Published in Journal of advanced research
Integral transforms are important to solve real problems. Appropriate choice of integral transforms helps to convert differential equations as well as integral equations into terms of an algebraic equation that can be solved easily.During last two decades many integral transforms in the class of Laplace transform are introduced such as Sumudu, Elza...
Published in Journal of advanced research
This study describes a novel meshless technique for solving one of common problem within cell biology, computer graphics, image processing and fluid flow. The diffusion mechanism has extremely depended on the properties of the structure. The present paper studies why diffusion processes not following integer-order differential equations, and presen...
Published in Zeitschrift für angewandte Mathematik und Physik
Foundations of the modified Poisson kernel method were laid out by Finkelstein and Scheinberg in 1975 in the context of explicit solvability for the adaptive Dirichlet problem in a half plane. Over the past decade, this method has been further developed, and new applications have appeared both in the field of harmonic analysis and operator theory a...
Published in GEM - International Journal on Geomathematics
In this survey paper, we present a multiscale post-processing method in exploration. Based on a physically relevant mollifier technique involving the elasto-oscillatory Cauchy–Navier equation, we mathematically describe the extractable information within 3D geological models obtained by migration as is commonly used for geophysical exploration purp...
Published in Complex Analysis and Operator Theory
In the present work we obtain some analogues of the Hilbert formulas on the unit circle for iterated Cauchy-Riemann operator in one-dimensional complex analysis involving higher order Lipschitz classes. Furthermore, a Poincaré-Bertrand formula related to the corresponding singular iterated Cauchy integral over the boundary of a smoothly bounded dom...
Published in Journal of Inverse and Ill-posed Problems
We consider a fixed angle inverse scattering problem in the presence of a known Riemannian metric. First, assuming a no caustics condition, we study the direct problem by utilizing the progressing wave expansion. Under a symmetry assumption on the metric, we obtain uniqueness and stability results in the inverse scattering problem for a potential w...
Published in Journal of Fourier Analysis and Applications
Given a graph G=(V,E)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G=(V,E)$$\end{document}, suppose we are interested in selecting a sequence of vertices (xj)j=1n\doc...
Published in Zeitschrift für angewandte Mathematik und Physik
The novelty of the approach contains several aspects: the method of derivation of the governing equations, the form and number of equations, the optimal choice of elastic constants. While majority of published articles derives the governing equations from the Green’s function for the compound space and the use of the reciprocal theorem, we use the ...
Published in Acta Mathematica Sinica, English Series
The paper provides integral representations for solutions to a certain first order partial differential equation natural arising in the factorization of the Lamé—Navier system with the help of Clifford analysis techniques. These representations look like in spirit to the Borel—Pompeiu and Cauchy integral formulas both in three and higher dimensiona...
Published in Journal of Inverse and Ill-posed Problems
We are concerned with the inverse scattering problems associated with incomplete measurement data. It is a challenging topic of increasing importance that arise in many practical applications. Based on a prototypical working model, we propose a machine learning based inverse scattering scheme, which integrates a CNN (convolution neural network) for...
