Nonlinear partial differential equation (PDE) models are established approaches for image/signal processing, data analysis and surface construction. Most previous geometric PDEs are utilized as low-pass filters which give rise to image trend information. In an earlier work, we introduced mode decomposition evolution equations (MoDEEs), which behave like high-pass filters and are able to systema...

The method of partial Fourier transform is used to find explicit formulas for two remarkable fundamental solutions for a generalized Tricomi operator. These fundamental solutions reflect clearly the mixed type of the Tricomi operator. In proving these results, we establish explicit formulas for Fourier transforms of some functions involving Bessel functions.

In this paper we prove analogous theorems like Leindler’s [3] using the so-called A-transform of the B-transform of the partial sums of Fourier series. In addition, more than two such transforms are introduced and for them analogous results are showed as well.

Communication over doubly selective channels (both time and frequency selective) suffers from significant intercarrier interference (ICI). This problem is severe in underwater acoustic communications. In this paper, a novel partial fractional (PFrFT)-MIMO-OFDM system proposed implemented to further mitigate ICI. A new iterative band minimum mean square error (BMMSE) weight combining based on LD...

— For a regular twistor D-module and for a given function f , we compare the nearby cycles at f =∞ and the nearby or vanishing cycles at τ = 0 for its partial Fourier-Laplace transform relative to the kernel e−τf .

The nonequispaced or nonuniform fast Fourier transform (NUFFT) arises in a variety of application areas, including imaging processing and the numerical solution of partial differential equations. In its most general form, it takes as input an irregular sampling of a function and seeks to compute its Fourier transform at a nonuniform sampling of frequency locations. This is sometimes referred to...

In the paper the question Is the q-Fourier transform of a qGaussian a q ′ -Gaussian (with some q ′ ) up to a constant factor? is studied for the whole range of q ∈ (−∞, 3). This question is connected with applicability of the q-Fourier transform in the study of limit processes in nonextensive statistical mechanics. We prove that the answer is affirmative if and only if q ≥ 1, excluding two part...