• Journal of the Korea Institute of Military Science and Technology
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• v.7 no.3 s.18
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• pp.157-164
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• 2004

This is a boundary integral formulation for elastic shallow shell structures subjected to both membrane and bending loads. Fundamental solutions for shell actions are determined from the plate solutions and, finally the corresponding kernel functions for shell BIEs can be constructed. It is illustrated by solving an example of uniform load of spherical cap.

• Structural Engineering and Mechanics
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• v.26 no.5
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• pp.557-568
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• 2007

The elastic T-stress is increasingly being recognized as an important second parameter to the stress intensity factor for fracture and fatigue assessments. In this paper, the mutual or M-contour integral approach is employed in conjunction with the Boundary Element Method (BEM) to determine the numerical T-stress solutions for cracks in plates with multiple holes. The problems investigated include plates of infinite width with multiple holes at which single or double, symmetric cracks have grown from. Comparisons of these results are also made with the corresponding solutions of finite plates with a single hole. For completeness, stress intensity factor solutions for the cracked geometries analyzed are presented as well. These results will be useful for failure assessments using the two-parameter linear elastic fracture mechanics approach.

• Journal of applied mathematics & informatics
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• v.36 no.1_2
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• pp.1-14
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• 2018

In this paper, we prove the existence, uniqueness and stability of solution for some nonlinear functional-integral equations by using generalized coupled Lipschitz condition. We prove a fixed point theorem to obtain the mentioned aim in Banach space $X=C([a,b],{\mathbb{R}})$. As application we study some volterra integral equations with linear, nonlinear and single kernel.

• Korean Journal of Mathematics
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• v.18 no.4
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• pp.425-440
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• 2010

Using Green's theorem, elliptic boundary value problems can be converted to boundary integral equations. A numerical methods for boundary integral equations are boundary elementary method(BEM). BEM has advantages over finite element method(FEM) whenever the fundamental solutions are known. Helmholtz type equations arise naturally in many physical applications. In a boundary integral formulation for the exterior Neumann there occurs a hypersingular operator which exhibits a strong singularity like $\frac{1}{|x-y|^3}$ and hence is not an integrable function. In this paper we are going to remove this hypersingularity by reducing the regularity of test functions.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.209-224
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• 2013

The problem of finding rational or integral points of an elliptic curve basically boils down to solving a cubic equation. We look closely at the cubic formula of Cardano to find a criterion for a cubic polynomial to have a rational or integral roots. Also we show that existence of a rational root of a cubic polynomial implies existence of a solution for certain Diophantine equation. As an application we find some integral solutions of some special type for $y^2=x^3+b$.

• Korean Journal of Mathematics
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• v.25 no.3
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• pp.323-334
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• 2017

In this paper, we propose a combined form for solving nonlinear interval Volterra-Fredholm integral equations of the second kind based on the modifying Laplace Adomian decomposition method. We find the exact solutions of nonlinear interval Volterra-Fredholm integral equations with less computation as compared with standard decomposition method. Finally, an illustrative example has been solved to show the efficiency of the proposed method.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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• pp.121-136
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• 2008

Some new explicit bounds on the solutions to a class of new nonlinear retarded Volterra-Fredholm type integral inequalities in two independent variables are established, which can be used as effective tools in the study of certain integral equations. Some examples of application are also indicated.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.165-182
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• 2003

Toeplitz matrix method and the product Nystrom method are described for mixed Fredholm-Volterra singular integral equation of the second kind with Carleman Kernel and logarithmic kernel. The results are compared with the exact solution of the integral equation. The error of each method is calculated.

• The Pure and Applied Mathematics
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• v.18 no.1
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• pp.63-78
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• 2011

In the present paper, we obtain integral inequalities involving the Kurzweil-Stieltjes integrals which generalize Gronwall-Bellman inequality and we use the inequalities to verify existence of solutions of a certain integral equation. Such inequalities will play an important role in the study of impulsively perturbed systems [9].

• Journal of the Korean Magnetics Society
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• v.1 no.2
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• pp.79-84
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• 1991

A variational approach employing localized functional is presented to solve alternating magnetic field problems with open boundary. The functional used in the approach consists of the domain integral of finite element region only and the boundary integral of the interfacial boundary between the finite and infinite element regions. The boundary integral is obtained by transforming the infinite domain integral for the infinite element region into the interfacial boundary integral. The proposed algorithm is then applied to a simple two-dimensional problem where the analytic solutions are available. It is shown that the algorithm makes it possible to yield good agreements between the numerical and analytic solutions. and that it requires less computer storage memory and computation time than the conventional finite element method due to the reduction of the computing region.