• Journal of the Computational Structural Engineering Institute of Korea
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• v.12 no.2
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• pp.251-264
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• 1999

본 연구에서는 추계론적 동적시스템의 응답거동을 예측할 수 있는 반해석적 절차를 개발하였으며, 이를 이용하여 구분적선형시스템의 동적거동특성을 확률적 영역에서 분석하였다. 반 해석적 절차는 시스템의 추계론적 미분방정식에 상응하는 Fokker-Planck 방정식을 path-integral solotion을 이용하여 풂으로써 구할 수 있다. 결합확률밀도함수의 시간에 따른 전개과정을 통하여 시스템의 동적 응답거동 특성의 예측과 분석을 하고 시스템의 거동에 미치는 외부노이즈의 영향 또한 조사하였다. 반 해석적 방법은 위상면 상에서 결합확률밀도 함수를 통하여 응답거동의 예측은 물론 거동특성에 대하여 적절한 정보를 제공하는 것을 밝혔다. 혼돈거동의 특성은 외부노이즈가 존재하는 상황에서도 시스템의 응답 안에 잔재하는 것을 밝혔다.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.17 no.1
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• pp.83-91
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• 2004

Nonlinear system responses of an impact system under randomly perturbed harmonic excitations are predicted in the probability domain by adopting the semi-analytical procedure previously developed. The semi-analytical procedure is obtained by solving the Fokker-Planck equation corresponding to the stochastic differential equation of the given impact system by utilizing the path-integral solution. The evolutionary joint probability density functions are generated by using the method, and the characteristics of nonlinear dynamic response behaviors of the system are examined. Noise effects on the responses are also examined. It Is found that the semi-analytical method can provides the accurate information of the responses via the joint probability functions for the impact system. It is found that the noises weaken and eventually terminate the chaos in the responses, but it is also found that the chaotic signatures reside in the presence of the external noise with relatively high intensity. The joint probability density function shows that the ensemble of the system responses are weakly stationary.

• Journal of the Earthquake Engineering Society of Korea
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• v.9 no.6 s.46
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• pp.53-58
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• 2005

Semi-analytical methodology to examine the dynamic responses of a bridge is developed via the joint probability density function. The evolution of joint probability density function is evaluated by the semi-analytical procedure developed. The joint probability function of the bridge responses can be obtained by solving the path-integral solution of the Fokker-Planet equation corresponding to the stochastic differential equations of the system. The response characteristics are observed from the joint probability density function and the boundary of the envelope of the probability density function can provide the maxima ol the bridge responses.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.337-348
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• 2001

The unitary Lie-Trotter-Kato product formula gives in a simplest way a meaning to the Feynman path integral for the Schroding-er equation. In this note we want to survey some of recent results on the norm convergence of the selfadjoint Lie-Trotter Kato product formula for the Schrodinger operator -1/2Δ + V(x) and for the sum of two selfadjoint operators A and B. As one of the applications, a remark is mentioned about an approximation therewith to the fundamental solution for the imaginary-time Schrodinger equation.

• Proceedings of the KIEE Conference
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• summer
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• pp.1403-1405
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• 2004

The method proposed by Carson contains indefinite complex integral which simulates earth return current. Although the Carson solution is proposed with power series, the solution is limited and valid at special range of frequency. We proposed a simplified Carson solution by modelling earth current path analytical method using ground transmission line return current. In this paper, we studied on trying to find the equivalent distance for earth current return path.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.757-769
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• 2019

A solution of the heat equation with a distribution-valued potential is constructed by regularization. When the potential is the generalized derivative of a $H{\ddot{o}}lder$ continuous function, regularity of the resulting solution is in line with the standard parabolic theory.

• Transactions of the Korean Society of Mechanical Engineers
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• v.13 no.3
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• pp.479-489
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• 1989

The $J_{k}$ integral method for determining mixed mode stress intensity factors separately in the cracked anisotropic plate is developed. Stress intensity factors are indirectly determined from the values of $J_{1}$ and $J_{2}$. The $J_{2}$ integral can be evaluated efficiently from a finite element solution, neglecting the contribution from the portion of the integration contour along the crack faces, by selecting the integration contour in the vicinity of the crack tip. Using functions of a complex variable, the complete relations between $J_{1}$, $J_{2}$ and $K_{I}$ , $K_{II}$ for anisotropic materials are derived conveniently by selecting narrow rectangular contours shrinking to the crack tip. Compared to the existing path independent integral methods, the present method does not involve calculating the auxiliary solution and hence numerical procedures become quite simple. Numerical results to various problems are given and demonstrate the accuracy, stability and versatility of the method.

• Management Science and Financial Engineering
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• v.11 no.2
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• pp.85-103
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• 2005

In this paper, we consider the routing and wavelength assignment problem in survivable WDM transport network without wavelength conversion. We assume the single-link failure and a path protection scheme in optical layer. When a physical network and a set of working paths are given, the problem is to select a link-disjoint protection path for each working path and assign a wavelength for each working and protection path. We give an integer programming formulation of the problem and propose an algorithm to solve it. Though the formulation has exponentially many variables, we solve the linear programming relaxation of it by using column generation technique. We devise a branch-and price algorithm to solve the column generation problem. After solving the linear programming relaxation, we apply a variable fixing procedure combined with the column generation to get an integral solution. We test the proposed algorithm on some randomly generated data and test results show that the algorithm gives very good solutions.

• International Journal of Precision Engineering and Manufacturing
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• v.2 no.3
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• pp.11-18
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• 2001

A simple and convenient method of analysis for obtaining the individual stress intensity factors in a three-dimensional mixed mode crack is proposed. The procedures presented here are based on the path independence of J integral and mutual or two-state conservation integral, which involves two elastic fields. The problem is reduced to the determination of mixed mode stress intensity factor solutions in terms of conservation integrals involving known auxiliary solutions. Some numerical examples are presented to investigate the effectiveness and applicability of the method for a three-dimensional penny-shaped crack problem under mixed mode. This procedure is applicable to a three-dimensional mixed mode curved crack.

• The Journal of the Acoustical Society of Korea
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• v.13 no.2E
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• pp.83-91
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• 1994

Three components contribute to the acoustic field propagating in a wedge or over a ridge : a direct path arrival, an image component due to reflection from the boundaries and a component diffracted by the apex. All three contributions are included in a new, exact solution of the Helmholtz equation for the three-dimensional time harmonic field from a point source in a wedge(or over a ridge) formed by two intersecting, pressure-release plane boundaries. The solution is obtained by applying three integral transforms, and consists of and infinite sum of uncoupled normal nodes. The mode coefficients are given by a finite integral involving a Gegenbauer polynomial in the integrand, which may be computed relatively efficiently. Results of the theory for propagation over a 90 degree ridge is discussed.