• Journal of applied mathematics & informatics
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• 제26권3_4호
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• pp.811-818
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• 2008

Biological systems with both protein-protein and protein-gene interactions can be modeled by differential equations for concentrations of the proteins with time-delay terms because of the time needed for DNA transcription to mRNA and translation of mRNA to protein. Values of some parameters in the mathematical model can not be measured owing to the difficulty of experiments. Also values of some parameters obtained in a normal stress condition can be changed under pathological stress stimuli. Thus it is important to find the effective way of determining parameters values. One approach is to use optimization algorithms. Here we construct an optimal system used to find optimal parameters in the equations with nonnegative time delays and apply this optimization result to the Nuclear factor-${\kappa}B$ pathway.

• 한국공작기계학회논문집
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• 제12권2호
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• pp.71-78
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• 2003

This research proposes an implementation method of linearized equations of motion for multibody systems with closed loops. The null space of the constraint Jacobian is first pre-multiplied to the equations of motion to eliminate the Lagrange multiplier and the equations of motion are reduced down to a minimum set of ordinary differential equations. The resulting differential equations are functions of all relative coordinates, velocities, and accelerations. Since the variables are tightly coupled by the position, velocity, and acceleration level coordinates, direct substitution of the relationships among these variables yields very complicated equations to be implemented. As a consequence, the reduced equations of motion are perturbed with respect to the variations of all variables, which are coupled by the constraints. The position velocity and acceleration level constraints are also perturbed to obtain the relationships between the variations of all relative coordinates, velocities, and accelerations and variations of the independent ones. The Perturbed constraint equations are then simultaneously solved for variations of all variables only in terms of the variations of the independent variables. Finally, the relationships between the variations of all variables and these of the independent ones are substituted into the variational equations of motion to obtain the linearized equations of motion only in terms of the independent variables variations.

• Advances in environmental research
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• 제3권2호
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• pp.131-149
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• 2014

Two different model selection indices, the Akaike information criterion (AIC) and the coefficient of determination ($R^2$), are used to discriminate competing isotherm equations for aqueous pollutant removal systems. The former takes into account model accuracy and complexity while the latter considers model accuracy only. The five types of isotherm shape in the Brunauer-Deming-Deming-Teller (BDDT) classification are considered. Sorption equilibrium data taken from the literature were correlated using isotherm equations with fitting parameters ranging from two to five. For the isotherm shapes of types I (favorable) and III (unfavorable), the AIC favors two-parameter equations which can easily track these simple isotherm shapes with high accuracy. The $R^2$ indicator by contrast recommends isotherm equations with more than two parameters which can provide marginally better fits than two-parameter equations. To correlate the more intricate shapes of types II (multilayer), IV (two-plateau) and V (S-shaped) isotherms, both indices favor isotherm equations with more than two parameters.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1987년도 한국자동제어학술회의논문집; 한국과학기술대학, 충남; 16-17 Oct. 1987
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• pp.52-57
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• 1987

In this paper, it is dealt with the dynamic motion equations for a robot arm. Four kinds of the dynamic equations which are the Lagrange-Euler equations, the Recursive L-E equations, the Newton-Euler equations and the improved N-E equation are derived on robot PUMA 600. Finally the algorithms on these equations are programmed using PASCAL. and are compared with each other. As the results, it is found that the improved N-E equations has the most fastest execution time among the equations and can be used in real time processing.

• 한국CDE학회논문집
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• 제20권1호
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• pp.84-92
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• 2015

In this study, we describe a method to analysis dynamic behavior of an offshore wind turbine in the frequency domain and expected effects of the method. An offshore wind turbine, which is composed of platform, tower, nacelle, hubs, and blades, can be considered as multibody systems. In general, the dynamic analysis of multibody systems are carried out in the time domain, because the equations of motion derived based on the multibody dynamics are generally nonlinear differential equations. However, analyzing the dynamic behavior in time domain takes longer than in frequency domain. In this study, therefore, we describe how to analysis the system multibody systems in the frequency domain. For the frequency domain analysis, the non-linear differential equations are linearized using total derivative and Taylor series expansions, and then the linearized equations are solved in time domain. This method was applied to analysis of double pendulum system for the verification of its effectiveness, and the equations of motion for the offshore wind turbine was derived with assuming that the wind turbine is rigid multibody systems. Using this method, the dynamic behavior analysis of the offshore wind turbine can be expected to take less time.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2004년도 춘계학술대회
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• pp.893-898
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• 2004

This research proposes an implementation method of linearized equations of motion for multibody systems with closed loops. The null space of the constraint Jacobian is first pre multiplied to the equations of motion to eliminate the Lagrange multiplier and the equations of motion are reduced down to a minimum set of ordinary differential equations. The resulting differential equations are functions of all relative coordinates, velocities, and accelerations. Since the coordinates, velocities, and accelerations are tightly coupled by the position, velocity, and acceleration level constraints, direct substitution of the relationships among these variables yields very complicated equations to be implemented. As a consequence, the reduced equations of motion are perturbed with respect to the variations of all coordinates, velocities, and accelerations, which are coupled by the constraints. The position, velocity and acceleration level constraints are also perturbed to obtain the relationships between the variations of all relative coordinates, velocities, and accelerations and variations of the independent ones. The perturbed constraint equations are then simultaneously solved for variations of all coordinates, velocities, and accelerations only in terms of the variations of the independent coordinates, velocities, and accelerations. Finally, the relationships between the variations of all coordinates, velocities, accelerations and these of the independent ones are substituted into the variational equations of motion to obtain the linearized equations of motion only in terms of the independent coordinate, velocity, and acceleration variations.

• 한국수자원학회논문집
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• 제40권5호
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• pp.397-407
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• 2007

건기 때의 합류식 관거 내 고형물의 퇴적으로 인해 통수능이 감소하여 여름철 우기시 국지적인 침수가 발생하며 이로 인해 관거 내 퇴적을 더욱 초래할 수가 있다. 이와 같은 문제를 해결하고 관거 시스템을 효율적으로 관리하기 위해서는 관거 내 고형물 퇴적량을 산정하기 위한 식을 개발할 필요가 있다. 그러나 이러한 산정식을 개발하기 전에 컴퓨터 모형 등을 이용한 고형물 퇴적량을 산정하여야 한다. 따라서 본 연구에서는 국내 군자매수유역에 대해 MOUSE 모형을 적용하여 관거 내 고형물 퇴적량을 산정하였으며, 이를 미환경보호청(EPA)에서 개발한 산정식을 이용하여 산정한 퇴적량과 검토하였다. MOUSE 모형을 적용하여 산정한 값은 EPA에서 1977년에 개발한 초기의 산정식에 의한 결과보다는 작지만 1984년에 개발된 산정식에 의한 결과보다는 다소 크게 나타나고 있다. 퇴적고형물의 관측자료가 구비되어 있지 않아 모형에 의한 산정치를 비교하기는 곤란하지만 모형에 의해 산정결과가 신뢰성이 있다고 판단되며, 추후 군자배수유역에 대한 산정식을 유도하는데 이용할 수 있다고 본다.

• Journal of Mechanical Science and Technology
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• 제14권2호
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• pp.159-167
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• 2000

A computational method for the dynamic analysis of a constrained mechanical system is presented in this paper. The partial velocity matrix, which is the null space of the Jacobian of the constraint equations, is used as the key ingredient for the derivation of reduced equations of motion. The acceleration constraint equations are solved simultaneously with the equations of motion. Thus, the total number of equations to be integrated is equivalent to that of the pseudo generalized coordinates, which denote all the variables employed to describe the configuration of the system of concern. Two well-known conventional methods are briefly introduced and compared with the present method. Three numerical examples are solved to demonstrate the solution accuracy, the computational efficiency, and the numerical stability of the present method.

• Journal of information and communication convergence engineering
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• 제12권1호
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• pp.39-45
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• 2014

A numerical method for solving Hamiltonian equations is said to be symplectic if it preserves the symplectic structure associated with the equations. Various symplectic methods are widely used in many fields of science and technology. A symplectic method preserves an approximate Hamiltonian perturbed from the original Hamiltonian. It theoretically supports the effectiveness of symplectic methods for long-term integration. Although it is also related to long-term integration, numerical stability of symplectic methods have received little attention. In this paper, we consider explicit symplectic methods defined for Hamiltonian equations with Hamiltonians of the special form, and study their numerical stability using the harmonic oscillator as a test equation. We propose a new stability criterion and clarify the stability of some existing methods that are visually based on the criterion. We also derive a new method that is better than the existing methods with respect to a Courant-Friedrichs-Lewy condition for hyperbolic equations; this new method is tested through a numerical experiment with a nonlinear wave equation.

• 충청수학회지
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• 제26권4호
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• pp.869-878
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• 2013

We study boundedness of solutions of dynamic equations on time scales by using Lyapunov-type functions.