• International Journal of Oral Biology
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• 제33권1호
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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.

• 대한수학회보
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• 제57권2호
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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^∞.

• 호남수학학술지
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• 제31권3호
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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 ${\sigma}^2$.

• 한국산림과학회지
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• 제58권1호
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• pp.48-53
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• 1982

현행(現行)의 형태학적수목분류법(形態學的樹木分類法)에 계획적특성(計劃的特性)을 이용(利用)한 소위(所謂) 판별분석법(判別分析法)에 의(依)할 독일(獨逸)가문비(Picea abies(L.) Karsten)와 종비나무(樅榧)(Picea koraiensis Nak.)와의 분류시험(分類試驗)을 실시(實施)하고 그 결과(結果)를 다음과 같이 요약(要約)한다. 1) 본(本) 시험(試驗)에서 얻은 판별식(判別式)과 판별영역(判別領域)은, Z(x)=Z($x_1,\;x_2$)=$0.000379x_1+0.004354x_2-0.311061$ 또는 Z(x)=Z($x_1,\;x_2$)=$0.000379(x_1-60.4428)+0.004354(x_2-66.1851)$, $$R_1=\{x{\mid}0.000379x_1+0.004354x_2-0.311061{\geq_-}0\}$$, $R_2$={$x{\mid}0.000379x_1+0.004354x_2-0.311061$ <0)} 또는 $$R_1=\{x{\mid}0.000379(x_1-60.4428)+0.004354(x_2-66.1851){\geq_-}0%\}$$, $R_2$={$x{\mid}0.000379(x_1-60.4428)+0.004354(x_2-66.1851)$ <0}. 2) 위의 판별영역(判別領域)에 의(依)한 오판율(誤判率)(오분류확율(誤分類確率))은, P($2{\mid}1$)=($P1{\mid}2$)=0.444로서, P($2{\mid}1$)와 P($P1{\mid}2$)의 동시오판율(同時誤判率)은 P=44.4%. 3) 본(本) 시험(試驗)에서 얻은 판별식(判別式)에 의(依)한 오판율(誤判率)은 상당(相當)히 높게 나타났지만 그의 정도(精度)보다는 오히려 판별(判別)에 대(對)한 신뢰도(信賴度)를 알 수 있다는데 보다 큰 의의(意義)가 있는 것으로 사료(思料)된다.

• 대한의생명과학회지
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• 제13권3호
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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.

• 대한수학회논문집
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• 제38권4호
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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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• 제28권3호
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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.

• 호남수학학술지
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• 제42권3호
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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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• 제31권1호
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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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• 제22권1_2호
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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.