• 대한수학회보
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• 제33권2호
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• pp.177-186
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• 1996

Colton and Wendland [1] have considered acoustic wave propagations in a spherically symmetric medium. They used constructive method for in a spherically symmetric medium. They used constructive method for solving the exterior Neumann problem. Jones [2] has derived an integral equation for the exterior acoustic problem. Jones has also discussed analytical and numerical solution of the acoustic problem.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제26권1호
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• pp.49-66
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• 2022

The G-Euler process has been proposed to overcome the difficulties of the calculation of the exponential function of the Jacobian. It is an explicit method that uses the exponential function of the scalar skew-symmetric matrix. We define the moving shapes of true solutions and the moving shapes of numerical solutions. It is discussed whether the moving shape of the numerical solution matches the moving shape of the true solution. The match rates of these two kinds of moving shapes are sequentially calculated by the G-Euler process without using the true solution. It is shown that the closer the minimum match rate is to 100%, the more closely the numerical solutions follow the true solutions to the end. The minimum match rate indicates the reliability of the numerical solution calculated by the G-Euler process. The graphs of the Lorenz system in Perko [1] are different from those drawn by the G-Euler process. By the way, there is no basis for claiming that the Perko's graphs are reliable.

• Kyungpook Mathematical Journal
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• 제27권1호
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• pp.43-46
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• 1987

In this paper we consider the semilinear hyperbolic symmetric system of the first-order. The existence and uniqueness of the solution are proved, under certain conditions, some properties of the solution are investigated.

• 대한수학회보
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• 제54권6호
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• pp.2165-2182
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• 2017

Let G be a group and $\mathbb{C}$ the field of complex numbers. Suppose ${\sigma}:G{\rightarrow}G$ is an endomorphism satisfying ${{\sigma}}({{\sigma}}(x))=x$ for all x in G. In this paper, we first determine the central solution, f : G or $G{\times}G{\rightarrow}\mathbb{C}$, of the functional equation $f(xy)+f({\sigma}(y)x)=2f(x)+2f(y)$ for all $x,y{\in}G$, which is a variant of the quadratic functional equation. Using the central solution of this functional equation, we determine the general solution of the functional equation f(pr, qs) + f(sp, rq) = 2f(p, q) + 2f(r, s) for all $p,q,r,s{\in}G$, which is a variant of the equation f(pr, qs) + f(ps, qr) = 2f(p, q) + 2f(r, s) studied by Chung, Kannappan, Ng and Sahoo in [3] (see also [16]). Finally, we determine the solutions of this equation on the free groups generated by one element, the cyclic groups of order m, the symmetric groups of order m, and the dihedral groups of order 2m for $m{\geq}2$.

• 대한토목학회논문집
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• 제28권4B호
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• pp.413-419
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• 2008

본 연구에서는, 바닥의 수심이 반경의 임의 차수의 제곱 꼴로 표현되는 다양한 형태의 축 대칭 지형 위를 통과하는 장파의 해석해를 유도하였다. 첫 번째 지형은 둔덕 위에 원기둥 모양의 섬이 있는 경우이며 두 번째는 원형의 섬이 있는 경우이다. 해를 구하기 위하여 변수 분리법, Taylor 급수전개법 및 Frobenius 급수법을 사용하였다. 유도된 해석해를 기존에 유도된 해석해와 비교를 하여 그 정확성을 검증 하였다. 또한, 입사파의 주기, 둔덕의 반지름 및 차수를 가지는 경우에 대하여 분석하였다.

• 멤브레인
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• 제25권4호
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• pp.320-326
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• 2015

본 연구에서는 0.5 wt% 에멀젼형 절삭유 수용액에 평막형 분리막을 침지시키고 대칭 및 비대칭 사인파형 투과유속 연속운전(SFCO) 방식으로 실험하였다. 사용한 정밀여과막은 유효 막면적이 $0.02m^2$이고 공칭 세공크기가 $0.15{\mu}m$이었다. 탁도 기준으로 에멀젼형 절삭유의 99% 이상이 제거되었으며 산기량이 증가할수록 TMP가 낮게 상승하였다. 비대칭형 SFCO 운전방식은 투과유속이 낮은 $10{\sim}15L/m^2{\cdot}h$ 영역에서 대칭형 SFCO 운전방식보다 다소 유리하였다. 하지만, 투과유속이 높은 $25{\sim}30L/m^2{\cdot}h$에서는 대칭형 SFCO 운전이 매우 효과적임을 확인할 수 있었다.

• Advances in Computational Design
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• 제5권3호
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• pp.305-321
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• 2020

In this paper is presented the solution method for three-dimensional problem of transversely isotropic body's elastoplastic deformation by the finite element method (FEM). The process of problem solution consists of: determining the effective parameters of a transversely isotropic medium; construction of the finite element mesh of the body configuration, including the determination of the local minimum value of the tape width of non-zero coefficients of equation systems by using of front method; constructing of the stiffness matrix coefficients and load vector node components of the equation for an individual finite element's state according to the theory of small elastoplastic deformations for a transversely isotropic medium; the formation of a resolving symmetric-tape system of equations by summing of all state equations coefficients summing of all finite elements; solution of the system of symmetric-tape equations systems by means of the square root method; calculation of the body's elastoplastic stress-strain state by performing the iterative process of the initial stress method. For each problem solution stage, effective computational algorithms have been developed that reduce computational operations number by modifying existing solution methods and taking into account the matrix coefficients structure. As an example it is given, the problem solution of fibrous composite straining in the form of a rectangle with a system of circular holes.

• International Journal of Aeronautical and Space Sciences
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• 제14권2호
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• pp.112-121
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• 2013

An approach for composing a performance optimized computational code is suggested for the latest microprocessors. The concept of the code optimization, termed localization, is maximizing the utilization of the second level cache that is common to all the latest computer systems, and minimizing the access to system main memory. In this study, the localized optimization of the LU-SGS (Lower-Upper Symmetric Gauss-Seidel) code for the solution of fluid dynamic equations was carried out in three different levels and tested for several different microprocessor architectures widely used these days. The test results of localized optimization showed a remarkable performance gain of more than two times faster solution than the baseline algorithm for producing exactly the same solution on the same computer system.

• 한국콘텐츠학회논문지
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• 제15권6호
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• pp.539-546
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• 2015

본 연구에서는 수심이 해안선에서 0이 되며 임의로 변하는 축 대칭 지형의 주변을 통과하는 파를 해석하기 위하여 타원형 완경사 방정식을 이용한 수치모델을 개발하였다. 수치해석을 위해 전체 영역을 세 부분으로 구분하였는데, 안쪽 및 바깥쪽 영역에서는 기존 해석해를 활용하였으며, 가운데 영역에서는 지배방정식에서 유한요소기법을 적용하였다. 영역 1에서의 해석해는 변수분리법 및 Frobenius 급수를 사용하였다. 개발된 수치해는 기존에 존재하는 해석해와 비교하여 타당성을 검증하였으며 다양한 경우에 적용하여 활용성을 검토하였다.

• 한국공간구조학회논문집
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• 제2권3호
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• pp.115-122
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• 2002

It is often hard to obtain analytical solutions of boundary value problems of shells. Introducing some approximations into the governing equations may allow us to get analytical solutions of boundary value problems. Instead of an analytical procedure, we can apply a numerical method to the governing equations. Since the governing equations of shells of revolution under symmetric load are expressed by ordinary differential equations, a numerical solution of ordinary differential equations is applicable to solve the equations. In this paper, the governing equations of orthotropic spherical shells under symmetric load are derived from the classical theory based on differential geometry, and the analysis is numerically carried out by computer program of Runge-Kutta methods. The numerical results are compared to the solutions of a commercial analysis program, SAP2000, and show good agreement.