• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.119-126
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• 1989

Throughout this paper, X will always denote a Banach space over the complex numbers C, and L(X) will denote the Banach algebra of all continuous linear operators on X. Operator will always mean continuous linear operator. An n-tuple of operators T$_{1}$,..,T$_{n}$ on X will be denoted by over ^ T=(T$_{1}$,..,T$_{n}$ ). Let L$^{n}$ (X) be the set of all n-tuples of operators on X. X' will denote the dual space of X, S(X) its unit sphere and .PI.(X) the subset of X*X' defined by .PI.(X)={(x,f).mem.X*X': ∥x∥=∥f∥=f(x)=1}.

• Journal of Sericultural and Entomological Science
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• v.10
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• pp.35-40
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• 1969

Various formulae for estimation of spring leaf production in mulberry trees were calculated and obtained. Four varieties of mulberry trees were used as the materials, and four characters, namely branch length (X$_1$), node number (X$_2$), branch diameter (X$_3$) and branch number per stock (X$_4$) were studied. The formulae to estimate the leaf yield of spring mulberry trees are as follows: 1. $Y_1$v$_1$= -26.8939＋50.3950X$_1$＋1.1403X$_2$ $Y_1$v$_2$= -372.1091＋116.6371X$_1$＋0.1984X$_2$ $Y_1$v$_3$= 149.8203＋90.5125X$_1$-0.9775X$_2$ $Y_1$v$_4$= 108, 1496＋59.4533X$_1$＋1.4965X$_2$ Where $Y_1$v$_1$, $Y_1$v$_2$, $Y_1$v$_3$, $Y_1$v$_4$, are showed the estimated yield of the each variety, namely Gaeryang Seuban, Ilchirye, Nosang, and Suwon Sang No. 4, respectively. X$_1$ and X$_2$ denote the measured values of branch length and node number, respectively. 2. $Y_{7}$v$_1$= -54.4411＋32.9869c1.1127X$_2$＋21.7600X$_3$ $Y_{7}$v$_2$= -494.1480-1.8756X$_1$＋0.9788X$_2$＋110.0039X$_3$ $Y_{7}$v$_3$= 143.2836＋29.1779X$_1$＋0.1644X$_2$＋48.4135X$_3$ $Y_{7}$v$_4$= 1243.2549＋1.9454X$_1$＋2.7118X$_2$-75.6669X$_3$ Where $Y_{7}$v$_1$, $Y_{7}$v$_2$, $Y_{7}$v$_3$, $Y_{7}$v$_4$, are the estimated yield of the each variety, namely Gaeryang-Seuban, Ilchirye, Nosang, Suwon Sang No 4, respectively. X$_1$, X$_2$, X$_3$ denote the measured values of each character, branch length, node number, branch diameter and branch number per stock, respectively. 3. $Y_{11}$v$_1$=233.4780＋74.3713X$_1$＋1.2912X$_2$＋39.0420X$_3$-148.9300X$_4$ $Y_{11}$v$_2$=-317.0150＋15.l524X$_1$＋1.0861X$_2$＋156.7973X$_3$-148.3742X$_4$ $Y_{11}$v$_3$=178.7011＋29.8664X$_1$-0.2562X$_2$＋102.4632X$_3$-83.2693X$_4$ $Y_{11}$v$_4$= 264.0062＋47.7742X$_1$＋2.6996X$_2$＋92.8882X$_3$-192.3464X$_4$ Where $Y_{11}$v$_1$, $Y_{11}$v$_2$, $Y_{11}$v$_3$, $Y_{11}$v$_4$, are the estimated yield values of four varieties, and X$_1$, X$_2$, X$_3$, X$_4$, denote the measured values of four characters, namely branch length, node number, branch diameter and branch number per stock, respectively. The estimation method of mulberry spring leaf yield by measurement of some characters, in autumn the year before, could be the better method to determine the leaf yield of mulberry trees without destroying the leaves and without weighting the leaves of mulberry trees than the other methods.

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.465-490
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• 1998

In this paper, we consider the existence and asymptotic behavior of solutions of the following problem: $u_{tt}$ -(t, x) - (∥∇u(t, x)∥(equation omitted) ＋ ∥∇v(t, x) (equation omitted)$^{\gamma}$ $\Delta$u(t, x)＋$\delta$│ $u_{t}$ (t, x)│sup p-1/ $u_{t}$ (t, x) = $\mu$│u(t, x) $^{q-1}$u(t, x), x$\in$$\Omega$, t$\in$[0, T], $v_{tt}$ (t, x) - (∥∇uu(t, x) (equation omitted) ＋ ∥∇v(t, x) (equation omitted)sup ${\gamma}$/ $\Delta$v(t, x)＋$\delta$ │ $v_{t}$ (t, x)│sup p-1/ $u_{t}$ (t, x) = $\mu$ u(t, x) $^{q-1}$u(t, x), x$\in$$\Omega$, t$\in$[0, T], u(0, x) = $u_{0}$ (x), $u_{t}$ (0, x) = $u_1$(x), x$\in$$\Omega$, u(0, x) = $v_{0}$ (x), $v_{t}$ (0, x) = $v_1$(x), x$\in$$\Omega$, u│∂$\Omega$=v│∂$\Omega$=0 T > 0, q > 1, p $\geq$1, $\delta$ > 0, $\mu$ $\in$ R, ${\gamma}$ $\geq$ 1 and $\Delta$ is the Laplacian in $R^{N}$.X> N/.

• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.503-507
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• 2006

Let X be a Tychonoff space and ${\sum}(X)$ the set of all the subrings of C(X) that contain $C^*(X)$. For any A(X) in ${\sum}(X)$ suppose $_{{\upsilon}A}X$ is the largest subspace of ${\beta}X$ containing X to which each function in A(X) can be extended continuously. Let us write A(X) ~ B(X) if and only if $_{{\upsilon}A}X=_{{\upsilon}B}X$, thereby defining an equivalence relation on ${\sum}(X)$. We have shown that an A(X) in ${\sum}(X)$ is isomorphic to C(Y ) for some space Y if and only if A(X) is the largest member of its equivalence class if and only if there exists a subspace T of ${\beta}X$ with the property that A(X)={$f{\in}C(X):f^*(p)$ is real for each $p$ in T}, $f^*$ being the unique continuous extension of $f$ in C(X) from ${\beta}X$ to $\mathbb{R}^*$, the one point compactification of $\mathbb{R}$. As a consequence it follows that if X is a realcompact space in which every $C^*$-embedded subset is closed, then C(X) is never isomorphic to any A(X) in ${\sum}(X)$ without being equal to it.

• Journal of Korean Ophthalmic Optics Society
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• v.14 no.1
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• pp.47-56
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• 2009

Purpose: To find optimized luminosity factor of color from light transmission filter. Methods: To make $Y_{1-x}G_{x}$, $Y_{1-x}P_{x}$ by using CR-39 compound within dipping method, mixing up Y(Yellow), G(green) and P(pink) for optimize eye sensitivity. Modeling for relative luminous efficiency(relative sensitivity) curves in Luminose transmission, it could be resolved by Multiplying sensitivity of eye within transmission rate of Lens ($P_f({\lambda}=T({\lambda}){\cdot}P({\lambda}).)$.). To evaluate Wavelength between 400~700 nm, relative luminous efficiency curve in Area and Height value is being used. Results: In color filter of $Y_{1-x}G_{x}$ position of x equals to 0.04, 0.1, 0.08, 0.12, 0.14, 0.5 at ${\beta}=S_1/S_0{\cdot}100$ each consist value of 76.1, 77.9, 80.7, 81.6, 80.2, 18.6 In color filter of $Y_{1-x}P_{x}$ position of x equals to 1.00, 0.2, 0.6, 0.8 at ${\beta}=S_1/S_0{\cdot}100$ each consist value of 74.3, 74.0, 70.5, 33.0 The result from experiment $Y_{1-x}P_{x}$ value less than $Y_{1-x}G_{x}$, from evaluating luminous efficiency curve and test was successfully optimized. Conclusions: Optimized relative luminous efficiency curve result have value of X=0.12-0.14 at $Y_{1-x}G_{x}$.

• Honam Mathematical Journal
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• v.35 no.2
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• pp.303-310
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• 2013

In this paper, we first show that $z_{{\kappa}X}:E_{cc}({\kappa}X){\rightarrow}{\kappa}X$ is $z^{\sharp}$-irreducible and that if $\mathcal{G}(E_{cc}({\beta}X))$ is a base for closed sets in ${\beta}X$, then $E_{cc}({\kappa}X)$ is $C^*$-embedded in $E_{cc}({\beta}X)$, where ${\kappa}X$ is the extension of X such that $vX{\subseteq}{\kappa}X{\subseteq}{\beta}X$ and ${\kappa}X$ is weakly Lindel$\ddot{o}$f. Using these, we will show that if $\mathcal{G}({\beta}X)$ is a base for closed sets in ${\beta}X$ and for any weakly Lindel$\ddot{o}$f space Y with $X{\subseteq}Y{\subseteq}{\kappa}X$, ${\kappa}X=Y$, then $kE_{cc}(X)=E_{cc}({\kappa}X)$ if and only if ${\beta}E_{cc}(X)=E_{cc}({\beta}X)$.

• Journal of the Korean Vacuum Society
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• v.2 no.2
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• pp.227-235
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• 1993

$SbS_{1-x}Se_xI,\;BiS_{1-x}Se_xI,\;Sb_{1-x}Bi_xSI,\;Sb_{1-x}Bi_xSeI,\;SbS_{1-x}Se_xI:Co,\;BiS_{1-x}Se_xI:Co,\;Sb_{1-x}Bi_xSI:Co$, and $Sb_{1-x}Bi_xSeI:Co$ single crystals were grown by the vertical Bridgman method using the ingots. It has been found that these single crystals have an orthorhombic structure and indirect optical transition. The composition dependences of energy gaps are given by $E_g(x)=E_g(0)-Ax+Bx^2$. The impurity optical absorption peaks due to cobalt deped with impurity are attributed to the electron transitions between the split energy levels of $Co^{2+}$ and $Co^{3+}$ ions sited at $T_d$symmetry of the host lattice.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.535-540
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• 2002

Let X$_1$, X$_2$‥‥,X$\_$n/ be n independent and identically distributed random variables with continuous cumulative distribution function F(x). Let us rearrange the X's in the increasing order X$\_$1:n/ $\leq$ X$\_$2:n/ $\leq$ ‥‥ $\leq$ X$\_$n:n/. We call X$\_$k:n/ the k-th order statistic. Then X$\_$n:n/ - X$\_$n-1:n/ and X$\_$n-1:n/ are independent if and only if f(x) = 1-e(equation omitted) with some c > 0. And X$\_$j/ is an upper record value of this sequence lf X$\_$j/ > max(X$_1$, X$_2$,¨¨ ,X$\_$j-1/). We define u(n) = min(j|j > u(n-1),X$\_$j/ > X$\_$u(n-1)/, n $\geq$ 2) with u(1) = 1. Then F(x) = 1 - e(equation omitted), x > 0 if and only if E[X$\_$u(n+3)/ - X$\_$u(n)/ | X$\_$u(m)/ = y] = 3c, or E[X$\_$u(n+4)/ - X$\_$u(n)/|X$\_$u(m)/ = y] = 4c, n m+1.

• The Pure and Applied Mathematics
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• v.23 no.4
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• pp.347-375
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• 2016

Let R be a 3!-torsion free noncommutative semiprime ring, U a Lie ideal of R, and let $D:R{\rightarrow}R$ be a Jordan derivation. If [D(x), x]D(x) = 0 for all $x{\in}U$, then D(x)[D(x), x]y - yD(x)[D(x), x] = 0 for all $x,y{\in}U$. And also, if D(x)[D(x), x] = 0 for all $x{\in}U$, then [D(x), x]D(x)y - y[D(x), x]D(x) = 0 for all $x,y{\in}U$. And we shall give their applications in Banach algebras.

• The Korean Journal of Applied Statistics
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• v.27 no.1
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• pp.133-146
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• 2014

The United States Census Bureau released a new version of X-13ARIMA-SEATS that integrates X-12-ARIMA with TRAMO-SEATS. This paper compares a seasonal adjusted series from X-13ARIMA-SEATS and those from X-12-ARIMA. An X11 filter and SEATS filter were used for the X-13ARIMA-SEATS. The result of the comparison suggests that seasonal adjusted series using X-13ARIMA-SEATS with the X11 filter are similar to those of X-12-ARIMA.