• Journal of Life Science
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• v.15 no.6 s.73
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• pp.972-978
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• 2005

The present study was carried out to investigate the blood markers of Jeju horses. The redcell cypes (blood groups) and blood protein types (biochemical polymorphisms) were tested from 102 Jeju horses by serological and electrophoretc procedure, and their phenotypes and gene frequencies were estimated. The blood group and biochemical polymorphism phenotypes observed with high frequency were $A^{af}\;(27.45\%$), $C^{a}\;(99.02\%$), $K^{-}\;(97.06\%$), $U^{a}\;(62.75\%$), $P^{b}\;(36.27\%$), $Q^{c}\;(47.06\%$), $D^{cgm/dghm}\;(13.73\%$), $D^{adn/cgm}\;(9.80\%$), $D^{ad/cgm}$\;(8.82\%$), $D^{dghm/dghm}(7.84\%$), $D^{cgm/cgm}(7.84\%$), $AL^{B}\;(48.04\%$), $GC^{F}\;(99.02\%$), $AlB^{K}\;(97.06\%$), $ES^{FI}\;(36.27\%$), $TF^{F2}\;(25.49\%$), $HB^{B1}\;(45.10\%$), and $PGD^{F}\;(86.27\%$) in Jeju horses, respectively. Alleles observed with high gene frequency were $A^{af}$ (0.3726), $A^{C}$ (0.2647), $C^{-}$ (0.5050), $K^{-}$ (0.9853), $U^{-}$ (0.6863), $P^{b}$ (0.4657), $Q^{c}$ (0.5294), $D^{cgm}$ (0.3039), $HB^{B1}$(0.6863), $PGD^{F}$ (0.9265), $AL^{B}$ (0.6912), $ALB^{K}$ (0.9852), $GC^{F}$ (0.9950), $ES^{I}$ (0.5000) and $TF^{F2}$ (0.4950) in Jeju horses, and sfecific alleles, $D^{cgm(f)}$ (0.0196), $HB^{A}$ (0.0147), $HB^{A2}$ (0.0196), $ES^{G}$ (0.0441), $ES^{H}$ (0.0098), $TF^{E}$TF'(0.0246), $TF^{H2}$ (0.0049) and $PGD^{D}$ (0.0098) were detected in Jeju horses. These preliminary results present basic information for detecting the genetic markers in Jeju horse. and developing a system for parentage verification and individuals identification in jeju horses.

• Applied Chemistry for Engineering
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• v.9 no.3
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• pp.372-376
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• 1998

Supported Pd($Pd/AlF_3$, $Pd/{\gamma}-Al_2O_3$) catalysts and solid-acid catalysts(${\gamma}-Al_2O_3$, ${\alpha}-Al_2O_3$, $AlF_3$) were used to perform dechlorination of HCFC-142b(1-chloro-1,1-difluoroethane) in the presence of excess hydrogen. In the reactions the effects of reaction temperature, the mole ratio(r) of $H_2$ to HCFC-142b and the amount of supported Pd on dechlorination of HCFC-142b into HFC-143a(1,1,1-trifluoroethane) or HFC-152a(1,1-difluoroethane) were investigated. The experimental results showed that the conversion of HCFC-142b to product gases were 60% and 92%, respectively, and the selectivity to HFC-143a in the product gases were 58% and 64% for $Pd/AlF_3$ and $Pd/{\gamma}-Al_2O_3$ catalysts, respectively. On these catalysts an optimum reaction condition was found at $200^{\circ}C$ with the space time of reactant gases as 1.05 second and the mole ratio of $H_2$ to HCFC-142b as 3. Solid-acid catalysts were also tested at the same reaction condition. The results showed that the conversions of HCFC-142b to product gases were 12%, 8% and 7%, and the selectivities to HFC-152a were 94%, 92% and 90% for ${\gamma}-Al_2O_3$, ${\alpha}-Al_2O_3$ and $AlF_3$ catalysts, respectively.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.65-74
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• 2014

The well known quadratic transformation formula due to Gauss: $$(1-x)^{-2a}{_2F_1}\[{{a,b;}\\\hfill{21}{2b;}}\;-\frac{4x}{(1-x)^2}\]={_2F_1}\[{{a,a-b+\frac{1}{2};}\\\hfill{65}{b+\frac{1}{2};}}\;x^2\]$$ plays an important role in the theory of (generalized) hypergeometric series. In 2001, Rathie and Kim have obtained two results closely related to the above quadratic transformation for $_2F_1$. Our main objective of this paper is to deduce some interesting known or new results for the series $_2F_1(x)$ by using the above Gauss's quadratic transformation and its contiguous relations and then apply our results to provide a list of a large number of integrals involving confluent hypergeometric functions, some of which are (presumably) new. The results established here are (potentially) useful in mathematics, physics, statistics, engineering, and so on.

• Korean Journal of Mathematics
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• v.26 no.1
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• pp.75-85
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• 2018

In this paper, we study nonconstant warping functions on an Einstein warped product manifold $M=B{\times}_{f^2}F$ with a warped product metric $g=g_B+f(t)^2g_F$. And we consider a 2-dimensional base manifold B with a metric $g_B=dt^2+(f^{\prime}(t))^2du^2$. As a result, we prove the following: if M is an Einstein warped product manifold with a 2-dimensional base, then there exist generally nonconstant warping functions f(t).

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1157-1163
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• 2009

Let G be a graph with vertex set V(G) and let f be a nonnegative integer-valued function defined on V(G). A spanning subgraph F of G is called a fractional f-factor if $d^h_G$(x)=f(x) for all x $\in$ for all x $\in$ V (G), where $d^h_G$ (x) = ${\Sigma}_{e{\in}E_x}$ h(e) is the fractional degree of x $\in$ V(F) with $E_x$ = {e : e = xy $\in$ E|G|}. In this paper it is proved that if ${\delta}(G){\geq}{\frac{b^2(k-1)}{a}},\;n>\frac{(a+b)(k(a+b)-2)}{a}$ and $|N_G(x_1){\cup}N_G(x_2){\cup}{\cdots}{\cup}N_G(x_k)|{\geq}\frac{bn}{a+b}$ for any independent subset ${x_1,x_2,...,x_k}$ of V(G), then G has a fractional f-factor. Where k $\geq$ 2 be a positive integer not larger than the independence number of G, a and b are integers such that 1 $\leq$ a $\leq$ f(x) $\leq$ b for every x $\in$ V(G). Furthermore, we show that the result is best possible in some sense.

• Fashion & Textile Research Journal
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• v.13 no.5
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• pp.661-671
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• 2011

This study was designed to produce rounded belt pattern and tight-skirt pattern drafting method using 3D body scan data. Subjects were thirty women in their early twenties. In order to figure out the optimum cutting points, namely, where darts are made, using CAD program, curve ratio inflection points on the horizontal curve of waist, abdomen, and hip to find 1 point in the front, two points in the back part. The average length from center front point to maximum curve ratio was 7.7 cm(46.3%) on the waist curve; 7.9 cm(39.4%) on the abdomen curve. And the average length from center back point to maximum curve ratio point was 6.9 cm(39.0%) for first dart and 11.2 cm(63.3%) for second dart on the waist curve; 8.9 cm(35.8%) for first dart and 15.7 cm(63.3%) for second dart on the hip curve respectively. The cutting lines from were made up by connecting curve inflection points. After divided using cutting lines, each patch was flattened onto the plane and all the technical design factors related with patternmaking were measured, such as dart amount, lifting amount of side waist point, etc. Based on the results of correlation analysis among these factors, regression analysis was done to produce equations to estimate the variables necessary to draw up pattern draft method; F1=F8+1.1, $F4=2.5{\times}F2+0.9$, $F5=0.9{\times}F4+1.0$, $F6=0.3{\times}F4+0.4$, $B1=0.9{\times}B8+2.3$, $B4=2.1{\times}B2+1.3$, $B5=0.9{\times}B4+3.5$, and $B6=0.3{\times}B4+0.4$.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.29-42
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• 2018

In this paper, we investigate the stability of two functional equations f(ax+by + cz) - abf(x + y) - bcf(y + z) - acf(x + z) + bcf(y) - a(a - b - c)f(x) - b(b - a)f(-y) - c(c - a - b)f(z) = 0, f(ax+by + cz) + abf(x - y) + bcf(y - z) + acf(x - z) - a(a + b + c)f(x) - b(a + b + c)f(y) - c(a + b + c)f(z) = 0 by applying the direct method in the sense of Hyers and Ulam.

• Kyungpook Mathematical Journal
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• v.13 no.2
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• pp.235-240
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• 1973

A k-dimensional vector bundle is a bundle ${\xi}=(E,P,B,F^k)$ with fibre $F^k$ satisfying the local triviality, where F is the field of real numbers R or complex numbers C ([1], [2] and [3]). Let $Vect_k(X)$ be the set consisting of all isomorphism classes of k-dimensional vector bundles over the topological space X. Then $Vect_F(X)=\{Vect_k(X)\}_{k=0,1,{\cdots}}$ is a semigroup with Whitney sum (${\S}1$). For a pair (X, A) of topological spaces, a difference isomorphism over (X, A) is a vector bundle morphism ([2], [3]) ${\alpha}:{\xi}_0{\rightarrow}{\xi}_1$ such that the restriction ${\alpha}:{\xi}_0{\mid}A{\longrightarrow}{\xi}_1{\mid}A$ is an isomorphism. Let $S_k(X,A)$ be the set of all difference isomorphism classes over (X, A) of k-dimensional vector bundles over X with fibre $F^k$. Then $S_F(X,A)=\{S_k(X,A)\}_{k=0,1,{\cdots}}$, is a semigroup with Whitney Sum (${\S}2$). In this paper, we shall prove a relation between $Vect_F(X)$ and $S_F(X,A)$ under some conditions (Theorem 2, which is the main theorem of this paper). We shall use the following theorem in the paper. THEOREM 1. Let ${\xi}=(E,P,B)$ be a locally trivial bundle with fibre F, where (B, A) is a relative CW-complex. Then all cross sections S of ${\xi}{\mid}A$ prolong to a cross section $S^*$ of ${\xi}$ under either of the following hypothesis: (H1) The space F is (m-1)-connected for each $m{\leq}dim$ B. (H2) There is a relative CW-complex (Y, X) such that $B=Y{\times}I$ and $A=(X{\times}I)$ ${\cap}(Y{\times}O)$, where I=[0, 1]. (For proof see p.21 [2]).

• Polymer(Korea)
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• v.31 no.6
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• pp.497-504
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• 2007

We have prepared the dinuclear half-sandwich CGC(constrained geometry catalyst) with polymethylene bridge $[Zr(({\eta}^5\;:\;{\eta}^1-C_9H_5SiMe_2NCMe_3)Me_2)_2\;[(CH_2)_n]$ [n=6(4), 9(5), 12(6)] by treating 2 equivalents of MeLi with the corresponding dichlorides compounds. To study the catalytic behavior of the dinuclear catalysts we conducted copolymerization of ethylene and 1-hexene in the presence of three kinds of boron cocatalysts, $Ph_3C^+[B(C_6F_5)_4]^-\;(B_1),\;B(C_6F_5)_3\;(B_3)$, and $Ph_3C^+[(C_6F_5)_3B-C_6F_4-B(C_6F_5)_3]^{2-}\;(B_2)$. It turned out that all active species formed by the combination of three dinuclear CGCs with three cocatalyst were very efficient catalysts for the polymerization of olefins. The activities increase as the bridge length of the dinuclear CGCs increases. At the same time the dinuclear cocatalyst exhibited the lowest activity among three cocatalysts. The prime observation is that the dinuclear cocatalyst gave rise to the formation of the copolymers with the least branches on the polyethylene backbone.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.17-33
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• 2007

Suppose F is an arbitrary field. Let ${\mid}F{\mid}$ be the number of the elements of F. Let $T_{n}(F)$ be the space of all $n{\times}n$ upper-triangular matrices over F. A map ${\Psi}\;:\;T_{n}(F)\;{\rightarrow}\;T_{n}(F)$ is said to preserve idempotence if $A-{\lambda}B$ is idempotent if and only if ${\Psi}(A)-{\lambda}{\Psi}(B)$ is idempotent for any $A,\;B\;{\in}\;T_{n}(F)$ and ${\lambda}\;{\in}\;F$. It is shown that: when the characteristic of F is not 2, ${\mid}F{\mid}\;>\;3$ and $n\;{\geq}\;3,\;{\Psi}\;:\;T_{n}(F)\;{\rightarrow}\;T_{n}(F)$ is a map preserving idempotence if and only if there exists an invertible matrix $P\;{\in}\;T_{n}(F)$ such that either ${\Phi}(A)\;=\;PAP^{-1}$ for every $A\;{\in}\;T_{n}(F)\;or\;{\Psi}(A)=PJA^{t}JP^{-1}$ for every $P\;{\in}\;T_{n}(F)$, where $J\;=\;{\sum}^{n}_{i-1}\;E_{i,n+1-i}\;and\;E_{ij}$ is the matrix with 1 in the (i,j)th entry and 0 elsewhere.