• Kyungpook Mathematical Journal
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• 제46권2호
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• pp.255-260
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• 2006

Let $m$ and $k$ be any positive integers, let $\mathbb{Z}_k$ the ring of integers of modulo $k$, let $G_m(\mathbb{Z}_k)$ the group of all $m$ by $m$ nonsingular matrices over $\mathbb{Z}_k$ and let ${\phi}_m(k)$ the order of $G_m(\mathbb{Z}_k)$. In this paper, ${\phi}_m(k)$ can be computed by the following investigation: First, for any relatively prime positive integers $s$ and $t$, $G_m(\mathbb{Z}_{st})$ is isomorphic to $G_m(\mathbb{Z}_s){\times}G_m(\mathbb{Z}_t)$. Secondly, for any positive integer $n$ and any prime $p$, ${\phi}_m(p^n)=p^{m^2}{\cdot}{\phi}_m(p^{n-1})=p{^{2m}}^2{\cdot}{\phi}_m(p^{n-2})={\cdots}=p^{{(n-1)m}^2}{\cdot}{\phi}_m(p)$, and so ${\phi}_m(k)={\phi}_m(p_1^n1){\cdot}{\phi}_m(p_2^{n2}){\cdots}{\phi}_m(p_s^{ns})$ for the prime factorization of $k$, $k=p_1^{n1}{\cdot}p_2^{n2}{\cdots}p_s^{ns}$.

• 한국정보과학회논문지:시스템및이론
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• 제29권12호
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• pp.665-679
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• 2002

그래프 G의 고장지름이란 임의의 연결도-1 개 이하의 정점들에 고장이 났을 경우, 모든 두 정점사이의 최단경로 길이의 최대 값을 말한다. 본 논문에서는 $k{\geq}3$인 재귀원형군 $G(2{\leq}m,2{\leq}k)$의 고장 지름을 분석한다. $ dia_{m.k}$를$ G(2^m,2^k)$의 지름이라 하자. $G(2{\leq}m,2{\leq}k/)$일 때, $G(2{\leq}m,2{\leq}k)$의 고장지름은 $2^m-2이고$, m=k+1일 때, 고장지름은 $2^k-1$임을 보인다. 그리고 m>k+1인 재귀원형군 $G(2{\leq}m,2{\leq}k)$에서, m=1 (mod 2k)이면 고장지름은 $dia_{m.k+1}$과 같고, $m{\neq}1$ (mod 2k)이면 고장지름은 $dia_{m.k+2}$ 이하임을 보인다.

• Journal of Plant Biology
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• 제39권1호
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• pp.41-48
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• 1996

발아 후 8일된 해녀콩 자엽에서 성질이 서로 다른 두 개의 homoserine dehydrogenase를 분리하였다. 자엽에서 얻은 조효소액을 열처리, 황산 암모늄 침전, DEAE-Sephacel 및 Sephacryl S-300 겔 크로마토그래피와 Procion red dye, Cibacron blue dye 및 Resource Q 컬럼 크로마토그래피로 정제하였다. 겔 크로마토그래피에서 얻은 2개의 활성분획 중 T-형(트레오닌 감수성)과 K-형(트레오닌 비감수성)의 분자량은 각각 230 kD과 135 kD이었다. 10mM 트레오닌 첨가로 T-형 효소는 70% 이상의 활성저해를 받았으나 K-형 효소는 전혀 억제를 받지 않았다. Homoserine에 대한 Km은 T-형이 1.6mM, K-형이 0.3mM이었고, NAD에 대한 Km은 T-형이 2.34mM, K-형이 0.03mM이었으며 NADP에 대한 Km은 두 효소에서 동일하게 0.01mM로 산출되었다. 400mM KCl에서 T-형은 4.9배, K-형은 2.8배의 활성증가를 보였다. 부분정체(Sephacryl S-300 겔 크로마토그래피)된 상태의 T-형과 K-형은 조건에 따라 쉽게 상호전환되었다.

• Journal of Applied Biological Chemistry
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• 제42권1호
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• pp.12-18
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• 1999

Sucrose synthase (EC 2.4.1.13) has been purified from the plant cytosolic fraction of chickpea (Cicer arietinum L. cv. Amethyst) nodules. The native enzyme had a molecular mass of $356{\pm}15kD$. The subunit molecular mass was $87{\pm}2kD$, and a tetrameric structure is proposed for sucrose synthase of chickpea nodule. Optimum activities in the sucrose cleavage and synthesis directions were at pH 6.5 and 9.0, respectively. The purified enzyme displayed typical hyperbolic kinetics with substrates in cleavage and synthesis reactions. Chickpea nodules sucrose synthase had a high affinity for UDP ($K_m$, $8.0{\mu}M$) and relatively low affinities for ADP ($K_m$, 0.23 mM), CDP ($K_m$, 0.87 mM), and GDP ($K_m$, 1.51 mM). The $K_m$ for sucrose was 29.4 mM. In the synthesis reaction, UDP-glucose ($K_m$, $24.1{\mu}M$) was a more effective glucosyl donor than ADP-glucose ($K_m$, 2.7 mM), and the $K_m$ for fructose was 5.4 mM. Divalent cations, such as $Ca^{2+}$, $Mg^{2+}$, and $Mn^{2+}$, stimulated the enzyme activity in both the cleavage and synthesis directions, and the enzyme was very sensitive to inhibition by $HgCl_2$ and $CuSO_4$.

• The Korean Journal of Physiology and Pharmacology
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• 제3권4호
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• pp.415-425
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• 1999

$[K^+]_o$ can be increased under a variety of conditions including subarachnoid hemorrhage. The increase of $[K^+]_o$ in the range of $5{\sim}15$ mM may affect tensions of blood vessels and cause relaxation of agonist-induced precontracted vascular smooth muscle $(K^+-induced$ relaxation). In this study, effect of the increase in extracellular $K^+$ concentration on the agonist-induced contractions of various arteries including resistant arteries of rabbit was examined, using home-made Mulvany-type myograph. Extracellular $K^+$ was increased in three different ways; from initial 1 to 3 mM, from initial 3 to 6 mM, or from initial 6 to 12 mM. In superior mesenteric arteries, the relaxation induced by extracellular $K^+$ elevation from initial 6 to 12 mM was the most prominent among the relaxations induced by the elevations in three different ways. In cerebral arteries, the most prominent relaxation was produced by the elevation of extracellular $K^+$ from initial 1 to 3 mM and a slight relaxation was provoked by the elevation from initial 6 to 12 mM. In superior mesenteric arteries, $K^+-induced$ relaxation by the elevation from initial 6 to 12 mM was blocked by $Ba^{2+}\;(30\;{\mu}M)$ and the relaxation by the elevation from 1 to 3 mM or from 3 to 6 mM was not blocked by $Ba^{2+}.$ In cerebral arteries, however, $K^+-induced$ relaxation by the elevation from initial 3 to 6 mM was blocked by $Ba^{2+},$ whereas the relaxation by the elevation from 1 to 3 mM was not blocked by $Ba^{2+}.$ Ouabain inhibited all of the relaxations induced by the extracellular $K^+$ elevations in three different ways. In cerebral arteries, when extracellular $K^+$ was increased to 14 mM with 2 or 3 mM increments, almost complete relaxation was induced at 1 or 3 mM of initial $K^+$ concentration and slight relaxation occurred at 6 mM. TEA did not inhibit $Ba^{2+}-sensitive$ relaxation at all and NMMA or endothelial removal did not inhibit $K^+-induced$ relaxation. Most conduit arteries such as aorta, carotid artery, and renal artery were not relaxed by the elevation of extracellular $K^+.$ Among conduit arteries, trunk of superior mesenteric artery and basilar artery were relaxed by the elevations of $[K^+]_o.$ These data suggest that $K^+-induced$ relaxation has two independent components, $Ba^{2+}-sensitive$ and $Ba^{2+}-insensitive$ one and there are different mechanisms for $K^+-induced$ relaxation in various arteries.

• The Korean Journal of Physiology and Pharmacology
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• 제2권6호
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• pp.695-703
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• 1998

$[K^+]_o$ can be increased under a variety of conditions including subarachnoid hemorrhage. The increase of $[K^+]_o$ in the range of $5{\sim}15$ mM may affect tensions of blood vessels and can change their sensitivity to various vasoactive substances. Therefore, it was examined in the present study whether the sensitivity of cerebral arteries to vasoactive substances can be changed with the moderate increase of $[K^+]_o$, using Mulvany-type myograph and $[Ca^{2+}]_c$ measurement. The contractions of basilar artery and branch of middle cerebral artery induced by histamine were not increased with the elevation of $[K^+]_o$ from 6 mM to 9 mM or 12 mM. On the contrary, the contractions induced by serotonin were significantly increased with the elevation of $[K^+]_o$. The contractions were also significantly increased by the treatment with nitro-L-arginine $(10^{-4}$ M for 20 minutes). In the nitro-L-arginine treated arteries, the contractions induced by serotonin were significantly increased with the elevation of $[K^+]_o$ from 6 mM to 12 mM. $K^+-induced$ relaxation was evoked with the stepwise increment of extracellular $K^+$ from 0 or 2 mM to 12 mM by 2 mM in basilar arterial rings, which were contracted by histamine. But $[K^+]_o$ elevation from 4 or 6 mM to 12 mM by the stepwise increment evoked no significant relaxation. Basal tension of basilar artery was increased with $[K^+]_o$ elevation from 6 mM to 12 mM by 2 mM steps or by the treatment with ouabain and the increase of basal tension was blocked by verapamil. The cytosolic free $Ca^{2+}$ level was not increased by the single treatment with serotonin or with the elevation of $[K^+]_o$ from 4 mM to 8 or 12 mM. In contrast to the single treatment, the $Ca^{2+}$ level was increased by the combined treatment with serotonin and the elevation of $[K^+]_o$. The increase of free $Ca^{2+}$ concentration was blocked by the treatment with verapamil. These data suggest that the sensitivity of cerebral artery to serotonin is increased with the moderate increase of $[K^+]_o$ and the increased sensitivity to serotonin is due to the increased $[Ca^{2+}]_i$ induced by extracellular $Ca^{2+}$ influx.

• 대한수학회논문집
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• 제38권4호
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• pp.1075-1090
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• 2023

In this paper, we study new classes of operators k-quasi (m, n)-paranormal operator, k-quasi (m, n)^*-paranormal operator, k-quasi (m, n)-class 𝒬 operator and k-quasi (m, n)-class 𝒬^* operator which are the generalization of (m, n)-paranormal and (m, n)^*-paranormal operators. We give matrix characterizations for k-quasi (m, n)-paranormal and k-quasi (m, n)^*-paranormal operators. Also we study some properties of k-quasi (m, n)-class 𝒬 operator and k-quasi (m, n)-class 𝒬^* operators. Moreover, these classes of composition operators on L² spaces are characterized.

• 대한수학회논문집
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• 제12권1호
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• pp.59-67
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• 1997

Let $K'_M$ be the space of distributions on $R^m$ which grow no faster than $e^{M(kx)}$ for some k > 0 and an index function M(x) and $K'_M$ be the Fourier transform of $K'_M$. We establish the characterizations of the space $O_M(K'_m;K'_M)$ of multipliers in $K'_M$.

• 대한수학회지
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• 제49권2호
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• pp.435-447
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• 2012

Let G be a group. Let R be a G-graded commutative ring with identity and M be a G-graded multiplication module over R. A proper graded submodule Q of M is semiprime if whenever $I^nK{\subseteq}Q$, where $I{\subseteq}h(R)$, n is a positive integer, and $K{\subseteq}h(M)$, then $IK{\subseteq}Q$. We characterize semiprime submodules of M. For example, we show that a proper graded submodule Q of M is semiprime if and only if grad$(Q){\cap}h(M)=Q+{\cap}h(M)$. Furthermore if M is finitely generated then we prove that every proper graded submodule of M is contained in a graded semiprime submodule of M. A proper graded submodule Q of M is said to be almost semiprime if (grad(Q)$\cap$h(M))n(grad$(0_M){\cap}h(M)$) = (Q$\cap$h(M))n(grad$(0_M){\cap}Q{\cap}h(M)$). Let K, Q be graded submodules of M. If K and Q are almost semiprime in M such that Q + K $\neq$ M and $Q{\cap}K{\subseteq}M_g$ for all $g{\in}G$, then we prove that Q + K is almost semiprime in M.

• 한국통신학회논문지
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• 제32권10C호
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• pp.929-934
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• 2007

이 논문에서는 M진 Sidel'nikov 수열을 생성하는 원시원을 바꾸었을 때, 생성된 수열의 서로 다른 자기 상관 분포의 개수를 계산한다. p는 소수이고 M은 $p^n-1$의 약수일 때 M진 Sidel'nikov 수열의 서로 다른 자기 상관 분포는 M=2일 때, 유일하다. M은 2보다 크고 어떤 $k(1{\leq}k)에 대해서 $p^k+1$의 약수일 때, M진 Sidel'nikov 수열의 자기 상관 분포는 1개이다. M은 2보다 크고 어떤 $k(1{\leq}k)에 대해서 $p^k+1$의 약수가 아닐 때, 서로 다른 자기 상관 분포의 개수는 ${\phi}(M)/k'$(혹은 ${\phi}(M)/2k'$)보다 작거나 같다. 여기서 k'는 $M|p^{k'}-1$를 만족하는 가장 작은 정수이다.