• Title/Summary/Keyword: B.T.X

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THE BOUNDEDNESS OF SOLUTIONS FOR STOCHASTIC DIFFERENTIAL INCLUSIONS

  • Yun, Yong-Sik
    • Bulletin of the Korean Mathematical Society
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    • v.40 no.1
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    • pp.159-165
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    • 2003
  • We consider the stochastic differential inclusion of the form $dX_t\;\in\;\sigma(t,\;X_t)db_t+b(t,\;X_t)dt$, where $\sigma$, b are set-valued maps, B is a standard Brownian motion. We prove the boundedness of solutions under the assumption that $\sigma$ and b satisfy the local Lipschitz property and linear growth.

SUBTOURNAMENTS ISOMORPHIC TO W5 OF AN INDECOMPOSABLE TOURNAMENT

  • Belkhechine, Houmem;Boudabbous, Imed;Hzami, Kaouthar
    • Journal of the Korean Mathematical Society
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    • v.49 no.6
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    • pp.1259-1271
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    • 2012
  • We consider a tournament T = (V,A). For each subset X of V is associated the subtournament T(X) = (X,$A{\cap}(X{\times}X)$) of T induced by X. We say that a tournament T' embeds into a tournament T when T' is isomorphic to a subtournament of T. Otherwise, we say that T omits T'. A subset X of V is a clan of T provided that for a, $b{\in}X$ and $x{\in}V{\backslash}X$, $(a,x){\in}A$ if and only if $(b,x){\in}A$. For example, ${\emptyset}$, $\{x\}(x{\in}V)$ and V are clans of T, called trivial clans. A tournament is indecomposable if all its clans are trivial. In 2003, B. J. Latka characterized the class ${\tau}$ of indecomposable tournaments omitting a certain tournament $W_5$ on 5 vertices. In the case of an indecomposable tournament T, we will study the set $W_5$(T) of vertices $x{\in}V$ for which there exists a subset X of V such that $x{\in}X$ and T(X) is isomorphic to $W_5$. We prove the following: for any indecomposable tournament T, if $T{\notin}{\tau}$, then ${\mid}W_5(T){\mid}{\geq}{\mid}V{\mid}$ -2 and ${\mid}W_5(T){\mid}{\geq}{\mid}V{\mid}$ -1 if ${\mid}V{\mid}$ is even. By giving examples, we also verify that this statement is optimal.

Common Fixed Point Theorems of Commuting Mappinggs

  • Park, Wee-Tae
    • The Mathematical Education
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    • v.26 no.1
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    • pp.41-45
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    • 1987
  • In this paper, we give several fixed point theorems in a complete metric space for two multi-valued mappings commuting with two single-valued mappings. In fact, our main theorems show the existence of solutions of functional equations f($\chi$)=g($\chi$)$\in$S$\chi$∩T$\chi$ and $\chi$=f($\chi$)=g($\chi$)$\in$S$\chi$∩T$\chi$ under certain conditions. We also answer an open question proposed by Rhoades-Singh-Kulsherestha. Throughout this paper, let (X, d) be a complete metric space. We shall follow the following notations : CL(X) = {A; A is a nonempty closed subset of X}, CB(X)={A; A is a nonempty closed and founded subset of X}, C(X)={A; A is a nonempty compact subset of X}, For each A, B$\in$CL(X) and $\varepsilon$>0, N($\varepsilon$, A) = {$\chi$$\in$X; d($\chi$, ${\alpha}$) < $\varepsilon$ for some ${\alpha}$$\in$A}, E$\sub$A, B/={$\varepsilon$ > 0; A⊂N($\varepsilon$ B) and B⊂N($\varepsilon$, A)}, and (equation omitted). Then H is called the generalized Hausdorff distance function fot CL(X) induced by a metric d and H defined CB(X) is said to be the Hausdorff metric induced by d. D($\chi$, A) will denote the ordinary distance between $\chi$$\in$X and a nonempty subset A of X. Let R$\^$+/ and II$\^$+/ denote the sets of nonnegative real numbers and positive integers, respectively, and G the family of functions ${\Phi}$ from (R$\^$+/)$\^$s/ into R$\^$+/ satisfying the following conditions: (1) ${\Phi}$ is nondecreasing and upper semicontinuous in each coordinate variable, and (2) for each t>0, $\psi$(t)=max{$\psi$(t, 0, 0, t, t), ${\Phi}$(t, t, t, 2t, 0), ${\Phi}$(0, t, 0, 0, t)} $\psi$: R$\^$+/ \longrightarrow R$\^$+/ is a nondecreasing upper semicontinuous function from the right. Before sating and proving our main theorems, we give the following lemmas:

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VIABILITY FOR SEMILINEAR DIFFERENTIAL EQUATIONS OF RETARDED TYPE

  • Dong, Qixiang;Li, Gang
    • Bulletin of the Korean Mathematical Society
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    • v.44 no.4
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    • pp.731-742
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    • 2007
  • Let X be a Banach space, $A:D(A){\subset}X{\rightarrow}X$ the generator of a compact $C_0-semigroup\;S(t):X{\rightarrow}X,\;t{\geq}0$, D a locally closed subset in X, and $f:(a,b){\times}C([-q,0];X){\rightarrow}X$ a function of Caratheodory type. The main result of this paper is that a necessary and sufficient condition in order that D be a viable domain of the semi linear differential equation of retarded type $$u#(t)=Au(t)+f(t,u_t),\;t{\in}[t_0,\;t_0+T],{u_t}_0={\phi}{\in}C([-q,0];X)$$ is the tangency condition $$\limits_{h{\downarrow}0}^{lim\;inf\;h^{-1}d(S(h)v(0)+hf(t,v);D)=0}$$ for almost every $t{\in}(a,b)$ and every $v{\in}C([-q,0];X)\;with\;v(0){\in}D$.

An x-dB Bandwidth Measurement Method for Terrestrial Digital Broadcasting Signals in the Field Environments (필드 환경에 적합한 지상파 디지털 방송 신호의 x-dB 대역폭 측정 방법)

  • Hwang, Tae-Wook;Kim, Young-Soo;Yang, Hoon-Gee;Yook, Jong-Gwan;Suh, Doug-Young;Kim, Jin-Sang
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.18 no.6 s.121
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    • pp.629-638
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    • 2007
  • The methods of bandwidth measurement in the field environments are notified in ITU-R spectrum monitoring(SM) documents. But, these methods for terrestrial DTV and T-DMB are not informed yet. The x-dB bandwidth is the most suitable method fer the bandwidth measurement of terrestrial digital broadcasting signals. So, we proposed the suitable x-dB value for x-dB bandwidth measurement of the digital broadcasting signal that is not notified in ITU-R SM documents. As a result, we derived the x dB value of -12 dB and -8 dB that can be used fer estimation of occupied bandwidth of DTV and T-DMB signals respectively by x dB bandwidth measurement in field environments.

TWO GENERALIZATIONS OF LCM-STABLE EXTENSIONS

  • Chang, Gyu Whan;Kim, Hwankoo;Lim, Jung Wook
    • Journal of the Korean Mathematical Society
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    • v.50 no.2
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    • pp.393-410
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    • 2013
  • Let $R{\subseteq}T$ be an extension of integral domains, X be an indeterminate over T, and R[X] and T[X] be polynomial rings. Then $R{\subseteq}T$ is said to be LCM-stable if $(aR{\cap}bR)T=aT{\cap}bT$ for all $0{\neq}a,b{\in}R$. Let $w_A$ be the so-called $w$-operation on an integral domain A. In this paper, we introduce the notions of $w(e)$- and $w$-LCM-stable extensions: (i) $R{\subseteq}T$ is $w(e)$-LCM-stable if $((aR{\cap}bR)T)_{w_T}=aT{\cap}bT$ for all $0{\neq}a,b{\in}R$ and (ii) $R{\subseteq}T$ is $w$-LCM-stable if $((aR{\cap}bR)T)_{w_R}=(aT{\cap}bT)_{w_R}$ for all $0{\neq}a,b{\in}R$. We prove that LCM-stable extensions are both $w(e)$-LCM-stable and $w$-LCM-stable. We also generalize some results on LCM-stable extensions. Among other things, we show that if R is a Krull domain (resp., $P{\upsilon}MD$), then $R{\subseteq}T$ is $w(e)$-LCM-stable (resp., $w$-LCM-stable) if and only if $R[X]{\subseteq}T[X]$ is $w(e)$-LCM-stable (resp., $w$-LCM-stable).

CHARACTERIZATIONS OF STABILITY OF ABSTRACT DYNAMIC EQUATIONS ON TIME SCALES

  • Hamza, Alaa E.;Oraby, Karima M.
    • Communications of the Korean Mathematical Society
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    • v.34 no.1
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    • pp.185-202
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    • 2019
  • In this paper, we investigate many types of stability, like (uniform stability, exponential stability and h-stability) of the first order dynamic equations of the form $$\{u^{\Delta}(t)=Au(t)+f(t),\;\;t{\in}{\mathbb{T}},\;t>t_0\\u(t_0)=x{\in}D(A),$$ and $$\{u^{\Delta}(t)=Au(t)+f(t,u),\;\;t{\in}{\mathbb{T}},\;t>t_0\\u(t_0)=x{\in}D(A),$$ in terms of the stability of the homogeneous equation $$\{u^{\Delta}(t)=Au(t),\;\;t{\in}{\mathbb{T}},\;t>t_0\\u(t_0)=x{\in}D(A),$$ where f is rd-continuous in $t{\in}{\mathbb{T}}$ and with values in a Banach space X, with f(t, 0) = 0, and A is the generator of a $C_0$-semigroup $\{T(t):t{\in}{\mathbb{T}}\}{\subset}L(X)$, the space of all bounded linear operators from X into itself. Here D(A) is the domain of A and ${\mathbb{T}}{\subseteq}{\mathbb{R}}^{{\geq}0}$ is a time scale which is an additive semigroup with property that $a-b{\in}{\mathbb{T}}$ for any $a,b{\in}{\mathbb{T}}$ such that a > b. Finally, we give illustrative examples.

STABILITY FOR INTEGRO-DELAY-DIFFERENTIAL EQUATIONS

  • Goo, Yoon-Hoe;Ryu, Hyun Sook
    • Journal of the Chungcheong Mathematical Society
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    • v.13 no.1
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    • pp.45-51
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    • 2000
  • We will investigate some properties of integro-delay-differential equations, $$x^{\prime}(t)=A(t)x(t-g_1(t,x_t))+{\int}_{t_0}^{t}B(t,s)x(s-g_2(s,x_s))ds,\;t_0{\geq}0,\\x(t_0)={\phi}$$,

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A Study on Evaluation of Accuracy and Precision on B, T, X Analysis Using Thermal Desorption/Gas Chromatograph/Flams Ionization Detector (열탈착/GC/FID를 이용한 B, T, X 분석의 정확도 및 정밀도 평가)

  • 박정근;유기호
    • Journal of Korean Society for Atmospheric Environment
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    • v.16 no.3
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    • pp.265-275
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    • 2000
  • By using thermal desorption/gas chromatograph/flame ionization detector(TD/GC/FID), this study was carried out to evalute an accuracy and a precision on Benzene(B), Toluene(T), o-Xylene(X) analysis in an industrial hygiene laboratory. Limits of detection of TD/GC/FID on B, T, X were showed 13.75ng/sample or less. For the accuracy of the method by concentration levels, overall bias was showed 7.7% as an absolute value, and the pooled coefficient of variation showed 3.51%. For the precision on repeatability of peak area and retention time between within-run and between-run of analytical system, it is showed the results of within-run gave better than those of between-run. Also the accuracy by sorbents(Tenax TA and Chromosorb 106)was evaluated, and the precision on reproducibility between MDHS72 and this study was compared. It is showed it is possible for TD/GC/FID to evaluate accurately B, T, X concentration levels of less than 1ppm at indoor or outdoor of workplaces in Korea.

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