• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.9-18
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• 2020

In this paper, we investigate the stability of a quadratic-cubic-quartic functional equation $$f(x+ky)+f(x-ky)-k^2f(x+y)-k^2f(x-y)-2(1-k^2)f(x)-{\frac{k^2(k^2-1)}{6}}(f(2y)+2f(-y)-6f(y))=0$$ by applying the direct method in the sense of Gǎvruta.

• Communications for Statistical Applications and Methods
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• v.2 no.1
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• pp.32-47
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• 1995

The coefficient of determination R/sup 2/, as the proprtation of by explained by a set of independent variavles x/sub 1/, x/sub 2, .cdots., x/sub k/ through a linear regression model, is a very useful tool in linear regression analysis. Suppose R/sup 2//sub yx/ is the coefficient of determination when y is regressed only on x/sub i/ alone. If the independent variables are correlaated, the sum, R/sup 2//sub {yx/sub 1/}/ +R/sup 2//sub {yx/sub 2/}/+.cdots.R/sup 2//sub {yx/sub k/}/, is not equal to R/sup 2/sub {yx/sub 1/x/sub 2/.cots.x/sub k/}/, where R/sup 2//sub {yx/sub 1/x/sub 2/.cdots.x/sub k/}/ is the coefficient of determination when y is regressed simultaneously on x/sub 1/, x/sub 2/,.cdots., x/sub k/. In this paper it is discussed that under what conditions the sum is greater than, equal to, or less than R/sup 2//sub {yx/sub 1/x/sub 2/.cdots.x/sub k/}/, and then the proofs for these conditions are given. Also illustrated examples are provided. In addition, we will discuss about inequality between R/sup 2//sub {yx/sub 1/x/sub 2/.cdots.x/sub k/}/ and the sum, R/sup 2//sub {yx/sub 1/}/+R/sup 2//sub {yx/sub 2/}/+.cdots.+R/sup 2//sub {yx/sub k/}/.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.40 no.3
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• pp.491-496
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• 2015

In this paper, we introduce two classes of optimal codes, [$2^k-1$, k, $2^{k-1}$] simplex codes and [$2^k-1+k$, k, $2^{k-1}+1$] codes, attaining Griesmer bound with equality. We further present and compare the locality of them. The [$2^k-1+k$, k, $2^{k-1}+1$] codes have good locality property as well as optimal code length with given code dimension and minimum distance. Therefore, we expect that [$2^k-1+k$, k, $2^{k-1}+1$] codes can be applied to various distributed storage systems.

• Bulletin of the Korean Chemical Society
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• v.27 no.6
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• pp.841-846
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• 2006

$Y_2O_2S$:Eu phosphors were synthesized via solid-state reactions. $Y_2O_2S$:Eu phosphor particles of various sizes were obtained by varying the firing temperature and firing time. The photoluminescence properties of these $Y_2O_2S$:Eu phosphors were examined. In addition, the cathodoluminescence properties of the $Y_2O_2S$:Eu phosphors were examined for applied voltages of 3-8 kV. The relationship between the luminescence intensity and particle size of the$Y_2O_2S$:Eu phosphors was investigated. The photoluminescence and cathodoluminescence of the $Y_2O_2S$:Eu phosphors are affected differently by variations in particle size.

• Analytical Science and Technology
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• v.9 no.4
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• pp.411-415
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• 1996

The new potentially heptadentate $N_7$ ligand 1, 15-bis(2-pyridyl)-2, 5, 8, 11, 14-pentaazapentadecane(pytetren) has been synthesized and characterized by EA, IR, NMR, and mass spectrometry. Its proton association constants (log $K{_H}^n$) and stability constants(log $K_{ML}$) for $Co^{2+}$, $Ni^{2+}$, $Cu^{2+}$, and $Zn^{2+}$ ions were determined at 298.1K and ionic strength=0.100M($KNO_3$) by potentiometry: log $K{_H}^1=9.36$, log $K{_H}^2=9.12$, log $K{_H}^3=8.09$, log $K{_H}^4=6.62$, log $K{_H}^5=4.02$, log $K{_H}^6=2.54$: log $K_{ML}(CO^{2+})=22.67$, log $K_{ML}(Ni^{2+})=26.25$. log $K_{ML}(Cu^{2+})=28.46$, log $K_{ML}(Zn^{2+})=19.90$.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.343-355
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• 2019

In this paper, we investigate the stability of the functional equation $$f(x+ky)-kf(x+y)+kf(x-y)-f(x-ky)-f(ky)+{\frac{k^3+k^2-2k}{2}}f(-y)-{\frac{k^3-k^2-2k}{2}}f(y)=0$$ by using the fixed point theory in the sense of L. $C{\breve{a}}dariu$ and V. Radu.

• The Pure and Applied Mathematics
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• v.26 no.4
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• pp.247-254
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• 2019

In this paper, we investigate Hyers-Ulam-Rassias stability of the functional equation f(x + ky) - k²f(x + y) + 2(k² - 1)f(x) - k²f(x - y) + f(x - ky) - k²(k² - 1)(f(y) + f(-y)) = 0, where k is a fixed real number with |k| ≠ 0, 1.

• Proceedings of the Korean Information Science Society Conference
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• 2001.10a
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• pp.589-591
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• 2001

본 논문에서는 재귀원형군 G(2$^{m}$ , 2$^{k}$ )에서 노드에 고장이 났을 경우 임의의 두 노드사이의 고장이 없는 최단경로의 길이를 분석한다. m > k+1인 G(2$^{m}$ , 2$^{k}$ )에서 m = nk+r이라 하자. 여기서 n $\geq$ 이고, 1$\leq$ r$\leq$ k이다. m > k+1인 G(2$^{m}$ , 2$^{k}$ )에서 임의의 연결도-1개 이하의 노드에 고장이 있을 경우, 모든 두 노드 사이의 고장이 없는 가장 짧은 경로들의 길이의 최대값, 즉 G(2$^{m}$ , 2$^{k}$ )의 고장지름은 n이 짝수이면 di $a_{m, k}$+2 이하이고, n이 흘수이면 di $a_{m, k}$+3 이하이다. 여기서 di $a_{m, k}$는 G(2$^{m}$ , 2$^{k}$ )의 지름이다.

• Journal of the Korean Data and Information Science Society
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• v.15 no.4
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• pp.717-729
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• 2004

The contour method which was originally designed for $2{\times}2{\times}2$ contingency table is studied for $2{\times}2{\times}K$ and $2{\times}3{\times}K$ tables. Whereas a contour plot for a $2{\times}2{\times}K$ table is represented on unit squared two dimensional plane, a contour plot of a $2{\times}3{\times}K$ table can be expressed with a regular hexahedron on three dimensional space. Based on contour plots for categorical data fitted to all possible three dimensional log-linear models, one might identify whether $2{\times}2{\times}k$ or $2{\times}3{\times}K$ tables are collapsible over the third variable.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2012.05a
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• pp.228-231
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• 2012

In this paper we propose a new family of nonlinear binary sequences generated by $m$-sequences for decimations $d=2^{k-1}(2^{s+1}-2^k+2^{k(i+1)}-2^{ki}-1)/(2^s-1)$ where $n=2k$, $i$ is odd and $s$ is such that $2s$ divides $k$. And we analyze the cross-correlation function between two $m$-sequences for new decimations $d$. Proposed sequences is extension of Rosendahl's sequnces and Dobbertin's sequences.