• The Transactions of The Korean Institute of Electrical Engineers
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• v.67 no.2
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• pp.277-284
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• 2018

In this paper, a new numerical method of finding the roots of a nonlinear system is proposed, which extends the conventional fixed point iterative method by relaxing the constraints on it. The proposed method determines the real valued roots and expands the convergence region by relaxing the constraints on the conventional fixed point iterative method, which transforms the diverging root searching iterations into the converging iterations by employing the metric induced by the geometrical characteristics of a polynomial. A metric is set to measure the distance between a point of a real-valued function and its corresponding image point of its inverse function. The proposed scheme provides the convenience in finding not only the real roots of polynomials but also the roots of the nonlinear systems in the various application areas of science and engineering.

• Bulletin of the Korean Mathematical Society
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• v.25 no.2
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• pp.243-246
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• 1988

Let M(z)=exp (-1+z/1-z) be the unit singular inner function. See [1] or [2] for the basic facts about inner functions. We define the iterations of M9z) as (Fig.) Since the composition M$_{2}$(z)=M.M(z) is known (see [5] for example) to be singular inner function it has the "cannonical" representation (Fig.) where .mu. is a finite, positive singular Borel measure on the unit circle T. In section 2, we have explicit cannonical representation of M$_{2}$(z) by determining the singular measure .mu. In section 3 we show that (Fig.) These facts might have been known but could not be found in the literature.iterature.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.983-992
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• 1996

Let p(x, dy) be a transition probability function on $(S, \rho)$, where S is a complete separable metric space. Then a Markov process $X_n$ which has p(x, dy) as its transition probability may be generated by random iterations of the form $X_{n+1} = f(X_n, \varepsilon_{n+1})$, where $\varepsilon_n$ is a sequence of independent and identically distributed random variables (See, e.g., Kifer(1986), Bhattacharya and Waymire(1990)).

• Korean Journal of Mathematics
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• v.28 no.3
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• pp.449-457
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• 2020

We focus on the interations of the weighted Berezin transform T_α on L^p(τ), where τ is the invariant measure on the complex unit ball B_n. Iterations of T_α on L¹_R(τ) the space of radial integrable functions played important roles in proving 𝓜-harmonicity of bounded functions with invariant mean value property. Here, we introduce more properties on iterations of T_α on L¹_R(τ) and observe differences between the iterations of T_α on L1(τ) and L^p(τ) for 1 < p < ∞.

• Journal of the Korean Operations Research and Management Science Society
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• v.19 no.1
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• pp.113-122
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• 1994

This study proposes a new procedure to find an initial solution to reduce the number of iterations of goal programming. The process of computing an initial solution is divided into two steps in this study. Decision variables which satisfy feasibility using Gaussian eliminations construct an initial solution reducing the iterations in the first step. It uses LHS as a tool that decision variables construct an initial solution. The initial solution which is constructed by the first step computes the updated coefficient of the objective function in the second step. If the solution does not satisfy the optimality, the optimal solution using the Modified Simplex Method is sought. The developed method doesn't reduce the overall computing time of goal programming problems, because time is more required for the process of constructing an initial solution. But The result of this study shows that the proposed procedure can reduce the large number of iterations in the first step effectively.

• Journal of Powder Materials
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• v.29 no.4
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• pp.303-308
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• 2022

The plastic deformation behavior of additively manufactured anisotropic structures are analyzed using the finite element method (FEM). Hill's quadratic anisotropic yield function is used, and a modified return-mapping method based on dual potential is presented. The plane stress biaxial loading condition is considered to investigate the number of iterations required for the convergence of the Newton-Raphson method during plastic deformation analysis. In this study, incompressible plastic deformation is considered, and the associated flow rule is assumed. The modified return-mapping method is implemented using the ABAQUS UMAT subroutine and effective in reducing the number of iterations in the Newton-Raphson method. The anisotropic tensile behavior is computed using the 3-dimensional FEM for two tensile specimens manufactured along orthogonal additive directions.

• Journal of electromagnetic engineering and science
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• v.4 no.3
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• pp.102-106
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• 2004

A novel Genetic Algorithm(GA)-based method is suggested to transform a coupling matrix to another, without the procedure of Matrix Rotation. This can remove tedious work like pivoting and deciding rotation angles needed for each of the iterations. The error function for the GA is simply formed and used as part of error minimization for obtaining the solution. An 8th order dual-mode elliptic integral function response filter is taken as an example to validate the present method.

• Journal of electromagnetic engineering and science
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• v.6 no.3
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• pp.155-159
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• 2006

An efficient method is presented to design filters without the similarity transform of their coupling coefficient matrix as circuit parameters, which is very tedious due to pivoting and deciding rotation angles needed during the iterations. The transfer function of a filter is directly used for the design and its desired form is derived by the optimized rational-function fitting technique. A 3rd order coaxial lowpass filter is taken as an example to validate the proposed method.

• Nuclear Engineering and Technology
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• v.54 no.7
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• pp.2625-2634
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• 2022

Discretization errors are extremely challenging conundrums of discrete ordinates calculations for radiation transport problems with void regions. In previous work, we have presented a multi-collision source method (MCS) to overcome discretization errors, but the efficiency needs to be improved. This paper proposes a goal-oriented algorithm for the MCS method to adaptively determine the partitioning of the geometry and dynamically change the angular quadrature in remaining iterations. The importance factor based on the adjoint transport calculation obtains the response function to get a problem-dependent, goal-oriented spatial decomposition. The difference in the scalar fluxes from one high-order quadrature set to a lower one provides the error estimation as a driving force behind the dynamic quadrature. The goal-oriented algorithm allows optimizing by using ray-tracing technology or high-order quadrature sets in the first few iterations and arranging the integration order of the remaining iterations from high to low. The algorithm has been implemented in the 3D transport code ARES and was tested on the Kobayashi benchmarks. The numerical results show a reduction in computation time on these problems for the same desired level of accuracy as compared to the standard ARES code, and it has clear advantages over the traditional MCS method in solving radiation transport problems with reflective boundary conditions.

• Korean Journal of Mathematics
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• v.26 no.1
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• pp.1-7
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• 2018

In this paper, we will study a generalized version of Josephus where a serial execution occurs at each iteration and give a non-recursive formula for the initial positions of survivors.