• Journal of applied mathematics & informatics
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• 제7권2호
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• pp.391-408
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• 2000

In the curved geometries, from the solution of the classical Riemann problem in the plane, the asymptotic solutions of the compressible Euler equation are presented. The explicit formulae are derived for the third order approximation of the generalized Riemann problem form the conventional setting of a planar shock-interface interaction.

• Journal of applied mathematics & informatics
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• 제7권1호
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• pp.175-181
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• 2000

The purpose of this to measure, with explicit constants as small as possible, a priori error bounds for approximation by picewise polynomials. These constants play an important role in the numerical verification method of solutions for obstacle problems by using finite element methods .

• 충청수학회지
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• 제31권1호
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• pp.161-166
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• 2018

This paper deals an impulsive fractional integral inequality with singular kernel which can be used in getting the explicit estimate of solutions of impulsive fractional differential equations.

• 호남수학학술지
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• 제33권2호
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• pp.223-229
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• 2011

In investigation of boundary-value problems for certain partial differential equations arising in applied mathematics, we often need to study the solution of system of partial differential equations satisfied by hypergeometric functions and find explicit linearly independent solutions for the system. Here we choose the Exton functions $X_1$ and $X_2$ among his twenty functions to show how to find the linearly independent solutions of partial differential equations satisfied by these functions $X_1$ and $X_2$.

• 대한의용생체공학회:의공학회지
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• 제5권1호
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• pp.9-14
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• 1984

The asymptotic solution using the Tailor series has been given explicit form for the solute concentration and overall solute removal in hemodiafilter using one dimensional model. The numerical solutions have been calculated within 0.001% error by the Romberg integration method. Compared with the numerical solutions, the oneterm asymptotic solutions were found to be within 3% error for the condition > 3.0 and three-terms asymtotic solutions were required for the condition >0.7 where denotes measure of convection over diffusional transport and a the ratio of blood flow rate over dialysate flow rate.

• Structural Engineering and Mechanics
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• 제35권4호
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• pp.409-430
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• 2010

The present paper will be concerned to the investigation of the stress-strain field around the cavity that is loaded or partially loaded at the inner surface by the rotationally symmetric loading. The cavity of the spherical, cylindrical or elliptical shape is situated in a stressed elastic continuum, subjected to the gravitation field. As the contribution to the similar investigations, the paper introduces the new function of loading in the form of the infinite sine series. Besides, in this paper the solution of stresses around an oblong ellipsoid cavity, has been obtained using appropriate curvilinear elliptical coordinates. This analytical approach avoids the solutions of the same problem that lead to expressions that contain rather complex integrations. Thus the presented solutions provide the applicable and explicit expressions for stresses and strains developed in infinite series with easily determinable coefficients by the use of contemporary mathematical packages. The numerical examples are also included to confirm the convergence of the obtained solutions.

• 대한기계학회논문집A
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• 제27권1호
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• pp.66-76
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• 2003

The arbitrary V-notched crack problem is considered. The general expressions for the stress components on this problem are obtained as explicit series forms composed of independent unknown coefficients which are denoted by coefficients of eigenvector. For this results eigenvalue equation is performed first through introducing complex stress functions and applying the traction free boundary conditions. Next solving this equation, eigenvalues and corresponding eigenvectors are obtained respectively, and finally inserting these results into stress components, the general equations are obtained. These results are also shown to be applicable to the symmetric V-notched crack or straight crack. It can be shown that this solutions are composed of the linear combination of Mode I and Mode II solutions which are obtained from different characteristic equations, respectively. Through performing asymptotic analysis for stresses, the stress intensity factor is given as a closed form equipped with the unknown coefficients of eigenvector. In order to calculate the unknown coefficients. based on these general explicit equations, numerical programming using the overdetermined boundary collocation method which is algorithmed originally by Carpenter is also worked out. As this programming requires the input data, the commercial FE analysis for stresses is performed. From this study, for some V-notched problems, unknown coefficients can be calculated numerically and also fracture parameters are determined.

• 한국산학기술학회논문지
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• 제11권9호
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• pp.3583-3589
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• 2010

본 연구에서는 2차원 천수방정식을 풀이 하는데 Backhaus가 제안한 반음해법의 유한차분법을 도입하였다. 이 기법을 사용하여 금강하구 해역의 조위와 유속을 구하는 수치모형을 구성하였다. 본 모형에 의한 수치해를 검증하기 위하여 양해법의 모형으로 잘 알려진 Heaps모형의 결과와 비교하였다. 두 모형의 수치해는 거의 일치하였다. 반음해법에서 선택한 계산시간간격은 엄격한 CFL 조건에 의존하는 양해법보다 6배를 증가 시킬 수 있었다. 총 계산 시간은 50%정도 감소하였다. 이와 같은 사실은 본 수치해법이 금강하구 해역에 널리 분포되어 있는 간사지의 처리가 원활하였으며 장기간 동안의 계산에서도 안정적인 수치해석이 가능하였다.

• 한국해안해양공학회지
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• 제16권2호
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• pp.57-63
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• 2004

지진해일파는 조석에 비하면 파장이 짧아 상대적으로 분산성이 장하므로, 먼 거리를 전파하는 경우에는 분산성을 고려하여 해석하여야 한다. 본 연구에서는 파동방정식에 기초한 일차원 유한요소모형을 이용하여 지진해일 전파를 수치모의할 때 시간단계를 2단계로 나누어 양해법을 사용하면서도 분산효과를 고려할 수 있는 능동적인 분산보정기법을 개발하였다. 제안된 기법을 이용하여 계산한 수치해와 파의 분산효과를 고려한 해석해의 비교를 통해 본 연구에서 제안한 분산보정기법의 타당성을 확인하였다.

• 대한수학회보
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• 제37권4호
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• pp.803-810
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• 2000

Let N($d_1,...,{\;}d_n;c_1,...,{\;}c_n$) be the number of solutions $(x_1,...,{\;}x_n){\in}F^{n}_p$ of the diagonal equation $c_lx_1^{d_1}+c_2x_2^{d_2}+{\cdots}+c_nx_n^{d_n}{\;}={\;}0{\;}n{\geq},{\;}c_j{\;}{\in}{\;}F^{*}_q,{\;}j=1,2,...,{\;}n$ where $d_j{\;}>{\;}1{\;}and{\;}d_j{\;}$\mid${\;}q{\;}-{\;}1$ for all j = 1,2,..., n. In this paper, we find all n-tuples ($d_1,...,{\;}d_n$) such that the reduced form of ($d_1,...,{\;}d_n$) and N($d_1,...,{\;}d_n;c_1,...,{\;}c_n$) are the same as in the theorem obtained by Sun Qi [3]. Improving this, we also get an explicit formula for the number of solutions of the diagonal equation, unver a certain natural restriction on the exponents.