• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.27-41
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• 2019

We determine explicit formulas for the number of representations of a positive integer n by quaternary quadratic forms with coefficients 1, 2, 5 or 10. We use a modular forms approach.

• Honam Mathematical Journal
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• v.38 no.4
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• pp.753-782
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• 2016

In this paper we deduce the number of representations of a positive integer n by each of the six triangular forms as $${\frac{1}{2}}x_1(x_1+1)+{\frac{3}{2}}x_2(x_2+1)+{\frac{3}{2}}x_3(x_3+1)+{\frac{3}{2}}x_4(x_4+1),\\{\frac{1}{2}}x_1(x_1+1)+{\frac{1}{2}}x_2(x_2+1)+{\frac{3}{2}}x_3(x_3+1)+{\frac{3}{2}}x_4(x_4+1),\\{\frac{1}{2}}x_1(x_1+1)+{\frac{1}{2}}x_2(x_2+1)+{\frac{1}{2}}x_3(x_3+1)+{\frac{3}{2}}x_4(x_4+1),\\x_1(x_1+1)+x_2(x_2+1)+{\frac{3}{2}}x_3(x_3+1)+{\frac{3}{2}}x_4(x_4+1),\\x_1(x_1+1)+{\frac{3}{2}}x_2(x_2+1)+{\frac{3}{2}}x_3(x_3+1)+3x_4(x_4+1),\\{\frac{1}{2}}x_1(x_1+1)+{\frac{1}{2}}x_2(x_2+1)+3x_3(x_3+1)+3x_4(x_4+1).$$

• Journal of the Korean Statistical Society
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• v.20 no.1
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• pp.67-76
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• 1991

The empirical Bayes version involves ″independent″ repetitions(a sequence) of the component decision problem. With the varying sample size possible, these are not identical components. However, we impose the usual assumption that the parameters sequence $\theta$=($\theta$$_1$, $\theta$$_2$, …) consists of independent G-distributed parameters where G is unknown. We assume that G $\in$ g, a known family of distributions. The sample size $N_i$ and the decisin rule $d_i$ for component i of the sequence are determined in an evolutionary way. The sample size $N_1$ and the decision rule $d_1$$\in$ $D_{N1}$ used in the first component are fixed and chosen in advance. The sample size $N_2$and the decision rule $d_2$ are functions of *see full text($\underline{X}^1$equation omitted), the observations in the first component. In general, $N_i$ is an integer-valued function of *see full text(equation omitted) and, given $N_i$, $d_i$ is a $D_{Ni}$/-valued function of *see full text(equation omitted). The action chosen in the i-th component is *(equation omitted) which hides the display of dependence on *(equation omitted). We construct an empirical Bayes decision rule for estimating normal mean and show that it is asymptotically optimal.

• Journal of The Korean Astronomical Society
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• v.5 no.1
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• pp.7-14
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• 1972

We have investigated the structure of the general relativistic polytrope(G.R.P.) of n=5. The numerical solutions of the general relativistic Lane-Emden functions ${\upsilon}\;and\;{\theta}$ for the ratio of the central pressure to the central density ${\sigma}=0.1$, 0.3, 0.5 and 0.8333 are plotted graphically. We may summarize the results as follows: 1. As the invariant radius $\bar{\xi}$ increases, the numerical value of the mass parameter ${\upsilon}$ does not approach toward the assymptotic limit, as it does in the classical case $({\upsilon}{\sim}{\sqrt{3}})$, but it increases continuously with progressively smaller rate as compared with the classical case. 2. When $\bar{\xi}$ is less than ${\sim}5.5$, the value of the density function ${\theta}$ drops more rapidly than the classical one, whereas when $\bar{\xi}$ is greater than ${\sim}5.5$, ${\theta}$ becomes greater than the classical value. For the greater values of ${\sigma}$ these phenomena become significant. 3. From the above results it is expected that the equilibrium mass of the G.R.P. of n=5 must be larger than the classical masse $({\sqrt{3}})$ and the mass is more dispersed than the classical configuration (i.e. equilibrium with infinite radius).

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1549-1556
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• 2011

In this paper, we give an estimate on the difference between $x^n(t)$ and x(t) and it clearly shows that one can use the Picard iteration procedure to the approximate solutions to stochastic functional differential equations with infinite delay at phase space BC(($-{\infty}$, 0] : $R^d$) which denotes the family of bounded continuous $R^d$-valued functions ${\varphi}$ defined on ($-{\infty}$, 0] with norm ${\parallel}{\varphi}{\parallel}={\sup}_{-{\infty}<{\theta}{\leq}0}{\mid}{\varphi}({\theta}){\mid}$ under non-Lipschitz condition being considered as a special case and a weakened linear growth condition.

• International Journal of Contents
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• v.12 no.3
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• pp.12-16
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• 2016

Brain computer interfaces (BCI) usually have focused on classifying the explicitly-expressed intentions of humans. In contrast, implicit intentions should be considered to develop more intelligent systems. However, classifying implicit intention is more difficult than explicit intentions, and the difficulty severely increases for subject independent classification. In this paper, we address the subject independent classification of implicit intention based on electroencephalography (EEG) signals. Among many machine learning models, we use the support vector machine (SVM) with radial basis kernel functions to classify the EEG signals. The Fisher scores are evaluated after extracting the gamma, beta, alpha and theta band powers of the EEG signals from thirty electrodes. Since a more discriminant feature has a larger Fisher score value, the band powers of the EEG signals are presented to SVM based on the Fisher score. By training the SVM with 1-out of-9 validation, the best classification accuracy is approximately 65% with gamma and theta components.

• The Pure and Applied Mathematics
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• v.21 no.4
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• pp.271-279
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• 2014

Let $T_l$ be a transformation on the interval [-1, 1] defined by Chebyshev polynomial of degree $l(l{\geq}2)$, i.e., $T_l(cos{\theta})=cos(l{\theta})$. In this paper, we consider $T_l$ as a measure preserving transformation on [-1, 1] with an invariant measure $\frac{1}{\sqrt[\pi]{1-x^2}}dx$. We show that If f(x) is a nonconstant step function with finite k-discontinuity points with k < l-1, then it satisfies the Central Limit Theorem. We also give an explicit method how to check whether it satisfies the Central Limit Theorem or not in the cases of general step functions with finite discontinuity points.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.417-437
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• 2009

The notions of $\mathcal{N}$-subalgebras, (closed, commutative, retrenched) $\mathcal{N}$-ideals, $\theta$-negative functions, and $\alpha$-translations are introduced, and related properties are investigated. Characterizations of an $\mathcal{N}$-subalgebra and a (commutative) $\mathcal{N}$-ideal are given. Relations between an $\mathcal{N}$-subalgebra, an $\mathcal{N}$-ideal and commutative $\mathcal{N}$-ideal are discussed. We verify that every $\alpha$-translation of an $\mathcal{N}$-subalgebra (resp. $\mathcal{N}$-ideal) is a retrenched $\mathcal{N}$-subalgebra (resp. retrenched $\mathcal{N}$-ideal).

• Communications of the Korean Mathematical Society
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• v.25 no.4
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• pp.655-669
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• 2010

In this paper we propose new primal-dual interior point methods (IPMs) for $P_*(\kappa)$ linear complementarity problems (LCPs) and analyze the iteration complexity of the algorithm. New search directions and proximity measures are defined based on a class of kernel functions, $\psi(t)=\frac{t^2-1}{2}-{\int}^t_1e{^{q(\frac{1}{\xi}-1)}d{\xi}$, $q\;{\geq}\;1$. If a strictly feasible starting point is available and the parameter $q\;=\;\log\;\(1+a{\sqrt{\frac{2{\tau}+2{\sqrt{2n{\tau}}+{\theta}n}}{1-{\theta}}\)$, where $a\;=\;1\;+\;\frac{1}{\sqrt{1+2{\kappa}}}$, then new large-update primal-dual interior point algorithms have $O((1\;+\;2{\kappa})\sqrt{n}log\;n\;log\;{\frac{n}{\varepsilon}})$ iteration complexity which is the best known result for this method. For small-update methods, we have $O((1\;+\;2{\kappa})q{\sqrt{qn}}log\;{\frac{n}{\varepsilon}})$ iteration complexity.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.18 no.9
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• pp.1323-1331
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• 1993

In this paper, novel anti-multipath mod/demodulation techniques are introduced, The principal anti-multipath concepts of the double phase shift keying(DSK) system with a differntial detector and the diversity effect to be obtained from the phase shifts at the middle of symbol duration T are described. A generalized form of DSK, referred to as the $\theta$-DSK, is studied, and comparison of bandwidth is mode for various values of $\theta$ and shaping functions.