• Korean Journal of Mathematics
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• v.18 no.3
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• pp.311-322
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• 2010

In this paper, we prove stabilities of the reciprocal difference functional equation $$r(\frac{x+y+z}{3})-r(x+y+z)=\frac{2r(x)r(y)r(z)}{r(x)r(y)+r(y)r(z)+r(z)r(x)}$$ and the reciprocal adjoint functional equation $$r(\frac{x+y+z}{3})+r(x+y+z)=\frac{4r(x)r(y)r(z)}{r(x)r(y)+r(y)r(z)+r(z)r(x)}$$ with three variables. Stabilities of the reciprocal difference functional equation and the reciprocal adjoint functional equation in two variables was proved by K. Ravi, J. M. Rassias and B. V. Senthil Kumar. We extend their results to three variables in similar types.

• Journal of Fisheries and Marine Sciences Education
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• v.29 no.3
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• pp.785-798
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• 2017

This study was conducted to evaluated the surface(10 variables) and bottom(10 variables) water quality, and sediment(3 variables) in the cage fish farm off Baegyado in Gamak Bay using a multivariate analysis from January 2013 to November 2014. Generally, the environmental data did not show a certain tendency by months during two years investigated. The pairwise simple correlation matrices among variables were also shown. The first four principal components of the surface water in 2013 explain 93% of the total sample variance; the first principal component($z_1$) showed the freshwater inflow and/or precipitation, $z_2$, $z_3$ and $z_4$ related to freshwater inflow and/or precipitation, organic matters and eutrophy, respectively; the first four principal components of the bottom water in 2013 explain 93% of the total sample variance; the $z_1$, $z_2$ and $z_4$ related to freshwater inflow and/or precipitation, and $z_3$ water temperature. In 2014, at the surface water the first three principal components explain 87%; the $z_1$, $z_2$ and $z_3$ related to water temperature, eutrophy and freshwater inflow and/or precipitation, respectively; at the bottom water the first three principal components explain 93%; $z_1$, $z_2$ and $z_3$ related to water temperature, freshwater inflow and/or precipitation and eutrophy. Half of the principal components related to freshwater inflow and/or precipitation.

• 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.

• The Journal of the Acoustical Society of Korea
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• v.7 no.2
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• pp.65-73
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• 1988

In this paper, V(z) curve has been analyzed theoretically and compared with the experimental result, and the relation between the V(z) curve and the material characteristic has been studied. Angular spectrum and ray optics theory have been used for theoretical analysis and the acoustic microscope operating at a center frequency of 3 MHz has been used for experiment. In experiment, it has been shown that each material has a V(z) curve of a unique form and the interval of dips appearing in the V(z) curves have been used to determine the Rayleigh wave velocity.

• Korean Journal of Medicinal Crop Science
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• v.19 no.1
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• pp.1-8
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• 2011

Biological characteristics of 5 Zanthoxylum schinifolium (Zs) fruits such as Z1 (early August), Z2 (middle August), Z3 (middle September), Z4 (early October) and Z5 (middle October) according to harvesting time were evaluated. As fruits ripened, average weight of Zs increased from 4.8mg (Z1) to 50.7mg (Z5), while moisture contents decreased from 74.6% (Z1) to 55.2% (Z5). Crude fat contents of the fruits during ripening increased from 1% (Z1) to 10.6% (Z5). The major fatty acids in Zs were palmitic (C16:0), palmitoleic (C16:1), oleic (C18:1), and linoleic (C18:2) acids. Linoleic acid (C18:2) was a main fatty acid in Z1 and Z2, whereas oleic acid (C18:1) was found as a main one in the other Zs. The ratio of unsaturated fatty acid to total fatty acids increased from 60% (Z1) to 80% (Z3~Z5) during ripening. Among ripening stages, Z4 had the highest contents of total fatty acids ($3,355{\mu}g/g$) and total unsaturated fatty acids ($2,753{\mu}g/g$). Forty six volatile compounds in Zs were also identified. The major volatile compounds were ${\alpha}-pinene$, ${\beta}-myrcene$, ${\beta}-ocimene$, 2-nonanone, estragole, 2-undecanone, and ${\beta}-caryophyllene$. Major volatile components of Z1 were ${\beta}-ocimene$ (20.8 peak area %) and ${\alpha}-pinene$ (9.7 peak area %). In Z2, estragole (30.1 peak area %) was a main volatile compound, but the contents of ${\alpha}-pinene$ (0.4 peak area %), ${\beta}-myrcene$ (0.3 peak area %), and ${\beta}-ocimene$ (0.6 peak area %) were lower than those in Z1. Especially, estragole used as perfumes and as a food additive for flavor was drastically increased to 91.2 (Z3) and 92% (Z4) as fruits ripened.

• The Pure and Applied Mathematics
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• v.11 no.3
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• pp.207-215
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• 2004

Let W(z) be a power series with operator coefficients such that multiplication by W(z) is contractive in extC(z). The overlapping space $\varepsilon$(W) of D(W) in C(z) is a Herglotz space with Herglotz function $\varphi$(z) which satisfies $\varphi$(z) + ${\varphi}^*(z^{-1})$ = 2[1-W$^*(z^{-1})W(z)]$.

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.199-209
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• 2002

In this paper, we investigate the problem of stability of the quadratic functional equation f(x+y+z)+f(y-z)+f(y-z)+f(x-z) = 3f(x)+3f(y)+3f(z) on abelian group.

• Korean Journal of Mathematics
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• v.29 no.3
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• pp.631-638
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• 2021

In this paper, some sharp inequalities for ordinary derivative P'(z) and polar derivative D_αP(z) = nP(z) + (α - z)P'(z) are obtained by including some of the coefficients and modulus of each individual zero of a polynomial P(z) of degree n not vanishing in the region |z| > k, k ≥ 1. Our results also improve the bounds of Turán's and Aziz's inequalities.

• Korean journal of applied entomology
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• v.53 no.1
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• pp.7-13
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• 2014

This study was performed to investigate the response of the lacewing Chrysopa cognata to both Aphis gossypii-induced plant volatiles and lacewing-derived volatiles. The results of a Y-tube olfactometer bioassay showed that more C. cognata males were attracted to green pepper plants infected with A. gossypii than to uninfected green pepper plants alone or clean air and C. cognata males were attractive to C. cognata females. Gas chromatography-electroantennographic detection (GC-EAD) analysis showed that the antennae of C. cognata females elicited EAD-active responses to the volatiles entrained from A. gossypii-infected green pepper plants. 4-Ethylacetophenone, 3-ethylbenzaldehyde, 3-ethylacetophenone, and 4-ethylbenzaldehyde from A. gossypii-induced green pepper volatiles, and (Z,Z)-4,7-tridecadiene, (Z)-4-tridecene, and (Z)-4-undecene from C. cognata female entrainment were elucidated by further analysis using GC coupled nuclear magnetic resonance spectroscopy. Of the A. gossypii-induced plant volatiles identified in this study, 4-ethylacetophenone and 3-ethylbenzaldehyde significantly increased the attraction of C. cognata males to nepetalactol, but (Z)-4-tridecene and (Z)-4-undecene did not. (Z,Z)-4,7-Tridecadiene significantly reduced the attractiveness of nepetalactol to C. cognata.

• 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.