• Bulletin of the Korean Mathematical Society
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• 제39권1호
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• pp.141-151
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• 2002

Let X and Y be real Banach spaces and $\varepsilon$, p $\geq$ 0. A mapping T between X and Y is called an ($\varepsilon$, p)-isometry if ｜∥T(x)-T(y)∥-∥x-y∥｜$\leq$ $\varepsilon$∥x-y∥$^{p}$ for x, y$\in$X. Let H be a real Hilbert space and T : H longrightarrow H an ($\varepsilon$, p)-isometry with T(0) = 0. If p$\neq$1 is a nonnegative number, then there exists a unique isometry I : H longrightarrow H such that ∥T(x)-I(y)∥$\leq$ C($\varepsilon$)(∥x∥$^{ 1+p)/2}$+∥x∥$^{p}$ ) for all x$\in$H, where C($\varepsilon$) longrightarrow 0 as $\varepsilon$ longrightarrow 0.

• Journal of the Mineralogical Society of Korea
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• 제3권1호
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• pp.7-17
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• 1990

화산 유리질 암석을 출발 물질로 사용하여 저온 ($80^{\circ}C$)에서 수열 처리하여 Na-P Na-X 및 Na-A 제올라이트를 합성하였다. 합성과정은 (1) 유리질 분말 시료와 알칼리 용액과의 용해.변질 반응에 의한 1차적인 Na-P의 합성 방식과 (2) 여기서 잔류된 규산질 모액에 Al(OH)3나 NaAlO2의 수용액을 공급하여 보다 고순도의 Na-P, Na-X 및 Na-A를 효과적으로 합성할 수 있었다. 원암의 암상과 조성은 제올라이트들의 화학 조성과 순도 및 백색도같은 물리적 특성에는 영향을 주지만, 합성된 제올라이트의 광물종을 규제하는 주된 요인은 아닌 것으로 해석된다. 합성된 제올라이트의 광물상은 반응 용액의 pH, Al(OH)4 및 Na+에 대한 농도 조건에 주로 의존되는 경향을 나타낸다. 또한 화산 유리질 암석을 제올라이트 합성원료로 활용하는 데에 있어서 (2)와 같음 합성 방안이 보완적으로 시행되면 그 생산성과 효율성을 제고시킬 수 있을 것으로 여겨진다.

• Bulletin of the Korean Mathematical Society
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• 제58권3호
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• pp.659-668
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• 2021

Let R be a semiprime ring with maximal right ring of quotients Q_mr(R), and let n₁, n₂, …, n_k be k fixed positive integers. Suppose that R is (n₁+n₂+⋯+n_k)!-torsion free, and that f : 𝜌 → Q_mr(R) is an additive map, where 𝜌 is a nonzero right ideal of R. It is proved that if [[…[f(x), x^n₁], …], x^n_k] = 0 for all x ∈ 𝜌, then [f(x), x] = 0 for all x ∈ 𝜌. This gives the result of Beidar et al. [2] for semiprime rings. Moreover, it is also proved that if R is p-torsion, where p is a prime integer with p = Σ^k_i=1 n_i and if f : R → Q_mr(R) is an additive map satisfying [[…[f(x), x^n₁], …], x^n_k] = 0 for all x ∈ R, then [f(x), x] = 0 for all x ∈ R.

• Bulletin of the Korean Mathematical Society
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• 제54권6호
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• pp.2165-2182
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• 2017

Let G be a group and $\mathbb{C}$ the field of complex numbers. Suppose ${\sigma}:G{\rightarrow}G$ is an endomorphism satisfying ${{\sigma}}({{\sigma}}(x))=x$ for all x in G. In this paper, we first determine the central solution, f : G or $G{\times}G{\rightarrow}\mathbb{C}$, of the functional equation $f(xy)+f({\sigma}(y)x)=2f(x)+2f(y)$ for all $x,y{\in}G$, which is a variant of the quadratic functional equation. Using the central solution of this functional equation, we determine the general solution of the functional equation f(pr, qs) + f(sp, rq) = 2f(p, q) + 2f(r, s) for all $p,q,r,s{\in}G$, which is a variant of the equation f(pr, qs) + f(ps, qr) = 2f(p, q) + 2f(r, s) studied by Chung, Kannappan, Ng and Sahoo in [3] (see also [16]). Finally, we determine the solutions of this equation on the free groups generated by one element, the cyclic groups of order m, the symmetric groups of order m, and the dihedral groups of order 2m for $m{\geq}2$.

• Bulletin of the Korean Mathematical Society
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• 제56권1호
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• pp.1-12
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• 2019

For a finite poset $P=(X,{\preceq})$ the fractional weak discrepancy of P, denoted $wd_F(P)$, is the minimum value t for which there is a function $f:X{\rightarrow}{\mathbb{R}}$ satisfying (1) $f(x)+1{\leq}f(y)$ whenever $x{\prec}y$ and (2) ${\mid}f(x)-f(y){\mid}{\leq}t$ whenever $x{\parallel}y$. In this paper, we determine the range of the fractional weak discrepancy of (M, 2)-free posets for $M{\geq}5$, which is a problem asked in [9]. More precisely, we showed that (1) the range of the fractional weak discrepancy of (M, 2)-free interval orders is $W=\{{\frac{r}{r+1}}:r{\in}{\mathbb{N}}{\cup}\{0\}\}{\cup}\{t{\in}{\mathbb{Q}}:1{\leq}t<M-3\}$ and (2) the range of the fractional weak discrepancy of (M, 2)-free non-interval orders is $\{t{\in}{\mathbb{Q}}:1{\leq}t<M-3\}$. The result is a generalization of a well-known result for semiorders and the main result for split semiorders of [9] since the family of semiorders is the family of (4, 2)-free posets.

• International Journal of Oral Biology
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• 제36권3호
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• pp.143-148
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• 2011

The present study investigated the role of peripheral P2X receptors in inflammatory pain transmission in the orofacial area in rats. Experiments were carried out on male Sprague-Dawley rats weighing 220 to 280 g. Formalin (5%, 50 ${\mu}L$) and complete Freund's adjuvant (CFA, 25 ${\mu}L$) was applied subcutaneously to the vibrissa pad to produce inflammatory pain. TNP-ATP, a $P2X_{2,2/3,4}$ receptor antagonist, or OX-ATP, a $P2X_7$ receptor antagonist, was then injected subcutaneously at 20 minutes prior to formalin injection. One of the antagonists was administered subcutaneously at three days after CFA injection. The subcutaneous injection of formalin produced a biphasic nociceptive behavioral response. Subcutaneous pretreatment with TNP-ATP (80, 160 or 240 ${\mu}g$) significantly suppressed the number of scratches in the second phase produced by formalin injection. The subcutaneous injection of 50 ${\mu}g$ of OX-ATP also produced significant antinociceptive effects in the second phase. Subcutaneous injections of CFA produced increases in mechanical and thermal hypersensitivity. Both TNP-ATP (480 ${\mu}g$) and OX-ATP (100 ${\mu}g$) produced an attenuation of mechanical hypersensitivity. However, no change was observed in thermal hypersensitivity after the injection of either chemical. These results suggest that the blockade of peripheral P2X receptors is a potential therapeutic approach to the onset of inflammatory pain in the orofacial area.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.829-842
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• 2009

Let {$X_{ni}|1\;{\le}\;i\;{\le}\;n$, $n\;{\ge}\;1$} be an array of rowwise negatively associated random variables and let $\alpha$ > 1/2, 0 < p < 2 ${\alpha}p\;{\ge}\;1$. In this paper we discuss $n^{{\alpha}p-2}h(n)$ max $_{1\;{\le}\;k{\le}n}\;|\;{\sum}^k_{i=1}\;X_{ni}|/n^{\alpha}\;{\to}\;0$ completely as $n\;{\to}\;{\infty}$ under not necessarily identically distributed with a suitable conditions and h(x) > 0 is a slowly varying function as $x\;{\to}\;{\infty}$. In addition, we obtained that $n^{{\alpha}p-2}h(n)$ max $_{1\;{\le}\;k{\le}n}\;|\;{\sum}^k_{i=1}\;X_{ni}|/n^{\alpha}\;{\to}\;0$ completely as $n\;{\to}\;{\infty}$ if and only if $E|X_{11}|^ph(|X_{11}|^{1/\alpha})\;<\;{\infty}$ and $EX_{11}\;=\;0$ under identically distributed case and some corollaries are obtained.

• Nonlinear Functional Analysis and Applications
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• 제29권2호
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• pp.333-360
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• 2024

This paper is concerned with the radial solutions of a nonlinear elliptic equation ∆_pu + |x|^𝑙₁ |u|^q₁-1 u + |x|^𝑙₂ |u|^q₂-1 u = 0, x ∈ ℝ^N, where p > 2, N ≥ 1, q₂ > q₁ ≥ 1, -p < 𝑙₂ < 𝑙₁ ≤ 0 and -N < 𝑙₂ < 𝑙₁ ≤ 0. We prove the existence of global solutions, we give their classification and we present the explicit behavior of positive solutions near the origin and infinity.

• The Korean Journal of Physiology and Pharmacology
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• 제14권5호
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• pp.311-316
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• 2010

It is well-known that electrical field stimulation (EFS)-induced contraction is mediated by a cholinergic mechanism and other neurotransmitters. NO, ATP, calcitonin gene-related peptide (CGRP), and substance P are released by EFS. To investigate the purinergic mechanism involved in the EFS-induced contraction, purinegic receptors antagonists were used. Suramine, a non-selective P2 receptor antagonist, reduced the contraction induced by EFS. NF023 ($10^{-7}{\sim}10^{-4}M$), a selective P2X antagonist, inhibited the contraction evoked by EFS. Reactive blue ($10^{-6}{\sim}10^{-4}M$), selective P2Y antagonist, also blocked the contraction in a dose-dependent manner. In addition, P2X agonist ${\alpha}$,${\beta}$-methylene 5'-adenosine triphosphate (${\alpha}{\beta}MeATP$, $10^{-7}{\sim}10^{-5}M$) potentiated EFS-induced contraction in a dose-dependent manner. P2Y agonist adenosine 5'-[${\beta}$-thio]diphosphate trilithium salt ($ADP{\beta}S$, $10^{-7}{\sim}10^{-5}M$) also potentiated EFS-induced contractions in a dose-dependent manner. Ecto-ATPase activator apyrase (5 and 10 U/ml) reduced EFS-induced contractions. Inversely, 6-N,$N$-diethyl-D-${\beta}$,${\gamma}$- dibromomethylene 5'-triphosphate triammonium (ARL 67156, $10^{-4}M$) increased EFS-induced contraction. These data suggest that endogenous ATP plays a role in EFS-induced contractions which are mediated through both P2X-receptors and P2Y-receptors stimulation in cat esophageal smooth muscle.

• Journal of the Korean Chemical Society
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• 제30권5호
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• pp.441-448
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• 1986

Dioxobis(sub.-salicylaldiminato) molybdenum (VI) complexes, $MoO_2\;(X-sal-N-R)_2,\;(X=H,\;5-CH_3,\;R=C_6H_5,\;p-F-C_6H_4,\;m-Cl-C_6H_4,p-I-C_6H_4\;and\;p-C_2H_5-C_6H_4)$, have been prepared by reactions of dioxobis(sub.-salicylaldehydato) molybdenum (VI), $MoO_2(X-sal)_2$ with primary amines, in which $MoO_2(X-sal)_2$ complexes were obtained by acidification of a mixture solution of ammonium paramolybdate in water and appropriate salicylaldehyde in methanol. All these complexes show two strong Mo=O stretching imodes in the 900-940$cm^{-1}$ and p.m.r. spectra exhibited only one signal for the azomethine group. These results confirmed that the complexes are six-coordinated octahedron with a $cis-MoO_2$ group and the geometrical configurations of the complexes possess a C2 axis of symmetry. From the mass analyses of the complexes, it found that the composition ratios of $MoO_2$ : ligand are 1 : 2. The charge transfer transition corresponding to N-Mo, and O-Mo occured at 29,000$cm^{-1}$ and 32,000$cm^{-1}$ respectively. Where, the complexes were found to be non-ionic materials by conductivity measurements in dimethylformamide.