Kac-Akhiezer formula for normal integral operators

The Kac-Akhiezer formula for finite section normal Wiener-Hopf integral operators is proved. This is an extension of the corresponding result for symmetric operator [2, 3, 4, 5, 6, 7].

A Legendre spectral element model for sloshing and acoustic analysis in nearly incompressible fluids

A new spectral finite element formulation is presented for modeling the sloshing and the acoustic waves in nearly incompressible fluids. The formulation makes use of the Legendre polynomials in deriving the finite element interpolation shape functions in the Lagrangian frame of reference. The formulated element uses Gauss-Lobatto-Legendre quadrature scheme for integrating the volumetric stiffness and the mass matrices while the conventional Gauss-Legendre quadrature scheme is used on the rotational stiffness matrix to completely eliminate the zero energy modes, which are normally associated with the Lagrangian FE formulation. The numerical performance of the spectral element formulated here is examined by doing the inf-sup test oil a standard rectangular rigid tank partially filled with liquid The eigenvalues obtained from the formulated spectral element are compared with the conventional equally spaced node locations of the h-type Lagrangian finite element and the predicted results show that these spectral elements are more accurate and give superior convergence The efficiency and robustness of the formulated elements are demonstrated by solving few standard problems involving free vibration and dynamic response analysis with undistorted and distorted spectral elements. and the obtained results are compared with available results in the published literature (C) 2009 Elsevier Inc All rights reserved

A quantum stochastic Lie-Trotter product formula

A Trotter product formula is established for unitary quantum stochastic processes governed by quantum stochastic differential equations with constant bounded coefficients.

An alternate form of the ramberg-osgood formula for matrix displacement analysis

A new stress-strain law, which is a three parameter representation of stress in terms of strain has been proposed for the matrix displacement analysis of structures made of non-hookean materials. This formula has been utilized to study three typical problems. These studies brought out the effectiveness and suitability of this law for matrix displacement analysis.

Investigations of superconducting bismuth cuprates of the general formula Bi2-xPbx(Ca,Sr,Y)n 1 Cun O2n 4 δ

In the (Bi,Pb)-Sr-Cu-O system we have examined many compositions which are either metallic or semiconducting. In the Bi2-xPbx(Ca, Sr)n+1 Cun O2n+4+δ system, we have established the superconducting properties of the n = 1 to 4 members. The Tc increases from n = 1 to 3 and does not increase further when n = 4. In Bi2Ca1-x,YxSr2Cu2Oy, the Tc decreases with increase in x.

On the unreasonable effectiveness of Gutzmer's formula

In this article we plan to demonstrate the usefulness of `Gutzmer's formula' in the study of various problems related to the Segal-Bargmann transform. Gutzmer's formula is known in several contexts: compact Lie groups, symmetric spaces of compact and noncompact type, Heisenberg groups and Hermite expansions. We apply Gutzmer's formula to study holomorphic Sobolev spaces, local Peter-Weyl theorems, Paley-Wiener theorems and Poisson semigroups.

A series of metallic oxides of the formula La3LnBaCu5O13+δ (Ln = rare earth or Y)

Oxides of the formula La3LnBaCu5O13+δ (Ln = Nd, Sm, Gd, Dy, or Y) exhibiting metallic resistivity have been prepared and characterized. In the case of yttrium, a composition close to La2Y2BaCu5O13+δ, which is also metallic, could be prepared.

Transformation formula for exponential sums involving fourier coefficients of modular forms

In 1984 Jutila [5] obtained a transformation formula for certain exponential sums involving the Fourier coefficients of a holomorphic cusp form for the full modular group SL(2, Z). With the help of the transformation formula he obtained good estimates for the distance between consecutive zeros on the critical line of the Dirichlet series associated with the cusp form and for the order of the Dirichlet series on the critical line, [7]. In this paper we follow Jutila to obtain a transformation formula for exponential sums involving the Fourier coefficients of either holomorphic cusp forms or certain Maass forms for congruence subgroups of SL(2, Z) and prove similar estimates for the corresponding Dirichlet series.

A formula for the solution of general Abel integral equation

A new formula for the solution of the general Abel Integral equation is derived, and an important special case is checked with the known result.

Fast computation of Legendre and Zernike moments

This paper presents recursive algorithms for fast computation of Legendre and Zernike moments of a grey-level image intensity distribution. For a binary image, a contour integration method is developed for the evaluation of Legendre moments using only the boundary information. A method for recursive calculation of Zernike polynomial coefficients is also given. A square-to-circular image transformation scheme is introduced to minimize the computation involved in Zernike moment functions. The recursive formulae can also be used in inverse moment transforms to reconstruct the original image from moments. The mathematical framework of the algorithms is given in detail, and illustrated with binary and grey-level images.

Phosphate derivatives of 123 cuprates of the formula LnSr(2)Cu(3)O(7) (Ln=Gd, Dy, Ho)

Partial substitution of Cu in the chain by the phosphate ion stabilizes LnSr(2)Cu(3)O(7) (Ln = Gd, Dy or Ho) in the 123 structure. The LnSr(2)Cu(2.8)(PO4)(0.2)O-y derivatives exhibit incommensurately modulated structures. The holmium oxy-phosphate derivative has been rendered superconducting by the partial substitution of Ho by Ca.

Non-resonant perturbation formula for interaction impedance measurement for a folded-waveguide SWS

The non-resonant perturbation formula for the measurement of interaction impedance of a folded-waveguide slow-wave structure was derived for the relevant electromagnetic field configuration at the axis of the beam-hole of the structure. Efficacy of the theory was benchmarked through virtual measurement using 3D electromagnetic modeling in CST-studio.