• Journal of the Korean Mathematical Society
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• v.31 no.3
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• pp.467-475
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• 1994

In 1983 Harmand and Lima [5] proved that if X is a Banach space for which K(X), the space of compact linear operators on X, is an M-ideal in L(X), the space of bounded linear operators on X, then it has the metric compact approximation property. A strong converse of the above result holds if X is a closed subspace of either $\elll_p(1 < p < \infty) or c_0 [2,15]$. In 1979 J. Johnson [7] actually proved that if X is a Banach space with the metric compact approximation property, then the annihilator K(X)^\bot$ of K(X) in $L(X)^*$ is the kernel of a norm-one projection in $L(X)^*$, which is the case if K(X) is an M-ideal in L(X).

• East Asian mathematical journal
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• v.24 no.2
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• pp.169-176
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• 2008

The aim of this paper is to prove a common fixed point theorem in normed linear spaces for noncompatible, discontinuous mappings without assuming completeness of the space. We also give an application of our theorem to best approximation theory.

• Interaction and multiscale mechanics
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• v.2 no.2
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• pp.129-151
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• 2009

This paper presents a meshfree procedure using a convex generalized meshfree (GMF) approximation for the large deformation analysis of particle-reinforced rubber compounds on microscopic level. The convex GMF approximation possesses the weak-Kronecker-delta property that guarantees the continuity of displacement across the material interface in the rubber compounds. The convex approximation also ensures the positive mass in the discrete system and is less sensitive to the meshfree nodal support size and integration order effects. In this study, the convex approximation is generated in the GMF method by choosing the positive and monotonic increasing basis function. In order to impose the periodic boundary condition in the unit cell method for the microscopic analysis, a singular kernel is introduced on the periodic boundary nodes in the construction of GMF approximation. The periodic boundary condition is solved by the transformation method in both explicit and implicit analyses. To simulate the interface de-bonding phenomena in the rubber compound, the cohesive interface element method is employed in corporation with meshfree method in this study. Several numerical examples are presented to demonstrate the effectiveness of the proposed numerical procedure in the large deformation analysis.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.1
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• pp.251-268
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• 1996

In this paper, a higher-order feedforward neural network called ridge polynomial network (RPN) which shows good approximation capability for nonlnear continuous functions defined on compact subsets in multi-dimensional Euclidean spaces, is presented. This network provides more efficient and regular structure as compared to ordinary higher-order feedforward networks based on Gabor-Kolmogrov polynomial expansions, while maintating their fast learning property. the ridge polynomial network is a generalization of the pi-sigma network (PSN) and uses a specialform of ridge polynomials. It is shown that any multivariate polynomial can be exactly represented in this form, and thus realized by a RPN. The approximation capability of the RPNs for arbitrary continuous functions is shown by this representation theorem and the classical weierstrass polynomial approximation theorem. The RPN provides a natural mechanism for incremental function approximation based on learning algorithm of the PSN. Simulation results on several applications such as multivariate function approximation and pattern classification assert nonlinear approximation capability of the RPN.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.28 no.2
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• pp.59-70
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• 2024

In this paper we present the approximation method of the circular helix by G² cubic polynomial curves. The approximants are G¹ Hermite interpolation of the circular helix and their approximation order is four. We obtain numerical examples to illustrate the geometric continuity and the approximation order of the approximants. The method presented in this paper can be extended to approximating the elliptical helix. Using the property of affine transformation invariance we show that the approximant has G² continuity and the approximation order four. The numerical examples are also presented to illustrate our assertions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.4
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• pp.307-314
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• 2009

In this work, we introduce a new quatnary approximating subdivision scheme for curve and deal with its analysis (convergence and regularity) using Laurent polynomials method. We also discuss various properties, such as approximation order and support of basic limit function.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1677-1703
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• 2008

In this paper, we introduce and study various locally convex vector topologies on the space of bounded linear operators between Banach spaces. We also apply these topologies to approximation properties.

• East Asian mathematical journal
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• v.28 no.5
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• pp.543-552
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• 2012

The aim of this paper is to prove a common fixed point theorem in normed linear spaces for discontinuous, occasionally weakly biased mappings without assuming completeness of the space. We give an example to illustrare our theorem. We also give an application of our theorem to best approximation theory. Our theorem improve the results of Gregus [9], Jungck [12], Pathak, Cho and Kang [22], Sharma and Deshpande [26]-[28].

• Proceedings of the Korean Institute of Communication Sciences Conference
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• 1986.10a
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• pp.68-71
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• 1986

A new circuit configuration for charge-balancing successive approximation Analog-to-Digital converters is described. This consists of a improved successive approximation register(SAR) and a weighted capacitor Digital-to-Analog converter (WCDAC). Due to the inherent conversion property of the WCDAC, the A/D converter using the WCDAC can be simply implemented by successive approximation conversion method, and 4bit monotonicity conversion with differential nonlinearity less 1/2LSB is completed in 80 US.

• Communications for Statistical Applications and Methods
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• v.24 no.6
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• pp.673-683
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• 2017

The least absolute shrinkage and selection operator (LASSO) has been a popular regression estimator with simultaneous variable selection. However, LASSO does not have the oracle property and its robust version is needed in the case of heavy-tailed errors or serious outliers. We propose a robust penalized regression estimator which provide a simultaneous variable selection and estimator. It is based on the rank regression and the non-convex penalty function, the smoothly clipped absolute deviation (SCAD) function which has the oracle property. The proposed method combines the robustness of the rank regression and the oracle property of the SCAD penalty. We develop an efficient algorithm to compute the proposed estimator that includes a SCAD estimate based on the local linear approximation and the tuning parameter of the penalty function. Our estimate can be obtained by the least absolute deviation method. We used an optimal tuning parameter based on the Bayesian information criterion and the cross validation method. Numerical simulation shows that the proposed estimator is robust and effective to analyze contaminated data.