• Bulletin of the Korean Mathematical Society
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• v.22 no.1
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• pp.11-15
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• 1985

Manddelberg [9] has shown that a Clifford algebra of a free quadratic space over an arbitrary semi-local ring R in Brawer-Wall group BW(R) is determined by its rank, determinant, and Hasse invariant. In this paper, we prove a corresponding result when R is a full ring.Throughout this paper, unless otherwise specified, we assume that R is a commutative ring having 2 a unit. A quadratic space (V, B, .phi.) over R is a finitely generated projective R-module V with a symmetric bilinear mapping B: V*V.rarw.R which is non-degenerate (i.e., the natural mapping V.rarw.Ho $m_{R}$(V,R) induced by B is an isomorphism), and with a quadratic mapping .phi.: V.rarw.R such that B(x,y)=1/2(.phi.(x+y)-.phi.(x)-.phi.(y)) and .phi.(rx) = $r^{2}$.phi.(x) for all x, y in V and r in R. We denote the group of multiplicative units of R by U9R). If (V, B, .phi.) is a free rank n quadratic space over R with an orthogonal basis { $x_{1}$,.., $x_{n}$}, we will write < $a_{1}$,.., $a_{n}$> for (V, B, .phi.) where the $a_{i}$=.phi.( $x_{i}$) are in U(R), and denote the space by the table [ $a_{ij}$ ] where $a_{ij}$ =B( $x_{i}$, $x_{j}$). In the case n=2 and B( $x_{1}$, $x_{2}$)=1/2 we reserve the notation [a $a_{11}$, $a_{22}$] for the space. A commutative ring R having 2 a unit is called full [10] if for every triple $a_{1}$, $a_{2}$, $a_{3}$ of elements in R with ( $a_{1}$, $a_{2}$, $a_{3}$)=R, there is an element w in R such that $a_{1}$+ $a_{2}$w+ $a_{3}$ $w^{2}$=unit.TEX>=unit.t.t.t.

• Bulletin of the Korean Mathematical Society
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• v.22 no.2
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• pp.121-126
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• 1985

D.K. Harrison [5] has shown that if R and S are fields of characteristic different from 2, then two Witt rings W(R) and W(S) are isomorphic if and only if W(R)/I(R)$^{3}$ and W(S)/I(S)$^{3}$ are isomorphic where I(R) and I(S) denote the fundamental ideals of W(R) and W(S) respectively. In [1], J.K. Arason and A. Pfister proved a corresponding result when the characteristics of R and S are 2, and, in [9], K.I. Mandelberg proved the result when R and S are commutative semi-local rings having 2 a unit. In this paper, we prove the result when R and S are 2-fold full rings. Throughout this paper, unless otherwise specified, we assume that R is a commutative ring having 2 a unit. A quadratic space (V, B, .phi.) over R is a finitely generated projective R-module V with a symmetric bilinear mapping B: V*V.rarw.R which is nondegenerate (i.e., the natural mapping V.rarw.Ho $m_{R}$ (V, R) induced by B is an isomorphism), and with a quadratic mapping .phi.:V.rarw.R such that B(x,y)=(.phi.(x+y)-.phi.(x)-.phi.(y))/2 and .phi.(rx)= $r^{2}$.phi.(x) for all x, y in V and r in R. We denote the group of multiplicative units of R by U(R). If (V, B, .phi.) is a free rank n quadratic space over R with an orthogonal basis { $x_{1}$, .., $x_{n}$}, we will write < $a_{1}$,.., $a_{n}$> for (V, B, .phi.) where the $a_{i}$=.phi.( $x_{i}$) are in U(R), and denote the space by the table [ $a_{ij}$ ] where $a_{ij}$ =B( $x_{i}$, $x_{j}$). In the case n=2 and B( $x_{1}$, $x_{2}$)=1/2, we reserve the notation [ $a_{11}$, $a_{22}$] for the space.the space.e.e.e.

• Korean Journal of Microbiology
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• v.45 no.4
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• pp.430-434
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• 2009

Bacterial 16S rRNA gene sequences have been widely used for the studies on molecular phylogeny, evolutional history, and molecular detections. Bacterial genomes have multiple rRNA operons, of which gene sequences sometimes are variable. In the present study, heterogeneity of the Vibrio 16S rRNA gene sequences were investigated. Vibrio 16S rRNA sequences were obtained from GenBank databases, considering the completion of gene annotation of Vibrio genome sequences. These included V. cholerae, V. harveyi, V. parahaemolyticus, V. splendidus, and V. vulnificus. Chromosome 1 of the studied Vibrio had 7~10 copies of the 16S rRNA gene, and their intragenomic variations were less than 0.9% dissimilarity (more than 99.1% DNA similarity). Chromosome 2 had none or single 16S rRNA gene. Intragenomic 16S rRNA genotypes were detected at least 5 types (V. vulnificus #CMCP6) to 8 types (V. parahaemolyticus #RIMD 2210633, V. harveyi #ATCC BAA-1116). These suggest that Vibrio has high heterogeneity of the 16S rRNA gene sequences.

• Journal of Astronomy and Space Sciences
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• v.26 no.2
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• pp.157-170
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• 2009

BVR observations for 52 standard stars were performed using the 1-m reflecter with 2K CCD System of Chungbuk National University Observatory (CBNUO) in 2008. We obtained 1,322 CCD images to establish a correlation between our bvr system and the standard Johnson-Cousins BVR system. We derived the tentative equations of transformation between then as follows; V = v-0.0303(B - V) + 0.0466 B - V = 1.3475(b - v) - 0.0251 V - R = 1.0641(v - r) - 0.0125 Using these equations the magnitudes in V, B-V, and V-R for 197 stars were obtained.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.40 no.1
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• pp.92-97
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• 1995

The objective of this study is to investigate the growth characters of overhead flooded soybean plants at four growth stage. Overhead flooding treatments were applied at the vegetative growth stage ($V_3,\;V_6$) and the reproductive stage ($R_2,\;R_4$) for 6.12.24 hrs, respectively. Yield and yield components were more decreased as the overhead flooding duration was longer and the growth stage was later. Yield was not reduced significantly in soybean plants flooded at $V_3$ stage regardless of flooding duration, and flooded 6 or 12 hrs at $V_6$ stage. When compared to the control, 27 to 36% of yield reduction was observed in soybean plants flooded for 24 hrs at $V_6$ stage, 6 or 12 hrs at $R_2$ stage, and 6 hrs at $R_4$ stage. And 43%, 53% and 66% of yield were reduced through the flooding treatment for 24 hrs at $R_2$ stage 12 hrs and 24 hrs at $R_4$ stage, respectively. So yield reduction was higher in overhead flooded soybean plants at the reproductive stage than that at the vegetative growth stage.

• 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 Astronomy and Space Sciences
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• v.25 no.2
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• pp.87-100
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• 2008

A total of 792 CCD images of V523 Cas were obtained on four nights of Jan. 2003 with the bvri CCD photometric system attached to a 61cm reflector of Sobaeksan Optical Astronomy Observatory (SOAO). The 17 standard stars in the images were used to establish transformation relations between our bvri system and the standard Johnson-Cousins BVRI system. We derived the tentative equations of transformation between two photometric systems as follows; V=v-0.0689(B-V)+0.0063, B-V=1.3197(b-v)-0.1733, V-R=0.9210(v-r)-0.1309, R-I=0.8892(r-i)-0.1055. Using these equations standard V magnitudes and their color indexes (B-V, V-R, R-I) for 57 stars in the field of the image were determined.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.661-677
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• 2015

In this paper, we consider the following Kirchhoff-type Schr$\ddot{o}$dinger system $$\{-\(a_1+b_1{\int}_{\mathbb{R^3}}{\mid}{\nabla}u{\mid}^2dx\){\Delta}u+{\gamma}V(x)u=\frac{2{\alpha}}{{\alpha}+{\beta}}{\mid}u{\mid}^{\alpha-2}u{\mid}v{\mid}^{\beta}\;in\;\mathbb{R}^3,\\-\(a_2+b_2{\int}_{\mathbb{R^3}}{\mid}{\nabla}v{\mid}^2dx\){\Delta}v+{\gamma}W(x)v=\frac{2{\beta}}{{\alpha}+{\beta}}{\mid}u{\mid}^{\alpha}{\mid}v{\mid}^{\beta-2}v\;in\;\mathbb{R}^3,\\u,v{\in}H^1(\mathbb{R}^3),$$ where $a_i$ and $b_i$ are positive constants for i = 1, 2, ${\gamma}$ > 0 is a parameter, V (x) and W(x) are nonnegative continuous potential functions. By applying the Nehari manifold method and the concentration-compactness principle, we obtain the existence and concentration of ground state solutions when the parameter ${\gamma}$ is sufficiently large.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.839-865
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• 2013

We deal with the existence of positive radial solutions concentrating on spheres for the following class of elliptic system $$\large(S) \hfill{400} \{\array{-{\varepsilon}^2{\Delta}u+V_1(x)u=K(x)Q_u(u,v)\;in\;\mathbb{R}^N,\\-{\varepsilon}^2{\Delta}v+V_2(x)v=K(x)Q_v(u,v)\;in\;\mathbb{R}^N,\\u,v{\in}W^{1,2}(\mathbb{R}^N),\;u,v&gt;0\;in\;\mathbb{R}^N,}$$ where ${\varepsilon}$ is a small positive parameter; $V_1$, $V_2{\in}C^0(\mathbb{R}^N,[0,{\infty}))$ and $K{\in}C^0(\mathbb{R}^N,[0,{\infty}))$ are radially symmetric potentials; Q is a $(p+1)$-homogeneous function and p is subcritical, that is, 1 < $p$ < $2^*-1$, where $2^*=2N/(N-2)$ is the critical Sobolev exponent for $N{\geq}3$.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.179-189
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• 1995

Let $V \subset R^n$ be a convex homogeneous cone which does not contain straight lines, so that the automorphism group $$ G = Aut(R^n, V)^\circ = { g \in GL(R^n) $\mid$ gV = V}^\circ $$ ($\circ$ denoting the identity component) acts transitively on V. A convex cone V is called "self-dual" if V coincides with its dual $$ (1.1) V' = { x' \in R^n $\mid$ < x, x' > > 0 for all x \in \bar{V} - {0}} $$ where $\bar{V}$ denotes the closure of V.sure of V.