• International Journal of Oral Biology
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• v.33 no.1
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• pp.1-5
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• 2008

Adenosine 5'-triphosphate (ATP) is an important extracellular signaling molecule which is involved in a variety of physiological responses in many different tissues and cell types, by acting at P2 receptors, either ionotropic (P2X) or G protein-coupled metabotropic receptors (P2Y). P2X receptors have seven isoforms designated as $P2X_{1^-}P2X_7$. In this study, we investigated the electrophysiological and pharmacological properties of rat $P2X_{1^-}P2X_4$ currents by using whole-cell patch clamp technique in a heterologous expression system. When ATP-induced currents were analyzed in human embryonic kidney (HEK293) cells following transient transfection of rat $P2X_{1^-}P2X_4$, the currents showed different pharmacological and electrophysiological properties. ATP evoked inward currents with fast activation and fast desensitization in $P2X_{^1-}$ or $P2X_{3^-}$ expressing HEK293 cells, but in $P2X_{2^-}$ or $P2X_{4^-}$ expressing HEK293 cells, ATP evoked inward currents with slow activation and slow desensitization. While PPADS and suramin inhibited $P2X_2$ or $P2X_3$ receptor-mediated currents, they had little effects on $P2X_4$ receptor-mediated currents. Ivermectin potentiated and prolonged $P2X_4$ receptor-mediated currents, but did not affect $P2X_2$ or $P2X_3$ receptor-mediated currents. We suggest that distinct pharmacological and electrophysiological properties among P2X receptor subtypes would be a useful tool to determine expression patterns of P2X receptors in the nervous system including trigeminal sensory neurons and microglia.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.429-441
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• 2020

Let M(X, Y) denote the space of multipliers from X to Y, where X and Y are analytic function spaces. As we known, for Dirichlet-type spaces 𝓓_α^p, M(𝓓_p-1^p, 𝓓_q-1^q) = {0}, if p ≠ q, 0 < p, q < ∞. If 0 < p, q < ∞, p ≠ q, 0 < s < 1 such that p + s, q + s > 1, then M(𝓓_p-2+s^p, 𝓓_q-2+s^q) = {0}. However, X ∩ 𝓓_p-1^p ⊆ X ∩ 𝓓_q-1^q and X ∩ 𝓓_p-2+s^p ⊆ X ∩ 𝓓_q-2+s^p whenever X is a subspace of the Bloch space 𝓑 and 0 < p ≤ q < ∞. This says that the set of multipliers M(X ∩ 𝓓 _p-2+s^p, X∩𝓓_q-2+s^q) is nontrivial. In this paper, we study the multipliers M(X ∩ 𝓓_p-2+s^p, X ∩ 𝓓_q-2+s^q) for distinct classical subspaces X of the Bloch space 𝓑, where X = 𝓑, BMOA or 𝓗^∞.

• Honam Mathematical Journal
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• v.31 no.3
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• pp.369-380
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• 2009

Let $X,X_1,X_2,\;{\cdots}$ be identically distributed and negatively associated random variables with mean zeros and positive, finite variances. We prove that, if $E{\mid}X_1{\mid}^r$ < ${\infty}$, for 1 < p < 2 and r > $1+{\frac{p}{2}}$, and $lim_{n{\rightarrow}{\infty}}n^{-1}ES^2_n={\sigma}^2$ < ${\infty}$, then $lim_{{\epsilon}{\downarrow}0}{\epsilon}^{{2(r-p}/(2-p)-1}{\sum}^{\infty}_{n=1}n^{{\frac{r}{p}}-2-{\frac{1}{p}}}E\{{{\mid}S_n{\mid}}-{\epsilon}n^{\frac{1}{p}}\}+={\frac{p(2-p)}{(r-p)(2r-p-2)}}E{\mid}Z{\mid}^{\frac{2(r-p)}{2-p}}$, where $S_n\;=\;X_1\;+\;X_2\;+\;{\cdots}\;+\;X_n$ and Z has a normal distribution with mean 0 and variance ${\sigma}^2$.

• Journal of Korean Society of Forest Science
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• v.58 no.1
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• pp.48-53
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• 1982

This experiment was carried out to distinguish between picea abies (L.) Karsten and Picea koraiensis Nak by the method of discriminant analysis which is used the metrical continuous characteristic on current inorphological plant taxanomy. The results are summarized as follows 1) The discriminant function and discriminant region from the experiment are Z(x)=Z($x_1,\;x_2$)=$0.000379x_1+0.004354x_2-0.311061$ or Z(x)=Z($x_1,\;x_2$=$0.000379(x_1-60.442800)+0.004354(x_2-66.185100)$, $$R_1=(x{\mid}0.000379x_1+0.004354x_2-0.311061{\geq_-}0)$$, $R_2$=($x{\mid}0.000379x_1+0.004354x_2-0.311061$ <0). 2) The probability of misclassification based on the above discriminant region is P($2{\mid}1$)=$P(1{\mid}2)$=0.444 therefore the probability of simultaneous misclassification of P($2{\mid}1$) and $P(1{\mid}2)$ is about 44.4%. 3) the probability of misclassification by the discriminant function resulted from the experiment if recorded as high but it is thought that there is a considerable meaning to perceive the probability of confidence about the discrimination better than its precision.

• Biomedical Science Letters
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• v.13 no.3
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• pp.197-206
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• 2007

P2X receptors are membrane-bound ion channels that conduct $Na^+,\;K^+$, and $Ca^{2+}$ in response to ATP and its analogs. There are seven subunits identified so far ($P2X_1-P2X_7$). $P2X_2$ receptors are known to be expressed in a wide range of organs including brains and adrenal grands. PC12 cells are originated from adrenal grand and differentiated by nerve growth factor or pituitary adenylate cyclase activating poly peptide (PACAP). Previous studies indicate that $P2X_2$ receptor activation in PC12 cells couples to $Ca^{2+}-dependent$ release of catecholamine and ATP. It is known that acidic pH potentiates ATP currents at $P2X_2$ receptors. This leads to a hypothesis that $P2X_2$ receptors may play an important role in PC12 cell differentiation, one of the characteristics of which is neurite outgrowth, induced by the hormones under lower pH. In the present study, we isolated several clones which potentiate neurite outgrowth by PACAP in acidic pH (6.8), but not in alkaline pH (7.6). RT-PCR and electrophysiology data indicate that these clones express only functional $P2X_2$ receptors in the absence or presence of PACAP for 3 days. Potentiation of neurite outgrowth resulted from PACAP (100 nM) in acidic pH is inhibited by the two P2X receptor antagonists, suramin and PPADS ($100\;{\mu}M)$ each), and exogenous exprerssion of ATP-binding mutant $P2X_2$ receptor subunit ($P2X_2[K69A]$). However, acid sensing ion channels (ASICs) are not involved in PACAP-induced neurite outgrowth potentiation in lower pH since treatments of an inhibitor of ASICs, amyloride ($10\;{\mu}M$), did not give any effects to neurite extension. The vesicular proton pump ($H^+-ATPase$) inhibitor, bafilomycin (100 nM), reduced neurite extension indicating that ATP release resulted from $P2X_2$ receptor activation in PC12 cells is needed for neurite outgrowth. These were confirmed by activation of mitogen activated protein kinases, such as ERKs and p38. These results suggest roles of ATP and $P2X_2$ receptors in hormone-induced cell differentiation or neuronal synaptogenesis in local acidic environments.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1045-1061
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• 2023

Using variational methods, Krasnoselskii's genus theory and symmetric mountain pass theorem, we introduce the existence and multiplicity of solutions of a parameteric local equation. At first, we consider the following equation $$\{-div[a(x,{\mid}{\nabla}u{\mid}){\nabla}u]\,=\,{\mu}(b(x){\mid}u{\mid}^{s(x)-2}-{\mid}u{\mid}^{r(x)-2})u\;in\;{\Omega},\\u\,=0\,on\;{\partial}{\Omega},$$ where Ω⊆ ℝ^N is a bounded domain, µ is a positive real parameter, p, r and s are continuous real functions on ${\bar{\Omega}}$ and a(x, ξ) is of type |ξ|^p(x)-2. Next, we study boundedness and simplicity of eigenfunction for the case a(x, |∇u|)∇u = g(x)|∇u|^p(x)-2∇u, where g ∈ L^∞(Ω) and g(x) ≥ 0 and the case $a(x,\,{\mid}{\nabla}u{\mid}){{\nabla}u}\,=\,(1\,+\,{\nabla}u{\mid}^2)^{\frac{p(x)-2}{2}}{\nabla}u$ such that p(x) ≡ p.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.801-812
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• 2023

In this paper, we investigate the superstability for the p-power-radical sine functional equation $$f\(\sqrt[p]{\frac{x^p+y^p}{2}}\)^2-f\(\sqrt[p]{\frac{x^p-y^p}{2}}\)^2=f(x)f(y)$$ from an approximation of the p-power-radical functional equation: $$f(\sqrt[p]{x^p+y^p})-f(\sqrt[p]{x^p-y^p})={\lambda}g(x)h(y),$$ where p is an odd positive integer and f, g, h are complex valued functions. Furthermore, the obtained results are extended to Banach algebras.

• Honam Mathematical Journal
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• v.42 no.3
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• pp.569-576
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• 2020

An element x ∈ E is called a norming point of P ∈ P(ⁿE) if ║x║ = 1 and |P(x)| = ║P║. For P ∈ P(ⁿE), we define Norm(P) = {x ∈ E : x is a norming point of P}. Norm(P) is called the norming set of P. We classify Norm(P) for P ∈ 𝒫(²𝑙²_∞).

• East Asian mathematical journal
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• v.31 no.1
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• pp.103-107
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• 2015

We use some known contiguous function relations for $_2F_1$ to show how simply the following three recurrence relations for Jacobi polynomials $P_n^{({\alpha},{\beta)}(x)$: (i) $({\alpha}+{\beta}+n)P_n^{({\alpha},{\beta})}(x)=({\beta}+n)P_n^{({\alpha},{\beta}-1)}(x)+({\alpha}+n)P_n^{({\alpha}-1,{\beta})}(x);$ (ii) $2P_n^{({\alpha},{\beta})}(x)=(1+x)P_n^{({\alpha},{\beta}+1)}(x)+(1-x)P_n^{({\alpha}+1,{\beta})}(x);$ (iii) $P_{n-1}^{({\alpha},{\beta})}(x)=P_n^{({\alpha},{\beta}-1)}(x)+P_n^{({\alpha}-1,{\beta})}(x)$ can be established.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.361-372
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• 2006

In this paper, we consider the multi-point boundary value problems for one-dimensional p-Laplacian at resonance: $({\phi}_p(x'(t)))'=f(t,x(t),x'(t))$, subject to the boundary value conditions: ${\phi}_p(x'(0))={\sum}^{n-2}_{i=1}{\alpha}_i{\phi}_p(x'({\epsilon}i)),\;{\phi}_p(x'(1))={\sum}^{m-2}_{i=1}{\beta}_j{\phi}_p(x'({\eta}_j))$ where ${\phi}_p(s)=/s/^{p-2}s,p>1,\;{\alpha}_i(1,{\le}i{\le}n-2){\in}R,{\beta}_j(1{\le}j{\le}m-2){\in}R,0<{\epsilon}_1<{\epsilon}_2<...<{\epsilon}_{n-2}1,\;0<{\eta}1<{\eta}2<...<{\eta}_{m-2}<1$, By applying the extension of Mawhin's continuation theorem, we prove the existence of at least one solution. Our result is new.