• Journal of the Korean Chemical Society
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• v.22 no.6
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• pp.417-422
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• 1978

Rather than undergo photooxygenation, the Z-configuration benzalpyrrolinones (Z-2, Z-4) photoisomerized to the E-configuration isomers under direct or sensitized irradiation. Rose bengal sensitized photochemical stereoisomerzation of benzalpyrrolinones (Z-2, Z-4 and E-2) with monochromatic light (at 557 nm, excitation of rose bengal only) showed that the triplet of benzalpyrrolinones was involved in the photoisomerization, since oxygen inhibited the photoisomerization.

• The Transactions of the Korea Information Processing Society
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• v.2 no.1
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• pp.55-65
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• 1995

Existing multiple-row downdating algorithms have adopted a CFD(Cholesky Factor Downdating) that recursively downdates one row at a time. The CFD based algorithm requires 5/2p $n^{2}$ flops(floating point operations) downdating a p$\times$n observation matrix $Z^{T}$ . On the other hands, a HCFD(Hybrid CFD) based algorithm we propose in this paper, requires p $n^{2}$＋6/5 $n^{3}$ flops v hen p$\geq$n. Such a HCFD based algorithm factorizes $Z^{T}$ at first, such that $Z^{T}$ = $Q_{z}$ RT/Z, and then applies the CFD onto the upper triangular matrix Rt/z, so that the total number of floating point operations for downdating $Z^{T}$ would be significantly reduced compared with that of the CFD based algorithm. Benchmark tests on the Sun SPARC/2 and the Tolerant System also show that performance of the HCFD based algorithm is superior to that of the CFD based algorithm, especially when the number of rows of the observation matrix is large.rge.

• Honam Mathematical Journal
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• v.1 no.1
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• pp.11-14
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• 1979

S^{**}를 S의 subclass로서$f(z)=z+a_zz^2+{\cdots}\;{\cdots}\;{\cdots}\;{\cdots}$가 $Re\{zf^'(z)[f(z)-f(-z)]^{-1}\}$>0, ${\left|z\right|}$<1을 만족하는 함수족(函數族)이라 하자. M.S. Robertson은 1961년에 subordination의 원리를 이용하여 $f(z)=z+a_zz^2+{\cdots}\;{\cdots}\;{\cdots}$가 S^{**}에 속하기 위한 충분조건을 구하였다. 본(本) 논문(論文)은 Robertson의 조건에 약간의 수정을 가해서 f(Z)가 S^{**}에 속하기 위한 필요 충분 조건을 만들고, 그것을 증명하였다.

• Kyungpook Mathematical Journal
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• v.46 no.2
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• pp.255-260
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• 2006

Let $m$ and $k$ be any positive integers, let $\mathbb{Z}_k$ the ring of integers of modulo $k$, let $G_m(\mathbb{Z}_k)$ the group of all $m$ by $m$ nonsingular matrices over $\mathbb{Z}_k$ and let ${\phi}_m(k)$ the order of $G_m(\mathbb{Z}_k)$. In this paper, ${\phi}_m(k)$ can be computed by the following investigation: First, for any relatively prime positive integers $s$ and $t$, $G_m(\mathbb{Z}_{st})$ is isomorphic to $G_m(\mathbb{Z}_s){\times}G_m(\mathbb{Z}_t)$. Secondly, for any positive integer $n$ and any prime $p$, ${\phi}_m(p^n)=p^{m^2}{\cdot}{\phi}_m(p^{n-1})=p{^{2m}}^2{\cdot}{\phi}_m(p^{n-2})={\cdots}=p^{{(n-1)m}^2}{\cdot}{\phi}_m(p)$, and so ${\phi}_m(k)={\phi}_m(p_1^n1){\cdot}{\phi}_m(p_2^{n2}){\cdots}{\phi}_m(p_s^{ns})$ for the prime factorization of $k$, $k=p_1^{n1}{\cdot}p_2^{n2}{\cdots}p_s^{ns}$.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.1
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• pp.41-56
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• 2007

A 3-partite 2-digraph is an orientation of a 3-partite multi-graph that is without loops and contains at most two edges between any pair of vertices from distinct parts. Let D(X, Y, Z) be a 3-partite 2-digraph with ${\mid}X{\mid}=l,\;{\mid}Y{\mid}=m,\;{\mid}Z{\mid}=n$. For any vertex v in D(X, Y, Z), let $d^+_{\nu}\;and\;d^-_{\nu}$ denote the outdegree and indegree respectively of v. Define $p_x=2(m+n)+d^+_x-d^-_x,\;q_y=2(l+n)+d^+_y-d^-_y\;and\;r_z=2(l+m)+d^+_z-d^-_z$ as the marks (or 2-scores) of x in X, y in Y and z in Z respectively. In this paper, we characterize the marks of 3-partite 2-digraphs and give a constructive and existence criterion for sequences of non-negative integers in non-decreasing order to be the mark sequences of some 3-partite 2-digraph.

• Kyungpook Mathematical Journal
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• v.47 no.1
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• pp.69-76
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• 2007

Let $f$ denote a mapping from an orthogonality space ($\mathcal{X}$, ${\bot}$) into a real Banach space $\mathcal{Y}$. In this paper, we prove the Hyers-Ulam-Rassias stability of the orthogonally cubic functional equations $f(2x+y)+f(2x-y)=2f(x+y)+2f(x-y)+12f(x)$ and $f(x+y+2z)+f(x+y-2z)+f(2x)+f(2y)=2f(x+y)+4f(x+z)+4f(x-z)+4f(y+z)+4f(y-z)$, where $x{\bot}y$, $y{\bot}z$, $x{\bot}z$.

• Korean Journal of Medicinal Crop Science
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• v.11 no.1
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• pp.40-45
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• 2003

Volatile components in the leaves and fruits of Z. schinjfolium and Z. piperitum were analyzed by Headspace SPME(Solid phase Microextraction). Fifty two and 48 components in the leaves and fruits, repectively, were identified in Z. schinifolium. (E)-2-hexenal, ${\alpha}-pinene$, (Z)-ocimene+limonene, estragole, germacrene-d were detected at common components in the leaves and estragole in the fruits of Z. schinjfolium. Regardless of collection sites hexanal, (Z)-3-hexenol, (E)-2-hexenal, n-hexanol were appeared in the leaves while undecanone in the fruits. Thirty and 27 components in the leaves and fruits, respectively, were identified in Z. piperitum. ${\alpha}-pinene,\;{\beta}-phellandrene$, 1,8-cineole, citronellal and myrcene, (Z)-ocimene+limonene, ${\beta}-phellandrene$ were appeared as common components in the leaves and fruits collected from Baeck-yang-sa and Nae-jang-sa. (Z)-3-hexenol, (E)-2-hexenal, ${\alpha}-pinene\;myrcene\;and\;{\beta}-phellandrene$, citronellal, geranyl acetate were major components in the leaves and fruits from Tong-do-sa.

• Journal of Korean Society on Water Environment
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• v.28 no.5
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• pp.723-728
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• 2012

In this study, zeolites were synthesized by a fusion and a hydrothermal methods using a coal fly ash and a waste catalyst. The recovery performance of metal ions on the structure property of synthetic zeolites was evaluated as comparing the adsorption kinetics (Lagergen 2nd order model) and isotherm (Langmuir model) of $Co^{2+},\;Ni^{2+}$, and $Cu^{2+}$ ions. The synthetic zeolites (Z-C1 and Z-W5) were similarly assigned to XRD peaks in a reagent grade Na-A zeolite (Z-WK : $Na_{12}Al_{12}Si_{12}O_{48}\;27.4H_2O$). Adsorption rates of Z-W5 and Z-C1 were in the order of $Cu^{2+}\;>\;Co^{2+}\;>\;Ni^{2+}\;and\;Ni^{2+}\;>\;Cu^{2+}\;>\;Co^{2+}$, respectively. They had influenced upon structure properties of zeolite. Selectivities of metal ions and maximum equilibrium adsorption capacities, $q_{max}$, in Z-C1 and Z-W5 were in the order of $Ni^{2+}$ (127.9 mg/g) > $Cu^{2+}$ (94.7 mg/g) > $Co^{2+}$ (82.6 mg/g) and $Cu^{2+}$ (141.3 mg/g) > $Co^{2+}$ (122.2 mg/g) > $Ni^{2+}$ (87.6 mg/g), respectively. The results show that the synthetic zeolites, Z-C1 and Z-W5, are able to recover metal ions selectively in wastewater.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.91-102
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• 2000

Let ${\gamma}{\equiv}{\gamma}^{(2n)}$ denote a sequence of complex numbers ${\gamma}{00},{\gamma}{01},\cdots,{\gamma}0, 2n,...,{\gamma}{2n},0\;with\; {\gamma}{00}\;>\;0,{\gamma}{ji}={{\overline}{\gamma_{ij}}}$,and let K denote a closed subset of the complex plane C. The truncated K complex moment problem entails finding a positive Borel measure $\mu$ such that ${\gamma}{ij}={\int}{{\overline}{z}}^{i}z^{j}d{\mu}\;(0{\leq}\;i+j\;{\leq}\;2n)$ and supp ${\mu}{\subseteq}\;K$. If n=2, then is called the quartic moment problem. In this paper, we give partial solutions for the singular quartic moment problem with rank M(2)=5 and ${{\overline}{Z}}Z{\in}\;<1,Z,{{\overline}{Z}},Z^{2},{{\overline}{Z}}^2>$.

• Archives of Pharmacal Research
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• v.28 no.12
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• pp.1381-1385
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• 2005

Further investigation of Lycium chinense fruits gave a mixture of (6'-O-palmitoyl)- and (6'-O­stearoyl)-$\beta$-sitosterol-3-O-$\beta$-D-glucopyranoside (1) and two glycolipids, 1-O-(9Z, 12Z, 15Z-octa­decatrienoyl)-2-O-(9Z, 12Z, 15Z-octadecatrienoyl)-3-O-$\beta$-D-galactopyranosyl glycerol (2) and 1-O-(9Z, 12Z-octadecadienoyl)-2-O-(9Z, 12Z, 15Z-octadecatrienoyl)-3-O-$\beta$-D-galactopyranosyl glycerol (3). These compounds were newly isolated as constituents of L. chinense.