• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.471-480
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• 2005

This paper deals with some useful methods of solving the one-dimensional integral equation of Fredholm type. Application of the reduction techniques with a view to inverting a class of integral equation with Lauricella function in the kernel, Riemann-Liouville fractional integral operators as well as Weyl operators have been made to reduce to this class to generalized Stieltjes transform and inversion of which yields solution of the integral equation. Use of Mellin transform technique has also been made to solve the Fredholm integral equation pertaining to certain polynomials and H-functions.

• East Asian mathematical journal
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• v.23 no.2
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• pp.257-260
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• 2007

Using the center instead of the Lipschitz condition we show how to provide weaker sufficient convergence conditions of the modified Newton Kantorovich method for the solution of nonlinear singular integral equations with Curleman shift (NLSIES). Finer error bounds on the distances involved and a more precise information on the location of the solution are also obtained and under the same computational cost than in [1].

• Structural Engineering and Mechanics
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• v.43 no.5
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• pp.561-582
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• 2012

Despite popularity of FEM in analysis of static and dynamic structural problems and the routine applicability of FE softwares, analytical methods based on simple mathematical relations is still largely sought by many researchers and practicing engineers around the world. Development of such analytical methods for analysis of free vibration of non-prismatic beams is also of primary concern. In this paper a new and simple method is proposed for determination of vibration frequencies of non-prismatic beams under variable axial forces. The governing differential equation is first obtained and, according to a harmonic vibration, is converted into a single variable equation in terms of location. Through repetitive integrations, integral equation for the weak form of governing equation is derived. The integration constants are determined using the boundary conditions applied to the problem. The mode shape functions are approximated by a power series. Substitution of the power series into the integral equation transforms it into a system of linear algebraic equations. Natural frequencies are determined using a non-trivial solution for system of equations. Presented method is formulated for beams having various end conditions and is extended for determination of the buckling load of non-prismatic beams. The efficiency and convergence rate of the current approach are investigated through comparison of the numerical results obtained to those obtained using available finite element software.

• Kyungpook Mathematical Journal
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• v.51 no.3
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• pp.251-260
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• 2011

The aim of this paper is to obtain a solution of a certain multidimensional convolution integral equation of Fredholm type whose kernel involves a generalized polynomial set. A number of results follow as special cases from the main theorem by specifying the parameters of the generalized polynomial set.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.36D no.1
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• pp.22-28
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• 1999

An exact asymptotic solution for a perfect conducting wedge with H-polarized plane wave incidence is analytically derived by substituting the exact boundary fields of the perfeet conducting wedge, the well known series solution, into the dual integral exquation in the spectral domain. The validity of the derivation is assured by showing that the analytic integration gives the null fields in the complementary region. The merits taking the dual integral equation for derivation of an asymptotic solution for a perfect conduction wedge is discussed.

• 한국초전도학회:학술대회논문집
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• 2009.07a
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• pp.44-44
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• 2009

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.363-370
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• 2005

In this paper, we obtain a new fixed point theorem in complete probabilistic ${\Delta}$-inner product space. As an example of applications, we utilize the results of this paper to study the existence and uniqueness of solutions for linear Valterra integral equation.

• Proceedings of the IEEK Conference
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• 1998.10a
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• pp.613-616
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• 1998

In this paper, a model of a Eddy-current probe coil with a ferrite core in the presence of a half-space with a layer is developed. The half-space with a layer is accounted for by computing the appropriate Green's function by using Bessel transforms. Upon introducing equivalent Amperian currents within a core to explain effect to a impedance change in the coil due to a (ferrite) core, we derive a volume integral equation, The integral equation is transformed via the method of moments into a vector-matrix equation, which is then solved using a linear equation solver. Through the above processing, we computed impedance value in a Eddy-current probe coil due to a conductivity change of layer.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.241-252
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• 2011

Let $\{\Omega_{\tau}\}_{\tau{\in}I}$ be a family of strictly convex domains in $\mathbb{C}^n$. We obtain explicit estimates for the solution of the $\bar{\partial}$-equation on $\Omega{\times}I$ in H$\ddot{o}$lder space. We also obtain explicit point-wise derivative estimates for the $\bar{\partial}$-equation both in space and parameter variables.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.292-292
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• 2004

There are many difficulties to get the scattered field generated by obstacle which has arbitrary shape or irregular surface impedance by using analytic solution or numerical methods. In this study, we propose experimental method of acoustic scattering holography that can predict the far-field scattered field based on nearfield measurements. First of all, we express scattered field using K-H integral equation and compare the differences of which green's function we use. Also we consider analytic solution of scattered field by infinite cylinder to analysis for the errors due to apply cylinderical holography. So the errors which caused by holography due to frequency (ka) and microphone spacing are also analyzed by numerical simulation.