• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.721-730
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• 2010

In this paper we consider some results on convergence for arrays of rowwise and pairwise negatively quadrant dependent random variables.

• Journal of the Korean Data and Information Science Society
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• v.25 no.2
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• pp.423-429
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• 2014

This paper discusses a method for getting Type I sums of squares by projections under a two-way fixed-effects model when variances of errors are not equal. The method of weighted least squares is used to estimate the parameters of the assumed model. The model is fitted to the data in a sequential manner by using the model comparison technique. The vector space generated by the model matrix can be composed of orthogonal vector subspaces spanned by submatrices consisting of column vectors related to the parameters. It is discussed how to get the Type I sums of squares by using the projections into the orthogonal vector subspaces.

• Journal of Integrative Natural Science
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• v.10 no.1
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• pp.40-42
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• 2017

In this note, we study a generalization of a certain polynomial $z^n-{\sum\limits_{k=0}^{n-1}}a_kz^k$, where $\sum\limits_{k=0}^{n-1}a_k=1$, $a_k{\geq}0$ for each k, whose all zeros except for z=1 lie on the circle of radius 1/2 with center at the origin.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.4
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• pp.411-422
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• 2017

Let {$X_{ni}$, $i{\geq}1$, $n{\geq}1$} be an array of rowwise asymptotically negatively associated random variables and {$a_{ni}$, $i{\geq}1$, $n{\geq}1$} an array of constants. Some results concerning complete convergence of weighted sums ${\sum}_{i=1}^{n}a_{ni}X_{ni}$ are obtained. They generalize some previous known results for arrays of rowwise negatively associated random variables to the asymptotically negative association case.

• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.145-153
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• 2021

When {Xni|1 ≤ i ≤ n, n ≥ 1} be an array of rowwise negatively superadditive dependent(NSD) for semi-Gaussian random variables and {ani|1 ≤ i ≤ n, n ≥ 1} is an array of constants, we study the almost sure convergence of weighted sums ∑ni=1 aniXni under some appropriate conditions and we obtain some corollaries.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.679-688
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• 1995

Let $(B, \left\$\mid$ \right\$\mid$)$ be a real separable Banach space. Let $(\Omega, F, P)$ denote a probability space. A random elements in B is a function from $\Omega$ into B which is $F$-measurable with respect to the Borel $\sigma$-field $B$(B) in B.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.225-242
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• 2017

A family of $Ap{\acute{e}}ry$-like series involving reciprocals of central binomial coefficients is studied and it is shown that they represent transcendental numbers. The structure of such series is further examined in terms of finite combinations of logarithms and arctangents with arguments and coefficients belonging to a suitable algebraic extension of rationals. Monotonicity of certain quotients of weighted binomial sums which arise in the study of competitive cheap talk models is established with the help of a continuous extension of the discrete model at hand. The monotonic behavior of such quotients turns out to have important applications in game theory.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.363-370
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• 1995

A famous result of Chow and Robbins [8] asserts that if ${X_n, n \geq 1}$ are independent and identically distributed (i.i.d.) random variables with $E$\mid$X_1$\mid$ = \infty$, then for each sequence of constants ${M_n, n \geq 1}$ either $$ (1) lim inf_{n\to\infty} $\mid$\frac{M_n}{\sum_{j=1}^{n}X_j}$\mid$ = 0 almost certainly (a.c.) $$ or $$ (2) lim sup_{n\to\infty}$\mid$\frac{M_n}{\sum_{j=1}^{n}X_j}$\mid$ = \infty a.c. $$ and thus $P{lim_{n\to\infty} \sum_{j=1}^{n}X_j/M_n = 1} = 0$. Note that both (1) and (2) may indeed prevail.

• The KIPS Transactions:PartB
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• v.11B no.6
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• pp.717-722
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• 2004

This paper presents fuzzy rules to predict diagnosis of Wisconsin breast cancer using neural network with weighted fuzzy membership functions (NNWFM). NNWFM is capable of self-adapting weighted membership functions to enhance accuracy in prediction from the given clinical training data. n set of small, medium, and large weighted triangular membership functions in a hyperbox are used for representing n set of featured input. The membership functions are randomly distributed and weighted initially, and then their positions and weights are adjusted during learning. After learning, prediction rules are extracted directly from the enhanced bounded sums of n set of weighted fuzzy membership functions. Two number of prediction rules extracted from NNWFM outperforms to the current published results in number of rules and accuracy with 99.41%.

• Proceedings of the KIEE Conference
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• 1991.11a
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• pp.193-196
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• 1991

A method of extracting global, trend curves from input image that may locally not even contain small fragments of those curves using a hierarchical pyramid data structure is suggested. The smoothed input image is subsampled into a pyramid of lower-resolution versions by recursive computation of Gaussian-weighted sums. Trend curves are extracted by finding control points from ridges in these blurred images, and interpolating B-splines for those points.