• Communications of the Korean Mathematical Society
• /
• v.13 no.1
• /
• pp.151-158
• /
• 1998

In this note we derive inequalities of linearly positive quadrant dependent random variables and obtain a strong law of large numbers for linealy positive quardant dependent random variables. Our results imply an extension of Birkel's strong law of large numbers for associated random variables to the linear positive quadrant dependence case.

• Bulletin of the Korean Mathematical Society
• /
• v.35 no.4
• /
• pp.709-718
• /
• 1998

In this paper we obtain strong laws of large numbers for 2-dimensional arrays of random variables which are either pairwise positive quadrant dependent or associated. Our results imply extensions of Etemadi`s strong laws of large numbers for nonnegative random variables to the 2-dimensional case.

• Bulletin of the Korean Mathematical Society
• /
• v.38 no.3
• /
• pp.605-610
• /
• 2001

It is shown that for each 1 < p < 2 there exist identically distributed uncorrelated random variables $X_n\; with\;E({$\mid$X_1$\mid$}^p)\;<\;{\infty}$, not fulfilling the weak law of large numbers (WLLN). If, however, the random variables are moreover non-negative, the weaker integrability condition $E(X_1\;log\;X_1)\;<\;{\infty}$ already guarantees the strong law of large numbers.

• Communications of the Korean Mathematical Society
• /
• v.13 no.2
• /
• pp.385-391
• /
• 1998

In this note, we study a weak law of large numbers for sequences of exchangeable random variables. As a special case, we have an extension of Kolmogorov's generalization of Khintchine's weak law of large numbers to i.i.d. random variables.

• Journal of Institute of Control, Robotics and Systems
• /
• v.5 no.2
• /
• pp.139-144
• /
• 1999

The present paper is concerned with the robust decentralized stabilization problem of large-scale systems with time delays in the interconnections using sliding mode control. Based on Lyapunov stability theorem and H$_{\infty}$ theory, an existence condition of the sliding mode and a robust decentralized sliding mode controller are newly derived for large-scale systems under mismatched uncertainties. Finally, a numerical example is given to verify the validity of the results developed in this paper.

• 제어로봇시스템학회:학술대회논문집
• /
• 1991.10a
• /
• pp.601-605
• /
• 1991

In this paper an approximate solution method for the large-scale Traveling Salesman Problem(TSP) is presented. The method start with the subdivision of the problem domain into a number of clusters by considering their geometries. The clusters have limited number of nodes so as to get local solutions. They are linked to give the least path which covers the whole domain and become TSPs with start- and end-node. The approximate local solutions in each cluster are obtained by using geometrical property of the cluster, and combined to give an overall-approximate solution for the large-scale TSP.

• 제어로봇시스템학회:학술대회논문집
• /
• 1986.10a
• /
• pp.169-174
• /
• 1986

This thesis investigates the scanning time ; one of the most important performance index of Programmable Controller(PC). The multiprocessor architecture of the large PC considered in this thesis are classified as architecture 1 and architecture 2 by the bus control methods. The queuing model of each architecture is developed. Form the analysis it is observed that in the case of the number of processors less than 3 the best architecture of the large PC is the architecture 2 and in the case of the number of processors greater than 2 the best architecture of the large PC is the architecture 1.

• Journal of applied mathematics & informatics
• /
• v.22 no.1_2
• /
• pp.331-338
• /
• 2006

The Paley-type inequalities for the complete convergence and lower and upper bounds in the Baum-Katz law of large numbers for i.i.d. random variables sequence are obtained. The results obtained generalize the result of Pruss [8].

• Journal of applied mathematics & informatics
• /
• v.29 no.1_2
• /
• pp.201-210
• /
• 2011

In this paper, we obtain the H$\`{a}$jeck-R$\`{e}$nyi type inequality and the strong law of large numbers for asymptotically linear negative quadrant dependent random variables by using this inequality. We also give the strong law of large numbers for the linear process under asymptotically linear negative quadrant dependence assumption.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.1
• /
• pp.195-206
• /
• 2020

The fundamental idea of this article is to present an effective way to obtain the large groups in terms of the split extension obtained by a finite cyclic group and a free abelian group rank 2. The proof of the main result on largeness property of this specific split extension groups will be given by using the connection of large groups with the groups having deficiency one presentations.