• Korean Journal of Mathematics
• /
• v.26 no.2
• /
• pp.215-269
• /
• 2018

Orders and types of entire functions have been actively investigated by many authors. In this paper, we investigate some basic properties in connection with sum and product of relative (p, q, t) L-th order, relative (p, q, t) L-th type, and relative (p, q, t) L-th weak type of entire functions with respect to another entire function where $p,q{\in}{\mathbb{N}}$ and $t{\in}{\mathbb{N}}{\cup}\{-1,0\}$.

• Journal of the Korean Mathematical Society
• /
• v.60 no.1
• /
• pp.195-212
• /
• 2023

In this paper, two weight conditions are introduced and the multiple weighted strong and weak characterizations of the multilinear fractional new maximal operator 𝓜_ϕ,β are established. Meanwhile, we introduce the ${\mathcal{S}}_{({\vec{p}},q),{\beta}}({\varphi})$ and $B_{({\vec{p}},q),{\beta}}({\varphi})$ conditions and obtain the characterization of two-weighted inequalities for 𝓜_ϕ,β. Finally, the relationships of the conditions ${\mathcal{S}}_{({\vec{p}},q),{\beta}}({\varphi}),\,{\mathcal{A}}_{({\vec{p}},q),{\beta}}({\varphi})$ and $B_{({\vec{p}},q),{\beta}}({\varphi})$ and the characterization of the one-weight $A_{({\vec{p}},q),{\beta}}({\varphi})$ are given.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.26 no.6
• /
• pp.1401-1411
• /
• 2016

The Multi-Prime RSA and the Prime Power RSA are the variants of the RSA cryptosystem, where the Multi-Prime RSA uses the modulus $N=p_1p_2{\cdots}p_r$ for distinct primes $p_1,p_2,{\cdots},p_r$ (r>2) and the Prime Power RSA uses the modulus $N=p^rq$ for two distinct primes p, q and a positive integer r(>1). This paper analyzes the security of these systems by using the technique given by Heninger and Shacham. More specifically, this paper shows that if the $2-2^{1/r}$ random portion of bits of $p_1,p_2,{\cdots},p_r$ is given, then $N=p_1p_2{\cdots}p_r$ can be factorized in the expected polynomial time and if the $2-{\sqrt{2}}$ random fraction of bits of p, q is given, then $N=p^rq$ can be factorized in the expected polynomial time. The analysis is then validated with experimental results for $N=p_1p_2p_3$, $N=p^2q$ and $N=p^3q$.

• Korean Journal of Head & Neck Oncology
• /
• v.24 no.1
• /
• pp.33-42
• /
• 2008

Head and neck squamous cell carcinoma(HNSCC) is notorious for its poor outcome and increasing incidence. But, the studies of cytogenetic analysis in HNSCC are relatively rare, because of difficulties in culturing solid tumor cells and complexity in chromosomal DNA abberations associated with the lesions. The purpose of this study is to evaluate the location of chromosomal aberrations in Korean HNSCC cell lines (SNU-1041, 1066, and 1076) with comparative genomic hybridization(CGH) and array based CGH(array-CGH). Chromosomal gains of 3q23-q27, 5p13-p15.3, 7p21-pter, 8q11.2-q12, 8q21.1-qter, 9q22-q34, 16q22-q24, and 20q11.2-qter, as well as chromosomal losses on 3p10-p14 were found in all 3 SNU cell lines. Losses on 3p15- p23, 4q22-q27, 4q31.3-qter, 6q14-q15, 7q31-q34, 8p12-pter, 18q21-q23, and 21q11.2-q12 were observed in 2 of 3 cell lines. In array-CGH, many genes were altered including gains of PIK3CA, MYC, EVI1, MAD1L1 genes and losses of SERPIN genes. These aberrations of gene and chromosome coincide with other results of study, generally. These data about the patterns of chromosomal aberrations could be a basic step for understanding more detailed genetic events in the carcinogenesis and also provide information for diagosis and treatment in HNSCC.

• Kyungpook Mathematical Journal
• /
• v.53 no.1
• /
• pp.117-124
• /
• 2013

We show that for 1 < $p$ < ${\infty}$, $k$, $m{\in}\mathbb{N}$, $n^{(k)}(l_p)=inf\{n^{(k)}(l^m_p):m{\in}\mathbb{N}\}$ and that for any positive measure ${\mu}$, $n^{(k)}(L_p({\mu})){\geq}n^{(k)}(l_p)$. We also prove that for every $Q{\in}P(^kl_p:l_p)$ (1 < $p$ < ${\infty}$), if $v(Q)=0$, then ${\parallel}Q{\parallel}=0$.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.2
• /
• pp.521-533
• /
• 2020

In this paper, we compute the Bergman kernel for Ω_p,q,r = {(z, z', w) ∈ ℂ² × Δ : |z|^2p < (1 - |z'|^2q)(1 - |w|²)^r}, where p, q, r > 0 in terms of multivariable hypergeometric series. As a consequence, we obtain the behavior of K_Ωp,q,r (z, 0, 0; z, 0, 0) when (z, 0, 0) approaches to the boundary of Ω_p,q,r.

• Molecules and Cells
• /
• v.24 no.1
• /
• pp.105-112
• /
• 2007

Most neuroblastoma cells have chromosomal aberrations such as gains, losses, amplifications and deletions of DNA. Conventional approaches like fluorescence in situ hybridization (FISH) or metaphase comparative genomic hybridization (CGH) can detect chromosomal aberrations, but their resolution is low. In this study we used array-based comparative genomic hybridization to identify the chromosomal aberrations in human neuroblastoma SH-SY5Y cells. The DNA microarray consisting of 4000 bacterial artificial chromosome (BAC) clones was able to detect chromosomal regions with aberrations. The SH-SY5Y cells showed chromosomal gains in 1q12~ q44 (Chr1:142188905-246084832), 7 (over the whole chro-mosome), 2p25.3~p16.3 (Chr2:18179-47899074), and 17q 21.32~q25.3 (Chr17:42153031-78607159), while chromosomal losses detected were the distal deletion of 1p36.33 (Chr1:552910-563807), 14q21.1~q21.3 (Chr14:37666271-47282550), and 22q13.1~q13.2 (Chr22:36885764-4190 7123). Except for the gain in 17q21 and the loss in 1p36, the other regions of gain or loss in SH-SY5Y cells were newly identified.

• Journal of the Korean Mathematical Society
• /
• v.44 no.4
• /
• pp.915-929
• /
• 2007

The main result of this paper is to construct the derivative twisted p-adic (h, q)-L-functions at s = 0. We obtain twisted version of Theorem 4 in [17]. We also obtain twisted (h, q)-extension of Proposition 1 in [3].

• Korean Journal of Microbiology
• /
• v.46 no.1
• /
• pp.46-51
• /
• 2010

Coenzyme Q10 (CoQ10) is an essential lipid-soluble component of membrane-bound electron transport chains. CoQ10 is involved in several aspects of cellular metabolism and is increasingly being used in therapeutic applications for several diseases. Despite the recent accomplishments in metabolic engineering of Escherichia coli for CoQ10 production, the production levels are not yet competitive with those by fermentation or isolation. So we tested several microorganisms obtained from the KCTC of Biological Resource Center to find novel sources of strain-development for CoQ10-production. Then we selected two strains, Paracoccus denitrificans (KCTC 2530) and Asaia siamensis (KCTC 12914), and tested to optimize the CoQ10 production conditions. Among the carbon sources tested, CoQ10 production was the highest when fructose was supplied about 4% concentration. Yeast extract produced the highest CoQ10 production about 2% concentration. The highest CoQ10 production was obtained at pH 6.0 for P. denitrificans and pH 8.0 for A. siamensis. And two strains showed the highest CoQ10 production at $30^{\circ}C$, but the highest DCW was obtained at $37^{\circ}C$. In the fed-batch culture, P. denitrificans yielded $14.34{\pm}0.473$ mg and A. siamensis yielded $12.53{\pm}0.231$ mg of final CoQ10 production.

• Journal of the Korean Mathematical Society
• /
• v.48 no.2
• /
• pp.431-447
• /
• 2011

We investigate the asymptotic behavior of positive solutions to the elliptic equation (0.1) ${\Delta}u+|x|^{l_1}u^p+|x|^{l_2}u^q=0$ in $\mathbb{R}^n$. We obtain a conclusion that, for n $\geq$ 3, -2 < $l_2$ < $l_1$ $\leq$ 0 and q > p > 1, any positive radial solution to (0.1) has the following properties: $lim_{r{\rightarrow}{\infty}}r^{\frac{2+l_1}{p-1}}\;u$ and $lim_{r{\rightarrow}0}r^{\frac{2+l_2}{q-1}}\;u$ always exist if $\frac{n+1_1}{n-2}$ < p < q, $p\;{\neq}\;\frac{n+2+2l_1}{n-2}$, $q\;{\neq}\;\frac{n+2+2l_2}{n-2}$. In addition, we prove that the singular positive solution of (0.1) is unique under some conditions.