• Korean Journal of Mathematics
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• v.16 no.3
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• pp.323-334
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• 2008

We define injective and projective representations of quivers with two vertices with n arrows. In the representation of quivers we denote n edges between two vertices as ${\Rightarrow}$ and n maps as $f_1{\sim}f_n$, and $E{\oplus}E{\oplus}{\cdots}{\oplus}E$ (n times) as ${\oplus}_nE$. We show that if E is an injective left R-module, then $${\oplus}_nE{\Longrightarrow[50]^{p_1{\sim}p_n}}E$$ is an injective representation of $Q={\bullet}{\Rightarrow}{\bullet}$ where $p_i(a_1,a_2,{\cdots},a_n)=a_i,\;i{\in}\{1,2,{\cdots},n\}$. Dually we show that if $M_1{\Longrightarrow[50]^{f_1{\sim}f_n}}M_2$ is an injective representation of a quiver $Q={\bullet}{\Rightarrow}{\bullet}$ then $M_1$ and $M_2$ are injective left R-modules. We also show that if P is a projective left R-module, then $$P\Longrightarrow[50]^{i_1{\sim}i_n}{\oplus}_nP$$ is a projective representation of $Q={\bullet}{\Rightarrow}{\bullet}$ where $i_k$ is the kth injection. And if $M_1\Longrightarrow[50]^{f_1{\sim}f_n}M_2$ is an projective representation of a quiver $Q={\bullet}{\Rightarrow}{\bullet}$ then $M_1$ and $M_2$ are projective left R-modules.

• Kyungpook Mathematical Journal
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• v.54 no.3
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• pp.401-411
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• 2014

In this paper, we prove the generalized Hyers-Ulam stability of the following Jensen type functional equation $$f(\frac{x-y}{n}+z)+f(\frac{y-z}{n}+x)+f(\frac{z-x}{n}+y)=f(x)+f(y)+f(z)$$ in p-Banach spaces for any fixed nonzero integer n.

• Journal of the Korean Magnetics Society
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• v.10 no.3
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• pp.106-111
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• 2000

The magnetic thin films can be prepared without vacuum process and under the low temperature (<100 $^{\circ}C$) by ferrite plating. We have performed ferrite plating of M $n_{x}$Z $n_{0.22}$F $e_{2.78-x}$ $O_4$(x=0.00~0.08) films and N $i_{x}$Z $n_{0.22}$F $e_{*}$2.78-x/ $O_4$(x=0.00~0.15) films on cover glass at the substrate temperature 90 $^{\circ}C$. The crystal structure of the samples has been identified as a single phase of polycrystal spinel structure by x-ray diffraction technique. The lattice constant in the M $n_{x}$Z $n_{0.22}$F $e_{2.78-x}$ $O_4$films increases but in the N $i_{x}$Z $n_{0.22}$F $e_{*}$2.78-x/ $O_4$films decrease with the composition parameter, x. The saturation magnetization in the M $n_{x}$Z $n_{0.22}$F $e_{2.78-x}$ $O_4$films does not greatly change, in agreement with observations on bulk samples.k samples.k samples.

• Parasites, Hosts and Diseases
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• v.56 no.5
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• pp.453-461
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• 2018

The aim of this study is to delineate 'admixed hybrid' and 'introgressive' Fasciola genotypes present in the Fasciola population in Vietnam. Adult liver flukes collected from ruminants in 18 Provinces were morphologically sorted out by naked eyes for small (S), medium (M) and large (L) body shapes; and human samples (n=14) from patients. Nuclear ribosomal (rDNA) ITS1 and ITS2, and mitochondrial (mtDNA) nad1 markers were used for determination of their genetic status. Total 4,725 worm samples of ruminants were tentatively classified by their size: 6% (n=284) small (S)-, 13% (n=614) medium (M)-, and 81% (n=3,827) large (L)-forms. All the representative (n=120, as 40 each group) and 14 human specimens, possessed maternal mtDNA of only F. gigantica and none of F. hepatica. Paternally, all (100%) of the L-(n=40) and 77.5% (n=31) of the M-flukes had single F. gigantica rDNA indicating 'pure' F. gigantica. A majority (90%, n=36) of the S- and 15% (n=6) of the M-worms had single F. hepatica rDNA, indicating their introgressive; the rest (10%, n=4) of the S- and 7.5% (n=3) of the M-flukes had mixture of both F. gigantica and F. hepatica rDNAs, confirming their admixed hybrid genetic status. Fourteen human samples revealed 9 (64%) of pure F. gigantica, 3 (22%) of introgressive and 2 (14%) of admixed hybrid Fasciola spp. By the present study, it was confirmed that the small worms, which are morphologically identical with F. hepatica, are admixed and/or introgressive hybrids of Fasciola spp., and able to be the pathogens of human fascioliasis.

• Korean Journal of Mathematics
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• v.16 no.3
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• pp.413-424
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• 2008

In [21], Th.M. Rassias proved that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed integer $n{\geq}2$ $$n{\parallel}\frac{1}{n}\sum\limits_{i=1}^{n}x_i{\parallel}^2+\sum\limits_{i=1}^{n}{\parallel}x_i-\frac{1}{n}\sum\limits_{j=1}^{n}x_j{\parallel}^2=\sum\limits_{i=1}^{n}{\parallel}x_i{\parallel}^2$$ holds for all $x_1,{\dots},x_n{\in}V$. We consider the functional equation $$nf(\frac{1}{n}\sum\limits^n_{i=1}x_i)+\sum\limits_{i=1}^{n}f(x_i-\frac{1}{n}\sum\limits_{j=1}^{n}x_j)=\sum\limits_{i=1}^nf(x_i)$$ Using fixed point methods, we prove the generalized Hyers-Ulam stability of the functional equation $$(1)\;2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})=f(x)+f(y)$$.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.15 no.3
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• pp.226-232
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• 1982

The measurements of the jerking force and the tail beat by hooked carp were carried out using a strain gauge at a fish pond from July to August 1981. The maximum jerking force was sustained for a while in the initial state after a carp was hooked, but the jerking force was gradually decreased as a function of the time elapsed until the fish was utterly exhausted, and it converged to the body weight at last. The results are as follows : 1. The maximum jerking force $F_m(g)$ can be expressed with empirical formula : $$F_m=3.23W+105$$ where W (g) is the body weight. 2. Dynamic change of the maximum jerking force $F_n(g)$ by one tail beat with time $t_{n}(-10T/2{\leq}\;t_n{\leq}10T/2)$ can he induced with the equation as follows : $$F_n=(0.27W-6.52)(|t_n|+C)^{-2.10}$$ where the period T (sec) is given by the following equation with the body weight : T=0.000385W+0.193 3. The jerking force at each of the peak points $F_p$ (g) varies with the time elapsed t (sec) as following equation : $$F_{p}=(2.23W+105)e^{-{\beta}t}+W$$. The value of durability index $\beta$ was nearly zero in the initial state and about 1.7 in the exhausted state at last. 4. It was clearly shown that the change of jerking force by hooked carp was closely related to the tail beat from a paired difference T-test.

• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.717-728
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• 2008

Let H be a real Hilbert space and S = {T(s) : $0\;{\leq}\;s\;<\;{\infty}$} be a nonexpansive semigroup on H such that $F(S)\;{\neq}\;{\emptyset}$ For a contraction f with coefficient 0 < $\alpha$ < 1, a strongly positive bounded linear operator A with coefficient $\bar{\gamma}$ > 0. Let 0 < $\gamma$ < $\frac{\bar{\gamma}}{\alpha}$. It is proved that the sequences {$x_t$} and {$x_n$} generated by the iterative method $$x_t\;=\;t{\gamma}f(x_t)\;+\;(I\;-\;tA){\frac{1}{{\lambda}_t}}\;{\int_0}^{{\lambda}_t}\;T(s){x_t}ds,$$ and $$x_{n+1}\;=\;{\alpha}_n{\gamma}f(x_n)\;+\;(I\;-\;{\alpha}_nA)\frac{1}{t_n}\;{\int_0}^{t_n}\;T(s){x_n}ds,$$ where {t}, {${\alpha}_n$} $\subset$ (0, 1) and {${\lambda}_t$}, {$t_n$} are positive real divergent sequences, converges strongly to a common fixed point $\tilde{x}\;{\in}\;F(S)$ which solves the variational inequality $\langle({\gamma}f\;-\;A)\tilde{x},\;x\;-\;\tilde{x}{\rangle}\;{\leq}\;0$ for $x\;{\in}\;F(S)$.

• Honam Mathematical Journal
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• v.16 no.1
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• pp.119-135
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• 1994

Let $Q_{n+p-1}(\alpha)$ denote the- dass of functions $$f(z)=z^{P}-\sum_{n=0}^\infty{a_{(p+k)}z^{p+k}$$ ($a_{p+k}{\geq}0$, $p{\in}N=\left{1,2,{\cdots}\right}$) which are analytic and p-valent in the unit disc $U=\left{z:{\mid}z:{\mid}<1\right}$ and satisfying $Re\left{\frac{D^{n+p-1}f(\approx))^{\prime}}{pz^{p-a}\right}>{\alpha},0{\leq}{\alpha}<1,n>-p,z{\in}U.$ In this paper we obtain sharp results concerning coefficient estimates, distortion theorem, closure theorems and radii of p-valent close-to- convexity, starlikeness and convexity for the class $Q_{n+p-1}$ ($\alpha$). We also obtain class preserving integral operators of the form $F(z)=\frac{c+p}{z^{c}}\int_{o}^{z}t^{c-1}f(t)dt.$ c>-p $F\left(z\right)=\frac{c+p}{z^{c}}\int_{0}^{z} t^{c-1}f\left(t \right)dt. \qquad c>-p$ for the class $Q_{n+p-1}$ ($\alpha$). Conversely when $F(z){\in}Q_{n+p-1}(\alpha)$, radius of p-valence of f(z) has been determined.

• Journal of Microbiology and Biotechnology
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• v.30 no.12
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• pp.1944-1949
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• 2020

Mutant sugar transporter ScGAL2-N376F was overexpressed in Kluyveromyces marxianus for efficient utilization of xylose, which is one of the main components of cellulosic biomass. K. marxianus ScGal2_N376F, the ScGAL2-N376F-overexpressing strain, exhibited 47.04 g/l of xylose consumption and 26.55 g/l of xylitol production, as compared to the parental strain (24.68 g/l and 7.03 g/l, respectively) when xylose was used as the sole carbon source. When a mixture of glucose and xylose was used as the carbon source, xylose consumption and xylitol production rates were improved by 195% and 360%, respectively, by K. marxianus ScGal2_N376F. Moreover, the glucose consumption rate was improved by 27% as compared to that in the parental strain. Overexpression of both wild-type ScGAL2 and mutant ScGAL2-N376F showed 48% and 52% enhanced sugar consumption and ethanol production rates, respectively, when a mixture of glucose and galactose was used as the carbon source, which is the main component of marine biomass. As shown in this study, ScGAL2-N376F overexpression can be applied for the efficient production of biofuels or biochemicals from cellulosic or marine biomass.

• Korean Journal of Mathematics
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• v.25 no.2
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• pp.215-227
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• 2017

Let D be an integral domain with quotient field K, X be an indeterminate over D, K[X] be the polynomial ring over K, and $R=\{f{\in}K[X]{\mid}f(0){\in}D\}$; so R is a subring of K[X] containing D[X]. For $f=a_0+a_1X+{\cdots}+a_nX^n{\in}R$, let C(f) be the ideal of R generated by $a_0$, $a_1X$, ${\ldots}$, $a_nX^n$ and $N(H)=\{g{\in}R{\mid}C(g)_{\upsilon}=R\}$. In this paper, we study two rings $R_{N(H)}$ and $Kr(R,{\upsilon})=\{{\frac{f}{g}}{\mid}f,g{\in}R,\;g{\neq}0,{\text{ and }}C(f){\subseteq}C(g)_{\upsilon}\}$. We then use these two rings to give some examples which show that the results of [4] are the best generalizations of Nagata rings and Kronecker function rings to graded integral domains.