• Korean Journal of Mathematics
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• v.16 no.1
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• pp.51-55
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• 2008

Let f be an analytic function with a simple zero in the reals or the complex numbers. An extraneous fixed-point of an iteration function is a fixed-point different from a zero of f. We prove that all extraneous fixed-points of Laguerre-like iteration functions and general Laguerre-like functions are repulsive.

• Journal of Powder Materials
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• v.30 no.1
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• pp.29-34
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• 2023

A fixed-point iteration is proposed to integrate the stress and state variables in the incremental analysis of plastic deformation. The Conventional Newton-Raphson method requires a second-order derivative of the yield function to generate a complicated code, and the convergence cannot be guaranteed beforehand. The proposed fixed-point iteration does not require a second-order derivative of the yield function, and convergence is ensured for a given strain increment. The fixed-point iteration is easier to implement, and the computational time is shortened compared with the Newton-Raphson method. The plane-stress condition is considered for the biaxial loading conditions to confirm the convergence of the fixed-point iteration. 3-dimensional tensile specimen is considered to compare the computational times in the ABAQUS/explicit finite element analysis.

• Communications of the Korean Mathematical Society
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• v.26 no.2
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• pp.229-235
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• 2011

In this paper, a continuous real function on the real line is considered. The necessary and sufficient conditions for the convergence of the Ishikawa iteration with error terms for the functional are obtained.

• The Pure and Applied Mathematics
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• v.14 no.2 s.36
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• pp.99-109
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• 2007

Being complicated in computation, iteration of a nonlinear 1-dimensional mapping makes many interesting problems, one of which is about the change of the number of vertices under iteration. In this paper we investigate iteration of polygonal functions which each have only one vertex and give conditions under which the number of vertices either does not increase or has a bound under iteration.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.369-378
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• 2001

In this paper, we obtain the following results: Let f be a transcendental entire function with log M(r,f)=$O(log r)^\beta (e^{log r}^\alpha)\; (0\leq\alpha<1,\beta>1$). Then every component of N(f) is bounded. This result generalizes the result of Baker.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.3
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• pp.189-202
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• 2009

In this paper we propose new primal-dual interior point algorithms for $P_*(\kappa)$ linear complementarity problems based on a new class of kernel functions which contains the kernel function in [8] as a special case. We show that the iteration bounds are $O((1+2\kappa)n^{\frac{9}{14}}\;log\;\frac{n{\mu}^0}{\epsilon}$) for large-update and $O((1+2\kappa)\sqrt{n}log\frac{n{\mu}^0}{\epsilon}$) for small-update methods, respectively. This iteration complexity for large-update methods improves the iteration complexity with a factor $n^{\frac{5}{14}}$ when compared with the method based on the classical logarithmic kernel function. For small-update, the iteration complexity is the best known bound for such methods.

• The Journal of the Korea Contents Association
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• v.7 no.2
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• pp.125-131
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• 2007

An iterative Green's function method (IGFM) is introduced in order to analyze complex electromagnetic waveguide stub structures in view of a university student. The IGFM utilizes a Green's function approach and an regional iteration scheme. A physical iteration mechanism with simple mathematical equations facilitates clear formulations of the IGFM. Scattering characteristics of a standard E-plane T-junction stub in a parallel-plate waveguide are theoretically investigated in terms of the IGFM. Numerical computations illustrate the characteristics of reflection and transmission powers versus frequency.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.13 no.5
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• pp.437-443
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• 1988

We calculate the distribution of the current on the strip by the incident waves on the infinite conducting strip line. The boundary equations represented as the spatial domain function become very complicated equations including convolution integral. Transformed it to the spectral domain, we have a very simple equation is composed by some algebraic multiplication of the current density function and Green's function. the acceleration of iteration procedure is achieved by Kastner's method. The result of iteration gives us the optimum value when it satisfies the iteration stop condition presented in this paper. We confirmed that the induced current density distribution on the stripline has been changed as variaties of the width.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.399-406
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• 2024

We point out an error appeared in the paper of Yuan et al. [3] and present a correction of their result under a more general assumption. Moreover, we discuss the validity of the conditions imposed on the sequences of error terms.

• Journal of the Chungcheong Mathematical Society
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• v.12 no.1
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• pp.1-13
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• 1999

The purpose of this paper is to show that if the Fatou set F(f) of a CF-meromorphic function f has two completely invariant components, then they are the only components of F(f) and that the Julia set of the entire transcendental function $E_{\lambda}(z)={\lambda}e^z$ for 0 < ${\lambda}$ < $\frac{1}{e}$ contains a Cantor bouquet by employing the Devaney and Tangerman's theorem[10].