• 제목/요약/키워드: absolutely continuous

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CHARACTERIZATIONS OF GAMMA DISTRIBUTION

  • Lee, Min-Young;Lim, Eun-Hyuk
    • 충청수학회지
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    • 제20권4호
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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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Comparative Analysis of Spectral Theory of Second Order Difference and Differential Operators with Unbounded Odd Coefficient

  • Nyamwala, Fredrick Oluoch;Ambogo, David Otieno;Ngala, Joyce Mukhwana
    • Kyungpook Mathematical Journal
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    • 제60권2호
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    • pp.297-305
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    • 2020
  • We show that selfadjoint operator extensions of minimal second order difference operators have only discrete spectrum when the odd order coefficient is unbounded but grows or decays according to specific conditions. Selfadjoint operator extensions of minimal differential operator under similar growth and decay conditions on the coefficients have a absolutely continuous spectrum of multiplicity one.

A geometric criterion for the element of the class $A_{1,aleph_0 $(r)

  • Kim, Hae-Gyu;Yang, Young-Oh
    • 대한수학회지
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    • 제32권3호
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    • pp.635-647
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    • 1995
  • Let $H$ denote a separable, infinite dimensional complex Hilbert space and let $L(H)$ denote the algebra of all bounded linear operators on $H$. A dual algebra is a subalgebra of $L(H)$ that contains the identity operator $1_H$ and is closed in the $weak^*$ operator topology on $L(H)$. For $T \in L(H)$, let $A_T$ denote the smallest subalgebra of $L(H)$ that contains T and $1_H$ and is closed in the $weak^*$ operator topology.

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SOME NECESSARY CONDITIONS FOR ERGODICITY OF NONLINEAR FIRST ORDER AUTOREGRESSIVE MODELS

  • Lee, Chan-Ho
    • 대한수학회지
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    • 제33권2호
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    • pp.227-234
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    • 1996
  • Consider nonlinear autoregressive processes of order 1 defined by the random iteration $$ (1) X_{n + 1} = f(X_n) + \epsilon_{n + 1} (n \geq 0) $$ where f is real-valued Borel measurable functin on $R^1, {\epsilon_n : n \geq 1}$ is an i.i.d.sequence whose common distribution F has a non-zero absolutely continuous component with a positive density, $E$\mid$\epsilon_n$\mid$ < \infty$, and the initial $X_0$ is independent of ${\epsilon_n : n > \geq 1}$.

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SOME NEW ČEBYŠEV TYPE INEQUALITIES

  • Zafar, Fiza;Mir, Nazir Ahmad;Rafiq, Arif
    • 대한수학회보
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    • 제47권2호
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    • pp.221-229
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    • 2010
  • Some new $\check{C}$eby$\check{s}$ev type inequalities have been developed by working on functions whose first derivatives are absolutely continuous and the second derivatives belong to the usual Lebesgue space $L_{\infty}[a,\;b]$. A unified treatment of the special cases is also given.

REPRESENTATION OF INTEGRAL OPERATORS ON W22(Ω) OF REPRODUCING KERNELS

  • LEE, DONG-MYUNG;LEE, JEONG-GON;CUI, MING-GEN
    • 호남수학학술지
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    • 제26권4호
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    • pp.455-462
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    • 2004
  • We prove that if ${\mathbb{K}}^*$ is adjoint operator on $W_2{^2}({\Omega})$, then ${\mathbb{K}}^*v(t,\;{\tau})=,\;v(x,\;y){\in}W_2{^2}({\Omega})$ ; it is also related to the decomposition of solution of Fredholm equations.

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A CHARACTERIZATION OF GAMMA DISTRIBUTION BY INDEPENDENT PROPERTY

  • Lee, Min-Young;Lim, Eun-Hyuk
    • 충청수학회지
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    • 제22권1호
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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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ON CHARACTERIZATIONS OF THE POWER DISTRIBUTION VIA THE IDENTICAL HAZARD RATE OF LOWER RECORD VALUES

  • Lee, Min-Young
    • 충청수학회지
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    • 제30권3호
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    • pp.337-340
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    • 2017
  • In this article, we present characterizations of the power distribution via the identical hazard rate of lower record values that $X_n$ has the power distribution if and only if for some fixed n, $n{\geq}1$, the hazard rate $h_W$ of $W=X_{L(n+1)}/X_{L(n)}$ is the same as the hazard rate h of $X_n$ or the hazard rate $h_V$ of $V=X_{L(n+2)}/X_{L(n+1)}$.

A NOTE ON THE CHARACTERIZATIONS OF THE GUMBEL DISTRIBUTION BASED ON LOWER RECORD VALUES

  • Jin, Hyun-Woo;Lee, Min-Young
    • 충청수학회지
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    • 제30권3호
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    • pp.285-289
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    • 2017
  • Let $\{X_n,\;n{\geq}1\}$ be a sequence of independent and identically distributed random variables with cdf F(x) which is absolutely continuous with pdf f(x) and F(x) < 1 for all x in ($-{\infty},\;{\infty}$). In this paper, we obtain the characterizations of the Gumbel distribution by lower record values.

ON CHARACTERIZATIONS OF THE NORMAL DISTRIBUTION BY INDEPENDENCE PROPERTY

  • LEE, MIN-YOUNG
    • Journal of applied mathematics & informatics
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    • 제35권3_4호
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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.