An Algorithm for Fresnel Diffraction Computing Based on Fractional Fourier Transform

The fractional Fourier transform (FrFT) is used for the solution of the diffraction integral in optics. A scanning approach is proposed for finding the optimal FrFT order. In this way, the process of diffraction computing is speeded up. The basic algorithm and the intermediate results at each stage are demonstrated.

The Automorphism Group of the Free Algebra of Rank Two

The theorem of Czerniakiewicz and Makar-Limanov, that all the automorphisms of a free algebra of rank two are tame is proved here by showing that the group of these automorphisms is the free product of two groups (amalgamating their intersection), the group of all affine automorphisms and the group of all triangular automorphisms. The method consists in finding a bipolar structure. As a consequence every finite subgroup of automorphisms (in characteristic zero) is shown to be conjugate to a group of linear automorphisms.

On the Error-Free Computation of Fast Cosine Transform

We extend our previous work into error-free representations of transform basis functions by presenting a novel error-free encoding scheme for the fast implementation of a Linzer-Feig Fast Cosine Transform (FCT) and its inverse. We discuss an 8x8 L-F scaled Discrete Cosine Transform where the architecture uses a new algebraic integer quantization of the 1-D radix-8 DCT that allows the separable computation of a 2-D DCT without any intermediate number representation conversions. The resulting architecture is very regular and reduces latency by 50% compared to a previous error-free design, with virtually the same hardware cost.

The Hough Transform and Uncertainity

The paper deals with the generalisations of the Hough Transform making it the mean for analysing uncertainty. Some results related Hough Transform for Euclidean spaces are represented. These latter use the powerful means of the Generalised Inverse for description the Transform by itself as well as its Accumulator Function.

On the Range of the Fourier Transform Associated with the Spherical Mean Operator

We characterize the range of some spaces of functions by the Fourier transform associated with the spherical mean operator R and we give a new description of the Schwartz spaces. Next, we prove a Paley-Wiener and a Paley-Wiener-Schawrtz theorems.

An Analogue of Beurling-Hörmander’s Theorem for the Dunkl-Bessel Transform

Mathematics Subject Classification: Primary 35R10, Secondary 44A15

Hankel Transform in Quantum Calculus and Applications

Mathematics Subject Classification: 44A15, 33D15, 81Q99

Spectrum of Functions for the Dunkl Transform on R^d

Mathematics Subject Classification: 42B10

On Hankel Transform of Generalized Mathieu Series

Mathematics Subject Classification: Primary 33E20, 44A10; Secondary 33C10, 33C20, 44A20

Representations of Inverse Functions by the Integral Transform with the Sign Kernel

Mathematics Subject Classification: Primary 30C40

On Y. Nievergelt's Inversion Formula for the Radon Transform

Mathematics Subject Classification 2010: 42C40, 44A12.

Bochner-Hecke Theorems for the Weinstein Transform and Application

MSC 2010: 42B10, 44A15

Hough Transform Approach to Identification of Flare Stars in Multi-exposure Plate Images

ACM Computing Classification System (1998): I.2.8 , I.2.10, I.5.1, J.2.

Factorizations of some Groups of Lie Type of Lie Rank 4

Еленка Генчева, Цанко Генчев В настоящата работа се разглеждат крайни прости групи G , които могат да се представят като произведение на две свои собствени неабелеви прости подгрупи A и B. Всяко такова представяне G = AB е прието да се нарича факторизация на G, а тъй като множителите A и B са избрани да бъдат прости подгрупи на G, то разглежданите факторизации са известни още като прости факторизации на G. Тук се предполага, че G е проста група от лиев тип и лиев ранг 4 над крайно поле GF (q). Ключови думи: крайни прости групи, групи от лиев тип, факторизации на групи.

Generalized Backscattering and the Lax-Phillips Transform

2000 Mathematics Subject Classification: 35P25, 35R30, 58J50.