• Title, Summary, Keyword: absolutely continuous function

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OSTROWSKI TYPE INEQUALITY FOR ABSOLUTELY CONTINUOUS FUNCTIONS ON SEGMENTS IN LINEAR SPACES

  • Kikianty, Eder;Dragomir, Sever S.;Cerone, Pietro
    • Bulletin of the Korean Mathematical Society
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    • v.45 no.4
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    • pp.763-780
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    • 2008
  • An Ostrowski type inequality is developed for estimating the deviation of the integral mean of an absolutely continuous function, and the linear combination of its values at k + 1 partition points, on a segment of (real) linear spaces. Several particular cases are provided which recapture some earlier results, along with the results for trapezoidal type inequalities and the classical Ostrowski inequality. Some inequalities are obtained by applying these results for semi-inner products; and some of these inequalities are proven to be sharp.

ON CHARACTERIZATIONS OF PARETO AND WEIBULL DISTRIBUTIONS BY CONSIDERING CONDITIONAL EXPECTATIONS OF UPPER RECORD VALUES

  • Jin, Hyun-Woo;Lee, Min-Young
    • Journal of the Chungcheong Mathematical Society
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    • v.27 no.2
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    • pp.243-247
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    • 2014
  • Let {$X_n$, $n{\geq}1$} be a sequence of i.i.d. random variables with absolutely continuous cumulative distribution function(cdf) F(x) and the corresponding probability density function(pdf) f(x). In this paper, we give characterizations of Pareto and Weibull distribution by considering conditional expectations of record values.

CHARACTERIZATIONS OF THE LOMAX, EXPONENTIAL AND PARETO DISTRIBUTIONS BY CONDITIONAL EXPECTATIONS OF RECORD VALUES

  • Lee, Min-Young;Lim, Eun-Hyuk
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.2
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    • pp.149-153
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    • 2009
  • Let {$X_{n},\;n\;\geq\;1$} be a sequence of independent and identically distributed random variables with absolutely continuous cumulative distribution function (cdf) F(x) and probability density function (pdf) f(x). Suppose $X_{U(m)},\;m = 1,\;2,\;{\cdots}$ be the upper record values of {$X_{n},\;n\;\geq\;1$}. It is shown that the linearity of the conditional expectation of $X_{U(n+2)}$ given $X_{U(n)}$ characterizes the lomax, exponential and pareto distributions.

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ON CHARACTERIZATIONS OF THE CONTINUOUS DISTRIBUTIONS BY INDEPENDENCE PROPERTY OF RECORD VALUES

  • JIN, HYUN-WOO;LEE, MIN-YOUNG
    • Journal of applied mathematics & informatics
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    • v.35 no.5_6
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    • pp.651-657
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    • 2017
  • A sequence {$X_n,\;n{\geq}1$} of independent and identically distributed random variables with absolutely continuous (with respect to Lebesque measure) cumulative distribution function F(x) is considered. We obtain two characterizations of a family of continuous probability distribution by independence property of record values.

HADAMARD-TYPE FRACTIONAL CALCULUS

  • Anatoly A.Kilbas
    • Journal of the Korean Mathematical Society
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    • v.38 no.6
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    • pp.1191-1204
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    • 2001
  • The paper is devoted to the study of fractional integration and differentiation on a finite interval [a, b] of the real axis in the frame of Hadamard setting. The constructions under consideration generalize the modified integration $\int_{a}^{x}(t/x)^{\mu}f(t)dt/t$ and the modified differentiation ${\delta}+{\mu}({\delta}=xD,D=d/dx)$ with real $\mu$, being taken n times. Conditions are given for such a Hadamard-type fractional integration operator to be bounded in the space $X^{p}_{c}$(a, b) of Lebesgue measurable functions f on $R_{+}=(0,{\infty})$ such that for c${\in}R=(-{\infty}{\infty})$, in particular in the space $L^{p}(0,{\infty})\;(1{\le}{\le}{\infty})$. The existence almost every where is established for the coorresponding Hadamard-type fractional derivative for a function g(x) such that $x^{p}$g(x) have $\delta$ derivatives up to order n-1 on [a, b] and ${\delta}^{n-1}[x^{\mu}$g(x)] is absolutely continuous on [a, b]. Semigroup and reciprocal properties for the above operators are proved.

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ON CHARACTERIZATIONS OF THE NORMAL DISTRIBUTION BY INDEPENDENCE PROPERTY

  • LEE, MIN-YOUNG
    • Journal of applied mathematics & informatics
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    • v.35 no.3_4
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    • pp.261-265
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    • 2017
  • Let X and Y be independent identically distributed nondegenerate random variables with common absolutely continuous probability distribution function F(x) and the corresponding probability density function f(x) and $E(X^2)$<${\infty}$. Put Z = max(X, Y) and W = min(X, Y). In this paper, it is proved that Z - W and Z + W or$(X-Y)^2$ and X + Y are independent if and only if X and Y have normal distribution.

A CHARACTERIZATION OF GAMMA DISTRIBUTION BY INDEPENDENT PROPERTY

  • Lee, Min-Young;Lim, Eun-Hyuk
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.1
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    • pp.1-5
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    • 2009
  • Let {$X_n,\;n{\geq}1}$ be a sequence of independent identically distributed(i.i.d.) sequence of positive random variables with common absolutely continuous distribution function(cdf) F(x) and probability density function(pdf) f(x) and $E(X^2)<{\infty}$. The random variables $\frac{X_i{\cdot}X_j}{(\Sigma^n_{k=1}X_k)^{2}}$ and $\Sigma^n_{k=1}X_k$ are independent for $1{\leq}i if and only if {$X_n,\;n{\geq}1}$ have gamma distribution.

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Anaerobic Microbial Degradation of Lignocellulose and Lignolic Compounds (미생물에 의한 섬유질과 리그닌 유도체의 혐기적 분해)

  • 김소자;김욱한
    • The Korean Journal of Food And Nutrition
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    • v.4 no.1
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    • pp.99-107
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    • 1991
  • Lignocellulose and lignolic compounds were absolutely given much weight In the biosphere, and their degradation was essential for continuous biological carbon circulation. Whereas aerobic cellulolytic microorganism dissolved the cellulose into their elements in the first stage, strict anaerobic cellulolytic microorganism's role was taken I increasing interest through the recent research. It was reviewed that anaerobic microbial degradation process of lignocellulose and its derivatives (cellulose, lignin, oligolignol and monoaromatic compound), and function of anaerobic microorganism on the. environmental ecology.

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CHARACTERIZATIONS OF GAMMA DISTRIBUTION

  • Lee, Min-Young;Lim, Eun-Hyuk
    • Journal of the Chungcheong Mathematical Society
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    • v.20 no.4
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    • pp.411-418
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    • 2007
  • Let $X_1$, ${\cdots}$, $X_n$ be nondegenerate and positive independent identically distributed(i.i.d.) random variables with common absolutely continuous distribution function F(x) and $E(X^2)$ < ${\infty}$. The random variables $X_1+{\cdots}+X_n$ and $\frac{X_1+{\cdots}+X_m}{X_1+{\cdots}+X_n}$are independent for 1 $1{\leq}$ m < n if and only if $X_1$, ${\cdots}$, $X_n$ have gamma distribution.

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CHARACTERIZATIONS OF THE GAMMA DISTRIBUTION BY INDEPENDENCE PROPERTY OF RANDOM VARIABLES

  • Jin, Hyun-Woo;Lee, Min-Young
    • Journal of the Chungcheong Mathematical Society
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    • v.27 no.2
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    • pp.157-163
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    • 2014
  • Let {$X_i$, $1{\leq}i{\leq}n$} be a sequence of i.i.d. sequence of positive random variables with common absolutely continuous cumulative distribution function F(x) and probability density function f(x) and $E(X^2)$ < ${\infty}$. The random variables X + Y and $\frac{(X-Y)^2}{(X+Y)^2}$ are independent if and only if X and Y have gamma distributions. In addition, the random variables $S_n$ and $\frac{\sum_{i=1}^{m}(X_i)^2}{(S_n)^2}$ with $S_n=\sum_{i=1}^{n}X_i$ are independent for $1{\leq}m$ < n if and only if $X_i$ has gamma distribution for $i=1,{\cdots},n$.