The Hartley transform, a real-valued alternative to the complex Fourier transform, is presented as an efficient tool for the analysis and simulation of earthquake accelerograms. This paper is introduced a novel method based on discrete Hartley transform (DHT) and radial basis function (RBF) neural network for generation of artificial earthquake accelerograms from specific target spectrums. Acce...

A three-dimensional wave packet generated by a local disturbance in a two-dimensional hypersonic boundary layer flow is studied with the aid of the previously solved initial-value problem. The solution to this problem can be expanded in a biorthogonal eigenfunction system as a sum of modes consisting of continuous and discrete spectra of temporal stability theory. A specific disturbance consist...

The study proposes an inversion method applicable to observations of deglacial land uplift and tilt near the margin of a major Pleistocene ice-sheet. This information allows the determination of the cross-section of the ice-sheet and the calculation of the thickness of the lithosphere. The method is applied to the Pleistocene glaciations in Fennoscandia and Laurentia and yields similar lithosph...

The inversion method proposed by Glück and Kawabe uses grammar programs as intermediate results that comprise sequences of operations (data generation, matching, etc.). The determinization method used in the inversion method fails for a grammar program of which the collection of item sets causes a conflict even if there exists a deterministic program equivalent to the grammar program. In this p...

It is proved that the Newton-Sabatier (NS) procedure is not a valid inversion method, in the following sense: 1) it is not possible to carry this procedure through for the phase shifts corresponding to a q ∈ L 1,1 such that ∞ 0 rq(r)dr = 0, where L 1,1 := {q : q = q, ∞ 0 r|q(r)|dr < ∞, 2) the ansatz (*) K(r, s) = ∞ l=0 c l ϕ l (r)u l (s), ∞ l=0 |c l | < ∞, similar to the one used in the NS proc...

This paper introduces a fast high-resolution imaging algorithm designed for ultra-wideband radar, and combines modified Kirchhoff migration and frequency-wavenumber (F-K) migration. The proposed algorithm also uses the texture method and inverse boundary scattering transform to calculate efficiently the integral arising in modified Kirchhoff migration, and thus enabling the integral in the F-K ...

In shape reconstruction, the celebrated Fourier slice theorem plays an essential role. By virtue of the relation between the Radon transform, the Fourier transform and the 2-dimensional inverse Fourier transform, the shape of an object can be reconstructed from the knowledge of the object’s Radon transform. Unfortunately, a discrete implementation requires the use of interpolation techniques, s...

The loop transform in quantum gauge field theory can be recognized as the Fourier transform (or characteristic functional) of a measure on the space of generalized connections modulo gauge transformations. Since this space is a compact Hausdorff space, conversely, we know from the Riesz-Markov theorem that every positive linear functional on the space of continuous functions thereon qualifies a...

Let μ be a compactly supported probability measure on R with expectation 1 and variance V. Let μn denote the n-time free multiplicative convolution of measure μ with itself. Then, for large n the length of the support of μn is asymptotically equivalent to eV n, where e is the base of natural logarithms, e = 2.71 . . . 1 Preliminaries and the main result First, let us recall the definition of th...