• The Korean Journal of Applied Statistics
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• v.7 no.2
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• pp.323-333
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• 1994

In this paper we present some approximation theorems related to the problem of finding optimal densities with prescribed moments. The implementation of the approximation theorems is to be done in some examples.

• Korean Journal of Materials Research
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• v.29 no.8
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• pp.477-482
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• 2019

The magnetic properties and electronic structures of the B20 crystal structure MnGe and MnSi were investigated using the density functional theory with local density approximation. The low symmetry of the B20 crystal structure plays a very important role to make electromagnetic characteristics of these materials. The important result of the calculations is that it can be observed the appearance of a pair of gaps in the density of states near the Fermi level in both compounds. These features are results from d-band splitting by the low symmetry of the crystal field from B20 crystal structure. It can be seen that there is half-metallic characteristics from the density of states in both compounds. The calculation shows that the value of magnetic moment of MnGe is 5 times bigger than that of MnSi even though they have same crystal structure. The electronic structures of paramagnetic case have a very narrow indirect gap just above the Fermi level in both compounds. These gaps acquire some significance in establishing the stability of the ferromagnetic states within the local density approximation. Calculation shows that the Mn 3d character dominates the density of states near the Fermi level in both materials.

• The Korean Journal of Applied Statistics
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• v.22 no.6
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• pp.1345-1353
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• 2009

We introduce a simple methodology, so-called generalized gamma-polynomial approximation, based on moment-matching technique to approximate survival and hazard functions in the context of parametric survival analysis. We use the generalized gamma-polynomial approximation to approximate the density and distribution functions of convolutions and finite mixtures of random variables, from which the approximated survival and hazard functions are obtained. This technique provides very accurate approximation to the target functions, in addition to their being computationally efficient and easy to implement. In addition, the generalized gamma-polynomial approximations are very stable in middle range of the target distributions, whereas saddlepoint approximations are often unstable in a neighborhood of the mean.

• Journal of Applied and Pure Mathematics
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• v.4 no.3_4
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• pp.185-209
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• 2022

Here we exhibit multivariate quantitative approximations of Banach space valued continuous multivariate functions on a box or ℝ^N, N ∈ ℕ, by the multivariate normalized, quasi-interpolation, Kantorovich type and quadrature type neural network operators. We treat also the case of approximation by iterated operators of the last four types. These approximations are achieved by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high order Fréchet derivatives. Our multivariate operators are defined by using a multidimensional density function induced by the generalized symmetrical sigmoid function. The approximations are point-wise and uniform. The related feed-forward neural network is with one hidden layer.

• Journal of Radiation Protection and Research
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• v.34 no.4
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• pp.155-164
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• 2009

In this paper, we used computerized glow curve deconvolution (CGCD) software with several models for the simulation of a TL glow curve which was used for analysis. By using the general approximation plus model, parameters values of the glow curve were analyzed and compared with the other models parameters (general approximation, mixed order kinetics, general order kinetics). The LiF:Mg,Cu,Si and the LiF:Mg,Cu,P material were used for the glow curve analysis. And we based on figure of merits (FOM) which was the goodness of the fitting that was monitored through the value between analysis model and TLD materials. The ideal value of FOM is 0 which represents a perfect fit. The main glow peak makes the most effect of radiation dose assessment of TLD materials. The main peak of the LiF:Mg,Cu,Si materials has a intensity rate 80.76% of the whole TL glow intensity, and that of LiF:Mg,Cu,P materials has a intensity rate 68.07% of the whole TL glow intensity. The activation energy of LiF:Mg,Cu,Si was analyzed as 2.39 eV by result of the general approximation plus(GAP) model. In the case of mixed order kinetics (MOK), the activation energy was analyzed as 2.29 eV. The activation energy was analyzed as 2.38 eV by the general order kinetics (GOK) model. In the case of LiF:Mg,Cu,P TLD, the activation energy was analyzed as 2.39 eV by result of the GAP model. In the case of MOK, the activation energy was analyzed as 2.55 eV. The activation energy was analyzed as 2.51 eV by the GOK model. The R value means different ratio of retrapping-recombination. The R value of LiF:Mg,Cu,Si TLD main peak analyzed as $1.12\times10^{-6}$ and $\alpha$ value analyzed as $1.0\times10^{-3}$. The R of LiF:Mg,Cu,P TLD analyzed as $7.91\times10^{-4}$, the $\alpha$ value means different ratio of initial thermally trapped electron density-initial trapped electron density (include thermally disconnected trap electrons density). The $\alpha$ value was analyzed as $9.17\times10^{-1}$ which was the difference from LiF:Mg,Cu,Si TLD. The deep trap electron density of LiF:Mg,Cu,Si was higher than the deep trap electron density of LiF:Mg,Cu,P.

• Communications for Statistical Applications and Methods
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• v.21 no.2
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• pp.115-124
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• 2014

In this paper we derive a Berry-Esseen type bound for the kernel density estimator of a random left truncated model, in which each datum (Y) is randomly left truncated and is sampled if $Y{\geq}T$, where T is the truncation random variable with an unknown distribution. This unknown distribution is estimated with the Lynden-Bell estimator. In particular the normal approximation rate, by choice of the bandwidth, is shown to be close to $n^{-1/6}$ modulo logarithmic term. We have also investigated this normal approximation rate via a simulation study.

• Journal of the Korean Statistical Society
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• v.10
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• pp.140-144
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• 1981

This paper approximates to a kernel density estimate by a truncated series of expansion involving Hermite polynomials, since this could ease the computing burden involved in the kernel-based density estimation. However, this truncated series may give a multimodal estimate when we are estiamting unimodal density. In this paper we will show a way to insure the truncated series to be positive and unimodal so that the approximation to a kernel density estimator would be maeningful.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.4C
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• pp.310-317
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• 2006

In this paper, we propose a new sequential message-passing decoding algorithm of low-density parity-check (LDPC) codes by partitioning check nodes. This new decoding algorithm shows better bit error rate(BER) performance than that of the conventional message-passing decoding algorithm, especially for small number of iterations. Analytical results tell us that as the number of partitioned subsets of check nodes increases, the BER performance becomes better. We also derive the recursive equations for mean values of messages at variable nodes by using density evolution with Gaussian approximation. Simulation results also confirm the analytical results.

• Communications for Statistical Applications and Methods
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• v.17 no.3
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• pp.367-376
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• 2010

Recently various methods were suggested and reviewed for estimating diffusion processes. Out of suggested estimation method, we mainly concerns on the estimation method using saddlepoint approximation method, and we suggest a term saddlepoint approximation(ASP) method which is the simplest saddlepoint approximation method. We will show that ASP method provides fast estimator as much as Euler approximation method(EAM) in computing, and the estimator also has good statistical properties comparable to the maximum likelihood estimator(MLE). By simulation study we compare the properties of ASP estimator with MLE and EAM, for Ornstein-Uhlenbeck diffusion processes.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1087-1095
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• 2009

In this paper, we study approximation method from scattered data to the derivatives of a function f by a radial basis function $\phi$. For a given function f, we define a nearly interpolating function and discuss its accuracy. In particular, we are interested in using smooth functions $\phi$ which are (conditionally) positive definite. We estimate accuracy of approximation for the Sobolev space while the classical radial basis function interpolation applies to the so-called native space. We observe that our approximant provides spectral convergence order, as the density of the given data is getting smaller.