• 대한수학회지
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• 제42권1호
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• pp.171-189
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• 2005

In this paper, we first establish some characterization of tightness for a sequence of random elements taking values in the space of normal and upper-semicontinuous fuzzy sets with compact support in $R^P$. As a result, we give some sufficient conditions for a sequence of fuzzy random sets to converge in distribution.

• 대한수학회논문집
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• 제35권3호
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• pp.843-854
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• 2020

The purpose of this present paper is to obtain inclusion relations between various subclasses of harmonic univalent functions by using the convolution operator associated with generalized distribution series. To be more precise, we obtain such inclusions with harmonic starlike and harmonic convex mappings in the plane.

• 대한수학회보
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• 제49권6호
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• pp.1163-1178
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• 2012

In this paper, we study the geometry of Einstein half lightlike submanifolds M of a semi-Riemannian space form $\bar{M}(c)$ subject to the conditions: (a) M is screen conformal, and (b) the coscreen distribution of M is a conformal Killing one. The main result is a classification theorem for screen conformal Einstein half lightlike submanifolds of a Lorentzian space form with a conformal Killing coscreen distribution.

• 호남수학학술지
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• 제30권4호
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• pp.671-676
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• 2008

We give the relation between the Riemann-Stieltjes integrals with respect to the Riesz-N$\'{a}$gy-Tak$\'{a}$cs(RNT) distribution $H_{a,p}$ satisfying the equation a = $(1-a)^m$ and those with respect to the dual RNT distribution $H_{1-a,1-p}$, which leads to a generalization of recent results for a = $\frac{1}{2}$.

• East Asian mathematical journal
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• 제34권3호
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• pp.287-293
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• 2018

We investigate the averaging value of a random sampling ${\zeta}(1/2+iX_t)$ of the Riemann zeta function on the critical line. Our result is that if $X_t$ is an increasing random sampling with Poisson distribution, then $${\mathbb{E}}{\zeta}(1/2+iX_t)=O({\sqrt{\;log\;t}}$$, for all sufficiently large t in ${\mathbb{R}}$.

• 충청수학회지
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• 제15권1호
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• pp.87-94
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• 2002

Trot(1999) considered how to calculate the expected area of a random triangle in the unit square $[0,1]{\times}[0,1]$. He used the Mathematica software package for the computational part. In this article, we study various aspects of the probability distribution of a triangle randomly chosen inside the circle of radius r. A simulation activity that can be conducted in statistics and probability classrooms is also considered.

• 충청수학회지
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• 제22권2호
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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.

• 충청수학회지
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• 제22권1호
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• pp.25-30
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• 2009

In this paper, we establish some characterizations which is satisfied by the independence of the upper record values from the Weibull distribution. One characterization of several results is that $X{\in}W$ EI(1, $\alpha$), $\alpha>0$, if and only if $\frac{X_{U(m)}}{X_{U(n)}}$ and $X_{U(n)}$, $1{\leq}m are independent.

• 충청수학회지
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• 제29권1호
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• pp.95-102
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• 2016

Multi-server queueing systems with retrials are widely used to model problems in a call center. We present an explicit formula for an approximation of the queue length distribution in a multi-server retrial queue, by using the Lerch transcendent. Accuracy of our approximation is shown in the numerical examples.

• 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.