• East Asian mathematical journal
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• v.16 no.1
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• pp.9-16
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• 2000

The authors aim at providing some identities involving the hypergeometric function via some known or presumably new formulas for the incomplete Beta and their associated functions. Some properties of the Beta and Gamma functions are also considered.

• Biomedical Science Letters
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• v.24 no.4
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• pp.305-310
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• 2018

Microglia are emerging as critical regulators of innate immune responses in AD and other neurodegenerative disorders, highlighting the importance of understanding their molecular and cellular mechanisms. We attempted to determine the role of crosstalk signaling between $IFN-{\gamma}$ and $TGF-{\beta}$ in $A{\beta}$ clearance by microglia cells. We used in vitro and in vivo mouse models that recapitulated acute and chronic aspects of microglial responses to $A{\beta}$ peptides. We showed that crosstalk signaling between $TGF-{\beta}$ and Smad2 was an important mediator of neuro-inflammation. These findings suggest that microglial $TGF-{\beta}$ activity enhances the pathological progression to AD. As $TGF-{\beta}$ displays broad regulatory effects on beneficial microglial functions, the activation of inflammatory crosstalk signaling between $TGF-{\beta}$ and Smad2 may be a promising strategy to restore microglial functions, halt the progression of $A{\beta}$-driven pathology, and prevent AD development.

• Kyungpook Mathematical Journal
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• v.29 no.2
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• pp.133-139
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• 1989

A generalization class $\sum_{P}$(${\alpha}$, ${\beta}$, ${\gamma}$) of certain meromorphic univalent functions with positive coefficients is introduced. The class $\sum_{P}$(${\alpha}$, ${\beta}$, ${\gamma}$) is a generalization of the class which was stuied by N.E. Cho, S.H. Lee and S. Qwa [1]. The object of the present paper is to prove some properties of functions in the class $\sum_{P}$(${\alpha}$, ${\beta}$, ${\gamma}$).

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1485-1502
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• 2014

The explicit formula for the hyperbolic metric ${\lambda}_{{\alpha},{\beta},{\gamma}}(z){\mid}dz{\mid}$ on the thrice-punctured sphere $\mathbb{P}{\backslash}\{0,1,{\infty}\}$ with singularities of order 0 < ${\alpha}$, ${\beta}$ < 1, ${\gamma}{\leq}1$, ${\alpha}+{\beta}+{\gamma}$ > 2 at 0, 1, ${\infty}$ was given by Kraus, Roth and Sugawa in [9]. In this article we investigate the asymptotic properties of the higher order derivatives of ${\lambda}_{{\alpha},{\beta},{\gamma}}(z)$ near the origin and give more precise descriptions for the asymptotic behavior of ${\lambda}_{{\alpha},{\beta},{\gamma}}(z)$.

• YAKHAK HOEJI
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• v.49 no.2
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• pp.168-173
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• 2005

Alzheimers disease (AD) is the most prevalent form of neurodegenerations associated with aging in the human population. This disease is characterized by the extracellular deposition of beta-amyloid (A ${\beta}$) peptide in cerebral plaques. The A ${\beta}$ peptide is derived from the ${\beta}$-amyloid precursor protein ( ${\beta}$APP). Photolytic processing of ${\beta}$APP by ${\beta}$-secretase(beta-site APP-cleaving enzyme, BASE) and ${\gamma}$-secretase generates the A ${\beta}$ peptide. Several lines of evidence support that A ${\beta}$-induced neuronal cell death is major mechanisms of development of AD. Accordingly, the ${\beta}$-and ${\gamma}$-secretase have been implicated to be excellent targets for the treatment of AD. We previously found that sesaminol glucosides have improving effect on memory functions through anti-oxidative mechanism. In this study, to elucidate possible other mechanism (inhibition of ${\beta}$-and ${\gamma}$-secretase) of sesaminol glucosides, we examined the improving effect of sesaminol glucosides in the scopolamine (1 mg/kg/mouse)-induced memory dysfunction using water maze test in the mice. Sesaminol glucosides (3.75, 7.5 mg/kg/6ml/day p.o., for 3 weeks) reversed the latency time, distance and velocity by scopolamine in dose dependent manner. Next, ${\beta}$-and ${\gamma}$-secretase activities were determined in different regions of brain. Sesaminol glucosides dose-dependently attenuated scopolamine-induced ${\beta}$-secretase activities in cortex and hippocampous and ${\gamma}$-secretase in cortex. This study therefore suggests that sesaminol glucosides may be a useful agent for prevention of the development or progression of AD, and its inhibitory effect on secretase may play a role in the improving action of sesaminol glucosides on memory function.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.661-677
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• 2015

In this paper, we consider the following Kirchhoff-type Schr$\ddot{o}$dinger system $$\{-\(a_1+b_1{\int}_{\mathbb{R^3}}{\mid}{\nabla}u{\mid}^2dx\){\Delta}u+{\gamma}V(x)u=\frac{2{\alpha}}{{\alpha}+{\beta}}{\mid}u{\mid}^{\alpha-2}u{\mid}v{\mid}^{\beta}\;in\;\mathbb{R}^3,\\-\(a_2+b_2{\int}_{\mathbb{R^3}}{\mid}{\nabla}v{\mid}^2dx\){\Delta}v+{\gamma}W(x)v=\frac{2{\beta}}{{\alpha}+{\beta}}{\mid}u{\mid}^{\alpha}{\mid}v{\mid}^{\beta-2}v\;in\;\mathbb{R}^3,\\u,v{\in}H^1(\mathbb{R}^3),$$ where $a_i$ and $b_i$ are positive constants for i = 1, 2, ${\gamma}$ > 0 is a parameter, V (x) and W(x) are nonnegative continuous potential functions. By applying the Nehari manifold method and the concentration-compactness principle, we obtain the existence and concentration of ground state solutions when the parameter ${\gamma}$ is sufficiently large.

• Honam Mathematical Journal
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• v.41 no.2
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• pp.381-390
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• 2019

In this paper, we introduce interesting subclasses ${\mathcal{H}}^{p,q,{\beta},{\alpha}}_{{\sigma}B}$ and ${\mathcal{H}}^{p,q,{\beta}}_{{\sigma}B}({\gamma})$ of bi-univalent functions by (p, q)-derivative operator. Furthermore, we find upper bounds for the second and third coefficients for functions in these subclasses. The results presented in this paper would generalize and improve some recent works of several earlier authors.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.911-927
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• 2019

Let $\mathscr{B}^{{\eta},{\mu}}_{p,n}\;({\alpha});\;({\eta},{\mu}{\in}{\mathbb{R}},\;n,\;p{\in}{\mathbb{N}})$ denote all functions f class in the unit disk ${\mathbb{U}}$ as $f(z)=z^p+\sum_{k=n+p}^{\infty}a_kz^k$ which satisfy: $$\|\[{\frac{f^{\prime}(z)}{pz^{p-1}}}\]^{\eta}\;\[\frac{z^p}{f(z)}\]^{\mu}-1\| <1-{\frac{\alpha}{p}};\;(z{\in}{\mathbb{U}},\;0{\leq}{\alpha}<p)$$. And $\mathscr{M}^{{\eta},{\mu}}_{p,n}\;({\alpha})$ indicates all meromorphic functions h in the punctured unit disk $\mathbb{U}^*$ as $h(z)=z^{-p}+\sum_{k=n-p}^{\infty}b_kz^k$ which satisfy: $$\|\[{\frac{h^{\prime}(z)}{-pz^{-p-1}}}\]^{\eta}\;\[\frac{1}{z^ph(z)}\]^{\mu}-1\|<1-{\frac{\alpha}{p}};\;(z{\in}{\mathbb{U}},\;0{\leq}{\alpha}<p)$$. In this paper several sufficient conditions for some classes of functions are investigated. The authors apply Jack's Lemma, to obtain this conditions. Furthermore, sufficient conditions for strongly starlike and convex p-valent functions of order ${\gamma}$ and type ${\beta}$, are also considered.

• Molecules and Cells
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• v.38 no.10
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• pp.866-875
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• 2015

COPI vesicles are essential to the retrograde transport of proteins in the early secretory pathway. The COPI coatomer complex consists of seven subunits, termed ${\alpha}-$, ${\beta}-$, ${\beta}^{\prime}-$, ${\gamma}-$, ${\delta}-$, ${\varepsilon}-$, and ${\zeta}$-COP, in yeast and mammals. Plant genomes have homologs of these subunits, but the essentiality of their cellular functions has hampered the functional characterization of the subunit genes in plants. Here we have employed virus-induced gene silencing (VIGS) and dexamethasone (DEX)-inducible RNAi of the COPI subunit genes to study the in vivo functions of the COPI coatomer complex in plants. The ${\beta}^{\prime}-$, ${\gamma}-$, and ${\delta}$-COP subunits localized to the Golgi as GFP-fusion proteins and interacted with each other in the Golgi. Silencing of ${\beta}^{\prime}-$, ${\gamma}-$, and ${\delta}$-COP by VIGS resulted in growth arrest and acute plant death in Nicotiana benthamiana, with the affected leaf cells exhibiting morphological markers of programmed cell death. Depletion of the COPI subunits resulted in disruption of the Golgi structure and accumulation of autolysosome-like structures in earlier stages of gene silencing. In tobacco BY-2 cells, DEX-inducible RNAi of ${\beta}^{\prime}$-COP caused aberrant cell plate formation during cytokinesis. Collectively, these results suggest that COPI vesicles are essential to plant growth and survival by maintaining the Golgi apparatus and modulating cell plate formation.

• Kyungpook Mathematical Journal
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• v.55 no.3
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• pp.695-703
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• 2015

Several interesting and useful extensions of some familiar special functions such as Beta and Gauss hypergeometric functions and their properties have, recently, been investigated by many authors. Motivated mainly by those earlier works, we establish some fractional integral formulas involving the extended generalized Gauss hypergeometric function by using certain general pair of fractional integral operators involving Gauss hypergeometric function $_2F_1$, Some interesting special cases of our main results are also considered.