• Korean Journal of Mathematics
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• 제16권3호
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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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• 제54권3호
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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.

• 한국자기학회지
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• 제10권3호
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• pp.106-111
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• 2000

페라이트 도금 방법으로 M $n_{x}$Z $n_{0.22}$F $e_{2.78-x}$ $O_4$(x=0.00~0.08)와 N $i_{x}$Z $n_{0.22}$F $e_{*}$2.78-x/ $O_4$(x=0.00~0.15)의 스피넬 페라이트 박막을 제작하였다. 반응용액의 조성비 변화에 따라 형성된 박막의 조성비와 성장속도를 조사하였다. 제조한 시료들의 결정성과 미세구조는 x-선 회절분석과 전자현미경으로 조사하고, 시료의 자기적 성질을 진동 시료형 자력계를 사용하여 조사했다. 조성비 x가 증가함에 따라 격자상수는 M $n_{x}$Z $n_{0.22}$F $e_{2.78-x}$ $O_4$(x=0.00~0.08) 박막에서 증가하지만, N $i_{x}$Z $n_{0.22}$F $e_{2.78-x}$ $O_4$(x=0.00~0.15) 박막에서 감소한다. M $n_{x}$Z $n_{0.22}$F $e_{2.78-x}$ $O_4$(x = 0.00~0.08) 박막의 포화자화는 419 emu/㎤에서 394 emu/㎤ 의 값을 가져 N $i_{x}$Z $n_{0.22}$F $e_{2.78-x}$ $O_4$(x=0.00~0.15)의 $M_{s}$ 보다 높게 나타났다. 보다 높게 나타났다. 보다 높게 나타났다.

• Parasites, Hosts and Diseases
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• 제56권5호
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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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• 제16권3호
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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 $$(1)\;2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})=f(x)+f(y)$$.

• 한국수산과학회지
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• 제15권3호
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• pp.226-232
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• 1982

낚시 어구 재료의 규격을 정하는데는 우선 낚시에 물련 고기가 순간적으로 잡아채는 충기하중, 피로하중 등을 기본적으로 고려하여야 할 것이다. 본 실험은 부산수산대학 양어장에서 잉어가 낚시에 물렸을 때 미치는 힘을 strain gauge를 사용하여 측정하고 아울러 꼬리 진동 측정장치를 만들어 꼬리의 진동과 힘의 변화를 동시에 기록하여 분석해 보았다. 잉어가 낚시에 물렸을 때 미치는 최대의 힘 $F_m$은 고기의 체중 W에 따라$$F_m=3.23W+105$$로 나타났다. 시간 $t_n$에 대한 최대의 힘의 변화 $F_n$은 $$F_n=a_n(|t_n|+C)^{-b}_n$$ (단, $$C=(\frac{a_n}{F_m})^\frac{1}{b_n} -10T/2{\leq}t_n{\leq}10T/2$$)에서 $a_n=0.27W-6.52$이고 $b_n$은 평균 2.10이며 주기는 체중에 따라 T=0.000385W+0.193으로 주어진다. 잉어가 낚인 직후부터의 시간 t에 따라 꼬리 진동에 의한 각 Peak점의 힘의 크기 $F_p$는$$F_p=(2.23W+105)e^{-{\beta}t}+W$$로 표시되는데, 낚시에 물린 초기단계에서는 지적지수 $\beta$가 거의 0에 가까우나 마지막 단계에서는 체중에 관계없이 평균 1.7정도 되었다. 또한, 잉어가 미치는 힘의 가 peak 점간의 주기는 재리 진동의 주기와 서로 밀접한 상관 관계가 있었다.

• 대한수학회보
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• 제45권4호
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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 $x\;{\in}\;F(S)$.

• 호남수학학술지
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• 제16권1호
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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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• 제30권12호
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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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• 제25권2호
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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.