• Journal of applied mathematics & informatics
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• 제35권1_2호
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• pp.121-130
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• 2017

This study is concerned with the existence of positive solution for the following nonlinear elliptic system $$\{-M_1(\int_{\Omega}{\mid}x{\mid}^{-ap}{\mid}{\nabla}u{\mid}^pdx)div({\mid}x{\mid}^{-ap}{\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)\\{\hfill{120}}={\mid}x{\mid}^{-(a+1)p+c_1}\({\alpha}_1A_1(x)f(v)+{\beta}_1B_1(x)h(u)\),\;x{\in}{\Omega},\\-M_2(\int_{\Omega}{\mid}x{\mid}^{-bq}{\mid}{\nabla}v{\mid}^qdx)div({\mid}x{\mid}^{-bq}{\mid}{\nabla}v{\mid}^{q-2}{\nabla}v)\\{\hfill{120}}={\mid}x{\mid}^{-(b+1)q+c_2}\({\alpha}_2A_2(x)g(u)+{\beta}_2B_2(x)k(v)\),\;x{\in}{\Omega},\\{u=v=0,\;x{\in}{\partial}{\Omega},$$ where ${\Omega}$ is a bounded smooth domain of ${\mathbb{R}}^N$ with $0{\in}{\Omega}$, 1 < p, q < N, $0{\leq}a$ < $\frac{N-p}{p}$, $0{\leq}b$ < $\frac{N-q}{q}$ and ${\alpha}_i,{\beta}_i,c_i$ are positive parameters. Here $M_i,A_i,B_i,f,g,h,k$ are continuous functions and we discuss the existence of positive solution when they satisfy certain additional conditions. Our approach is based on the sub and super solutions method.

• 대한수학회지
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• 제51권4호
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• pp.655-663
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• 2014

Let R be a ring with identity, X(R) the set of all nonzero, non-units of R and G(R) the group of all units of R. We show that for a matrix ring $M_n(D)$, $n{\geq}2$, if a, b are singular matrices of the same rank, then ${\mid}o_{\ell}(a){\mid}={\mid}o_{\ell}(b){\mid}$, where $o_{\ell}(a)$ and $o_{\ell}(b)$ are the orbits of a and b, respectively, under the left regular action. We also show that for a semisimple Artinian ring R such that $X(R){\neq}{\emptyset}$, $$R{{\sim_=}}{\oplus}^m_{i=1}M_n_i(D_i)$$, with $D_i$ infinite division rings of the same cardinalities or R is isomorphic to the ring of $2{\times}2$ matrices over a finite field if and only if ${\mid}o_{\ell}(x){\mid}={\mid}o_{\ell}(y){\mid}$ for all $x,y{\in}X(R)$.

• 대한수학회지
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• 제40권2호
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• pp.241-250
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• 2003

Let (B, m$_{B}$, k) be a maximal commutative $textsc{k}$-subalgebra of M$_{m}$(k). Then, for some element z $\in$ Soc(B), a k-algebra R = B［X,Y］/I, where I ＝ (m$_{B}$X, m$_{B}$Y, X$^2$- z,Y$^2$- z, XY) will create an interesting maximal commutative $textsc{k}$-subalgebra of a matrix algebra which is neither a $C_1$-construction nor a $C_2$-construction. This construction will also be useful to embed a maximal commutative $textsc{k}$-subalgebra of matrix algebra to a maximal commutative $textsc{k}$-subalgebra of a larger size matrix algebra.gebra.a.

• 미생물학회지
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• 제54권3호
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• pp.208-213
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• 2018

Nuclear factor kappa B ($NF{\kappa}B$)의 활성화는 염증을 일으킨다. 이 때, inducible nitric oxide synthase (iNOS)가 발현된다. 우리 선행 연구에 의하면 Bacillus licheniformis B1에 의해 제조된 발효대두에 있는 septapeptide (GVAWWMY)가 대식세포에서 iNOS mRNA 발현과 NO 생산을 억제하였다. 본 연구에서 septapeptide의 처리가 $I{\kappa}B{\alpha}$ ($NF{\kappa}B$ 억제 단백질)의 분해를 억제하여 LPS에 의해 유도되는 $NF{\kappa}B$의 활성화를 억제함을 확인했다. 분자 docking에 의해 septapeptide가 ${\kappa}B$ kinase ${\beta}$ ($IKK{\beta}$)에 부착하여 $I{\kappa}B{\alpha}$의 인산화를 방해할 가능성이 있다. Septapeptide는 높은 친화도로(-8.7 kcal/Mol) $IKK{\beta}$의 kinase domain에 부착해서 kinase 활성에 크게 영향을 미칠 수 있다.

• 충청수학회지
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• 제17권1호
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• pp.85-101
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• 2004

Let A be a Hopf algebra with a linear form ${\sigma}:k{\rightarrow}A{\otimes}A$, which is convolution invertible, such that ${\sigma}_{21}({\Delta}{\otimes}id){\tau}({\sigma}(1))={\sigma}_{32}(id{\otimes}{\Delta}){\tau}({\sigma}(1))$. We define Hopf algebras, ($A_{\sigma}$, m, u, ${\Delta}_{\sigma}$, ${\varepsilon}$, $S_{\sigma}$). If B and C are opposite skew copaired Hopf algebras and $A=B{\otimes}_kC$ then we find Hopf algebras, ($A_{[{\sigma}]}$, $m_B{\otimes}m_C$, $u_B{\otimes}u_C$, ${\Delta}_{[{\sigma}]}$, ${\varepsilon}B{\otimes}{\varepsilon}_C$, $S_{[{\sigma}]}$). Let H be a finite dimensional commutative Hopf algebra with dual basis $\{h_i\}$ and $\{h_i^*\}$, and let $A=H^{op}{\otimes}H^*$. We show that if we define ${\sigma}:k{\rightarrow}H^{op}{\otimes}H^*$ by ${\sigma}(1)={\sum}h_i{\otimes}h_i^*$ then ($A_{[{\sigma}]}$, $m_A$, $u_A$, ${\Delta}_{[{\sigma}]}$, ${\varepsilon}_A$, $S_{[{\sigma}]}$) is the dual space of Drinfeld double, $D(H)^*$, as Hopf algebra.

• 대한수학회논문집
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• 제23권4호
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• pp.511-528
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• 2008

Let (R, m) be a 2-dimensional regular local ring with algebraically closed residue field R/m. Let K be the quotient field of R and $\upsilon$ be a prime divisor of R, i.e., a valuation of K which is birationally dominating R and residually transcendental over R. Zariski showed that there are finitely many simple $\upsilon$-ideals $m\;=\;P_0\;{\supset}\;P_1\;{\supset}\;{\cdots}\;{\supset}\;P_t\;=\;P$ and all the other $\upsilon$-ideals are uniquely factored into a product of those simple ones [17]. Lipman further showed that the predecessor of the smallest simple $\upsilon$-ideal P is either simple or the product of two simple $\upsilon$-ideals. The simple integrally closed ideal P is said to be free for the former and satellite for the later. In this paper we describe the sequence of simple $\upsilon$-ideals when P is satellite of order 3 in terms of the invariant $b_{\upsilon}\;=\;|\upsilon(x)\;-\;\upsilon(y)|$, where $\upsilon$ is the prime divisor associated to P and m = (x, y). Denote $b_{\upsilon}$ by b and let b = 3k + 1 for k = 0, 1, 2. Let $n_i$ be the number of nonmaximal simple $\upsilon$-ideals of order i for i = 1, 2, 3. We show that the numbers $n_{\upsilon}$ = ($n_1$, $n_2$, $n_3$) = (${\lceil}\frac{b+1}{3}{\rceil}$, 1, 1) and that the rank of P is ${\lceil}\frac{b+7}{3}{\rceil}$ = k + 3. We then describe all the $\upsilon$-ideals from m to P as products of those simple $\upsilon$-ideals. In particular, we find the conductor ideal and the $\upsilon$-predecessor of the given ideal P in cases of b = 1, 2 and for b = 3k + 1, 3k + 2, 3k for $k\;{\geq}\;1$. We also find the value semigroup $\upsilon(R)$ of a satellite simple valuation ideal P of order 3 in terms of $b_{\upsilon}$.

• Archives of Pharmacal Research
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• 제27권1호
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• pp.111-117
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• 2004

Hepatic microcirculatory failure is a major component of reperfusion injury in the liver. Recent data provided some evidence that endothelium-derived vasoconstrictors and vasodilators may be functionally important to the control of the total hepatic blood flow under these conditions of circulatory failure. Since Kupffer cells provide signals that regulate the hepatic response in ischemia/reperfusion (I/R), the aim of this study was to investigate the role of Kupffer cells in the I/R-induced imbalance of vasoregulatory gene expression. Rats were subjected to 60 min hepatic ischemia, followed by 5 h of reperfusion. The Kupffer cells were inactivated by gadolinium chloride ($GdCl_3$, 7.5 mg/kg body weight, intravenously) 1 day prior to ischemia. Liver samples were obtained 5 hrs after reperfusion for RT-PCR analysis of the mRNA for genes of interest: endothelin-1 (ET-1), its receptors $ET_A and ET_B$, endothelial nitric oxide synthase (eNOS), inducible nitric oxide synthase (iNOS) and heme oxygenase-1 (HO-1). ET-1 mRNA expression was increased by I/R. mRNA levels for $ET_A$ receptors showed no change, whereas $ET_B$ receptor transcripts increased in the I/R group. The increases in ET-1 and $ET_B$ mRNA were not prevented by the $GdCI_3$ pretreatment. The mRNA levels for iNOS and eNOS significantly increased within the I/R group with no significant difference between the I/R group and the $GdCl_3$-treated I/R group. HO-1 mRNA expression significantly increased in the I/R group and this increase was attenuated by $GdCI_3$. In conclusion, we have demonstrated that an imbalance in hepatic vasoregulatory gene expression occurs during I/R. Our findings suggest that the activation of Kupffer cells is not required for I/R-induced hepatic microvascular dysfunction.

• Applied Biological Chemistry
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• 제25권3호
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• pp.177-181
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• 1982

Dicofol의 각종(各種) 유기용매(有機溶媒)에 대(對)한 안정성(安定性)을 조사(調査)하기 위하여 $-5^{\circ}C$에서 7일간(日間) 방치(放置)하여 그 침전생성유무(沈澱搬成有無)를 조사(調査)하고, $50^{\circ}C$에서 56일간(日間) 처리(處理)한 다음 각종용매(各種溶媒)에 대(對)해서 Dicofol의 분해형태(分解形態)를 T.L.C.로 확인(確認)하였으며, 그 주성분(主成分) 분해율(分解率)을 2주(週)간격으로 gas chromatography로 측정(測定)하였다. 그 결과(結果) Dicofol 수화제(水和劑)와 N.N-dimethylformamide 및 cyclohexanone용액(溶液)에서는 Dicofol의 주성분(主成分) 분해율(分解率)이 각각(各各) 1.2%, 6.7%, 13.3%이었으나 xylene, toluene, M.I.B.K. 및 isophorone용액(溶液)에서는 거의 주성분(主成分) 분해(分解)가 일어나지 않았다. 그러나 $-5^{\circ}C$에서 7일간(日間) 방치(放置)하였을 때 isophorone 을 제외(除外)한 xylene, toluene 및 M.I.B.K. 용액(溶液)에서는 침전(沈澱)이 생성(生成)되어 Dicofol의 용제(溶劑)로서는 적합하지 못하였다. 이러한 사실(事實)로 미루어 볼 때 공시(供試)된 각종(各種) 유기용매중(有機溶媒中)에서 Dicofol의 제제상(製劑上) 가장 적합한 용매(溶媒)는 isophorone임을 알았다.

• 대한수학회보
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• 제60권2호
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• pp.541-560
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• 2023

Let T be an m-linear Calderón-Zygmund operator. $T_{{\vec{b}S}}$ is the generalized commutator of T with a class of measurable functions {b_i}^∞_i=1. In this paper, we will give some new estimates for $T_{{\vec{b}S}}$ when {b_i}^∞_i=1 belongs to Orlicz-type space and Lipschitz space, respectively.

• 천문학회지
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• 제28권1호
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• pp.31-43
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• 1995

We present UBVRI CCD photometry of the Type Ie supernova SN 19941 in M51 which was discovered on April 2, 1994 (UT). UBVRI CCD photometry of SN 1994 I were obtained for the period of the first two months from April 4, 1994, using the Seoul National University Observatory 60 cm telescope. The light curves of SN 19941 show several interesting features: (a) SN 19941 reaches the maximum brightness at B-band on April 8.23 (B = 13.68 mag), at V-band on April 9.10 (V = 12.89 mag), and at I-band on April 10.32 (I = 12.48 mag); (b) The light curves around the maximum brightness are much narrower than those of other types of supernovae; (c) The light curves after the peak decline more steeply than those of other types of supernovae; and (d) The colors get redder from $(V-R){\approx}0.2 mag ((V - I){\approx} 0.3 mag, (B - V){\approx}0.7 mag)$ on April 4 to $(V-R){\approx}0.6 mag ((V-1){\approx}0.9 mag, (B-V){\approx}1.3 mag)$ on April 18. Afterwards (V - R) colors get bluer slightly $(by\~0.005 mag/day)$, while (V-I) colors stay almost constant around $(V-1){\approx}1.0 mag$. The color at the maximum brightness is (B-V)=0.9 mag, which is $\~1$mag redder than the mean color of typical Type la supernovae at the maximum brightness. The light curves of SN 1994I are similar to those of the Type Ie supernova SN 1962L in NGC 1073. Adopting the distance modulus of $(m-M)_0 = 29.2 mag$ and the reddening of E(B - V) = 0.45 mag [Iwamoto et al. 1994, preprint for ApJ], we derive absolute magnitudes at the maximum brightness of SN 1994I, Mv(max) = -17.7 mag and MB(max) = -17.4 mag. This result shows that SN 1994I was $\~2$mag fainter at the maximum brightness compared with typical Type Ia supernovae. A narrower peak and faster decline after the maximum in the light curve of SN 1994I compared with other types of supernovae indicate that the progenitor of SN 1994I might be a lower mass star compared with those of other types of supernovae.