• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.323-333
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• 2010

The biproduct bialgebra has been generalized to generalized biproduct bialgebra $B{\times}^L_H\;D$ in [5]. Let (D, B) be an admissible pair and let D be a bialgebra. We show that if generalized biproduct bialgebra $B{\times}^L_H\;D$ is a Hopf algebra with antipode s, then D is a Hopf algebra and the identity $id_B$ has an inverse in the convolution algebra $Hom_k$(B, B). We show that if D is a Hopf algebra with antipode $s_D$ and $s_B$ in $Hom_k$(B, B) is an inverse of $id_B$ then $B{\times}^L_H\;D$ is a Hopf algebra with antipode s described by $s(b{\times}^L_H\;d)={\Sigma}(1_B{\times}^L_H\;s_D(b_{-1}{\cdot}d))(s_B(b_0){\times}^L_H\;1_D)$. We show that the mapping system $B{\leftrightarrows}^{{\Pi}_B}_{j_B}\;B{\times}^L_H\;D{\rightleftarrows}^{{\pi}_D}_{i_D}\;D$ (where $j_B$ and $i_D$ are the canonical inclusions, ${\Pi}_B$ and ${\pi}_D$ are the canonical coalgebra projections) characterizes $B{\times}^L_H\;D$. These generalize the corresponding results in [6].

• Journal of Bio-Environment Control
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• v.21 no.3
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• pp.192-198
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• 2012

Experiments were conducted to investigate the optimum concentration of nutrient solution in hydroponics for strawberry 'Ssanta' bred at Gyongsangbuk-do Agricultural Research & Extension Services. Nutrient solutions for strawberry, which made by Yamazaki, were supplied EC (Electrical Conductivity) 0.6, 0.8, 1.2, and $1.8dS{\cdot}m^{-1}$ after planting on cocopeat medium during experiment period. Growth of shoot of strawberries did not show statistical differences among treatments. Fruit length showed the longest in EC $0.8dS{\cdot}m^{-1}$ in all clusters. In the second flower cluster, fruit length showed longer in EC 0.8 and $1.2dS{\cdot}m^{-1}$ than EC 0.6 and $1.8dS{\cdot}m^{-1}$. In the third flower cluster, it showed the longest in EC 0.8 and $1.2dS{\cdot}m^{-1}$, followed by 0.6 and $1.8dS{\cdot}m^{-1}$. The longest was in EC $0.8dS{\cdot}m^{-1}$ and the shortest in EC $1.8dS{\cdot}m^{-1}$ in the fourth flower cluster. Fruit diameter did not show significant differences among treatments, but longest in EC 0.8 and $1.2dS{\cdot}m^{-1}$ in all clusters. The heaviest mean fruit weight appeared in EC $0.8dS{\cdot}m^{-1}$ in all flower clusters. And heavier in EC $1.2dS{\cdot}m^{-1}$ in the second and third clusters. Also the weight was significantly light in plants grown in EC 0.6 and $1.8dS{\cdot}m^{-1}$ in the second and third cluster. Soluble solids of fruit was the highest in EC $0.6dS{\cdot}m^{-1}$ in all clusters. As the results, we came to the conclusion that the optimum EC for strawberry 'Ssanta' was EC $0.8{\sim}1.2dS{\cdot}m^{-1}$ in this experiment.

• The Korean Journal of Zoology
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• v.7 no.2
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• pp.13-18
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• 1964

The chromosomes of thirteen wild forms of Drosophila obtained from Kwangnung in Kyunggi Province, Korea were investigated with the ganglion cells of both male and female larvae using the aceto-lactic orcein squashed method. The male chromosome patterns of the species observed in the present study are summarized as follows:

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.455-462
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• 2012

The cyclic group $Cn={\langle}(12{\cdots}n){\rangle}$ acts on the set ($^{[n]}_k$) of all $k$-subsets of [$n$]. In this action of $C_n$ the number of orbits of size $d$, for $d|n$, is $$O^{n,k}_d=\frac{1}{d}\sum_{\frac{n}{d}|s|n}{\mu}(\frac{ds}{n})(^{n/s}_{k/s})$$. Stanton and White[7] generalized the above identity to construct the orbit polynomials $$O^{n,k}_d(q)=\frac{1}{[d]_{q^{n/d}}}\sum_{\frac{n}{d}|s|n}{\mu}(\frac{ds}{n})[^{n/s}_{k/s}]{_q}^s$$ and conjectured that $O^{n,k}_d(q)$ have non-negative coefficients. In this paper we give a combinatorial proof for the positivity of coefficients of the orbit polynomial $O^{n,3}_d(q)$.

• Korean Journal of Mathematics
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• v.25 no.3
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• pp.349-358
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• 2017

The cyclic group $C_n={\langle}(12{\cdots}n){\rangle}$ acts on the set $(^{[n]}_k)$ of all k-subsets of [n]. In this action of $C_n$ the number of orbits of size d, for d | n, is $$O^{n,k}_d={\frac{1}{d}}{\sum\limits_{{\frac{n}{d}}{\mid}s{\mid}n}}{\mu}({\frac{ds}{n}})(^{n/s}_{k/s})$$. Stanton and White [6] generalized the above identity to construct the orbit polynomials $$O^{n,k}_d(q)={\frac{1}{[d]_{q^{n/d}}}}{\sum\limits_{{\frac{n}{d}}{\mid}s{\mid}n}}{\mu}({\frac{ds}{n}})[^{n/s}_{k/s}]_{q^s}$$ and conjectured that $O^{n,k}_d(q)$ have non-negative coefficients. In this paper we give a constructive proof for the positivity of coefficients of the orbit polynomial $O^{n,2}_d(q)$.

• Journal of The Korean Astronomical Society
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• v.39 no.3
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• pp.57-71
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• 2006

We investigated the structural parameters of a sample of 30 dwarf galaxies(15 dEs and 15 dS0s) in the Virgo Cluster using i-band images from the Sloan Digital Sky Survey Data Release 4. Among 28 galaxies for which surface brightness profiles were derived from ellipse fittings, 23 galaxies had a single component that was adequately described by a generalized $S\acute{e}rsic$ function with a shape parameter ranging from n=0.5 to 2, while 5 galaxies(2 dEs and 3 dS0s) had bulge and disk components that were fitted by a generalized $S\acute{e}rsic$ function and an exponential function, respectively. Since the majority of dwarf galaxies in the present sample had a single component, it seems likely that genuine dS0 galaxies that have disk and bulge components are quite rare in the Virgo Cluster. The similarity in structural parameters of genuine dS0 galaxies in the Virgo Cluster with those of Magellanic-type galaxies implies that the progenitors of dwarf lenticular galaxies in the Virgo Cluster were most likely Magellanic-type galaxies if dS0s are harassed late-type spirals.

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.455-462
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• 2013

Let D be an integral domain, S be a saturated multi-plicative subset of D such that $D_S$ is a factorial domain, $\{X_{\alpha}\}$ be a nonempty set of indeterminates, and $D[\{X_{\alpha}\}]$ be the polynomial ring over D. We show that S is a splitting (resp., almost splitting, t-splitting) set in D if and only if every nonzero prime t-ideal of D disjoint from S is principal (resp., contains a primary element, is t-invertible). We use this result to show that $D{\backslash}\{0\}$ is a splitting (resp., almost splitting, t-splitting) set in $D[\{X_{\alpha}\}]$ if and only if D is a GCD-domain (resp., UMT-domain with $Cl(D[\{X_{\alpha}\}]$ torsion UMT-domain).

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.815-827
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• 2019

It is well known that the denominator of the Dedekind sum s(c, d) divides 2 gcd(d, 3)d and that no smaller denominator independent of c can be expected. In contrast, here we prove that we usually get a smaller denominator in S(H, d), the sum of the s(c, d)'s over all the c's in a subgroup H of order n > 1 in the multiplicative group $(\mathbb{Z}/d\mathbb{Z})^*$. First, we prove that for p > 3 a prime, the sum 2S(H, p) is a rational integer of the same parity as (p-1)/2. We give an application of this result to upper bounds on relative class numbers of imaginary abelian number fields of prime conductor. Finally, we give a general result on the denominator of S(H, d) for non necessarily prime d's. We show that its denominator is a divisor of some explicit divisor of 2d gcd(d, 3).

• Horticultural Science & Technology
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• v.29 no.4
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• pp.311-316
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• 2011

This study aimed to determine the effect of EC (electrical conductivity) levels of nutrient solution in hydroponic culture on allyl-isothiocyanate (AITC) content within plant tissues, Vitamin C content and physiological responses in wasabi plant (Wasabia japonica M. 'Darma'). The 'Darma' was grown for 5 weeks with a deep flow technique (DFT) system controlled at 5 different EC levels, including 0.5, 1, 2, 3, and $5dS{\cdot}m^{-1}$. In result, the highest total content of AITC showed at EC level 5 and $3dS{\cdot}m^{-1}$ for 1 or 5- week, respectively. The total content of AITC increased about 1.2-1.4 times when the plants were grown in the EC levels between 0.5 and $2dS{\cdot}m^{-1}$, whereas the content decreased about 6 and 56 % in the EC level 3 and $5dS{\cdot}m^{-1}$, respectively. The content of AITC was relatively higher in petiole tissue, about 53 %, taken from 1 week-grown plants when the EC was controlled between 0.5 and $2dS{\cdot}m^{-1}$. Root tissue also had relatively higher content of AITC, about 45.1 %, when the EC was controlled at 3 and $5dS{\cdot}m^{-1}$. However, a 5-fold decrease in the AITC content was found in blade tissue and a 6.8-fold decrease in root when the EC was controlled at $5dS{\cdot}m^{-1}$ for 5 weeks. There was no significant difference in the vitamin C content in 1-week grown leaf tissues under the different EC level treatments; but, the content increased about 27% in 5-week grown plants at the EC level between 0.5 and $2dS{\cdot}m^{-1}$, compared to the 1 week-grown leaf tissue. Electrolyte leakage of leaf tissue taken from 3-week grown plant was 3-fold higher at the EC level $5dS{\cdot}m^{-1}$, compared to the EC level between 0.5 and $2dS{\cdot}m^{-1}$. Chlorophyll content, photosynthesis rate and transpiration rate were decreased when the EC was controlled at higher than $2dS{\cdot}m^{-1}$. Leaf water content, specific leaf area and growth were decreased when the EC was controlled at $5dS{\cdot}m^{-1}$ for 5 weeks. All the integrated results in this study suggest that the EC level of nutrient solution should be maintained at lower than $3dS{\cdot}m^{-1}$ in order to improve nutritional value and quantity required for hydroponically grown wasabi as functional vegetable.

• Journal of Information Display
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• v.12 no.3
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• pp.159-165
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• 2011

This research entailed the production of stereoscopic 3D (S3D) contents using 2D-to-S3D conversion for exhibition at a museum and subjective evaluation. Hybrid production combining S3D images of existing live-action videos using the 2D-to-S3D conversion technology and computer graphic ones created via stereo rendering was conducted. Design and control of the chronological analysis of the parallactic angle was conducted on the produced contents, using binocular information as well as subjective evaluations, with the intent of conducting an investigation on the characteristics of such contents from the perspectives of the producers and viewers. An investigation was also conducted on the effects of the viewing position on the impressions of the S3D images.