• Journal of the Korean Mathematical Society
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• v.47 no.6
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• pp.1317-1328
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• 2010

In this paper, we study the properties of positive solutions for the reaction-diffusion equation $u_t$ = $\Delta_u+{\int}_\Omega u^pdx-ku^q$ in $\Omega\times(0,T)$ with nonlocal nonlinear boundary condition u (x, t) = ${\int}_{\Omega}f(x,y)u^l(y,t)dy$ $\partial\Omega\times(0,T)$ and nonnegative initial data $u_0$ (x), where p, q, k, l > 0. Some conditions for the existence and nonexistence of global positive solutions are given.

• Water Engineering Research
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• v.3 no.3
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• pp.195-202
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• 2002

The mean is generally used as a point estimator in water-quality data. Unfortunately, the nonnormal and skewed distributions of data hinder the direct application of the mean, which is inappropriate statistics in this case. The use of robust statistics such as L, M, and R-estimators are recommended and become more efficient. The median (L-estimator), the biweight (M-estimator), and the Hodges-Lehmann method (R-estimator) are briefly introduced and applied in this paper. From the actual data analyses, it is known that the median does not guarantee robustness for a small number of data sets, and robust measures of location or the arithmetic mean without outliers are highly recommended if the distribution has tails or outliers. Care must be taken to measure the location because water quality level within a water body can change depending on the selected point estimator.

• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.377-389
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• 2019

We evaluate the convolution sum $W_{a,b}(n):=\sum_{al+bm=n}{\sigma}(l){\sigma}(m)$ for (a, b) = (1, 28),(4, 7),(2, 7) for all positive integers n. We use a modular form approach. We also re-evaluate the known sums $W_{1,14}(n)$ and $W_{1,7}(n)$ with our method. We then use these evaluations to determine the number of representations of n by the octonary quadratic form $x^2_1+x^2_2+x^2_3+x^2_4+7(x^2_5+x^2_6+x^2_7+x^2_8)$. Finally we express the modular forms ${\Delta}_{4,7}(z)$, ${\Delta}_{4,14,1}(z)$ and ${\Delta}_{4,14,2}(z)$ (given in [10, 14]) as linear combinations of eta quotients.

• The Korean Journal of Applied Statistics
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• v.28 no.1
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• pp.9-21
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• 2015

The support vector machine has been successfully applied to various classification areas due to its flexibility and a high level of classification accuracy. However, when analyzing imbalanced data with uneven class sizes, the classification accuracy of SVM may drop significantly in predicting minority class because the SVM classifiers are undesirably biased toward the majority class. The weighted $L_2$-norm SVM was developed for the analysis of imbalanced data; however, it cannot identify irrelevant input variables due to the characteristics of the ridge penalty. Therefore, we propose the weighted $L_1$-norm SVM, which uses lasso penalty to select important input variables and weights to differentiate the misclassification of data points between classes. We demonstrate the satisfactory performance of the proposed method through simulation studies and a real data analysis.

• Journal of the Korean Data and Information Science Society
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• v.9 no.2
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• pp.299-303
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• 1998

In this paper weak laws of large numbers are obtained for random variables in $L^{1}(R)$ which satisfy a compact uniform integrability condition.

• Journal of the Korean Statistical Society
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• v.25 no.2
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• pp.255-263
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• 1996

Let $(X_{1j}, X_{2j}, … , X_{nj}, Y_j/)$j = 1, 2, … , n, be a sample of size n on an (m + l)-dimensional vector $(X_1, X_2, … , X_m, Y)$, m .geq. 1. If $Y_{(r)}$ denote the rth order statistic from Y, then the $X_{[r:n]}$ paired with $Y_(r)$ is termed the concomitant vector of the order statistics. The general distributions of concomitant of order statistics will be found. The mean, variance and covariance of$X_{[r:n]}$ Will be studied. Then we will apply the results to the multivariate normal variate case.e.

• International Journal of Reliability and Applications
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• v.8 no.2
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• pp.199-210
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• 2007

This paper presents estimations of the generalized Rayleigh distribution model based on grouped and censored data. The maximum likelihood method is used to derive point and asymptotic confidence estimates of the unknown parameters. The results obtained in this paper generalize some of those available in the literature. Finally, we test whether the current model fits a set of real data better than other models.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.1A
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• pp.34-42
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• 2000

In this paper, the closed form expression for the average bit error probability(BER) is derived for diversity reception using an L-branch maximal ratio combining(MRC) system which has same fading index and different fading index. Also, the BER to have same average power and Nakagami m-distribution for a generalized selection combining(SC) is derived, whereby the signal with the largest amplitude is selected from the original diversity branches in the channel, the order statistics is applied. Especially, when L is 1 in a selective diversity, the derived expression leads to that of DPSK in which SC is not applied in Nakagami fading. Changing the diversity branch L and fading index m, we compare the performance of MRC and SC.

• The Korean Journal of Applied Statistics
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• v.4 no.2
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• pp.129-135
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• 1991

A few simple methods to find $L_1$-unbiased estimators for location and scale parameters are summarized and examples utilizing diffusivity, a natural measure of dispersion for $L_1$-unbiased estimators, are given.

• Korean Journal of Mathematics
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• v.30 no.3
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• pp.555-560
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• 2022

Suppose L/K be a finite abelian extension of number fields of odd degree and suppose an abelian variety A defined over L is a K-variety. If the endomorphism algebra of A/L is a field F, the followings are equivalent : (1) The enodomorphiam algebra of the restriction of scalars from L to K is simple. (2) There is no proper subfield of L containing L^G_F on which A has a K-variety descent.