• 대한수학회보
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• 제39권1호
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• pp.123-131
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• 2002

Let A(p, k) (p, k$\in$N) be the class of functions f(z) = $z^{p}$ + $a_{p+k}$ $z^{p+k}$+… analytic in the unit disk. We introduce a subclass H(p, k, λ, $\delta$, A, B) of A(p, k) by using the Ruscheweyh derivative. The object of the present paper is to show some properties of functions in the class H(p, k, λ, $\delta$, A, B). B).

• 대한수학회지
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• 제58권3호
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• pp.571-595
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• 2021

In this paper we study the algebraic structure of ℤ_pℤ_p[u]/k>-cyclic codes, where u^k = 0 and p is a prime. A ℤ_pℤ_p[u]/k>-linear code of length (r + s) is an R_k-submodule of ℤ^r_p × R^s_k with respect to a suitable scalar multiplication, where R_k = ℤ_p[u]/k>. Such a code can also be viewed as an R_k-submodule of ℤ_p[x]/r - 1> × R_k[x]/s - 1>. A new Gray map has been defined on ℤ_p[u]/k>. We have considered two cases for studying the algebraic structure of ℤ_pℤ_p[u]/k>-cyclic codes, and determined the generator polynomials and minimal spanning sets of these codes in both the cases. In the first case, we have considered (r, p) = 1 and (s, p) ≠ 1, and in the second case we consider (r, p) = 1 and (s, p) = 1. We have established the MacWilliams identity for complete weight enumerators of ℤ_pℤ_p[u]/k>-linear codes. Examples have been given to construct ℤ_pℤ_p[u]/k>-cyclic codes, through which we get codes over ℤ_p using the Gray map. Some optimal p-ary codes have been obtained in this way. An example has also been given to illustrate the use of MacWilliams identity.

• 대한수학회보
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• 제40권3호
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• pp.509-520
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• 2003

Let p be a prime number, $Q_{p}$ the field of p-adic numbers, K a finite extension of $Q_{p}$, $\bar{K}}$ a fixed algebraic closure of K and $C_{p}$ the completion of K with respect to the p-adic valuation. Let E be a closed subfield of $C_{p}$, containing K. Given elements $t_1$...,$t_{r}$ $\in$ E for which the field K($t_1$...,$t_{r}$) is dense in E, we construct integral bases of E over K.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.573-578
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• 2005

For a positive integer k and a positive number 0 < p$\le$1, an operator T is said to be (p, k)-quasiposinormal if $T^{{\ast}k}(c^2(T^{\ast}T)P - (TT^{\ast})^P)T^k {\ge} 0$ for some c > o. In this paper we consider a structure for (p, k)-quasiposinormal.

• 한국작물학회:학술대회논문집
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• 한국작물학회 1989년도 춘계 학술대회지
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• pp.50-51
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• 1989

• 한국통신학회논문지
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• 제23권7호
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• pp.1851-1859
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• 1998

본 논문에서는 선행 논문인 [1]과 [2]에서 제안한 바 있는 패스워드 기반 인증 프로토콜 K1P의 특징을 요약하고 세가지의 확장된 프로토콜을 제안한다. 제안된 프로토콜들은 K1P의 설계 개념인 안전성과 효율성을 유지하도록 하였으며, 각기 다양한 목적에 따라 사용될 수 있도록 하였다. 새롭게 제안된 프로토콜은 일시 키-K1P, 사용자 공개키-K1P, 그리고 지수적 키 교환-K1P, 그리고 지수적 키 교환-K1P 등이다.

• Kyungpook Mathematical Journal
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• 제48권1호
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• pp.15-24
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• 2008

Let $N{\geq}1$ and p > 1. Let ${\Omega}$ be a domain of $\mathbb{R}^N$. In this article we shall establish Kato's inequalities for quasilinear degenerate elliptic operators of the form $A_pu$ = divA(x,$\nabla$u) for $u{\in}K_p({\Omega})$, ), where $K_p({\Omega})$ is an admissible class and $A(x,\xi)\;:\;{\Omega}{\times}\mathbb{R}^N{\rightarrow}\mathbb{R}^N$ is a mapping satisfying some structural conditions. If p = 2 for example, then we have $K_2({\Omega})\;= \;\{u\;{\in}\;L_{loc}^1({\Omega})\;:\;\partial_ju,\;\partial_{j,k}^2u\;{\in}\;L_{loc}^1({\Omega})\;for\;j,k\;=\;1,2,{\cdots},N\}$. Then we shall prove that $A_p{\mid}u{\mid}\;\geq$ (sgn u) $A_pu$ and $A_pu^+\;\geq\;(sgn^+u)^{p-1}\;A_pu$ in D'(${\Omega}$) with $u\;\in\;K_p({\Omega})$. These inequalities are called Kato's inequalities provided that p = 2. The class of operators $A_p$ contains the so-called p-harmonic operators $L_p\;=\;div(\mid{{\nabla}u{\mid}^{p-2}{\nabla}u)$ for $A(x,\xi)={\mid}\xi{\mid}^{p-2}\xi$.

• 대한의생명과학회지
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• 제13권2호
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• pp.75-81
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• 2007

Sodium salicylate (NaSal), a chemopreventive drug, has been shown to induce apoptosis and cell circle arrest depending on its concentrations in a variety of cancer cells. In A549 cells, low concentration of NaSal (5$\sim$10 mM) induces cell cycle arrest, whereas it induces apoptosis at higher concentration of 20 mM. In the present study, we examined the molecular mechanism for NaSal-induced cell cycle arrest. NaSal induced expression of p53, p21 (Wafl/Cipl), and p27 (Kipl) that play important roles in cell cycle arrest. p53 induction was mediated by its phosphorylation at Ser-15 that could be prevented by the PI3K-related kinase (ATM, ATR and DNA-PK) inhibitors including wortmannin, caffeine and LY294002. In addition, NaSal-induction of p2l (Wafl/Cipl) was detected in P53 (+/+) wild type A549 cells but not in p53 (-/-) mutant H1299 cells, indicating p53-dependent p21 (Wafl/Cipl) induction. In contrast, p27 (Kipl) that is a negative regulate. of cell cycle with p21 (Wafl/Cipl) was observed both in A549 cells and H1299 cells. Thus, 5 mM NaSal appeared to cause cell cycle arrest through inducing the cyclin-dependent kinase inhibitor p21 (Wafl/Cipl) via PI3K-related protein kinase-dependent p53 activation as well as by up-regulating p27 (Kipl) independently of p53 in A549 cells.

• Korean Journal of Mathematics
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• 제6권2호
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• pp.221-229
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• 1998

Let $k$ be a real abelian field and $k_{\infty}$ be its $\mathbb{Z}_p$-extension for an odd prime $p$. Let $A_n$ be the Sylow $p$-subgroup of the ideal class group of $k_n$, the $nth$ layer of the $\mathbb{Z}_p$-extension. By using the main conjecture of Iwasawa theory, we have the following: If $p$ does not divide $\prod_{{{\chi}{\in}\hat{\Delta}_k},{\chi}{\neq}1}B_{1,{\chi}{\omega}^{-1}$, then $A_n$ = {0} for all $n{\geq}0$, where ${\Delta}_k=Gal(k/\mathbb{Q})$ and ${\omega}$ is the Teichm$\ddot{u}$ller character for $p$. The converse of this statement does not hold in general. However, we have the following when $k$ is of prime conductor $q$: Let $q$ be an odd prime different from $p$. and let $k$ be a real subfield of $\mathbb{Q}({\zeta}_q)$. If $p{\mid}{\prod}_{{\chi}{\in}\hat{\Delta}_{k,p},{\chi}{\neq}1}B_{1,{\chi}{\omega}}-1$, then $A_n{\neq}\{0\}$ for all $n{\geq}1$, where ${\Delta}_{k,p}$ is the $Gal(k_{(p)}/\mathbb{Q})$ and $k_{(p)}$ is the decomposition field of $k$ for $p$.

• Korean Chemical Engineering Research
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• 제47권4호
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• pp.453-458
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• 2009

최근 환경문제가 크게 대두됨에 따라 고분자 합성과 가공 공정에서도 유기용매를 사용하지 않는 새로운 친환경적 공정의 개발이 요구되고 있다. 초임계 이산화탄소는 고분자 합성에서 용매로 사용될 경우, 기존의 유기용매와 비교하여 불연성이고 독성이 없으며 생성물과의 분리가 용이하다는 장점을 가지고 있다. 본 연구에서는 초임계 이산화탄소를 이용하여 의약학 및 화장품 분야에서 지능형 약물전달체로 사용할 수 있는 pH 감응형 하이드로젤인 P(MAA-co-EGMA) 하이드로젤을 수 백 nm 수준의 입자 형태로 합성하는 방법을 개발하였다. 그리고 중합과정에서 사용하는 분산안정제인 PtBuMA-PEO와 중합개시제인 AIBN이 하이드로젤 입자의 합성에 미치는 영향을 살펴보았다. 입자의 합성에서 PtBuMA-PEO의 함량이 증가할수록 입자 크기는 감소하였으나 AIBN의 함량에 따른 입자 크기의 변화는 관찰할 수 없었다. 합성된 P(MAA-co-EGMA) 하이드로젤 입자의 pH에 따른 팽윤 실험결과, PMAA의 $pK_a$인 pH 5를 전후하여 급격한 하이드로젤의 평형 질량팽윤비의 변화를 관찰할 수 있었다. 즉, pH 5보다 낮은 pH에서는 낮은 팽윤비를, 반면에 pH 5보다 높은 pH에서는 매우 높은 팽윤비를 나타내었다. 그리고 Rh-B를 이용한 방출실험에서는 높은 pH에서는 다량의 Rh-B가 하이드로젤 입자로부터 방출되었으나 낮은 pH에서는 Rh-B가 거의 방출되지 않는 pH에 따른 선택적 방출 특성을 나타내었다.