• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.205-235
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• 2023

In this paper, we introduce and study an iterative technique for solving quasimonotone split variational inequality problems and fixed point problem in the framework of real Hilbert spaces. Our proposed iterative technique is self adaptive, and easy to implement. We establish that the proposed iterative technique converges strongly to a minimum-norm solution of the problem and give some numerical illustrations in comparison with other methods in the literature to support our strong convergence result.

• Communications for Statistical Applications and Methods
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• v.19 no.4
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• pp.619-628
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• 2012

Noise reduction is an important issue in the field of image processing because image noise lowers the quality of the original pure image. The basic difficulty is that the noise and the signal are not easily distinguished. Simple smoothing is the most basic and important procedure to effectively remove the noise; however, the weakness is that the feature area is simultaneously blurred. In this research, we use ways to measure the degree of noise with respect to the degree of image features and propose a Bayesian noise reduction method based on MAP (maximum a posteriori). Simulation results show that the proposed adaptive noise reduction algorithm using Bayesian MAP provides good performance regardless of the level of noise variance.

• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.169-177
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• 2004

For a stationary field $\{X_{\b{j}},\b{j}{\;}\in{\;}{\mathbb{Z}}^d_{+}\}$ of associated random variables with distribution function $F(x)\;=\;P(X_{\b{1}}\;{\leq}\;x)$ we study strong consistency and asymptotic normality of the empirical distribution function, which is proposed as an estimator for F(x). We also consider strong consistency and asymptotic normality of the empirical survival function by applying these results.

• Bulletin of the Korean Mathematical Society
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• v.40 no.4
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• pp.715-722
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• 2003

A functional central limit theorem is obtained for a stationary linear process of the form $X_{t}=\;{\Sigma_{j=0}}^{\infty}a_{j}{\epsilon}_{t-j}, where {${\in}_{t}$｝is a strictly stationary associated sequence of random variables with $E_{{\in}_t}{\;}={\;}0.{\;}E({\in}_t^2){\;}<{\;}{\infty}{\;}and{\;}{a_j}$ is a sequence of real numbers with (equation omitted). A central limit theorem for a stationary linear process generated by stationary associated processes is also discussed.

• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.341-349
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• 2003

Let {$x_{nk}\;$\mid$1\;\leq\;k\;\leq\;n,\;n\;\geq\;1$} be an array of random varianbles and $\{a_n$\mid$n\;\geq\;1\}\;and\;\{b_n$\mid$n\;\geq\;1} be a sequence of constants with $a_n\;>\;0,\;b_n\;>\;0,\;n\;\geq\;1. In this paper, for array of row negatively associated(NA) random variables, we establish a general weak law of large numbers (WLLA) of the form (${\sum_{\kappa=1}}^n\;a_{\kappa}X_{n\kappa}\;-\;\nu_{n\kappa})\;/b_n$ converges in probability to zero, as $n\;\rightarrow\;\infty$, where {$\nu_{n\kappa}$\mid$1\;\leq\;\kappa\;\leq\;n,\;n\;\geq\;1$} is a suitable array of constants.

• Structural Engineering and Mechanics
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• v.8 no.5
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• pp.453-464
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• 1999

Safety monitoring systems of structures generally resort to detecting possible changes of dynamic system parameters. Sensitivity analysis of these dynamic system parameters may implement these techniques. Conventional structural eigenvalue problems are discussed in the scope of those systems with deterministic parameters. Large and flexible structures, such as suspension bridges, actually possess stochastic material properties and these random properties unavoidably affect the dynamic system parameters. The sensitivity matrix of structural modal parameters to basic design variables has been established in this paper. Moreover, second order statistics of natural frequencies due to the randomness of material properties have been discussed. It is concluded from numerical analysis of a modem suspension bridge that although the second order statistics of frequencies are small relatively to the change of basic design variables, such as density of mass and modulus of elasticity, the sensitivities of modal parameters to these variables at different locations change in magnitude.

• Journal of the Korean Statistical Society
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• v.33 no.3
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• pp.271-282
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• 2004

We discuss complete convergence of weighted sums for arrays of ø-mixing random variables. As application, we obtain the complete convergence of moving average processes for ø-mixing random variables. The result of Baum and Katz (1965) as well as the result of Li et al. (1992) on iid case are extended to ø-mixing setting.

• Journal of the Korean Statistical Society
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• v.31 no.4
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• pp.483-490
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• 2002

A weak convergence is obtained for a linear process of the form (equation omitted) where {$\varepsilon$$_{t}$ } is a strictly stationary sequence of associated random variables with E$\varepsilon$$_{t}$ = 0 and E$\varepsilon$$^{^2}$$_{t}$ < $\infty$ and {a $_{j}$ } is a sequence of real numbers with (equation omitted). We also apply this idea to the case of linearly positive quadrant dependent sequence.

• Genomics & Informatics
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• v.5 no.3
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• pp.118-123
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• 2007

The current existing literature offers little guidance on how to decide which method to use to analyze one-channel microarray measurements when dealing with large, grouped samples. Most previous methods have focused on two-channel data;therefore they can not be easily applied to one-channel microarray data. Thus, a more reliable method is required to determine an appropriate combination of individual basic processing steps for a given dataset in order to improve the validity of one-channel expression data analysis. We address key issues in evaluating the effectiveness of basic statistical processing steps of microarray data that can affect the final outcome of gene expression analysis without focusingon the intrinsic data underlying biological interpretation.

• Honam Mathematical Journal
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• v.24 no.1
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• pp.121-130
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• 2002

In this paper we prove a functional central limit theorem for a field $\{X_{\underline{j}}:{\underline{j}}{\in}Z_+^d\}$ of nonstationary associated random variables with $EX{\underline{j}}=0,\;E{\mid}X_{\underline{j}}{\mid}^{r+{\delta}}<{\infty}$ for some $r>2,\;{\delta}>0$and $u(n)=O(n^{-{\nu}})$ for some ${\nu}>0$, where $u(n):=sup_{{\underline{i}}{\in}Z_+^d{\underline{j}}:{\mid}{\underline{j}}-{\underline{i}}{\mid}{\geq}n}{\sum}cov(X_{\underline{i}},\;X_{\underline{j}}),\;{\mid}{\underline{x}}{\mid}=max({\mid}x_1{\mid},{\cdots},{\mid}x_d{\mid})\;for\;{\underline{x}}{\in}{\mathbb{R}}^d$. Our investigation implies and analogous result in the case associated random measure.