• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.689-707
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• 2017

In this paper, a boundary version of Schwarz lemma is investigated. We take into consideration a function f(z) holomorphic in the unit disc and f(0) = 0, f'(0) = 1 such that ${\Re}f^{\prime}(z)$ > ${\frac{1-{\alpha}}{2}}$, -1 < ${\alpha}$ < 1, we estimate a modulus of the second non-tangential derivative of f(z) function at the boundary point $z_0$ with ${\Re}f^{\prime}(z_0)={\frac{1-{\alpha}}{2}}$, by taking into account their first nonzero two Maclaurin coefficients. Also, we shall give an estimate below ${\mid}f^{{\prime}{\prime}}(z_0){\mid}$ according to the first nonzero Taylor coefficient of about two zeros, namely z = 0 and $z_1{\neq}0$. The sharpness of these inequalities is also proved.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.31-48
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• 2007

The paper deals with the solution of some fractional partial differential equations obtained by substituting modified Riemann-Liouville derivatives for the customary derivatives. This derivative is introduced to avoid using the so-called Caputo fractional derivative which, at the extreme, says that, if you want to get the first derivative of a function you must before have at hand its second derivative. Firstly, one gives a brief background on the fractional Taylor series of nondifferentiable functions and its consequence on the derivative chain rule. Then one considers linear fractional partial differential equations with constant coefficients, and one shows how, in some instances, one can obtain their solutions on bypassing the use of Fourier transform and/or Laplace transform. Later one develops a Lagrange method via characteristics for some linear fractional differential equations with nonconstant coefficients, and involving fractional derivatives of only one order. The key is the fractional Taylor series of non differentiable function $f(x+h)=E_{\alpha}(h^{\alpha}{D_x^{\alpha})f(x)$.

• Proceedings of the Korean Society of Applied Pharmacology
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• 2008.04a
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• pp.23-30
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• 2008

Mitochondria biogenesis requires a coordination of two genomes, nuclear DNA (nDNA) and mitochondrial DNA (mtDNA). Disruption of mitochondria function leads to a loss of mitochondrial membrane potential and ATP generating capacity and consequently results in chronic degenerative diseases including insulin resistance, metabolic syndrome and neurodegenerative diseases. Although PPAR-${\gamma}$ coactivator-$1{\alpha}$ (PGC-$1{\alpha}$) was discovered as a central regulator of mitochondria biogenesis and a transcriptional co-activator of nuclear respiratory factor (NRF) and mitochondrial transcription factor A (Tfam), the expressions of PGC-$1{\alpha}$, NRF and Tfam were not significantly altered in tissues showing abnormal mitochondria functions. This observation suggests that there should be another regulator(s) for mitochondria function. Here, we demonstrate microRNAs (miRNAs) can modulate mitochondria function. Overexpression of microRNA dissipated mitochondrial membrane potential and increased ROS production in vitro and in vivo. It will be discussed the target of microRNA and its role in metabolic syndrome.

• East Asian mathematical journal
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• v.35 no.1
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• pp.67-75
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• 2019

We investigate the averaging value of a random sampling of a Dirichlet series with some condition using Poisson distribution. Our result is the following: Let $L(s)={\sum}^{\infty}_{n=1}{\frac{a_n}{n^s}}$ be a Dirichlet series that converges absolutely for Re(s) > 1. If $X_t$ is an increasing random sampling with Poisson distribution and there exists a number $0<{\alpha}<{\frac{1}{2}}$ such that ${\sum}_{n{\leq}u}a_n{\ll}u^{\alpha}$, then we have $${\mathbb{E}}L(1/2+iX_t)=O(t^{\alpha}{\sqrt{{\log}t}})$$, for all sufficiently large t in ${\mathbb{R}}$. As a result, we get the behaviour of $L({\frac{1}{2}}+it)$ such that L is a Dirichlet L-function or a modular L-function, when t is sampled by the Poisson distribution.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.4
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• pp.763-769
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• 2012

In this paper, we define the strong $M_{\alpha}$-integral of Banach-valued functions and investigate some properties of the strong $M_{\alpha}$-integral.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.115-125
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• 2012

In this paper, we define the $M_{\alpha}$-integral of Banach-valued functions and investigate some properties of the $M_{\alpha}$-integral.

• Proceedings of the Korean Society of Life Science Conference
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• 2002.12a
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• pp.13-19
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• 2002

To elucidate the regulatory mechanism for expression of sialyl-glycoconjugates and their biological functions, ninetheen sialyltransferase cDNAs including eleven by our group or co-works have been cloned and characterized so far. The cloned sialyltransferases are classified into four families according to the carbohydrate linkages they synthesize: ${\alpha}2,3-sialyltransferase$ (ST3Gal I-VI), ${\alpha}$ 2,6-sialyltransferase (ST6Gal I), GalNAc ${\alpha}$ 2,6-sialyltransferase (ST6GalNAc I-VI), and ${\alpha}2,8-sialyltransferase$ (ST8Sia I-VI). Each of the sialyltransferase genes is differentially expressed in a tissue-, cell type-, and stage-specific manner. These enzymes differ in their substrate specificity and various biochemical parameters. However, enzymatic analysis conducted in vitro with recombinant enzyme revealed that one linkage can be synthesized by multiple enzymes. We present here an overview of structure and function of sialyltransferases performed by our group and co-works. Genomic structures and transcriptional regulation of two kinds of human sialyltransferase gene are also presented.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.443-455
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• 2014

Atanassov introduced the irrational factor function and the strong restrictive factor function, which he defined as $I(n)=\displaystyle\prod_{p^{\alpha}||n}^{}p^{1/{\alpha}}$ and $R(n)=\displaystyle\prod_{p^{\alpha}||n}^{}p^{{\alpha}-1}$ in [2] and [3]. Various properties of these functions have been investigated by Alkan, Ledoan, Panaitopol, and the authors. In the prequel, we expanded these functions to a class of elements of $PSL_2(\mathbb{Z})$, and studied some of the properties of these maps. In the present paper we generalize the previous work by introducing real moments and considering a larger class of maps. This allows us to explore new properties of these arithmetic functions.

• Communications for Statistical Applications and Methods
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• v.16 no.3
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• pp.549-556
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• 2009

Let $\{(X_{ni}|1{\leq}i{\leq}n,\;n{\geq}1)\}$ be an array of rowwise negatively associated random variables. In this paper we discuss $n^{{\alpha}p-2}h(n)max_{1{\leq}k{\leq}n}|{\sum}_{i=1}^kX_{ni}|/n^{\alpha}{\rightarrow}0$ completely as $n{\rightarrow}{\infty}$ under not necessarily identically distributed with suitable conditions for ${\alpha}$>1/2, 0${\alpha}p{\geq}1$ and a slowly varying function h(x)>0 as $x{\rightarrow}{\infty}$. In addition, we obtain the complete convergence of moving average process based on negative association random variables which extends the result of Zhang (1996).

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.113-119
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• 2010

If f is M-harmonic and integrable with respect to a weighted radial measure $\upsilon_{\alpha}$ over the unit ball $B_n$ of $\mathbb{C}^n$, then $\int_{B_n}(f\circ\psi)d\upsilon_{\alpha}=f(\psi(0))$ for every $\psi{\in}Aut(B_n)$. Equivalently f is fixed by the weighted Berezin transform; $T_{\alpha}f = f$. In this paper, we show that if a function f defined on $B_n$ satisfies $R(f\circ\phi){\in}L^{\infty}(B_n)$ for every $\phi{\in}Aut(B_n)$ and Sf = rf for some |r|=1, where S is any convex combination of the iterations of $T_{\alpha}$'s, then f is M-harmonic.