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

• Journal of the Korean Mathematical Society
• /
• v.43 no.4
• /
• pp.815-828
• /
• 2006

Let {$V_{nk},\;k\;{\geq}\;1,\;{\geq}\;1$} be an array of rowwise independent random elements which are stochastically dominated by a random variable X with $E\|X\|^{\frac{\alpha}{\gamma}+{\theta}}log^{\rho}(\|X\|)\;<\;{\infty}$ for some ${\rho}\;>\;0,\;{\alpha}\;>\;0,\;{\gamma}\;>\;0,\;{\theta}\;>\;0$ such that ${\theta}+{\alpha}/{\gamma}<2$. Let {$a_{nk},k{\geq}1,n{\geq}1$) be an array of suitable constants. A complete convergence result is obtained for the weighted sums of the form $\sum{^\infty_k_=_1}\;a_{nk}V_{nk}$.

• Journal of the Korean Mathematical Society
• /
• v.53 no.1
• /
• pp.45-55
• /
• 2016

Let {$X_n,n{\geq}1$} be a sequence of negatively superadditive dependent random variables. In the paper, we study the strong law of large numbers for general weighted sums ${\frac{1}{g(n)}}{\sum_{i=1}^{n}}{\frac{X_i}{h(i)}}$ of negatively superadditive dependent random variables with non-identical distribution. Some sufficient conditions for the strong law of large numbers are provided. As applications, the Kolmogorov strong law of large numbers and Marcinkiewicz-Zygmund strong law of large numbers for negatively superadditive dependent random variables are obtained. Our results generalize the corresponding ones for independent random variables and negatively associated random variables.

• Proceedings of the IEEK Conference
• /
• 2008.06a
• /
• pp.813-814
• /
• 2008

In this paper, we propose a new tracking algorithm which uses weighted sum of color bin's centroids to find the main centroid of the target. The weights are determined by the proportion of colors of the target and by the colors of background. That is, A color which has high occupation in forming the target is highly weighted and a color which has low occupation is lowly weighted. Moreover, the proposed algorithm prevent track failure by lowering the weight of the colors which forms the background. Therefore, the proposed algorithm performs stable tracking inspite of occlusion and existence of confusing backgrounds.

• Journal of the Korean Mathematical Society
• /
• v.54 no.6
• /
• pp.1879-1903
• /
• 2017

In this paper we study the closure property and probability tail asymptotics for randomly weighted sums $S^{\Theta}_n={\Theta}_1X_1+{\cdots}+{\Theta}_nX_n$ for long-tailed random variables $X_1,{\ldots},X_n$ and positive bounded random weights ${\Theta}_1,{\ldots},{\Theta}_n$ under similar dependence structure as in [26]. In particular, we study the case where the distribution of random vector ($X_1,{\ldots},X_n$) is generated by an absolutely continuous copula.

• Proceedings of the KIEE Conference
• /
• 2001.07a
• /
• pp.181-183
• /
• 2001

This paper presents a robust power system state estimator using linear programming(LP). LP state estimators minimize the weighted sum of the absolute values of the measurement residuals. In this paper, WLS(weighted least square) and WLAV(weighted least absolute value) state estimators are run with same measurement sets including bad data in order to compare the robustness to bad data and convergence characteristics of the two methods. Simulations with three test cases are performed and the results are presented, using IEEE 14 bus system.

• Bulletin of the Korean Mathematical Society
• /
• v.36 no.2
• /
• pp.273-285
• /
• 1999

In this paper we establish the weak law of large numbers for randomly weighted partial sums of random variables and study conditions imposed on the triangular array of random weights {$W_{nj}{\;}:{\;}1{\leq}j{\leq}n,{\;}n{\geq}1$} and on the triangular array of random variables {$X_{nj}{\;}:{\;}1{\leq}j{\leq}n,{\;}{\geq}1$} which ensure that $\sum_{j=1}^{n}{\;}W_{nj}{\mid}X_{nj}{\;}-{\;}B_{nj}{\mid}$ converges In probability to 0, where {$B_{nj}{\;}:{\;}1{\;}{\leq}{\;}j{\;}{\leq}{\;}n,{\;}n{\;}{\geq}{\;}1$} is a centering array of constants or random variables.

• Journal of the Korea Institute of Military Science and Technology
• /
• v.21 no.5
• /
• pp.614-622
• /
• 2018

Based on army operating road profile, the endurance test of military vehicle aims to reproduce the similar loading conditions with mixture of proving ground tracks. It is so called as endurance test mode and its optimal generation is important to meet high reliability of endurance test. In this paper, proving ground optimization is proposed to achieve a close match to the target profile. Several performance measures such as torque-revolution counts or transmission ratio for the powertrain system can be considered as one of the objective functions. However, the one-side optimal endurance test mode may give the poor solution in the whole system point of view. To incorporate several goals simultaneously, this paper employs multi-objective optimization technique to generate endurance test mode. One of the most widely used method, weighted-sum method is applied here and the case study is discussed.

• Environmental and Resource Economics Review
• /
• v.9 no.2
• /
• pp.349-371
• /
• 2000

Data Envelopment Analysis model is a linear programming based technique for measuring the relative performance of organizational units where the presence of multiple inputs and outputs makes comparison difficult. A common measure for relative efficiency is weighted sum of outputs divided by weighted sum of inputs. DEA model allows each unit to adopt a set of weight that shows it in the most favorable light in comparison to the other unit. In this paper, we present the mathematical background and characteristics of DEA model, and give a short case study where we apply the DEA model to evaluate the relative efficiencies of 51 global electricity companies. The technical efficiency and scale efficiency are also to be investigated. Generating capacity and the number of employees are used for input data, and revenue, net profit and electricity sales are used for output data. We find that the companies with 100% relative efficiency are only 9 among 51 electricity companies. And the technical and scale efficiency of KEPCO is 98.7% and 78.89%, respectively. This means that the inefficiency of KEPCO is caused by the scale inefficiency. The analysis shows that the employees should be decreased by 15% at minimum to get the 100% efficiency. The result suggests that KEPCO needs the structural reform to improve the efficiency.

• Smart Structures and Systems
• /
• v.25 no.5
• /
• pp.593-604
• /
• 2020

Temperature may have more significant influences on structural responses than operational loads or structural damage. Therefore, a comprehensive understanding of temperature distributions has great significance for proper design and maintenance of bridges. In this study, the temperature distribution of the steel box girder is systematically investigated based on the structural health monitoring system (SHMS) of the Sutong Cable-stayed Bridge. Specifically, the characteristics of the temperature and temperature difference between different measurement points are studied based on field temperature measurements. Accordingly, the probability density distributions of the temperature and temperature difference are calculated statistically, which are further described by the general formulas. The results indicate that: (1) the temperature and temperature difference exhibit distinct seasonal characteristics and strong periodicity, and the temperature and temperature difference among different measurement points are strongly correlated, respectively; (2) the probability density of the temperature difference distribution presents strong non-Gaussian characteristics; (3) the probability density function of temperature can be described by the weighted sum of four Normal distributions. Meanwhile, the temperature difference can be described by the weighted sum of Weibull distribution and Normal distribution.