scholarly journals Mathematical Aspects of Krätzel Integral and Krätzel Transform

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 526 ◽  
Author(s):  
Arak M. Mathai ◽  
Hans J. Haubold
Keyword(s):  
Integral Transform ◽  
Statistical Distributions ◽  
The Real ◽  
Real Scalar ◽  
Mathematical Properties ◽  
Scalar Variable ◽  
Krätzel Integral

A real scalar variable integral is known in the literature by different names in different disciplines. It is basically a Bessel integral called specifically Krätzel integral. An integral transform with this Krätzel function as kernel is known as Krätzel transform. This article examines some mathematical properties of Krätzel integral, its connection to Mellin convolutions and statistical distributions, its computable representations, and its extensions to multivariate and matrix-variate cases, in both the real and complex domains. An extension in the pathway family of functions is also explored.

M-convolutions of products and ratios, statistical distributions and fractional calculus

Analysis ◽  
2016 ◽  
Vol 36 (1) ◽  
Author(s):  
Arakaparampil M. Mathai
Keyword(s):  
Fractional Calculus ◽  
Random Variables ◽  
Positive Definite Matrix ◽  
Positive Definite ◽  
Positive Definite Matrices ◽  
The Real ◽  
Real Scalar ◽  
Scalar Variable ◽  
The Matrix

AbstractIt is shown that Mellin convolutions of products and ratios in the real scalar variable case can be considered as densities of products and ratios of two independently distributed real scalar positive random variables. It is also shown that these are also connected to Krätzel integrals and to the Krätzel transform in applied analysis, to reaction-rate probability integrals in astrophysics and to other related aspects when the random variables have gamma or generalized gamma densities, and to fractional calculus when one of the variables has a type-1 beta density and the other variable has an arbitrary density. Matrix-variate analogues are also discussed. In the matrix-variate case, the M-convolutions introduced by the author are shown to be directly connected to densities of products and ratios of statistically independently distributed positive definite matrix random variables in the real case and to Hermitian positive definite matrices in the complex domain. These M-convolutions reduce to Mellin convolutions in the scalar variable case.

The real scalar field in extreme RNdS space

2005 ◽  
Vol 37 (7) ◽  
pp. 1323-1330 ◽  
Author(s):  
Guanghai Guo ◽  
Yuanxing Gui ◽  
Jianxiang Tian
Keyword(s):  
Scalar Field ◽  
The Real ◽  
Real Scalar

Parametric instability of the real scalar pulsons

2005 ◽  
Vol 336 (1) ◽  
pp. 31-36 ◽  
Author(s):  
V.A. Koutvitsky ◽  
E.M. Maslov
Keyword(s):  
Parametric Instability ◽  
The Real ◽  
Real Scalar

Simulating the scalar field using the fuzzy sphere

2003 ◽  
Vol 18 (33n35) ◽  
pp. 2389-2396 ◽  
Author(s):  
XAVIER MARTIN
Keyword(s):  
Scalar Field ◽  
Numerical Scheme ◽  
Approximation Scheme ◽  
Fuzzy Sphere ◽  
Continuous Space ◽  
The Real ◽  
Matrix Algebras ◽  
Real Scalar ◽  
Fuzzy Space ◽  
Commutative Matrix

Fuzzy spaces provide a new approximation scheme using (non–commutative) matrix algebras to approximate the algebra of function of the continuous space. This paper describes how to implement a numerical scheme based on a fuzzy space approximation. In this first attempt, the simplest fuzzy space and field theory, respectively the fuzzy two–sphere and the real scalar field, are used to simulate the real scalar field on the plane. Along the way, this method is compared to its traditional lattice discretisation equivalent.

An integral transform related to quantization. II. Some mathematical properties

1983 ◽  
Vol 24 (2) ◽  
pp. 239-254 ◽  
Author(s):  
I. Daubechies ◽  
A. Grossmann ◽  
J. Reignier
Keyword(s):  
Integral Transform ◽  
Mathematical Properties

scholarly journals LINE DISCONTINUITIES, LOCAL ACTION WITH BOTH THE FIELD AND ITS DUAL, AND SPIN FROM NO SPIN IN TWO-DIMENSIONAL SCALAR THEORY

2013 ◽  
Vol 28 (01) ◽  
pp. 1350003
Author(s):  
CHANDRASEKHAR CHATTERJEE ◽  
E. HARIKUMAR ◽  
MANU MATHUR ◽  
INDRAJIT MITRA ◽  
H. S. SHARATCHANDRA
Keyword(s):  
Scalar Field ◽  
Scalar Fields ◽  
Local Action ◽  
Singular Line ◽  
Two Dimensional ◽  
Scalar Theory ◽  
The Real ◽  
Real Scalar ◽  
Wick’S Theorem

We consider a local action with both the real scalar field and its dual in two Euclidean dimensions. The role of singular line discontinuities is emphasized. Exotic properties of the correlation of the field with its dual, the generation of spin from scalar fields, and quantization of dual charges are pointed out. Wick's theorem and rotation properties of fermions are recovered for half-integer quantization.

scholarly journals Spectral Biomimetic Technique for Wood Classification Inspired by Human Echolocation

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Juan Antonio Martínez Rojas ◽  
Santiago Vignote Peña ◽  
Jesús Alpuente Hermosilla ◽  
Rocío Sánchez Montero ◽  
Pablo Luis López Espí ◽  
...  
Keyword(s):  
Individual Differences ◽  
The Real ◽  
Mathematical Properties ◽  
Nondestructive Techniques ◽  
Natural And Synthetic

Palatal clicks are most interesting for human echolocation. Moreover, these sounds are suitable for other acoustic applications due to their regular mathematical properties and reproducibility. Simple and nondestructive techniques, bioinspired by synthetized pulses whose form reproduces the best features of palatal clicks, can be developed. The use of synthetic palatal pulses also allows detailed studies of the real possibilities of acoustic human echolocation without the problems associated with subjective individual differences. These techniques are being applied to the study of wood. As an example, a comparison of the performance of both natural and synthetic human echolocation to identify three different species of wood is presented. The results show that human echolocation has a vast potential.

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