scholarly journals Advances in Laplace Type Integral Transforms with Applications

2014 ◽  
Vol 7 (6) ◽  
pp. 877-890 ◽  
Author(s):  
A. Aghili
Keyword(s):  
Integral Transforms ◽  
Type Integral ◽  
Laplace Type

scholarly journals New trends in Laplace type integral transforms with applications

2017 ◽  
Vol 35 (1) ◽  
pp. 173
Author(s):  
Arman Aghili
Keyword(s):  
Exact Solution ◽  
Fourier Transforms ◽  
Integral Transforms ◽  
Laplace Transforms ◽  
Two Dimensional ◽  
Stieltjes Transform ◽  
Special Series ◽  
Type Integral ◽  
Laplace Type

AbstractIn this paper, the authors provided a discussion on one and two dimensional Laplace transforms and generalized Stieltjes transform and their applications in evaluating special series and integrals. Finally, we implemented the joint Laplace – Fourier transforms to construct exact solution for a variant of the Kd.V equation. Illustrative examples are also provided.

scholarly journals On (p,q)-Analogues of Laplace-Typed Integral Transforms and Applications

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 631
Author(s):  
Sansumpan Jirakulchaiwong ◽  
Kamsing Nonlaopon ◽  
Jessada Tariboon ◽  
Sotiris K. Ntouyas ◽  
Hwajoon Kim
Keyword(s):  
Differential Equations ◽  
Integral Transforms ◽  
Type Integral ◽  
Laplace Type

In this paper, we establish (p,q)-analogues of Laplace-type integral transforms by using the concept of (p,q)-calculus. Moreover, we study some properties of (p,q)-analogues of Laplace-type integral transforms and apply them to solve some (p,q)-differential equations.

An Application to H2+ of Laplace Type Integral Transform and its Inverse

1985 ◽  
Vol 40 (3) ◽  
pp. 246-250 ◽  
Author(s):  
M. Primorac ◽  
K. Kovačević
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Integral Transform ◽  
Integral Transformation ◽  
Inverse Transform ◽  
Type Integral ◽  
Analytical Formulae ◽  
Molecular Computations ◽  
Laplace Type

Laplace type integral transformation (LIT) has been applied to wavefunctions. The effect of the inverse transform is also discussed. LIT wavefunctions are tested in the calculation of the ground-state energy of H2+, where the untransformed functions were 1s, 12s, 123s and 1234s- STO. The results presented here show that LIT wavefunctions are applicable in molecular computations. The analytical formulae for two-centre one-electron integrals over LIT wavefunctions are derived by use of a Barnett-Coulson-like expansion of rbN (rb + p)-v.

scholarly journals A complete analytical solution of the Fokker–Planck and balance equations for nucleation and growth of crystals

2018 ◽  
Vol 376 (2113) ◽  
pp. 20170327 ◽  
Author(s):  
Eugenya V. Makoveeva ◽  
Dmitri V. Alexandrov
Keyword(s):  
Distribution Function ◽  
Analytical Description ◽  
Supercooled Liquid ◽  
Intermediate Stage ◽  
Nucleation And Growth ◽  
Time Dependent ◽  
Supersaturated Solution ◽  
Nucleation Kinetics ◽  
Type Integral ◽  
Laplace Type

This article is concerned with a new analytical description of nucleation and growth of crystals in a metastable mushy layer (supercooled liquid or supersaturated solution) at the intermediate stage of phase transition. The model under consideration consisting of the non-stationary integro-differential system of governing equations for the distribution function and metastability level is analytically solved by means of the saddle-point technique for the Laplace-type integral in the case of arbitrary nucleation kinetics and time-dependent heat or mass sources in the balance equation. We demonstrate that the time-dependent distribution function approaches the stationary profile in course of time. This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’.

scholarly journals Matrix Expression of Convolution and Its Generalized Continuous Form

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1791
Author(s):  
Young Hee Geum ◽  
Arjun Kumar Rathie ◽  
Hwajoon Kim
Keyword(s):  
Neural Networks ◽  
Integral Transforms ◽  
Main Process ◽  
Continuous Form ◽  
Core Technology ◽  
New Variant ◽  
The Matrix ◽  
Matrix Expression ◽  
Almost All ◽  
Laplace Type

In this paper, we consider the matrix expression of convolution, and its generalized continuous form. The matrix expression of convolution is effectively applied in convolutional neural networks, and in this study, we correlate the concept of convolution in mathematics to that in convolutional neural network. Of course, convolution is a main process of deep learning, the learning method of deep neural networks, as a core technology. In addition to this, the generalized continuous form of convolution has been expressed as a new variant of Laplace-type transform that, encompasses almost all existing integral transforms. Finally, we would, in this paper, like to describe the theoretical contents as detailed as possible so that the paper may be self-contained.

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