Analogues of the Wiener-Tauberian and Schwartz theorems for radial functions on symmetric spaces

We prove a Wiener Tauberian theorem for the L-1 spherical functions on a semisimple Lie group of arbitrary real rank. We also establish a Schwartz-type theorem for complex groups. As a corollary we obtain a Wiener Tauberian type result for compactly supported distributions.

Generalized State Parameter for Partly Saturated Soils

Studies on compressibility and shear strength aspects are the concern of many investigators concerned with partly saturated soils. In soil engineering connected with partly saturated soils, there are no approaches connecting soil states and stress conditions. The present investigation is essentially a step in this direction. A generalized state parameter, identified with regard to material states is shown to be related to the compressibility and shear strength. The involved parameters are simple and normally determined in routine investigations. The advantage of this approach is that changes in soil states due to external stress conditions and the associated changes in strength can be examined particularly when different types of soils are involved.

Extended kac-akhiezer formulae and the fredholm determinant of finite section hilbert-schmidt kernels

This paper deals with some results (known as Kac-Akhiezer formulae) on generalized Fredholm determinants for Hilbert-Schmidt operators on L2-spaces, available in the literature for convolution kernels on intervals. The Kac-Akhiezer formulae have been obtained for kernels which are not necessarily of convolution nature and for domains in R(n).

Measurement of complex optical flow with use of an augmented generalized gradient scheme

We present a method for measuring the local velocities and first-order variations in velocities in a timevarying image. The scheme is an extension of the generalized gradient model that encompasses the local variation of velocity within a local patch of the image. Motion within a patch is analyzed in parallel by 42 different spatiotemporal filters derived from 6 linearly independent spatiotemporal kernels. No constraints are imposed on the image structure, and there is no need for smoothness constraints on the velocity field. The aperture problem does not arise so long as there is some two-dimensional structure in the patch being analyzed. Among the advantages of the scheme is that there is no requirement to calculate second or higher derivatives of the image function. This makes the scheme robust in the presence of noise. The spatiotemporal kernels are of simple form, involving Gaussian functions, and are biologically plausible receptive fields. The validity of the scheme is demonstrated by application to both synthetic and real video images sequences and by direct comparison with another recently published scheme Biol. Cybern. 63, 185 (1990)] for the measurement of complex optical flow.

Measurement of complex optical flow with use of an augmented generalized gradient scheme

We present a method for measuring the local velocities and first-order variations in velocities in a time-varying image. The scheme is an extension of the generalized gradient model that encompasses the local variation of velocity within a local patch of the image. Motion within a patch is analyzed in parallel by 42 different spatiotemporal filters derived from 6 linearly independent spatiotemporal kernels. No constraints are imposed on the image structure, and there is no need for smoothness constraints on the velocity field. The aperture problem does not arise so long as there is some two-dimensional structure in the patch being analyzed. Among the advantages of the scheme is that there is no requirement to calculate second or higher derivatives of the image function. This makes the scheme robust in the presence of noise. The spatiotemporal kernels are of simple form, involving Gaussian functions, and are biologically plausible receptive fields. The validity of the scheme is demonstrated by application to both synthetic and real video images sequences and by direct comparison with another recently published scheme [Biol. Cybern. 63, 185 (1990)] for the measurement of complex optical flow.

Toeplitz Operators with Special Symbols on Segal-Bargmann Spaces

We study the boundedness of Toeplitz operators on Segal-Bargmann spaces in various contexts. Using Gutzmer's formula as the main tool we identify symbols for which the Toeplitz operators correspond to Fourier multipliers on the underlying groups. The spaces considered include Fock spaces, Hermite and twisted Bergman spaces and Segal-Bargmann spaces associated to Riemannian symmetric spaces of compact type.

Capturability of realistic generalized true proportional navigation

The capturability of a realistic generalized true proportional navigation (RGTPN) guidance law, against a nonmaneuvering target, is analyzed. The RGTPN law is obtained by relaxing the somewhat unrealistic assumption of constant closing velocity, made in all earlier studies on generalized true proportional navigation (GTPN), and incorporating the actual time-varying value in the guidance law. Closed-form solutions for the complete capture region of RGTPN is obtained in terms of both zero and acceptable non-zero miss distances. It is shown that the capture region of RGTPN in the initial relative velocity space is significantly smaller than that of GTPN, for reasonable values of navigation constant (N) and angular direction (eta) of the missile commanded latax. However, for certain values of N and eta, capturability of RGTPN is found to be better. It is also shown that if in one of the versions of GTPN, which uses constant values of both the closing velocity and the line-of-sight (LOS) angular velocity in the guidance law, the corresponding realistic time-varying quantities are used, the capture region actually expands to cover the whole of the initial relative velocity space. A number of examples are given to compare the capture performance of RGTPN with other versions of the GTPN guidance laws.

Performance of the generalized delta rule in structural damage detection

The paper examines the suitability of the generalized data rule in training artificial neural networks (ANN) for damage identification in structures. Several multilayer perceptron architectures are investigated for a typical bridge truss structure with simulated damage stares generated randomly. The training samples have been generated in terms of measurable structural parameters (displacements and strains) at suitable selected locations in the structure. Issues related to the performance of the network with reference to hidden layers and hidden. neurons are examined. Some heuristics are proposed for the design of neural networks for damage identification in structures. These are further supported by an investigation conducted on five other bridge truss configurations.

Thomas-Fermi Method For Particles Obeying Generalized Exclusion Statistics

We use the Thomas-Fermi method to examine the thermodynamics of particles obeying Haldane exclusion statistics. Specifically, we study Calogero-Sutherland particles placed in a given external potential in one dimension. For the case of a simple harmonic potential (constant density of states), we obtain the exact one-particle spatial density and a {\it closed} form for the equation of state at finite temperature, which are both new results. We then solve the problem of particles in a $x^{2/3} ~$ potential (linear density of states) and show that Bose-Einstein condensation does not occur for any statistics other than bosons.

Direct Cartesian-Space Solutions of Generalized Bloch Equations in the Rotating Frame

Analytical solutions of the generalized Bloch equations for an arbitrary set of initial values of the x, y, and z magnetization components are given in the rotating frame. The solutions involve the decoupling of the three coupled differential equations such that a third-order differential equation in each magnetization variable is obtained. In contrast to the previously reported solutions given by Torrey, the present attempt paves the way for more direct physical insight into the behavior of each magnetization component. Special cases have been discussed that highlight the utility of the general solutions. Representative trajectories of magnetization components are given, illustrating their behavior with respect to the values of off-resonance and initial conditions. (C) 1995 Academic Press, Inc.

On an exact populationary model of genetic algorithms

Genetic algorithms (GAs) are search methods that are being employed in a multitude of applications with extremely large search spaces. Recently, there has been considerable interest among GA researchers in understanding and formalizing the working of GAs. In an earlier paper, we have introduced the notion of binomially distributed populations as the central idea behind an exact ''populationary'' model of the large-population dynamics of the GA operators for objective functions called ''functions of unitation.'' In this paper, we extend this populationary model of GA dynamics to a more general class of objective functions called functions of unitation variables. We generalize the notion of a binomially distributed population to a generalized binomially distributed population (GBDP). We show that the effects of selection, crossover, and mutation can be exactly modelled after decomposing the population into GBDPs. Based on this generalized model, we have implemented a GA simulator for functions of two unitation variables-GASIM 2, and the distributions predicted by GASIM 2 match with those obtained from actual GA runs. The generalized populationary model of GA dynamics not only presents a novel and natural way of interpreting the workings of GAs with large populations, but it also provides for an efficient implementation of the model as a GA simulator. (C) Elsevier Science Inc. 1997.

A fixed-grid finite element based enthalpy formulation for generalized phase change problems: role of superficial mushy region

The enthalpy method is primarily developed for studying phase change in a multicomponent material, characterized by a continuous liquid volume fraction (phi(1)) vs temperature (T) relationship. Using the Galerkin finite element method we obtain solutions to the enthalpy formulation for phase change in 1D slabs of pure material, by assuming a superficial phase change region (linear (phi(1) vs T) around the discontinuity at the melting point. Errors between the computed and analytical solutions are evaluated for the fluxes at, and positions of, the freezing front, for different widths of the superficial phase change region and spatial discretizations with linear and quadratic basis functions. For Stefan number (St) varying between 0.1 and 10 the method is relatively insensitive to spatial discretization and widths of the superficial phase change region. Greater sensitivity is observed at St = 0.01, where the variation in the enthalpy is large. In general the width of the superficial phase change region should span at least 2-3 Gauss quadrature points for the enthalpy to be computed accurately. The method is applied to study conventional melting of slabs of frozen brine and ice. Regardless of the forms for the phi(1) vs T relationships, the thawing times were found to scale as the square of the slab thickness. The ability of the method to efficiently capture multiple thawing fronts which may originate at any spatial location within the sample, is illustrated with the microwave thawing of slabs and 2D cylinders. (C) 2002 Elsevier Science Ltd. All rights reserved.

Generalized model for infrared perception from an engine exhaust

A comprehensive scheme has been developed for the prediction of radiation from engine exhaust and its incidence on an arbitrarily located sensor. Existing codes have been modified for the simulation of flows inside nozzles and jets. A novel view factor computation scheme has been applied for the determination of the radiosities of the discrete panels of a diffuse and gray nozzle surface. The narrowband model has been used to model the radiation from the gas inside the nozzle and the nonhomogeneous jet. The gas radiation from the nozzle inclusive of nozzle surface radiosities have been used as boundary conditions on the jet radiation. Geometric modeling techniques have been developed to identify and isolate nozzle surface panels and gas columns of the nozzle and jet to determine the radiation signals incident on the sensor. The scheme has been validated for intensity and heat flux predictions, and some useful results of practical importance have been generated to establish its viability for infrared signature analysis of jets.

On the explicit determination of the polar decomposition in n-dimensional vector spaces

A method for the explicit determination of the polar decomposition (and the related problem of finding tensor square roots) when the underlying vector space dimension n is arbitrary (but finite), is proposed. The method uses the spectral resolution, and avoids the determination of eigenvectors when the tensor is invertible. For any given dimension n, an appropriately constructed van der Monde matrix is shown to play a key role in the construction of each of the component matrices (and their inverses) in the polar decomposition.