• 한국해안해양공학회지
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• 제6권3호
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• pp.275-280
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• 1994

바닥영향을 받는 수평원형 실린더에 작용하는 힘에 대한 해석해를 복소포텐셜을 이용하여 재유도하였다. 본 연구에서 해석해를 재유도한 이유는 Yamamoto 등(1974)이 유도한 해석해는 부가질량제수가 거동하는 경향을 정확하게 설명하지 못하고있기 때문이다. 재유도한 부가질량계수 CM은 Yamamoto 등(1974)의 $C_{M}$ 과 다르며, 또한 부가질랑계수가 거동하는 경향을 만족하게 설명하고 있음을 알 수 있었다.

• East Asian mathematical journal
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• 제38권5호
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• pp.603-610
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• 2022

In [6, 7] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with homogeneous boundary conditions, compute the finite element solutions using standard FEM and use the extraction formula to compute the stress intensity factor(s), then they posed new PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor(s), which converges with optimal speed. From the solution they could get an accurate solution just by adding the singular part. They considered a partial differential equation with the input function f ∈ L²(Ω). In this paper we consider a PDE with the input function f ∈ H¹(Ω) and find the corresponding singular and dual singular functions. We also induce the corresponding extraction formula which are the basic element for the approach.

• Nuclear Engineering and Technology
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• 제14권3호
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• pp.103-109
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• 1982

여러가지 질산우라늄용액에 대한 우라늄의 용존농도, 질산의 노르말농도 및 용액의 밀도등을 측정하여 얻은 결과를 최소자승법으로 분석한 후 우라늄의 용존농도와 질산의 노르말농도만을 알므로서 질산우라늄용액속에 들어있는 물의 함량을 결정할 수 있는 실험식, Q=1-0.3628C-0.0327H$^{+}$,을 유도하였다. 여기서 Q, C 및 H$^{+}$는 각각 물함량(g/cc), 우라늄의 용존농도(g/cc)및 질산의 노르말농도를 뜻한다. 그리고 이 유도식을 써서 임의 우라늄용액에 대한 구성원소별 원자수밀도와 핵임계도를 산출하고 그 결과를 우라늄의 용존농도, 질산의 노르말농도 및 용액의 밀도를 근거로 하여 얻은 값과 비교해 보았다. 그 결과 유도식은 우라늄의 용존농도 0.004~0.2959g/cc 및 질산의 노르말농도 1.00~5.06사이에서 유용하게 쓰일 수 있을 것으로 보였다.

• 대한수학회논문집
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• 제36권3호
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• pp.549-555
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• 2021

We show the solvability of the ordinary differential equations describing curves on sphere or hyperbolic space. Making use of the geometric properties of the equations, we derive explicit solution formulae.

• ETRI Journal
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• 제15권3_4호
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• pp.35-45
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• 1994

In this paper we develop an approximation formalism on the queue length distribution for general queueing models. Our formalism is based on two steps of approximation; the first step is to find a lower bound on the exact formula, and subsequently the Chernoff upper bound technique is applied to this lower bound. We demonstrate that for the M/M/1 model our formula is equivalent to the exact solution. For the D/M/1 queue, we find an extremely tight lower bound below the exact formula. On the other hand, our approach shows a tight upper bound on the exact distribution for both the ND/D/1 and M/D/1 queues. We also consider the $M+{\Sigma}N_jD/D/1$ queue and compare our formula with other formalisms for the $M+{\Sigma}N_jD/D/1$ and M+D/D/1 queues.

• International Journal of Automotive Technology
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• 제6권4호
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• pp.375-381
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• 2005

This paper presents linear algebraic equations in the form of recursive formula to compute elastokinematic characteristics of a suspension system. Conventional methods of elastokinematic analysis are based on nonlinear kinematic constrant equations and force equilibrium equations for constrained mechanical systems, which require complicated and time-consuming implicit computing methods to obtain the solution. The proposed linearized elastokinematic equations in the form of recursive formula are derived based on the assumption that the displacements of elastokinematic behavior of a constrained mechanical system under external forces are very small. The equations can be easily computerized in codes, and have the advantage of sharing the input data of existing general multi body dynamic analysis codes. The equations can be applied to any form of suspension once the type of kinematic joints and elastic components are identified. The validity of the method has been proved through the comparison of the results from established elastokinematic analysis software. Error estimation and analysis due to piecewise linear assumption are also discussed.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제22권2호
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• pp.101-113
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• 2018

The dual singular function method(DSFM) is a numerical algorithm to get optimal solution including corner singularities for Poisson and Helmholtz equations. In this paper, we apply DSFM to solve heat equation which is a time dependent problem. Since the DSFM for heat equation is based on DSFM for Helmholtz equation, it also need to use Sherman-Morrison formula. This formula requires linear solver n + 1 times for elliptic problems on a domain including n reentrant corners. However, the DSFM for heat equation needs to pay only linear solver once per each time iteration to standard numerical method and perform optimal numerical accuracy for corner singularity problems. Because the Sherman-Morrison formula is rather complicated to apply computation, we introduce a simplified formula by reanalyzing the Sherman-Morrison method.

• Structural Engineering and Mechanics
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• 제25권6호
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• pp.717-732
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• 2007

A formula to approximate the fundamental period of a fixed-free mass-spring system with varying mass and varying stiffness is formulated. The formula is derived mainly by taking the dominant parts from the general form of the characteristic polynomial, and adjusting the initial approximation by a coefficient derived from the exact solution of a uniform case. The formula is tested for a large number of randomly generated structures, and the results show that the approximated fundamental periods are within the error range of 4% with 90% of confidence. Also, the error is shown to be normally distributed with zero mean, and the width of the distribution (as measured by the standard deviation) tends to decrease as the total number of discretized elements in the system increases. Other possible extensions of the formula are discussed, including an extension to a continuous cantilever structure with distributed mass and stiffness. The suggested formula provides an efficient way to estimate the fundamental period of building structures and other systems that can be modeled as mass-spring systems.

• 대한수학회보
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• 제55권2호
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• pp.431-448
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• 2018

This paper is concerned with the positive definite solutions of the nonlinear matrix equation $X-A^*{\bar{X}}^{-1}A=Q$, where A, Q are given complex matrices with Q positive definite. We show that such a matrix equation always has a unique positive definite solution and if A is nonsingular, it also has a unique negative definite solution. Moreover, based on Sherman-Morrison-Woodbury formula, we derive elegant relationships between solutions of $X-A^*{\bar{X}}^{-1}A=I$ and the well-studied standard nonlinear matrix equation $Y+B^*Y^{-1}B=Q$, where B, Q are uniquely determined by A. Then several effective numerical algorithms for the unique positive definite solution of $X-A^*{\bar{X}}^{-1}A=Q$ with linear or quadratic convergence rate such as inverse-free fixed-point iteration, structure-preserving doubling algorithm, Newton algorithm are proposed. Numerical examples are presented to illustrate the effectiveness of all the theoretical results and the behavior of the considered algorithms.

• 대한기계학회논문집A
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• 제24권3호
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• pp.645-652
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• 2000

A method for shape design sensitivity analysis is proposed utilizing commercial software ANSYS for thermal conduction problems. While the sensitivity formula is derived analytically by introduing adjoint variable concept, sensitivity calculation in practice as well as the primal and adjoint solution of thermal conduction is performed using the ANSYS very easily. Since the formula always takes boundary integral form, sensitivity evaluation in ANSYS requires a little more addition of post-processing routine which involves evaluation of boundary variable from the obtained solution. Though the BEM has been used as a better tool for this purpose, the present study shows it can also be calculated using any kind of analysis code such as ANSYS since the formula is based on analytic nature. Therefore the present study provides a new and efficient way of optimization which was not possible before using commercial software. The usefulness of the method is illustrated via a weight minimization problem of thermal diffuser.