• Korean Journal of Mathematics
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• v.24 no.2
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• pp.181-198
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• 2016

In this work, we suggest a new system of generalized nonlinear regularized nonconvex variational inequalities in a real Hilbert space and establish an equivalence relation between this system and fixed point problems. By using the equivalence relation we suggest a new perturbed projection iterative algorithms with mixed errors for finding a solution set of system of generalized nonlinear regularized nonconvex variational inequalities.

• Progress in Superconductivity and Cryogenics
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• v.17 no.2
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• pp.31-35
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• 2015

Mapping is a useful tool in the magnetic field analysis and design. In some specific research area, such as the nuclear magnetic resonance (NMR) or the magnetic resonance imaging (MRI), it is important to map the magnetic field in the interesting space with high accuracy. In this paper, an indirect mapping method in the center volume of an air-core solenoid is presented, based on the solution of the Laplace's equation for the field. Through the mathematical analysis on the mapping calculation, we know that the condition number of the matrix, generated by the measurement points, can greatly affect the error of mapping result. Two different arrangement methods of the measurement points in field mapping are described in this paper: helical cylindrical line (HCL) method and parallel cylindrical line (PCL) method. According to the condition number, the HCL method is recommended to measure the field components using one probe. As a simple example, we mapped the magnetic fields in a MRI main magnet system. Comparing the results in the different methods, it is feasible and convenient to apply the condition number to reduce the error in the field mapping calculation. Finally, some guidelines were presented for the magnetic field mapping in the center volume of the air-core solenoid.

• Bulletin of the Korean Mathematical Society
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• v.36 no.3
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• pp.565-578
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• 1999

In this paper some common fixed point theorems for pairs of condensing mappings in a Banach space are proved and applications are given to a pair of nonlinear first order ordinary differential equations in Banach spaces for proving the existence of common solution under suitable conditions.

• Journal of KIISE:Computer Systems and Theory
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• v.33 no.8
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• pp.486-494
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• 2006

In this paper, we introduce a new solution for the load balancing problem, an important issue in parallel processing. Our heuristic load balancing technique called MGA effectively combines the benefit of both mean-field annealing (MFA) and genetic algorithms (GA). We compare the proposed MGA algorithm with other mapping algorithms (MFA, GA-l, and GA-2). A multiprocessor mapping algorithm simulation has been developed to measure performance improvement ratio of these algorithms. Our experimental results show that our new technique, the composition of heuristic mapping methods improves performance over the conventional ones, in terms of solution quality with a longer run time.

• Wind and Structures
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• v.35 no.4
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• pp.243-253
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• 2022

The conformal mapping method (CMM) has been broadly exploited in the study of fluid flows over airfoils and other research areas, yet it's hard to find relevant research in bridge engineering. This paper explores the feasibility of CMM in streamlined box girder bridges. Firstly, the mapping function transforming a unit circle to the streamlined box girder was solved by CMM. Subsequently, the potential flow solution of aerostatic pressure on the streamlined box girder was obtained and was compared with numerical simulation results. Finally, the aerostatic pressure attained by CMM was utilized to estimate the aerostatic coefficient and flutter performance of the streamlined box girder. The results indicate that the solution of the aerostatic pressure by CMM on the windward side is satisfactory within a small angle of attack. Considering the windward aerostatic pressure and coefficient of correction, CMM can be employed to estimate the rate of change of the lift and moment coefficients with angle of attack and the influence of the geometric shape of the streamlined box girder on flutter performance.

• Journal of the Korean Mathematical Society
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• v.46 no.6
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• pp.1151-1164
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• 2009

Let E be a reflexive Banach space with a weakly sequentially continuous duality mapping, C be a nonempty closed convex subset of E, f : C $\rightarrow$C a contractive mapping (or a weakly contractive mapping), and T : C $\rightarrow$ C a nonexpansive mapping with the fixed point set F(T) ${\neq}{\emptyset}$. Let {$x_n$} be generated by a new composite iterative scheme: $y_n={\lambda}_nf(x_n)+(1-{\lambda}_n)Tx_n$, $x_{n+1}=(1-{\beta}_n)y_n+{\beta}_nTy_n$, ($n{\geq}0$). It is proved that {$x_n$} converges strongly to a point in F(T), which is a solution of certain variational inequality provided the sequence {$\lambda_n$} $\subset$ (0, 1) satisfies $lim_{n{\rightarrow}{\infty}}{\lambda}_n$ = 0 and $\sum_{n=0}^{\infty}{\lambda}_n={\infty}$, {$\beta_n$} $\subset$ [0, a) for some 0 < a < 1 and the sequence {$x_n$} is asymptotically regular.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1323-1339
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• 2008

In this paper, a new class of $(h,{\eta})$-proximal for proper functionals in Hilbert spaces is introduced. The existence and Lip-schitz continuity of the $(h,{\eta})$-proximal mappings for proper functionals are proved. A class of generalized nonlinear quasi-variational-like inclusions in Hilbert spaces is introduced. A perturbed three-step iterative algorithm with errors for the generalized nonlinear quasi-variational-like inclusion is suggested. The existence and uniqueness theorems of solution for the generalized nonlinear quasi-variational-like inclusion are established. The convergence and stability results of iterative sequence generated by the perturbed three-step iterative algorithm with errors are discussed.

• Progress in Superconductivity and Cryogenics
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• v.18 no.2
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• pp.30-36
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• 2016

For the magnetic field analysis or design, it is important to know the behavior of the magnetic field in an interesting space. Magnetic field mapping becomes a useful tool for the study of magnetic field. In this paper, a numerical way for mapping the magnetic field within the cylindrical center volume of magnet is presented, based on the solution of the Laplace's equation in the cylindrical coordinate system. The expression of the magnetic field can be obtained by the magnetic flux density, which measured in the mapped volume. According to the form of the expression, the measurement points are arranged with the parallel cylindrical line (PCL) method. As example, the magnetic flux density generated by an electron cyclotron resonance ion source (ECRIS) magnet and a quadrupole magnet were mapped using the PCL method, respectively. The mapping results show the PCL arrangement method is feasible and convenience to map the magnetic field within a cylindrical center volume generated by the general magnet.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.778-781
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• 2004

Recently, one of the reason of noise problems is urban planning has little concern about noise. For solving noise problems, strategic action is needed during urban planning. The noise map is one of the solution for concerning about noise in urban planning and EC has been studied the noise map for the strategic purpose since 1970s. The noise map is powerful tool for predicting sound level, calculating exposure population and evaluating the efficiency of the noise reduction plan. In Korea, The noise map is a unfamiliar field. The experience is few for noise-mapping and the noise mapping procedure has not been standardization yet. For activation of noise map, the study about fundamental problems of collecting data md noise-mapping procedure must be need. This paper is for studying on the noise-mapping procedure in Korea and application of noise map.

• Journal of The Korean Association For Science Education
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• v.32 no.2
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• pp.402-414
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• 2012

This study investigated the effects of the instructions using analogies in learning the concept of saturated solution by the analogy presentation types and the verbal learning styles upon the mapping understanding, the mapping errors, and the perceptions of the instruction. Fifth graders (N=123) at an elementary school were selected and assigned to VA (n=63) and VPA (n=60) groups. As a pretest, a test on the verbal learning style was administered. The students in the VA group learned the target concept with a verbal analogy, while those in the VPA group learned it with a verbal/pictorial analogy. After the students learned it, a mapping understanding test was administered. The students in the VPA group also administered the test on the perceptions of the instruction and some of them were interviewed in depth. The results revealed that the scores of the students with strong verbal learning preference in the VPA group were significantly lower than those in the VA group in the mapping understanding test. However, the scores of the students with weak verbal learning preference were not significantly different between the two groups. Five types of mapping errors were identified: failure to map, mismapping, rash mapping, impossible mapping, and mapping of a surficial feature. According to students' verbal learning styles, there were some differences in the frequencies of mapping errors in the two groups. Many students in the VPA group, regardless of their verbal learning styles, had positive perceptions of the instruction in various cognitive and motivational aspects. However, some of them also pointed out a few difficulties of the instruction. Educational implications of these findings are discussed.