A solution of the axisymmetric Boussinesq-type problem is derived for transient thermal stresses in a half-space under heating by using the Laplace and Hankel transforms. An analytical method is developed to predict the temperature field that satisfies the prescribed mechanical conditions. Several simple shapes of punches of arbitrary profile are considered and an expression for the total load ...

This paper analyzes the important steps of an O(n 2 log n) algorithm for nding the eigenvalues of a complex Hankel matrix. The three key steps are a Lanczos-type tridiagonalization algorithm, a fast FFT-based Hankel matrix-vector product procedure, and a QR eigenvalue method based on complex-orthogonal transformations. In this paper, we present an error analysis of the three steps, as well as r...

The significance of the similarity theorem for the fractional Fourier transform is discussed, and the properties of self-similar functions considered. The concept of the fractional Hankel transform is developed for use in the analysis of diffraction and imaging in symmetrical optical systems. The particular case of Fresnel diffraction from a circular aperture is discussed and the effects of the...

Asymptotic behavior of the integral '((w) = r e-"%(wx)f(x2)xdx is investigated, where J0(x) is the Bessel function of the first kind and w is a large positive parameter. It is shown that IAw) decays exponentially like e~y"' , y > 0, when/(z) is an entire function subject to a suitable growth condition. A complete asymptotic expansion is obtained when /( z ) is a meromorphic function satisfying ...

In the rst part 13] of the paper transformationsmappingToeplitz and Toeplitz-plus-Hankel matrices into generalizedCauchy matrices were studied. In this second part fast algorithms for LU-factorization and inversion of generalized Cauchy matrices are discussed. It is shown that the combinationof transformation pivoting techniques leads to algorithms for indeenite Toeplitz and Toeplitz-plus-Hanke...

A solution is presented to a doubly mixed boundary value problem of the torsion of an elastic layer, partially resting on a rigid circular base by a circular rigid punch attached to its surface. This problem is reduced to a system of dual integral equations using the Boussinesq stress functions and the Hankel integral transforms. With the help of the Gegenbauer expansion formula of the Bessel f...

Fast trigonometric transforms and periodic orthogonal wavelet transforms are essential tools for numerous practical applications. It is very important that fast algorithms work stable in a floating point arithmetic. This survey paper presents recent results on the worst case analysis of roundoff errors occurring in floating point computation of fast Fourier transforms, fast cosine transforms, a...

with u0 = 0, where the dot indicates differentiation with respect to t. In this note, we shall show how solutions to this equation can be formulated in the context of exponential Riordan arrays. The Riordan arrays we shall consider may be considered as parameterised (or “time”-dependent) Riordan arrays. We have already considered parameterized Riordan arrays [1], exploring the links between the...

In this note we announce an extension of these theorems to the setting of Stiefel manifolds and matrix space. Our work makes it possible to construct holomorphic discrete series representations for the real symplectic group by decomposing a tensor product of certain projective representations introduced earlier by Shale and Weil. (See Weil [11] and also Shalika [10].) Proofs of the results anno...