• 대한수학회논문집
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• 제16권2호
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• pp.287-290
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• 2001

Let X$_1$, X$_2$, … be a sequence of independent and identically distributed random variables with continuous cumulative distribution function F(x). X(sub)j is an upper record value of this sequence if X(sub)j > max {X$_1$, X$_2$, …, X(sub)j-1}. We define u(n) = min {j│j > u(n-1), X(sub)j > X(sub)u(n-1), n $\geq$ 2} with u(1) = 1. Then F(x) = 1 - e(sup)-x/c, x > 0 if and only if E[X(sub)n(n+1) - X(sub)u(n)│X(sub)u(m) = y] = c or E[X(sub)u(n+2) - X(sub)u(n)│X(sub)u(m) = y] = 2c, n $\geq$ m+1.

• 대한수학회보
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• 제51권2호
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• pp.329-338
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• 2014

In this paper, we study the method of upper and lower solutions and develop the generalized quasilinearization technique for the existence and approximation of solutions to some three-point nonlocal boundary value problems associated with higher order fractional differential equations of the type $$^c{\mathcal{D}}^q_{0+}u(t)+f(t,u(t))=0,\;t{\in}(0,1)$$ $$u^{\prime}(0)={\gamma}u^{\prime}({\eta}),\;u^{\prime\prime}(0)=0,\;u^{\prime\prime\prime}(0)=0,{\ldots},u^{(n-1)}(0)=0,\;u(1)={\delta}u({\eta})$$, where, n-1 < q < n, $n({\geq}3){\in}\mathbb{N}$, 0 < ${\eta},{\gamma},{\delta}$ < 1 and $^c\mathcal{D}^q_{0+}$ is the Caputo fractional derivative of order q. The nonlinear function f is assumed to be continuous.

• 대한수학회지
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• 제57권6호
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• pp.1551-1571
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• 2020

This paper is concerned with the following Kirchhoff-Schrödinger-Poisson system $$\begin{cases} -(a+b{\displaystyle\smashmargin{2}\int\nolimits_{\mathbb{R}^3}}{\mid}{\nabla}u{\mid}^2dx){\Delta}u+V(x)u+{\mu}{\phi}u={\lambda}f(x){\mid}u{\mid}^{p-2}u+g(x){\mid}u{\mid}^{p-2}u,&{\text{ in }}{\mathbb{R}}^3,\\-{\Delta}{\phi}={\mu}{\mid}u{\mid}^2,&{\text{ in }}{\mathbb{R}}^3, \end{cases}$$ where a > 0, b, µ ≥ 0, p ∈ (1, 2), q ∈ [4, 6) and λ > 0 is a parameter. Under some suitable assumptions on V (x), f(x) and g(x), we prove that the above system has at least two different nontrivial solutions via the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory. Some recent results from the literature are improved and extended.

• 대한수학회논문집
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• 제27권3호
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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 applied mathematics & informatics
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• 제13권1_2호
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• pp.441-446
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• 2003

Let { $X_{n}$ , n $\geq$ 1} be a sequence of independent and identically distributed random variables with a common continuous distribution function F(x) and probability density function f(x). Let $Y_{n}$ = max{ $X_1$, $X_2$, …, $X_{n}$ } for n $\geq$ 1. We say $X_{j}$ is an upper record value of { $X_{n}$ , n$\geq$1} if $Y_{j}$ > $Y_{j-1}$, j > 1. The indices at which the upper record values occur are given by the record times {u(n)}, n$\geq$1, where u(n) = min{j｜j>u(n-1), $X_{j}$ > $X_{u}$ (n-1), n$\geq$2} and u(1) = 1. We call the random variable X $\in$ Beta (1, c) if the corresponding probability cumulative function F(x) of x is of the form F(x) = 1-(1-x)$^{c}$ , c>0, 0$\leq$x$\leq$1. In this paper, we will give a characterization of the beta distribution of the first kind by considering conditional expectations of record values.s.

• 의료법학
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• 제14권2호
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• pp.87-112
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• 2013

Vor kurzer Zeit gibt es viele Diskussion $\ddot{u}$ber die Unterbrechung der Freiheitsstrafe aufgrund der Krankheit. Man wollte ihre Voraussetzungen einerseits durch 'Kommission f$\ddot{u}$r die Unterbrechung der Freiheitsstrafe' andererseits durch doppelte medizinische Gutachten strenger machen. Jedoch muss man auf die im voraus zu entscheidende Frage antworten, ob das Recht des Gefangenen auf Gesundheit geschutzt wird, insbesondere die Gefangenen in Justizvollzugsanstalten medizinische Behandlungen genug nutzen k$\ddot{o}$nnen. Meine Antwort ist 'Nein!'. Im kStvollzG bestehen die Regelungen f$\ddot{u}$r medizinische Behandlung mit staatlicher Beteilung und mit Selbstbeteiligung au${\ss}$er Justizvollzugsanstalten. Im Prinzip muss der Staat f$\ddot{u}$r die Behandlungskosten der Gefangenen bezahlen. In der Tat aber nicht. In diesem Beitrag wurden die Antwort auf die Vorfrage aufgrund der Erfolgen der zwei Rundfragen zu geben versucht, um die Voraussetzungen der Unterbrechung der Freiheitsstrafe strenger zu machen.

• 말소리와 음성과학
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• 제2권3호
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• pp.75-80
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• 2010

The present research investigated the characteristics of voice between genders and nationalities by measuring the acoustic parameter values of Korean and Chinese students. Sound Forge was used to collect voice samples and Praat was used to measure and analyze jitter, shimmer, NHR, $sF_0$, and pitch range. The results of this research are a follows. First, during prolongation of the vowels, there was no significant difference in $F_0$ between Korean and Chinese males and Korean and Chinese females. Korean males and females had higher $F_0$ values than Chinese males and females. Secondly, during sentence reading, there was no significant difference between Korean and Chinese males in $sF_0$. But between female groups, there was a significant difference in $sF_0$. Thirdly, during sentence reading, the pitch range in Korean males was found to be narrower compared to Korean and Chinese females who had wider pitch range, showing a significant difference. Fourthly, jitter in the five vowels /a, i, u, e, o/ was found to be higher in Chinese than Korean subjects. In the vowels /a, e, u/ females were higher than males showing a significant difference. Fifthly, shimmer in the vowels /a, e, u/ was found to be higher in Chinese than Korean subjects showing a significant difference. Finally, NHR in the vowels /a, u, o/ was found to be higher in Chinese than Korean subjects showing a significant difference.

• 대한수학회지
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• 제46권6호
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• pp.1309-1318
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• 2009

Let k be a positive integer, and let G be a simple graph with vertex set V (G). A Roman k-dominating function on G is a function f : V (G) $\rightarrow$ {0, 1, 2} such that every vertex u for which f(u) = 0 is adjacent to at least k vertices $\upsilon_1,\;\upsilon_2,\;{\ldots},\;\upsilon_k$ with $f(\upsilon_i)$ = 2 for i = 1, 2, $\ldot$, k. The weight of a Roman k-dominating function is the value f(V (G)) = $\sum_{u{\in}v(G)}$ f(u). The minimum weight of a Roman k-dominating function on a graph G is called the Roman k-domination number ${\gamma}_{kR}$(G) of G. Note that the Roman 1-domination number $\gamma_{1R}$(G) is the usual Roman domination number $\gamma_R$(G). In this paper, we investigate the properties of the Roman k-domination number. Some of our results extend these one given by Cockayne, Dreyer Jr., S. M. Hedetniemi, and S. T. Hedetniemi [2] in 2004 for the Roman domination number.

• 한국환경과학회지
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• 제19권9호
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• pp.1077-1082
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• 2010

This study was performed to investigate the nutritional conditions controlling keratinase activity in Bacillus megaterium F7-1. B. megaterium F7-1 produced keratinase using chicken feather as a sole source of carbon, nitrogen and sulfur. Addition of the feather medium with glucose enhanced keratinase production (68.9 U/ml), compared to control without glucose (63.2 U/ml). The synthesis of keratinase was repressed by addition of $NH_4Cl$ in B. megaterium F7-1. The highest keratinase production (70.9 U/ml) was obtained with the feather medium containing glucose and $MgSO_4{\cdot}7H_2O$. Keratinase was produced in the absence of feather (4.9 U/ml), indicating its constitutive synthesis. Feather degradation resulted in free SH group formation. B. megaterium F7-1 effectively degraded chicken feather meal (86%), whereas duck feather, human nail, human hair and sheep wool displayed relatively low degradation rates (8-34%).

• 음성과학
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• 제10권1호
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• pp.143-152
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• 2003

The present study was performed to investigate change in shimmer according to $F_{0}$ variation precisely, and to offer suggestions for a clinical application. The analysis for the present study was done by the fundamental frequency ($F_{0}$) and shimmer measurement results of the previous 120 Korean normal adults' voice study of Pyo et al. (2002), used three vowels, /i/, /a/, /and /u/. Through the analysis of 60 female samples from the previous study, we found that $F_{0}$ of the vowels was the highest in /u/, and the lowest in /a/, but, on the contrary, shimmer was highest in /a/and lowest in /u/. Thirty of 60 subjects showed such an inverse relationship between $F_{0}$ and shimmer, as a whole. In the vowel /a/, 47 of 60 subjects showed the increased $F_{0}$ and decreased shimmer, in /i/, 32 subjects, and in /u/, 33 subjects showed the same results. The decrease in shimmer means the improvement of voice quality, so by these results, we expect to answer the question why the patients with spasmodic dysphonia can improve their voice quality with increased pitched voice production.