• Journal of the Korean Data and Information Science Society
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• v.16 no.1
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• pp.127-136
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• 2005

We will derive some results on the perturbation of roots using Newton's interpolation formula. And we also compare our results with those obtained by Ostrowski by giving some numerical experiments with Wilkinson's polynomials.

• Journal of the Korean Mathematical Society
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• v.32 no.1
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• pp.61-76
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• 1995

Much research has been done to estimate the magnitudes of the changes of the roots from the perturbed polynomials. For more information and references on such work, see [2, 4, 5, 10, 17].

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.423-430
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• 2002

The object of this Paper is to Present a q-analogue of the Newton's forward-difference interpolation formula. We relate the q-beta function and the q-gamma function by the q-difference operators.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.135-145
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• 1995

A new algorithm was given to successively fit the multiexponential function/nonlinear function to data by a weighted least squares method, using Gauss-Newton, Marquardt, gradient and DUD methods for convergence. This study also considers the problem of linear-nonlimear weighted least squares estimation which is based upon the usual Taylor's formula process.

• Journal of Ocean Engineering and Technology
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• v.37 no.6
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• pp.256-265
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• 2023

Many numerical methods have been developed since 1961, but unresolved issues remain. This study developed a numerical method to address these issues and determine the coefficients and properties of rotational waves with a shear current in a finite water depth. The number of unknown constants was reduced significantly by introducing a wavelength-independent coordinate system. The reference depth was calculated independently using the shooting method. Therefore, there was no need for partial derivatives with respect to the wavelength and the reference depth, which simplified the numerical formulation. This method had less than half of the unknown constants of the other method because Newton's method only determines the coefficients. The breaking limit was calculated for verification, and the result agreed with the Miche formula. The water particle velocities were calculated, and the results were consistent with the experimental data. Dispersion relations were calculated, and the results are consistent with other numerical findings. The convergence of this method was examined. Although the required series order was reduced significantly, the total error was smaller, with a faster convergence speed.

• Bulletin of the Korean Chemical Society
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• v.34 no.2
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• pp.574-578
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• 2013

In this work, the friction and diffusion coefficients of a tracer in a mesoscopic solvent are evaluated as a function of the tracer size by a hybrid molecular dynamics simulation where solute molecules evolve by Newton's equations of motion but the solvent evolves through the multi-particle collision dynamics. The friction coefficient is shown to scale linearly with the tracer size for larger tracers in accord with predictions of hydrodynamic theories. The diffusion coefficient of tracer is found to be inversely proportional to tracer size. The behavior of Stokes-Einstein formula is validated as a function of tracer size.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.19 no.6
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• pp.1016-1026
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• 1994

In this paper, we have studied load balancing problems in distributed systems. The nodes of distributed systems exchange periodically system state information each other. The information is stored in history. Based on the information, we compute an expected load index(ELI) using a five-degree interpolation polynomial in Newton`s backward difference interpolation formula. A new location policy of dynamic load balancing systems makes use of the ELI. We show that its performance is better than that of the existing load balancing algorithm through a simulation study.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.1744-1746
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• 2004

This paper focuses on the problem of asymptotic stabilization for time-delay systems. To this end, a memoryless state feedback controller is proposed. Then, based on the Lyapunov method, a delay-dependent stabilization criterion is devised by taking the relationship between the terms in the Leibniz-Newton formula into account. Certain free weighting matrices are used to express this relationship and linear matrix inequalities (LMIs)-based algorithm to design the controller stabilizing the system.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.296-301
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• 2005

This paper describes the kinematics, dynamics and control of a 6-DOF shaking table with a bell crank structure, which converts the direction of reciprocating movements. In this shaking table, the bell crank mechanism is used to reduce the amount of space needed to install the shaking table and create horizontal displacement of the platform. In kinematics, joint design is performed using $Gr{\ddot{u}}bler's$ formula. The inverse kinematics of the shaking table is discussed. The derivation of the Jacobian matrix is presented to evaluate singularity conditions. Considering the maximum stroke of the hydraulic actuator, collision between links and singularity, workspace is computed. In dynamics, computations are based on the Newton-Euler formulation. To derive parallel algorithms, each of the contact forces is decomposed into one acting in the direction of the leg and the other acting in the plane orthogonal to the direction of the leg. Applying the Newton-Euler approach, the solution of inverse dynamics is almost completely parallel. Only one of the steps-the application of the Newton-Euler equations to the platform-must be performed on one single processor. Finally, the efficient control scheme is proposed for the tracking control of the motion platform.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 2000.11a
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• pp.63-71
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• 2000

In this study a drift prediction model based on fluid dynamics theory is introduced. The essential effects of environmental loads and target characteristics are taken into account from a fluid dynamics point of view. The governing equations of motion are derived from Newton's law of dynamics. In the mathematical formulation only three degrees of freedom(surge, sway, yaw) of the drifting object are assumed and the environmental loads considered are the forces and moments by wind and current. A computer algorithm for this model is implemented to obtain the numerical result in the time domain. The preliminary tests for model verification are conducted and the results are compared with the field experiment data as well as leeway formula suggested from the field test data.