• Bulletin of the Korean Mathematical Society
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• v.39 no.1
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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).

• Journal of the Korean Mathematical Society
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• v.58 no.3
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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.

• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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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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• v.19 no.1_2
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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.

• Proceedings of the Korean Society of Crop Science Conference
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• 1989.02a
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• pp.50-51
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• 1989

• The Journal of Korean Institute of Communications and Information Sciences
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• v.23 no.7
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• pp.1851-1859
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• 1998

We summarize the password-based authetication protocol K1P which was introduced in our easlier papers [1,2] and then propose three more extended protocols. These protocols preserve a design concept of K1P, i.e., security and efficiency, and canbe used for various purposes. They are a One-time key K1P, a Client public key K1P, and an Exponential key exchange K1P.

• Kyungpook Mathematical Journal
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• v.48 no.1
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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 $A(x,\xi)={\mid}\xi{\mid}^{p-2}\xi$.

• Biomedical Science Letters
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• v.13 no.2
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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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• v.6 no.2
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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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• v.47 no.4
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• pp.453-458
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• 2009

Recently, new methods to synthesize and process polymers without toxic organic solvents are needed in order to solve environmental problems. The use of supercritical carbon dioxide as a solvent for the polymer synthesis is attractive since it is non-toxic, non-flammable, naturally abundant, and the product may be easily separated from the solvent. In this study, we developed the method using super critical $CO_2$ to prepare P(MAA-co-EGMA) hydrogel nanoparticles as an intelligent drug delivery carrier. The effects of concentrations of PtBuMA-PEO as a dispersion stabilizer and AIBN as an initiator on the particle synthesis were investigated. When PtBuMA-PEO concentration increased, the particle size decreased. However, there was no significant difference in the particle size according to the AIBN concentration. There was a drastic change of the equilibrium weight swelling ratio of P(MAA-co-EGMA) hydrogel nanoparticles at a pH of around 5, which is the $pK_a$ of PMAA. At a pH below 5, the hydrogels were in a relatively collapsed state but at a pH higher than 5, the hydrogels swelled to a high degree. In release experiments using Rh-B as a model solute, the P(MAA-co-EGMA) hydrogel nanoparticles showed a pH-sensitive release behavior. At low pH(pH 4.0) a small amount of Rh-B was released while at high pH(pH 6.0) a relatively large amount of Rh-B was released from the hydrogels.