• Bulletin of the Korean Mathematical Society
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• v.43 no.1
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• pp.169-178
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• 2006

For double arrays of constants ${a_{ni},\;1{\leq}i{\leq}k_n,\;n{\geq}1}$ and sequences ${X_n,\;n{\geq}1}$ of asymptotically almost negatively associated (AANA) random variables the almost sure convergence of $\sum\limits{_{i=1}}{^{k_n}}\;a_{ni}X_i$ is derived.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.853-865
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• 2019

In this paper, we consider gradient estimates for positive solutions to the following nonlinear elliptic equation on a complete Riemannian manifold: $${\Delta}_Vu+cu^{\alpha}=0$$, where c, ${\alpha}$ are two real constants and $c{\neq}0$. By applying Bochner formula and the maximum principle, we obtain local gradient estimates for positive solutions of the above equation on complete Riemannian manifolds with Bakry-${\acute{E}}mery$ Ricci curvature bounded from below, which generalize some results of [8].

• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.1001-1016
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• 2019

We are concerned with optimization methods for the $L^2$-Wasserstein least squares problem of Gaussian measures (alternatively the n-coupling problem). Based on its equivalent form on the convex cone of positive definite matrices of fixed size and the strict convexity of the variance function, we are able to present an implementable (accelerated) gradient method for finding the unique minimizer. Its global convergence rate analysis is provided according to the derived upper bound of Lipschitz constants of the gradient function.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1329-1334
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• 2019

We define the concept of a generator for a ${\mathbb{Z}}^k$-action T and show that T is expansive if and only it has a generator. Further, we prove several properties of a ${\mathbb{Z}}^k$-action including that the least upper bound of the set of expansive constants is not an expansive constant.

• Honam Mathematical Journal
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• v.43 no.4
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• pp.627-639
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• 2021

Numerical techniques are used to determine the radius of convexity of the starlike functions related to cardioid shaped bounded domain. In addition, radius constants of certain starlikeness associated with right half plane of various starlike functions are computed.

• Honam Mathematical Journal
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• v.34 no.2
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• pp.241-252
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• 2012

Let $\{X_{ni},\;1{\leq}i{\leq}n,\;n{\geq}1\}$ be a sequence of LNQD which are dominated randomly by another random variable X. We obtain the complete convergence and almost sure convergence of weighted sums ${\sum}^n_{i=1}a_{ni}X_{ni}$ for LNQD by using a new exponential inequality, where $\{a_{ni},\;1{\leq}i{\leq}n,\;n{\geq}1\}$ is an array of constants. As corollary, the results of some authors are extended from i.i.d. case to not necessarily identically LNQD case.

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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• pp.273-285
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• 1999

In this paper we establish the weak law of large numbers for randomly weighted partial sums of random variables and study conditions imposed on the triangular array of random weights {$W_{nj}{\;}:{\;}1{\leq}j{\leq}n,{\;}n{\geq}1$} and on the triangular array of random variables {$X_{nj}{\;}:{\;}1{\leq}j{\leq}n,{\;}{\geq}1$} which ensure that $\sum_{j=1}^{n}{\;}W_{nj}{\mid}X_{nj}{\;}-{\;}B_{nj}{\mid}$ converges In probability to 0, where {$B_{nj}{\;}:{\;}1{\;}{\leq}{\;}j{\;}{\leq}{\;}n,{\;}n{\;}{\geq}{\;}1$} is a centering array of constants or random variables.

• Korean Journal of Mathematics
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• v.27 no.1
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• pp.81-92
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• 2019

We introduce a reciprocal-negative Fermat's equation generalized with constants coefficients and investigate its stability in a quasi-${\beta}$-normed space.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.3
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• pp.201-222
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• 2011

In the present work, the mathematical model of wire coating in a straight annular die is developed for unsteady second grade fluid in the form of partial differential equation. The Optimal Homotopy Asymptotic Method (OHAM) is applied for obtaining the solution of the model problem. This method provides us a suitable way to control the convergence of the series solution using the auxiliary constants which are optimally determined.

• Journal of the Korean Statistical Society
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• v.34 no.4
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• pp.263-272
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• 2005

Let {$X_n,\;n{\ge}1$} be a sequence of negatively associated random variables which are dominated randomly by another random variable. We discuss the limit properties of weighted sums ${\Sigma}^n_{i=1}a_{ni}X_i$ under some appropriate conditions, where {$a_{ni},\;1{\le}\;i\;{\le}\;n,\;n\;{\ge}\;1$} is an array of constants. As corollary, the results of Bai and Cheng (2000) and Sung (2001) are extended from the i.i.d. case to not necessarily identically distributed negatively associated setting. The corresponding results of Chow and Lai (1973) also are extended.