• Journal of the Korean Mathematical Society
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• v.50 no.1
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• pp.111-125
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• 2013

In this paper, we consider a continuous time risk model involving two types of dependent claims, namely main claims and by-claims. The by-claim is induced by the main claim and the occurrence of by-claim may be delayed depending on associated main claim amount. Using Rouch$\acute{e}$'s theorem, we first derive the closed-form solution for the Laplace transform of the survival probability in the dependent risk model from an integro-differential equations system. Then, using the Laplace transform, we derive a defective renewal equation satisfied by the survival probability. For the exponential claim sizes, we present the explicit formula for the survival probability. We also illustrate the influence of the model parameters in the dependent risk model on the survival probability by numerical examples.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.173-176
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• 1996

The transient behavior of the complex-LMS adaptive filter is studied when the adaptive filter is operating on a fixed or sweeping complex frequency sine-wave signal. The first-order difference equation is derived for the mean weights and its closed form solution is obtained. The transient response is represented as a function of the eigenvectors and eigenvalues of input correlation matrix. The mean-square error of the algorithm is evaluated as well. An optimal convergence parameter and filter length can be determined for sweeping frequency sine-wave signals as a function of frequency change rate and signal and noise powers.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.7
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• pp.877-884
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• 2001

A theoretical analysis is conducted on the Stokes flow in a narrow channel. A vertical fin is mounted on the bottom plate and the flow is induced by uniformly sliding top plate. The governing harmonic equation was solved in the transformed ζ-plane, which is obtained by applying conformal mappings to the physical plane. By using well-known transformation technique, closed-form expressions for velocity and skin frictional stress on the top and bottom plates were obtained.

• Journal of Advanced Marine Engineering and Technology
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• v.27 no.2
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• pp.218-228
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• 2003

A hydraulic system is modeled as the second order differential equation with uncertain system parameters and disturbance composed of modeling errors. To Position the load of the hydraulic system to a desired point. the servo valve of the hydraulic system is controlled. As a control scheme. a global sliding mode control(GSMC) is Proposed Since the servo valve has a torque limit. the GSMC is designed to coordinate the position of the load along the minimum time trajectory within the torque limit. The Proposed control scheme can be designed with ranges of parametric uncertainties and specified torque limits. By the proposed control scheme, the closed form solution of the arriving time at the desired position can be estimated.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.3
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• pp.339-352
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• 2001

The inverse kinematics problem of Stewart platform is straightforward, but no closed form solution of the forward kinematic problem has been presented. Since we need the real-time forward kinematic solution in MIMO control and the motion monitoring of the platform, it is important to acquire the 6 DOF displacements of the platform from measured lengths of six cylinders in small sampling period. Newton-Raphson method a simple algorithm and good convergence, but it takes too long calculation time. So we reduce 6 nonlinear kinematic equations to 3 polynomials using Nairs method and 3 polynomials to 2 polynomials. Then Newton-Raphson method is used to solve 3 polynomials and 2 polynomials respectively. We investigate operation counts and performance of three methods which come from the equation reduction and Newton-Raphson method, and choose the best method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.23 no.11 s.170
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• pp.2058-2066
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• 1999

The present paper proposes a new dynamic analysis method for multi-span Timoshenko beam structures supported by joints with damping subject to moving loads. An exact dynamic element matrix method is adopted to model Timoshenko beam structures. A generalized modal analysis method is applied to derive response formulae for beam structures subject to moving loads. The proposed method offers an exact and closed form solution. Two numerical examples are provided for validating and illustrating the proposed method. In the first numerical example, a single span beam with multiple moving loads is considered. A dynamic analysis on a multi-span beam under a moving load is considered as the second example, in which the flexibility and damping of supporting joints are taken into account. The numerical study proves that the proposed method is useful for the vibration analysis of multi-span beam-hype structures by moving loads.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.144-150
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• 2000

In this paper, we introduce a modified six-degrees-of-freedom parallel-link manipulator, which will be applied to the human vibration experiments. We analyze the inverse kinematics and workspace of this manipulator and comprehend the characteristics of kinematics analyzed. Additionally, solutions of forward kinematics are obtained through the iterative Newton-Raphson method known as one of the most used numerical analysis. Finally, dynamic equation of the manipulator is derived in closed form through the Newton-Euler approach, which will be used for the development of control software.

• Structural Engineering and Mechanics
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• v.30 no.5
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• pp.559-576
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• 2008

Having established the initial geometry and cable force of a typical three span suspension bridge under permanent load, the additional maximum response of the cable and the stiffening girder due to live load are determined, by means of an analytic procedure, considering the girder first hinged at its ends and then continuous through the main towers. The problem of interaction between the cable and the stiffening girder is examined taking under due consideration the second order effects, whereby, through the analogy to a fictitious tensioned beam under transverse load, a closed -form solution is achieved by means of a simple quadratic equation. It is found that the behavior of the whole system is governed by five simple dimensionless parameters which enable a quick determination of all the relevant design magnitudes of the bridge. Moreover, by introducing these parameters, a set of diagrams is presented, which enable the estimation of the influence of the geometric and loading data on the response and permit its immediate evaluation for preliminary design purposes.

• Journal of the Korean Operations Research and Management Science Society
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• v.37 no.2
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• pp.113-125
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• 2012

The logistic model and the Bass model have diverse names and formulae in diffusion theory. This diversity makes users or readers confused while it also contributes to the flexibility of modeling. The method of handling the integration constant, which is generated in process of deriving the closed form solution of the differential equation for a diffusion model, results in two different 'actual' models. We rename the actual four models and propose the usage of the models with respect to the purpose of model applications. The application purpose would be the explanation of historical diffusion pattern or the forecasting of future demand. Empirical validation with 86 historical diffusion data shows that misuse of the models can draw improper conclusions for the explanation of historical diffusion pattern.

• Proceedings of the KSME Conference
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• 2000.11a
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• pp.541-547
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• 2000

This paper presents the closed-form forward kinematics of the 6-6 Stewart platform of planar base and moving platform. Based on algebraic elimination method and with one extra linear sensor, it first derives an 8th-degree univariate equation and then finds tentative solution sets out of which the actual solution is to be selected. In order to provide more exact solution despite the error between measured sensor value and the theoretical one, a correction method is also used. The overall procedure requires so little computation time that it can be efficiently used for realtime applications. In addition, unlike the iterative schemes e.g. Newton-Raphson, the algorithm does not require initial estimates of solution and is free of the problems that it does not converge to actual solution within limited time. The presented method has been implemented in C language and a numerical example is given to confirm the effectiveness and accuracy of the developed algorithm.