• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.557-564
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• 2012

This study concerns the existence of positive solution for the following nonlinear system $$\{-div(|x|^{-ap}|{\nabla}u|^{p-2}{\nabla}u)=|x|^{-(a+1)p+c_1}({\alpha}_1f(v)+{\beta}_1h(u)),x{\in}{\Omega},\\-div(|x|^{-bq}|{\nabla}v|q^{-2}{\nabla}v)=|x|^{-(b+1)q+c_2}({\alpha}_2g(u)+{\beta}_2k(v)),x{\in}{\Omega},\\u=v=0,x{\in}{\partial}{\Omega}$$, where ${\Omega}$ is a bounded smooth domain of $\mathbb{R}^N$ with $0{\in}{\Omega}$, 1 < $p,q$ < N, $0{{\leq}}a<\frac{N-p}{p}$, $0{{\leq}}b<\frac{N-q}{q}$ and $c_1$, $c_2$, ${\alpha}_1$, ${\alpha}_2$, ${\beta}_1$, ${\beta}_2$ are positive parameters. Here $f,g,h,k$ : $[0,{\infty}){\rightarrow}[0,{\infty})$ are nondecresing continuous functions and $$\lim_{s{\rightarrow}{\infty}}\frac{f(Ag(s)^{\frac{1}{q-1}})}{s^{p-1}}=0$$ for every A > 0. We discuss the existence of positive solution when $f,g,h$ and $k$ satisfy certain additional conditions. We use the method of sub-super solutions to establish our results.

• Journal of the Korea Society of Computer and Information
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• v.4 no.4
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• pp.218-225
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• 1999

The purpose of this study is to investigate 1-10 year old kindergarten teachers of usage computer program in kindergarten. And the relations between the usage of computer program examined by students and kindergarten teachers were also investigated. The subjects were drawn from fifty kindergarten : 199 kindergarten teachers. The data were analyzed by frequency. percentage, $x^2$ test. The research findings were as follows: 1) There were differences in number of kindergarten teachers engaged by the computer. ( $x^2$＝ 138.486, df=36, p＜.001) 2) There were no differences in number of kindergarten teachers engaged by the kind of computer program. ($x^2$= 75.42, df=80 p＞.50) 3) There were differences in number of kindergarten teachers engaged by the kind of computer education program. ($x^2$= 519.566, df=64 p＜.001)

• The Mathematical Education
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• v.12 no.2
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• pp.5-12
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• 1974

단위원을 가지는 하환환에 있어서의 Prime Spectrum에 관하여 다음 세가지 사실을 증명하였다. 1. X를 환 R의 prime spectrum, C(X)를 X에서 정의되는 실연적함수의 환, X를 C(X)의 maximal spectrum이라 하면 X는 C(X)의 prime spectrum의 부분공간으로서의 한 T-space로 된다. N을 환 R의 nilradical이라 하면, R/N이 regula 이면 X와 X는 위상동형이다. 2. f: R$\longrightarrow$R'을 ring homomorphism, P를 R의 한 Prime ideal, $R_{p}$, R'$_{p}$를 각각 S=R-P 및 f(S)에 관한 분수환(ring of fraction)이라 하고, k(P)를 local ring $R_{p}$의 residue' field라 할 때, R'의 prime spectrum의 부분공간인 $f^{*-1}$(P)는 k(P)(equation omitted)$_{R}$R'의 prime spectrum과 위상동형이다. 단 f*는 f*(Q)=$f^{-1}$(Q)로서 정의되는 함수 s*:Spec(R')$\longrightarrow$Spec(R)이다. 3. X를 환 S의 prime spectrum, N을 R의 nilradical이라 할 때, 다음 네가지 사실은 동치이다. (1) R/N 은 regular 이다. (2) X는 Zarski topology에 관하여 Hausdorff 공간이다. (3) X에서의 Zarski topology와 constructible topology와는 일치한다. (4) R의 임의의 원소 f에 대하여 f를 포함하지 않는 R의 prime ideal 전체의 집합 $X_{f}$는 Zarski topology에 관하여 개집합인 동시에 폐집합이다.폐집합이다....

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.371-399
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• 2020

Let P_s := 𝔽₂[x₁, x₂, …, x_s] = ⊕_n⩾0(P_s)_n be the polynomial algebra viewed as a graded left module over the mod 2 Steenrod algebra, ${\mathfrak{A}}$. The grading is by the degree of the homogeneous terms (P_s)_n of degree n in the variables x₁, x₂, …, x_s of grading 1. We are interested in the hit problem, set up by F. P. Peterson, of finding a minimal system of generators for ${\mathfrak{A}}$-module P_s. Equivalently, we want to find a basis for the 𝔽₂-graded vector space ${\mathbb{F}}_2{\otimes}_{\mathfrak{A}}$ P_s. In this paper, we study the hit problem in the case s = 5 and the degree n = 5(2^t - 1) + 6 · 2^t with t an arbitrary positive integer.

• Journal of applied mathematics & informatics
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• v.42 no.1
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• pp.139-148
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• 2024

The purpose of this research is to investigate sufficient conditions for the existence of limit cycles of the fifth-order differential equation x⁽⁵⁾ + (p² + q²)$_{x}^{...}$ + p²q²$_{x}^{.}$ = εF(t, x, $_{x}^{.}$, $_{x}^{..}$, $_{x}^{...}$, $_{x}^{....}$), where p, q are rational numbers different from 0, p ≠ ±q, ε is a small real parameter, and F is a 2kπ-periodic function in the variable t. Also, we provide some applications.

• Kyungpook Mathematical Journal
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• v.49 no.2
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• pp.255-263
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• 2009

For an endomorphism ${\alpha}$ of R, in [1], a module $M_R$ is called ${\alpha}$-compatible if, for any $m{\in}M$ and $a{\in}R$, ma = 0 iff $m{\alpha}(a)$ = 0, which are a generalization of ${\alpha}$-reduced modules. We study on the relationship between the quasi-Baerness and p.q.-Baer property of a module MR and those of the polynomial extensions (including formal skew power series, skew Laurent polynomials and skew Laurent series). As a consequence we obtain a generalization of [2] and some results in [9]. In particular, we show: for an ${\alpha}$-compatible module $M_R$ (1) $M_R$ is p.q.-Baer module iff $M[x;{\alpha}]_{R[x;{\alpha}]}$ is p.q.-Baer module. (2) for an automorphism ${\alpha}$ of R, $M_R$ is p.q.-Baer module iff $M[x,x^{-1};{\alpha}]_{R[x,x^{-1};{\alpha}]}$ is p.q.-Baer module.

• Journal of Advanced Navigation Technology
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• v.23 no.1
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• pp.36-43
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• 2019

In this paper, a novel channel access scheme for the next-generation vehicle to anything (V2X) system based on IEEE 802.11p standard which is applied to recent connected car technologies is suggested and analyzed. The proposed scheme proposes a channel access method utilizing OFDMA multi-user transmission for IEEE 802.11p based system. In this paper, the authors examine geographical distance and network area performance of IEEE 802.11p system and the proposed scheme. Results of this research show that the proposed scheme is quite suitable for improving conventional V2X standards and systems. This paper also provides mathematical analysis and simulation results of the conventional IEEE 802.11p system and the proposed scheme.

• The Korean Journal of Physiology and Pharmacology
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• v.12 no.6
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• pp.315-321
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• 2008

Eugenol is widely used in dentistry to relieve pain. We have recently demonstrated voltage-gated $Na^+$ and $Ca^{2+}$ channels as molecular targets for its analgesic effects, and hypothesized that eugenol acts on $P2X_3$, another pain receptor expressed in trigeminal ganglion (TG), and tested the effects of eugenol by whole-cell patch clamp and $Ca^{2+}$ imaging techniques. In the present study, we investigated whether eugenol would modulate 5'-triphosphate (ATP)-induced currents in rat TG neurons and $P2X_3$-expressing human embryonic kidney (HEK) 293 cells. ATP-induced currents in TG neurons exhibited electrophysiological properties similar to those in HEK293 cells, and both ATP- and $\alpha$, $\beta$-meATP-induced currents in TG neurons were effectively blocked by TNP-ATP, suggesting that $P2X_3$ mediates the majority of ATP-induced currents in TG neurons. Eugenol inhibited ATP-induced currents in both capsaicin-sensitive and capsaicin-insensitive TG neurons with similar extent, and most ATP-responsive neurons were IB4-positive. Eugenol inhibited not only $Ca^{2+}$ transients evoked by $\alpha$, $\beta$-meATP, the selective $P2X_3$ agonist, in capsaicin-insensitive TG neurons, but also ATP-induced currents in $P2X_3$-expressing HEK293 cells without co-expression of transient receptor potential vanilloid 1 (TRPV1). We suggest, therefore, that eugenol inhibits $P2X_3$ currents in a TRPV1-independent manner, which contributes to its analgesic effect.

• Journal of the Korean Chemical Society
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• v.55 no.1
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• pp.38-45
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• 2011

The complexation behavior of the $\alpha$-ketostabilized phosphorus ylides $Ph_3P$=CHC(O) $C_6H_4-X$ (X=Br, Ph) towards the transition metal ions mercury (II) and Silver (I) was investigated. The mercury(II) complex {$HgX_2$ [Y]} 2 ($Y_1$=4-bromo benzoyl methylene triphenyl phosphorane; X=Cl(1), Br(2), I(3), $Y_2$=4-phenyl benzoyl methylene triphenyl phosphorane; X=Cl(4), Br(5), I(6)) have been prepared from the reaction of $Y_1$ and $Y_2$ with $HgX_2$ (X=Cl, Br, I) respectively. Silver complexes [$Ag(Y_2)_2]$ X(X=$BF_4$(7), OTf(8)) of the $\alpha$-keto-stabilized phosphorus ylides ($Y_2$) were obtained by reacting this ylide with AgX (X=$BF_4$, OTf) in $Me_2CO$. The crystal structure of complexes (1) and (4) was discussed. These reactions led to binuclear complexes C-coordination of ylide and trans-like structure of complexes $[Y_1HgCl_2]_2$. $CHCl_3$ (1) and $[Y_2HgCl_2]_2$ (4) is demonstrated by single crystal X-ray analyses. Not only all of complexes have been studied by IR, $^1H$ and $^{31}P$ NMR spectroscopy, but also complexes 1-3 have been characterized by $^{13}$CNMR.

• Analytical Science and Technology
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• v.13 no.2
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• pp.208-214
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• 2000

The formation and dissolution of hydroxides, carbonates and hydroxyapatite (HAp), which depend on the pH of solution, are important factor for the preparation of homogeneous and fine HAp, $Ca_{10-x}(HPO_4)_x(PO_4)_{6-x}(OH)_{2-x}(x=0)$, ceramic powder from the $Ca-PO_4-H_2O$ system. Since the solubility of each complex ion is a linear function of pH, the solubility diagram can be obtained by plotting the logarithmic molar concentrations calculated from the values of the equilibrium constants and solubility products for hydroxides, carbonates, and hydroxyapatite. The optimum pH condition for the formation of single phase $Ca_{10-x}(HPO_4)_x(PO_4)_{6-x}(OH)_{2-x}(x=0)$ powder in $Ca-PO_4-H_2O$ system at $25^{\circ}C$ was estimated as $10.5{\pm}0.5$ through the theoretical consideration. The HAp powder dried at $80^{\circ}C$ showed a fine agglomerated particles with a size of 75 nm. The HAp powder calcined at $1,000^{\circ}C$ consisted of nearly homogeneous particles with a size of 450 nm. Even though the dried HAp particles consisted of agglomeration, mechanical properties were superior due to fine microstructure after sintering.