

Fractional-factorial design of a porous-carbon fuel-cell electrode

The use of fractional-factorial methods in the optimization of porous-carbon electrode structure is discussed with respect to weight-loss of carbon during gas treatment, weight and mixing time of binder, compaction temperature, time and pressure, and pressure of feed gas. The experimental optimization of an air electrode in alkaline solution is described.

The nature of dislocation motion in quasicrystals

Calculations in a hydrodynamic model of quasicrystal dynamics show that dislocation motion in these systems is impeded by a drag far greater than that in crystals.

Exact path-integral evaluation of the heat distribution function of a trapped Brownian oscillator

Using path integrals, we derive an exact expression-valid at all times t-for the distribution P(Q,t) of the heat fluctuations Q of a Brownian particle trapped in a stationary harmonic well. We find that P(Q, t) can be expressed in terms of a modified Bessel function of zeroth order that in the limit t > infinity exactly recovers the heat distribution function obtained recently by Imparato et al. Phys. Rev. E 76, 050101(R) (2007)] from the approximate solution to a Fokker-Planck equation. This long-time result is in very good agreement with experimental measurements carried out by the same group on the heat effects produced by single micron-sized polystyrene beads in a stationary optical trap. An earlier exact calculation of the heat distribution function of a trapped particle moving at a constant speed v was carried out by van Zon and Cohen Phys. Rev. E 69, 056121 (2004)]; however, this calculation does not provide an expression for P(Q, t) itself, but only its Fourier transform (which cannot be analytically inverted), nor can it be used to obtain P(Q, t) for the case v=0.

Exact solution for the unsteady motion of a viscous-fluid in a porous annulus

An exact solution to the problem of time-dependent motion of a viscous fluid in an annulus with porous walls is obtained under the assumption that the rate of suction at one wall is equal to the rate of injection at the other. Finite Hankel transform is used to obtain a closed-form solution for the axial velocity. The average axial velocity profiles are depicted graphically.

Segal-Bargmann Transform and Paley-Wiener Theorems on Motion Groups

We study the Segal-Bargmann transform on a motion group R-n v K, where K is a compact subgroup of SO(n) A characterization of the Poisson integrals associated to the Laplacian on R-n x K is given We also establish a Paley-Wiener type theorem using complexified representations

Incipient motion design of sand bed channels affected by bed suction

Seepage through sand bed channels in a downward direction (suction) reduces the stability of particles and initiates the sand movement. Incipient motion of sand bed channel with seepage cannot be designed by using the conventional approach. Metamodeling techniques, which employ a non-linear pattern analysis between input and output parameters and solely based on the experimental observations, can be used to model such phenomena. Traditional approach to find non-dimensional parameters has not been used in the present work. Parameters, which can influence the incipient motion with seepage, have been identified and non-dimensionalized in the present work. Non-dimensional stream power concept has been used to describe the process. By using these non-dimensional parameters; present work describes a radial basis function (RBF) metamodel for prediction of incipient motion condition affected by seepage. The coefficient of determination, R-2 of the model is 0.99. Thus, it can be said that model predicts the phenomena very well. With the help of the metamodel, design curves have been presented for designing the sand bed channel when it is affected by seepage. (C) 2010 Elsevier B.V. All rights reserved.

On duality in linear fractional programming

In this paper, a dual of a given linear fractional program is defined and the weak, direct and converse duality theorems are proved. Both the primal and the dual are linear fractional programs. This duality theory leads to necessary and sufficient conditions for the optimality of a given feasible solution. A unmerical example is presented to illustrate the theory in this connection. The equivalence of Charnes and Cooper dual and Dinkelbach’s parametric dual of a linear fractional program is also established.