The free-space Green function for a two-dimensional exponentially graded elastic medium is derived. The shear modulus μ is assumed to be an exponential function of the Cartesian coordinates (x, y), i.e. μ ≡ μ(x, y) = μ0e12, where μ0, β1, and β2 are material constants, and the Poisson ratio is assumed constant. The Green function is shown to consist of a singular part, involving modified Bessel ...

We introduce a fast algorithm for the numerical application to arbitrary vectors of several special function transforms. The algorithm requires O(n log(n)) operations to apply to an arbitrary vector any n×n matrix such that the rank of any p×q contiguous submatrix is bounded by a constant times pq/n. These rank bounds are proven here for the case of the Fourier-Bessel transform. Numerical exper...

Short-time spectral attenuation is a common form of audio signal enhancement in which a time-varying filter, or suppression rule, is applied to the frequency-domain transform of a corrupted signal. The Ephraim and Malah suppression rule for speech enhancement is both optimal in the minimum mean-square error sense and wellknown for its associated colourless residual noise; however, it requires t...

By a highly–oscillating function we mean one with large number of local maxima and minima over some interval. The computation of integrals of highly–oscillating functions is one of the most important issues in numerical analysis since such integrals abound in applications in many branches of mathematics as well as in other sciences, e.g., quantum physics, fluid mechanics, electromagnetics, etc....

The pair-correlation functions for fluid ionic mixtures in arbitrary spatial dimensions are computed in hypernetted chain (HNC) approximation. In the primitive model (PM), all ions are approximated as nonoverlapping hyperspheres with Coulomb interactions. Our spectral HNC solver is based on a Fourier-Bessel transform introduced by Talman (J. Comput. Phys. 1978, 29, 35), with logarithmically spa...

A procedure leading to specific properties of the symmetric stable distribution functions results by subjecting certain generalizations of the Bessel functions Ja{t) to a limit process. 1 There arises the question as to the existence of the corresponding distributions in case the limit process involved is omitted. The object of this note is to delimit the conditions under which the answer is af...

We derive completeness criteria for sequences of functions of the form f(xλn), where λn is the nth zero of a suitably chosen entire function. Using these criteria, we construct complete nonorthogonal systems of FourierBessel functions and their q-analogues, as well as other complete sets of qspecial functions. We discuss connections with uncertainty principles over q-linear grids and the comple...

The present paper provides exact expressions for the probability distribution of linear functionals of the two–parameter Poisson–Dirichlet process PD(α, θ). Distributional results that follow from the application of an inversion formula for a (generalized) Cauchy– Stieltjes transform are achieved. Moreover, several interesting integral identities are obtained by exploiting a correspondence betw...

The out-of-equilibrium situation in which an initially sharp-edged cylindrical electron beam, that could e.g. model electrons flowing within a wire, is injected into a plasma is considered. A detailed computation of the subsequently produced magnetic field is presented. The control parameter of the problem is shown to be the ratio of the beam radius to the electron skin depth. Two alternative w...

Consider a Markov process with countably many states. In order to find a one-state occupation time distribution, we use a combination of Fourier and Laplace transforms in the way that allows for the inversion of the Fourier transform. We derive a closed-form expression for the occupation time distribution in the case of a simple continuous time random walk on Z and represent the one state occup...