• International Journal of Fuzzy Logic and Intelligent Systems
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• v.14 no.1
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• pp.57-65
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• 2014

In this paper, we investigate the properties of L-lower approximation operators as a generalization of fuzzy rough set in complete residuated lattices. We study relations lower (upper, join meet, meet join) approximation operators and Alexandrov L-topologies. Moreover, we give their examples as approximation operators induced by various L-fuzzy relations.

• Journal of the Chungcheong Mathematical Society
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• v.17 no.1
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• pp.77-83
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• 2004

The aim of this work is to generalize parametric approximation in order to apply them to an one-sided $L_1$-approximation. A natural question now arises : when is the parameter map $$P:f{\rightarrow}P_{K(f)}(f)$$ continuous on $C_1(X)$ ? We find some results with a monotone decreasing sequence about above question.

• Honam Mathematical Journal
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• v.27 no.1
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• pp.69-76
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• 2005

The aim of this work is to generalize $L_1$-approximation in order to apply them to a discrete approximation. In $L_1$-approximation, we use the norm given by $${\parallel}f{\parallel}_1={\int}{\mid}f{\mid}d{\mu}$$ where ${\mu}$ a non-atomic positive measure. In this paper, we go to the other extreme and consider measure ${\mu}$ which is purely atomic. In fact we shall assume that ${\mu}$ has exactly m atoms. For any ${\ell}$-tuple $b^1,\;{\cdots},\;b^{\ell}{\in}{\mathbb{R}}^m$, we defined the ${\ell}^m_1{w}$-norn, and consider $s^*{\in}S$ such that, for any $b^1,\;{\cdots},\;b^{\ell}{\in}{\mathbb{R}}^m$, $$\array{min&max\\{s{\in}S}&{1{\leq}i{\leq}{\ell}}}\;{\parallel}b^i-s{\parallel}_w$$, where S is a n-dimensional subspace of ${\mathbb{R}}^m$. The $s^*$ is called the Chebyshev center or a discrete simultaneous ${\ell}^m_1$-approximation from the finite dimensional subspace.

• Honam Mathematical Journal
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• v.28 no.1
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• pp.125-133
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• 2006

We investigate the approximation order to a function in $L_p$[-1, 1] for $0{\leq}p<{\infty}$ by generalized translation networks. In most papers related to neural network approximation, sigmoidal functions are adapted as an activation function. In our research, we choose an infinitely many times continuously differentiable function as an activation function. Using the integral modulus of continuity and the divided difference formula, we get the approximation order to a function in $L_p$[-1, 1].

• Journal of the Korean Mathematical Society
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• v.33 no.1
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• pp.155-167
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• 1996

Let X be a compact Hausdorff space, C(X) denote the set of all continuous real valued functions on X and $\ell \in N$ be any natural number.

• Kyungpook Mathematical Journal
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• v.50 no.4
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• pp.545-556
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• 2010

A good amount of work has been done on degree of approximation of functions belonging to Lip${\alpha}$, Lip($\xi$(t),r) and W($L_r,\xi(t)$) and classes using Ces$\`{a}$ro, N$\"{o}$rlund and generalised N$\"{o}$rlund single summability methods by a number of researchers ([1], [10], [8], [6], [7], [2], [3], [4], [9]). But till now, nothing seems to have been done so far to obtain the degree of approximation of functions using (N,$p_n$)(C, 1) product summability method. Therefore the purpose of present paper is to establish two quite new theorems on degree of approximation of function $f\;\in\;Lip({\alpha},r)$ class and $f\;\in\;W(L_r,\;\xi(t))$ class by (N, $p_n$)(C, 1) product summability means of its Fourier series.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.139-147
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• 2009

We study the neural network approximation to a function in $C^1$[0, 1] and its derivative. In [3], we used even trigonometric polynomials in order to get an approximation order to a function in $L_p$ space. In this paper, we show the simultaneous approximation order to a function in $C^1$[0, 1] using a Bernstein polynomial and a feedforward neural network. Our proofs are constructive.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2003.05e
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• pp.73-76
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• 2003

This paper describes the information for quantitative simulation of weakly ionized plasma. In previous paper, we calculated the electron transport coefficients in pure Xenon gas by using two-term approximation of Boltzmann equation. Therefore, in this paper, we calculated the electron transport coefficients(W, $N{\cdot}D_L$ and $D_{L/{\mu}}$) in pure Xenon gas for range of E/N values from 0.01 ~ 500[Td] at the temperature was 300[K] and pressure was 1[Torr] by using multi-term approximation of the Boltzmann equation by Robson and Ness, The results of two-term and multi-term approximation of the Boltzmann equation has been compared with the experimental data by L. S. Frost and A. V. Phelps for a range of E/N.

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.125-130
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• 2007

We propose a simple and intuitive method to derive the exact convergence rate of global $L_{2}-norm$ error for strong numerical approximation of stochastic differential equations the result of which has been reported by Hofmann and $M{\"u}ller-Gronbach\;(2004)$. We conclude that any strong numerical scheme of order ${\gamma}\;>\;1/2$ has the same optimal convergence rate for this error. The method clearly reveals the structure of global $L_{2}-norm$ error and is similarly applicable for evaluating the convergence rate of global uniform approximations.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.15 no.1
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• pp.79-84
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• 2002

An accurate cross sections set is necessary for the quantitatively understanding and modeling of plasma phenomena. By using the electron swarm method, we determine an accurate electron cross sections set for objective atoms or molecule at low electron energy range. It is general calculation that used in this method to an two-term approximation of Boltzmann equation. But it may give erroneous transport coefficients for CF$_4$ molecule treated in this paper having \`C2v symmetry\`, therefore, multi-term approximation of the Boltzmann equation analysis which can consider anisotropic scattering exactly is carried out. It is necessary to require understanding of the fundamental principle of analysis method. Therefore, in this paper, we compared the electron transport coefficients(W and ND$\_$L/) in pure Ar, O$_2$, and CF$_4$ gas calculated by using two-term approximation of the Boltzmann equation analysis code uses the algorithm proposed by Tagashira et al. with those by multi-term approximation by Rubson and Ness which was developed at James-Cook university, and discussed an application and/or validity of the calculation method by comparing these calculated results.