We describe in more detail the general relation uncovered our previous work between boundary correlators de Sitter (dS) and Euclidean anti-de (EAdS) space, at any order perturbation theory. Assuming Bunch-Davies vacuum early times, given diagram contributing to a correlator dS can be expressed as linear combination of Witten diagrams for corresponding process EAdS, where relative coefficients a...

Abstract. The reconstruction problem for the acoustic tomography with non-homogeneous background is discussed. We develop a method of beamlike solutions of a Helmholtz equation which is not sensitive to caustics. For small perturbations of the speed the inverse scattering problem is reduced to inversion of a ray integral transform. An explicit formula is given for beam-like solutions in a homog...

The X-ray transform on a compact symmetric space M is here inverted by means of an explicit inversion formula. The proof uses the conjugacy of the minimal closed geodesics in M and of the maximally curved totally geodesic spheres in M , proved in Math. Ann. 165 (1966), 309–317.

It is shown that any convolution operator in the time domain can be represented exactly as a multiplication operator in the time-scale (wavelet) domain. The Mellin transform gives a one-to-one correspondence between frequency filters (system functions) and scale filters (multiplication operators in the scale domain), subject to the convergence of the defining integrals. The usual wavelet recons...

This paper presents an algorithm that uses visual information to achieve the homing of an autonomous agent inside a previously visited environment. An image grabbed at the target position is compared with the currently perceived one to determine the relative position of the robot and of its target. Only particular regions of the image, called Visual References, are taken into account. A Visual ...

This paper presents a novel method for classifying an image into one of predeened classes in a data bank by applying mutual information to a representation of the Fourier amplitude domain. Template and test images are made translation and rotation invariant through the Fourier-Mellin transform. While mutual information could be employed here, we choose instead to apply it to the lower dimension...

In this paper, we present a novel integral transform known as the one-dimensional quaternion quadratic-phase Fourier (1D-QQPFT). We first define (1D-QQPFT) of integrable (and square integrable) functions on R. Later on, show that 1D-QQPFT satisfies all respective properties such inversion formula, linearity, Moyal’s convolution theorem, correlation theorem and uncertainty principle. Moreover, u...

In this paper we present an explicit (rank one) function transform which contains several Jacobi-type function transforms and Hankel-type transforms as degenerate cases. The kernel of the transform, which is given explicitly in terms of basic hypergeometric series, thus generalizes the Jacobi function as well as the Bessel function. The kernel is named the Askey-Wilson function, since it provid...

A new mathematical model of time fractional order heat equation and fractional order boundary condition have been constructed in the context of the generalized theory of thermo piezoelasticity. The governing equations have been applied to a semi infinite piezoelectric slab. The Laplace transform technique is used to remove the time-dependent terms in the governing differential equations and the...