• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1607-1619
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• 2015

We investigate some generalization of a class of Hankel-Clifford transformations having Fox H-function as part of its kernel on a class of Boehmians. The generalized transform is a one-to-one and onto mapping compatible with the classical transform. The inverse Hankel-Clifford transforms are also considered in the sense of Boehmians.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1055-1071
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• 2010

Recently, a number of algorithms have been proposed for numerical evaluation of Hankel transforms as these transforms arise naturally in many areas of science and technology. All these algorithms depend on separating the integrand $rf(r)J_{\upsilon}(pr)$ into two components; the slowly varying component rf(r) and the rapidly oscillating component $J_{\upsilon}(pr)$. Then the slowly varying component rf(r) is expanded either into a Fourier Bessel series or various wavelet series using different orthonormal bases like Haar wavelets, rationalized Haar wavelets, linear Legendre multiwavelets, Legendre wavelets and truncating the series at an optimal level; or approximating rf(r) by a quadratic over the subinterval using the Filon quadrature philosophy. The purpose of this communication is to take a different approach and replace rapidly oscillating component $J_{\upsilon}(pr)$ in the integrand by its Bernstein series approximation, thus avoiding the complexity of evaluating integrals involving Bessel functions. This leads to a very simple efficient and stable algorithm for numerical evaluation of Hankel transform.

• Structural Engineering and Mechanics
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• v.20 no.2
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• pp.209-223
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• 2005

A new method for deriving analytical solution of the annular elastic plate on elastic foundation under axisymmetric loading is presented. The formulation is based on application of Hankel integral transforms and Bessel functions' properties in the corresponding boundary-value problem. A representative example is studied and the obtained solution is compared with published numerical results indicating excellent agreement.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.521-535
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• 2022

In this paper, we introduce the k-Hankel-Wigner transform on R in some problems of time-frequency analysis. As a first point, we present some harmonic analysis results such as Plancherel's, Parseval's and an inversion formulas for this transform. Next, we prove a Heisenberg's uncertainty principle and a Calderón's reproducing formula for this transform. We conclude this paper by studying an extremal function for this transform.

• Kyungpook Mathematical Journal
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• v.17 no.1
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• pp.31-35
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• 1977

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.487-503
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• 2019

In this study, the author provided a discussion on one dimensional Laplace and Fourier transforms with their applications. It is shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve space fractional partial differential equation with non - constant coefficients. The object of the present article is to extend the application of the joint Fourier - Laplace transform to derive an analytical solution for a variety of time fractional non - homogeneous KdV. Numerous exercises and examples presented throughout the paper.

• Kyungpook Mathematical Journal
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• v.10 no.2
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• pp.165-175
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• 1970

• Geophysics and Geophysical Exploration
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• v.12 no.4
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• pp.361-366
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• 2009

Layered-earth Green's functions in electormagnetic (EM) surveys play a key role in modeling the response of exploration targets. They are computed through the Hankel transforms of analytic kernels. Computational precision depends upon the choice of algebraically equivalent forms by which these kemels are expressed. Since three-dimensional (3D) modeling can require a huge number of Green's function evaluations, total computational time can be influenced by computational time for the Hankel transform evaluations. Linear digital filters have proven to be a fast and accurate method of computing these Hankel transforms. In EM modeling for 3D inversion, electric fields are generally evaluated by the secondary field formulation to avoid the singularity problem. In this study, three components of electric fields for five different sources on the surface of homogeneous half-space were derived as primary field solutions. Moreover, reflection coefficients in TE and TM modes were produced to calculate EM responses accurately for a two-layered model having a sea layer. Accurate primary fields should substantially improve accuracy and decrease computation times for Green's function-based problems like MT problems and marine EM surveys.

• Coupled systems mechanics
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• v.13 no.3
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• pp.231-245
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• 2024

In the present work, a microelogated thermoelastic model based on Lord-Shulman (1967) and Green-Lindsay (1972) theories of thermoelasticity has been constructed. The governing equations for the simulated model are converted into two-dimensional case and made dimensionless for further simplification. Laplace and Hankel transforms followed by eigen value approach has been employed to solve the problem. The use of eigen value approach hasthe advantage of finding the solution of governing equationsin matrix form notations. This approach is straight forward and convenient for numerical computation and avoids the complicate nature of the problem. The components of displacement,stress and temperature distribution are obtained in the transformed domain. Numerical inversion techniques have been used to invert the resulting quantities in the physical domain. Graphical representation of the resulting quantities for describing the effect of microelongation are presented. A special case is also deduced from the present investigation. The problem find application in many engineering problems like thick-walled pressure vesselsuch as a nuclear containment vessel, a cylindricalroller etc.

• Geophysics and Geophysical Exploration
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• v.14 no.3
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• pp.185-190
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• 2011

In marine controlled-source electromagnetic (CSEM) modeling, it may be difficult to evaluate primary fields accurately using conventional linear filters because they decay very rapidly with distance. However, since there exists a closed-form solution to the Hankel transform in TM mode for a homogeneous half space, we can assess the accuracy of linear filters for evaluating the Hankel transform. As a result, only nine out of 36 source-receiver pairs show that EM fields decrease linearly in semi-log scale with an increase of source-receiver distance, while EM fields are either 0 or not reduced significantly due to an effect of the air layer. There also exist closed-form solutions for the nine pairs, and the others can be evaluated accurately with a relatively short filter. This paper proposes a method which uses closed-form solutions for TM-mode Hankel transforms and a filter with 61 coefficients for TE-mode ones.