• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.251-256
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• 1997

We show that a strong system of derivations ${D_0, D_1,\cdots,D_m}$ on a commutative Banach algebra A is contained in the radical of A if it satisfies one of the following conditions for separating spaces; (1) $\partial(D_i) \subseteq rad(A) and \partial(D_i) \subseteq K D_i(rad(A))$ for all i, where $K D_i(rad(A)) = {x \in rad(A))$ : for each $m \geq 1, D^m_i(x) \in rad(A)}$. (2) $(D^m_i) \subseteq rad(A)$ for all i and m. (3) $\bar{x\partial(D_i)} = \partial(D_i)$ for all i and all nonzero x in rad(A).

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.91-103
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• 2013

Let (D,B) be an admissible pair. Then recall that $B\;{\times}^L_HD^{{\rightarrow}{\pi}_D}_{{\leftarrow}i_D}\;D$ are bialgebra maps satisfying ${\pi}_D{\circ}i_D=I$. We have solved a converse in case D is a Hopf algebra. Let D be a Hopf algebra with antipode $S_D$ and be a left H-comodule algebra and a left H-module coalgebra over a field $k$. Let A be a bialgebra over $k$. Suppose $A^{{\rightarrow}{\pi}}_{{\leftarrow}i}D$ are bialgebra maps satisfying ${\pi}{\circ}i=I_D$. Set ${\Pi}=I_D*(i{\circ}s_D{\circ}{\pi}),B=\Pi(A)$ and $j:B{\rightarrow}A$ be the inclusion. Suppose that ${\Pi}$ is an algebra map. We show that (D,B) is an admissible pair and $B^{\leftarrow{\Pi}}_{\rightarrow{j}}A^{\rightarrow{\pi}}_{\leftarrow{i}}D$ is an admissible mapping system and that the generalized biproduct bialgebra $B{\times}^L_HD$ is isomorphic to A as bialgebras.

• Journal of the Korea Society of Computer and Information
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• v.20 no.2
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• pp.63-70
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• 2015

In the absence of a polynomial time algorithm capable of obtaining the exact solutions to it, the domatic number problem (DNP) of dominating set (DS) has been regarded as NP-complete. This paper suggests polynomial-time complexity algorithm about DNP. In this paper, I select a vertex $v_i$ of the maximum degree ${\Delta}(G)$ as an element of a dominating set $D_i,i=1,2,{\cdots},k$, compute $D_{i+1}$ from a simplified graph of $V_{i+1}=V_i{\backslash}D_i$, and verify that $D_i$ is indeed a dominating set through $V{\backslash}D_i=N_G(D_i)$. When applied to 15 various graphs, the proposed algorithm has succeeded in bringing about exact solutions with polynomial-time complexity O(kn). Therefore, the proposed domatic number algorithm shows that the domatic number problem is in fact a P-problem.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.517-523
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• 2007

Let R/I be an Artinian algebra of codimension 3 with Hilbert function H such that $h_{d-1}>h_d=h_{d+1}$. Ahn and Shin showed that A cannot be level if ${\beta}_{1,d+2}(Gin(I))={\beta}_{2,d+2}(Gin(I))$ where Gin(I) is a generic initial ideal of I. We prove that some certain graded Artinian algebra R/I cannot be level if either ${\beta}_{1,d}(I^{lex})={\beta}_{2,d}(I^{lex})+1\;or\;{\beta}_{1,d+1}(I^{lex})={\beta}_{2,d+1}(I^{lex})\;where\;I^{lex}$ is a lex-segment ideal associated to I.

• Korean Journal of Mathematics
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• v.17 no.1
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• pp.15-23
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• 2009

Let D be an integral domain, P be a nonzero prime ideal of D, $\{P_{\alpha}{\mid}{\alpha}{\in}{\mathcal{A}}\}$ be a nonempty set of prime ideals of D, and $\{I_{\beta}{\mid}{\beta}{\in}{\mathcal{B}}\}$ be a nonempty family of ideals of D with ${\cap}_{{\beta}{\in}{\mathcal{B}}}I_{\beta}{\neq}(0)$. Consider the following conditions: (i) If $P{\subseteq}{\cup}_{{\alpha}{\in}{\mathcal{A}}}P_{\alpha}$, then $P=P_{\alpha}$ for some ${\alpha}{\in}{\mathcal{A}}$; (ii) If ${\cap}_{{\beta}{\in}{\mathcal{B}}}I_{\beta}{\subseteq}P$, then $I_{\beta}{\subseteq}P$ for some ${\beta}{\in}{\mathcal{B}}$. In this paper, we prove that D satisfies $(i){\Leftrightarrow}D$ is a generalized weakly factorial domain of ${\dim}(D)=1{\Rightarrow}D$ satisfies $(ii){\Leftrightarrow}D$ is a weakly Krull domain of dim(D) = 1. We also study the t-operation analogs of (i) and (ii).

• Korean Journal of Mathematics
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• v.18 no.4
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• pp.335-342
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• 2010

Let D be an integral domain with quotient field K,$\mathcal{I}(D)$ be the set of nonzero ideals of D, and $w$ be the star-operation on D defined by $I_w=\{x{\in}K{\mid}xJ{\subseteq}I$ for some $J{\in}\mathcal{I}(D)$ such that J is finitely generated and $J^{-1}=D\}$. The D is called a Pr$\ddot{u}$fer $v$-multiplication domain if $(II^{-1})_w=D$ for all nonzero finitely generated ideals I of D. In this paper, we show that D is a Pr$\ddot{u}$fer $v$-multiplication domain if and only if $(A{\cap}(B+C))_w=((A{\cap}B)+(A{\cap}C))_w$ for all $A,B,C{\in}\mathcal{I}(D)$, if and only if $(A(B{\cap}C))_w=(AB{\cap}AC)_w$ for all $A,B,C{\in}\mathcal{I}(D)$, if and only if $((A+B)(A{\cap}B))_w=(AB)_w$ for all $A,B{\in}\mathcal{I}(D)$, if and only if $((A+B):C)_w=((A:C)+(B:C))_w$ for all $A,B,C{\in}\mathcal{I}(D)$ with C finitely generated, if and only if $((a:b)+(b:a))_w=D$ for all nonzero $a,b{\in}D$, if and only if $(A:(B{\cap}C))_w=((A:B)+(A:C))_w$ for all $A,B,C{\in}\mathcal{I}(D)$ with B, C finitely generated.

• The Korean Journal of Pharmacology
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• v.27 no.2
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• pp.135-144
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• 1991

Using T-lymphocytes obtained from rat peripheral blood, we found that the 44kD/pI6.8 protein was the major phosphoprotein of T-lymphocytes under basal condition, and that the 44kD/pI6.3 protein was a new phosphoprotein appeared in T-lymphocytes stimulated with ${\beta}-agonist$. The phosphorylation of the 44kD/pI6.3 protein was also induced by forskolin but inhibited by H-8 pretreatment. To clarify the character of the 44kD/pI6.3 protein, we used Con-A and kinase inhibitors, H-7 and W-7. Con-A stimulation induced phosphorylation of 44kD/pI 6.3 protein but that was inhibited by W-7 pretreatment. The phosphorytation of 44kD/pI6.3 protein was not induced by the PKC activator, PMA. Instead, the phosphorylation of 44kD/pI6.8 protein was reduced by H-7, a PKC inhibitor. From the above results,it can be concluded that the 44kD/pI6.3 protein can be a common substrate for A-kinase and CaM kinase. The two dimensional tryptic peptide mapping revealed that the 44kD/pI6.8 and 44kD/pI6.3 proteins are different.

• Nutrition Research and Practice
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• v.5 no.5
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• pp.464-470
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• 2011

Growing evidence suggests an elevated risk for colorectal neoplasia among individuals with low levels of vitamin D, the biological actions of which are mediated by the vitamin D receptor (VDR). To investigate the association among vitamin D status, VDR polymorphisms (FokI, and BsmI), and colorectal adenoma, we conducted a meta-analysis of nine studies of circulating levels of 25-hydroxyvitamin D (25(OH)D) and five studies of FokI or BsmI polymorphisms in relation to colorectal adenomas. Study-specific relative risks (RRs) and 95% confidence intervals (CIs) were pooled using a random-effects model. A total of 3398 coloreetal adenomas for 25(OH)D and 1754 colorectal adenomas for VDR were included in the meta-analysis. We identified a significant inverse association between colorectal adenoma (combined RR, 0.93; 95% CI, 0.87-0.98 per 10 ng/mL increase in 25(OH)D levels). When we examined FokI and BsmI polymorphisms in the meta-analysis, we found no association for either FokI (combined RR, 1.00; 95% CI, 0.95-1.06) or BsmI (combined RR, 0.99; 95% CI, 0.93-1.05) in the additive model. These data suggest an inverse association between circulating 25(OH)D levels and colorectal adenoma risk.

• Journal of the Society of Cosmetic Scientists of Korea
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• v.50 no.2
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• pp.153-161
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• 2024

Vitamin D is a fat-soluble vitamin that is mainly produced in the skin by UV rays. Along with melatonin, it is a representative chronobiotic substance, and the skin plays an important role in distinguishing between day and night. However, vitamin D cannot be used directly in cosmetics because it is a vitamin that acts as a coenzyme and plays a hormonal role in regulating the expression of various types of genes. Therefore, it was to investigate the skin efficacy of provitamin D (7-dehydrocholesterol), a vitamin D precursor that can be used in cosmetics. Our findings reveal that pro vitamin D can effectively inhibit the expression of tyrosinase, the melanin-producing enzyme, thereby attenuating melanin synthesis. This skin tone regulatory effect has been corroborated in vitro using artificial skin models. Additionally, pro vitamin D demonstrated anti-inflammatory properties by suppressing the expression of TNFa and, upon conversion to vitamin D through UV exposure, it was observed to induce the production of the antimicrobial peptide CAMP (LL-37). The inhibitory effect of pro vitamin D on melanin production appears to be a result of it reducing the UV absorption capacity of melanin, thereby inducing the conversion of pro D to vitamin D. Utilizing pro vitamin D in cosmetic formulations could not only modulate skin tone and enhance skin immunity but also expect to contribute to other cutaneous benefits as anti-aging and barrier function improvement with everyday UV exposure. This multifaceted efficacy positions pro vitamin D as a promising ingredient in advancing the formulation of skin care products.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1137-1146
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• 2011

Let {$X_i$, $i{\geq}1$} be a sequence of i.i.d. nondegenerate random variables which is in the domain of attraction of the normal law with mean zero and possibly infinite variance. Denote $S_n={\sum}_{i=1}^n\;X_i$, $M_n=max_{1{\leq}i{\leq}n}\;{\mid}S_i{\mid}$ and $V_n^2={\sum}_{i=1}^n\;X_i^2$. Then for d > -1, we showed that under some regularity conditions, $$\lim_{{\varepsilon}{\searrow}0}{\varepsilon}^2^{d+1}\sum_{n=1}^{\infty}\frac{(loglogn)^d}{nlogn}I\{M_n/V_n{\geq}\sqrt{2loglogn}({\varepsilon}+{\alpha}_n)\}=\frac{2}{\sqrt{\pi}(1+d)}{\Gamma}(d+3/2)\sum_{k=0}^{\infty}\frac{(-1)^k}{(2k+1)^{2d+2}}\;a.s.$$ holds in this paper, where If g denotes the indicator function.