• East Asian mathematical journal
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• v.31 no.3
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• pp.301-310
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• 2015

In this paper, we establish a strong convergence for the Noor iterative scheme associated with Lipschitz strongly pseudocontractive mappings in real Banach spaces. It's proof-method is very simple by comparing with the previous proofs known.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2001.05a
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• pp.244-249
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• 2001

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• Honam Mathematical Journal
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• v.9 no.1
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• pp.99-111
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• 1987

In this paper we shall construct a ridge estimator in a multiple linear model with the correlated error structure. The existence of the biasing parameter satisfying the Mean Squared Error Criterion is also proved. Furthermore, we shall determine the value of shrinkage factors by the iteration method.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.253-265
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• 2019

The aim of this paper is to study convergence behaviour of Thakur iteration scheme in CAT(0) spaces for generalized nonexpansive mappings. In process, several relevant results of the existing literature are generalized and improved.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1157-1162
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• 2019

In this paper, we extend the study of general convergence theorems for the Picard iteration of Proinov contraction from the class of continuous mappings to the class of discontinuous mappings. As a by product we provide a new affirmative answer to the open problem posed in [20].

• Korean Journal of Mathematics
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• v.31 no.1
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• pp.121-122
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• 2023

• Journal of the military operations research society of Korea
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• v.13 no.1
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• pp.91-100
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• 1987

This paper deals with an algorithm for solving nonlinear programming problems with equality constraints. Nonlinear programming problems are transformed into a square sums of nonlinear functions by the Lagrangian multiplier method. And an iteration method minimizing this square sums is suggested and then an algorithm is proposed. Also theoretical basis of the algorithm is presented.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.1129-1163
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• 2013

Based on finite element discretization, two linearization approaches to the defect-correction method for the steady incompressible Navier-Stokes equations are discussed and investigated. By applying $m$ times of Newton and Picard iterations to solve an artificial viscosity stabilized nonlinear Navier-Stokes problem, respectively, and then correcting the solution by solving a linear problem, two linearized defect-correction algorithms are proposed and analyzed. Error estimates with respect to the mesh size $h$, the kinematic viscosity ${\nu}$, the stability factor ${\alpha}$ and the number of nonlinear iterations $m$ for the discrete solution are derived for the linearized one-step defect-correction algorithms. Efficient stopping criteria for the nonlinear iterations are derived. The influence of the linearizations on the accuracy of the approximate solutions are also investigated. Finally, numerical experiments on a problem with known analytical solution, the lid-driven cavity flow, and the flow over a backward-facing step are performed to verify the theoretical results and demonstrate the effectiveness of the proposed defect-correction algorithms.

• Journal of The Korean Astronomical Society
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• v.30 no.1
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• pp.13-25
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• 1997

Sobolev approximation can be adopted to a macroscopic supersonic motion comparatively larger than a random (thermal) one. It has recently been applied not only to the winds of hot early type stars, but also to envelopes of late type giants and/or supergiants. However, since the ratio of wind velocity to stochastic one is comparatively small in the winds of these stars, the condition for applying the Sobolev approximation is not fulfilled any more. Therefore the validity of the Sobolev approximation must be checked. We have calculated exact P Cygni profiles with various velocity ratios, $V_\infty/V_{sto}$, using the accelerated lambda iteration method, comparing with those obtained by the Sobolev approximation. While the velocity ratio decrease, serious deviations have been occured over the whole line profile. When the gradual increase in the velocity structure happens near the surface of star, the amount of deviations become more serious even at the high velocity ratios. The investigations have been applied to observed UV line profile of CIV in the Copernicus spectrums $of\;\zeta\;Puppis\;and\;NV\;of\;\tau\;Sco$. In case of $\tau$ Sco which has an expanding envelope with the gradual velocity increase in the inner region, The Sobolev approximation has given the serious deviations in the line profiles.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.39 no.2
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• pp.27-38
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• 2002

A new self-consistent mathematical model for semiconductor quantum well device was developed. The model was based on the direct solution of the Boltzmann transport equation, coupled to the Schrodinger and Poisson equations. The solution yielded the distribution function for a two-dimensional electron gas(2DEG) in quantum well devices. To solve the Boltzmann equation, it was transformed into a tractable form using a Legendre polynomial expansion. The Legendre expansion facilitated analytical evaluation of the collision integral, and allowed for a reduction of the dimensionality of the problem. The transformed Boltzmann equation was then discretized and solved using sparce matrix algebra. The overall system was solved by iteration between Poisson, Schrodinger and Boltzmann equations until convergence was attained.