• Kyungpook Mathematical Journal
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• v.58 no.1
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• pp.19-35
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• 2018

Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [30] and the second Appell function [6], we introduce here the incomplete Lauricella functions ${\gamma}^{(n)}_A$ and ${\Gamma}^{(n)}_A$ of n variables. We then systematically investigate several properties of each of these incomplete Lauricella functions including, for example, their various integral representations, finite summation formulas, transformation and derivative formulas, and so on. We provide relevant connections of some of the special cases of the main results presented here with known identities. Several potential areas of application of the incomplete hypergeometric functions in one and more variables are also pointed out.

• Proceedings of the SAREK Conference
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• 2009.06a
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• pp.984-989
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• 2009

The present study has been conducted to predict the temperature distribution in the core of the scraper type ice generator. The analytic model was simplified as the flow in the annular type cylinder, which had an inside wall moving in axial direction due to the rotation of screw and a fixed outside wall. The governing equations were arranged by the method of separation of variables. The results corresponded to the exact solutions of the Bessel function. The qualitative results such as general characteristics of heat transfer in annulus flow from outer cylinder wall to the inside wall were obtained. However the amount of the heat transfer was underestimated as low as $1/5{\sim}1/6$ of the designed value.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.1
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• pp.1-15
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• 2013

In this paper the three dimensional wave propagation in a homogeneous isotropic thermo elastic cylindrical panel embedded in an elastic medium (Winkler model) is investigated in the context of the L-S (Lord-Shulman) theory of generalized thermo elasticity. The analysis is carried out by introducing three displacement functions so that the equations of motion are uncoupled and simplified. A Bessel function solution with complex arguments is then directly used for the case of complex Eigen values. This type of study is important for design of structures in atomic reactors, steam turbines, wave loading on submarine, the impact loading due to superfast train and jets and other devices operating at elevated temperature. In order to illustrate theoretical development, numerical solutions are obtained and presented graphically for a zinc material with the support of MATLAB.

• International Journal of Advanced Culture Technology
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• v.7 no.4
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• pp.268-273
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• 2019

The apparent soil resistivity is used for estimating multilayer soil parameters, such as, layer's depth and soil resistivity. The soil parameters are estimated by continuously revising those parameters until the error between the measured and calculated apparent soil resistivity reaches to allowable level. The equation for calculating the apparent soil resistivity is complicated and time consumed, because it is composed of an infinite integral which includes a zero order Bessel's function of the first kind. In this paper, a fast algorithm for calculating the apparent soil resistivity of horizontal multilayer earth structure is proposed using exponential sampling method.

• 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.

• The Proceedings of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.7 no.2
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• pp.31-35
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• 1993

The radial density distributions of the positive column of strongly modulated low -pressure gas discharges in mercury - rare gas mixtures at 10 tom pressure have been studied theoretically. The current was modulated inusoidally with a modulation depth of 50%. Calculations have shown that the radial profile of the excited atoms is ditferent form 0th Bessel function $J_0$(2.4r/R) and the invertion of the radial distribution of the excited atom can occur at some frequency. The hybrid method of FDM and 2nd order Runge-Kutta meth od is used for solving differenzial equations.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.49-55
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• 1995

This paper is the third of a series in which smoothness properties of function in several variables are discussed. The germ of the whole theory was laid in the works by Folland and Stein [4]. On nilpotent Lie groups, they difined analogues of the classical $L^p$ Sobolev or potential spaces in terms of fractional powers of sub-Laplacian, L and extended several basic theorems from the Euclidean theory of differentaiability to these spaces: interpolation properties, boundedness of singular integrals,..., and imbeding theorems. In this paper we study the analogue to the extension theorem for the Folland-Stein spaces. The analogue to Stein's restriction theorem were studied by M. Mekias [5] and Y.M. Kim [6]. First, we have the space of Bessel potentials on the Heisenberg group introduced by Folland [4].

• Kyungpook Mathematical Journal
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• v.52 no.2
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• pp.109-136
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• 2012

We aim at presenting certain unexpected functional relations among various hypergeometric functions of one or several variables (for example, see the identities in Corollary 5) by making use of Carlson's method employed in his work (Some extensions of Lardner's relations between $_0F_3$ and Bessel functions, SIAM J. Math. Anal. 1(2)(1970), 232-242).

• Convergence Security Journal
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• v.8 no.4
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• pp.153-159
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• 2008

Graded-Index Multimode Optical fibers have recently received a lot of attention as regards their application and lightwave behavior in relation to broadband communication links. Accordingly, this aticle presents a novel lightwave mode analysis that solves the wave equation using a numerical analysis based on an eigenvalue problem method, thereby avoiding the typical complicated Bessel function method. Angular depedences and number of modes were observed as well. Future research implications will be possibly noticed such areas as bending effects and mode coupling analyses thru this research.

• Proceedings of the IEEK Conference
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• 2002.07a
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• pp.9-11
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• 2002

We improve the free-space optical interconnection efficiency by using circular aperture computer-generated hologram (CGH). In free-space optical interconnection system using CGH, the single CGH is composed of sub-CGHs, which can change the direction of input beams to desired output positions, by Fourier transform. Each sub-CGH is rectangular shape, so the input beams through each sub-CGH are transformed to sinc functions in output plane. The side lobes of each sinc function are superimposed in output plane and they result in detection error in output plane, so the detection efficiency is low. We use the circular shaped sub-CGHs in order to reduce the side lobe value in output plane instead of rectangular shaped sub-CGHs. The each input beam is transformed to first-order Bessel functions through circular shaped sub-CGHs in output plane. The side lobes of first-order Bessel functions us low values compared with side lobes of sinc function, so we can improve the detection efficiency in output plane. We use binary phase modulated CGH, and confirm this improvement results by simulation.