• The Journal of Natural Sciences
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• v.8 no.2
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• pp.5-7
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• 1996

Let {X,$X_n$,n$\geq$1} be i.i.d. random variables with mean zero and {$a_ni$, 1$\leq$i$\leq$n,n$\geq$1} a triangular array of constants. In this paper we give sufficient conditions on X and {$a_ni$} such that $sum_{i=1}^n$$a_{ni}$$X_i$ converges to zero almostly surely.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.32B no.9
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• pp.62-70
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• 1995

In some practical applications of the LMS Algorithm the coefficient adaptation can be performed only after some fixed delay. The resulting algorithm is known as the Delayed Least Mean Square (DLMS) algorithm in the literature. There exist analyses for this algorithm, but most of them are based on the unrealistic independence assumption between successive input vectors. Inthis paper we consider the DLMS algorithm with decreasing step size .mu.(n)=n/a, a>0 and prove the almost-sure convergence ofthe weight vector W(n) to the Wiener solution W$_{opt}$ as n .rarw. .inf. under the mixing unput condition and the satisfaction of the law of large numbers. Computer simulations for decision-directed adaptive equalizer with decoding delay are performed to demonstrate the functioning of the proposed algorithm.m.

• 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.

• Journal of the Korean Mathematical Society
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• v.58 no.1
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• pp.237-264
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• 2021

In this work the stationary bootstrap of Politis and Romano [27] is applied to the empirical distribution function of stationary and associated random variables. A weak convergence theorem for the stationary bootstrap empirical processes of associated sequences is established with its limiting to a Gaussian process almost surely, conditionally on the stationary observations. The weak convergence result is proved by means of a random central limit theorem on geometrically distributed random block size of the stationary bootstrap procedure. As its statistical applications, stationary bootstrap quantiles and stationary bootstrap mean residual life process are discussed. Our results extend the existing ones of Peligrad [25] who dealt with the weak convergence of non-random blockwise empirical processes of associated sequences as well as of Shao and Yu [35] who obtained the weak convergence of the mean residual life process in reliability theory as an application of the association.

• East Asian mathematical journal
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• v.8 no.1
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• pp.9-17
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• 1992

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.455-469
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• 2002

The Purpose Of this Paper is to introduce the concept of a class of strictly successively hemicontractive mappings and construct certain stable and almost stable iteration procedures for the iterative approximation of fixed points for asymptotically nonexpansive and strictly successively hemicontractive mappings in Banach spaces.

• Journal of the Korean Society of Industry Convergence
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• v.25 no.2_2
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• pp.233-238
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• 2022

This study evaluated the fatigue limit depending on microcracks using 0.57 wt.% carbon steel with different Vickers hardness. The fatigue limit was almost constant up to a certain limit regardless of the carbon content. However, the fatigue limit decreased rapidly as the size of the crack increased. As the crack aspect ratio was smaller, the fatigue limit of the depth (point A) a lot decreased. The fatigue limit ratio of the depth decreased significantly because the crack propagation in the depth direction was fast as the crack aspect ratio became smaller. On the other hand, the fatigue limit ratio of surface cracks increased as the crack aspect ratio decreased.

• Journal of the Korean Society of Industry Convergence
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• v.9 no.1
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• pp.87-91
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• 2006

This research exposes the process of carbonization of solid waste from the city and the method of activated, as well as the process of meso-porous under several test conditions. In addition, it is expected that the active carbon obtained through this process can be used as filter for air and sewage treatment, and can absorb dioxin(as almost 60-80% of meso-porous and porous properties area) unlike the existing active carbon.

• Proceedings of the Korea Institute of Convergence Signal Processing
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• 2001.06a
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• pp.225-228
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• 2001

We propose a method which has effective scalable indexing characteristics of large color image archives. Color key and energy key method which uses provides high performance of fast accessing and has almost constant query response time over DH size.

• Proceedings of the Korea Institute of Convergence Signal Processing
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• 2001.06a
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• pp.113-116
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• 2001

The conventional K-means algorithm is widely used in vector quantizer design and clustering analysis. Recently modified K-means algorithm has been proposed where the codevector updating step is as fallows: new codevector = current codevector + scale factor (new centroid - current codevector). This algorithm uses a fixed value for the scale factor. In this paper, we propose a new algorithm for the enhancement of learning time in fuzzy c-means a1gorithm. Experimental results show that the proposed method produces codebooks about 5 to 6 times faster than the conventional K-means algorithm with almost the same Performance.