• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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• pp.431-452
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• 2022

For any positive integer 𝜇, we compute the mean value of the 𝜇-th derivative of quadratic Dirichlet L-functions over the rational function field 𝔽_q(t), where q is a power of 2.

• Wind and Structures
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• v.23 no.4
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• pp.367-383
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• 2016

The influence mechanism of mean value components, noted as $P_0$, on POD applications for complete random fields $P_C(t)$ and fluctuating random fields $P_F(t)$ are illustrated mathematically. The critical philosophy of the illustration is introduction of a new matrix, defined as the correlation function matrix of $P_0$, which connect the correlation function matrix of $P_C(t)$ and $P_F(t)$, and their POD results. Then, POD analyses for several different wind pressure fields were presented comparatively as validation. It's inevitable mathematically that the first eigenmode of $P_C(t)$ resembles the distribution of $P_0$ and the first eigenvalue of $P_C(t)$ is close to the energy of $P_0$, due to similarity of the correlation function matrixs of $P_C(t)$ and $P_0$. However, the viewpoint is not rigorous mathematically that the first mode represents the mean pressure and the following modes represent the fluctuating pressure when $P_C(t)$ are employed in POD application. When $P_C(t)$ are employed, POD results of all modes would be distorted by the mean value components, and it's impossible to identify $P_0$ and $P_F(t)$ separately. Consequently, characteristics of the fluctuating component, which is always the primary concern in wind pressure field analysis, can only be precisely identified with $P_0$ excluded in POD.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.44 no.1
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• pp.45-50
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• 2021

Machines and facilities are physically or chemically degenerated by continuous usage. The representative type of the degeneration is the wearing of tools, which results in the process mean shift. According to the increasing wear level, non-conforming products cost and quality loss cost are increasing simultaneously. Therefore, a preventive maintenance is necessary at some point. The problem of determining the maintenance period (or wear limit) which minimizes the total cost is called the 'process mean shift problem'. The total cost includes three items: maintenance cost (or adjustment cost), non-conforming cost due to the non-conforming products, and quality loss cost due to the difference between the process target value and the product characteristic value among the conforming products. In this study, we set the production volume as a decreasing function rather than a constant. Also we treat the process variance as a function to the increasing wear rather than a constant. To the quality loss function, we adopted the Cpm+, which is the left and right asymmetric process capability index based on the process target value. These can more reflect the production site. In this study, we presented a more extensive maintenance model compared to previous studies, by integrating the items mentioned above. The objective equation of this model is the total cost per unit wear. The determining variables are the wear limit and the initial process setting position that minimize the objective equation.

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1529-1547
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• 2021

In this series, we investigate the calculation of mean values of derivatives of Dirichlet L-functions in function fields using the analogue of the approximate functional equation and the Riemann Hypothesis for curves over finite fields. The present paper generalizes the results obtained in the first paper. For µ ≥ 1 an integer, we compute the mean value of the µ-th derivative of quadratic Dirichlet L-functions over the rational function field. We obtain the full polynomial in the asymptotic formulae for these mean values where we can see the arithmetic dependence of the lower order terms that appears in the asymptotic expansion.

• Journal of Korea Water Resources Association
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• v.33 no.1
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• pp.15-30
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• 2000

This study is to develop the applied method of reliability analysis to present risk - initial water level relationship in the small reservoir. To determine the reliability, the grasping of uncertainty sources is prerequisited and performance function is formulated. Reliability analysis method is a statistical method and the basic procedure of risk evaluation for overtopping of reservoir is as follows. 1. Define the risk criterion and performance function for the overtopping. 2. Determine the uncertainties of all the variables in the performance function. 3. Perform the risk analysis with suitable risk calculation method. Reliability analysis method such as Monte Carlo simulation(MCS) method and mean value first order second moment(MVFOSM) method are used to calculate the risk for reservoir. Finally, risk - initial water level relationship is established according to return period and it is useful for reservoir operation and safety assessment.ssment.

• Journal of the Korean Data and Information Science Society
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• v.25 no.3
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• pp.643-653
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• 2014

In this paper, we propose some estimators for the extreme value distribution based on the interval method and mid-point approximation method from the progressive Type-I interval censored sample. Because log-likelihood function is a non-linear function, we use a Taylor series expansion to derive approximate likelihood equations. We compare the proposed estimators in terms of the mean squared error by using the Monte Carlo simulation.

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.365-374
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• 2013

Let $k=\mathbb{F}_q(T)$ be a rational function field over the finite field $\mathbb{F}_q$, where q is a power of an odd prime number, and $\mathbb{A}=\mathbb{F}_q[T]$. Let ${\gamma}$ be a generator of $\mathbb{F}^*_q$. Let $\mathcal{H}_n$ be the subset of $\mathbb{A}$ consisting of monic square-free polynomials of degree n. In this paper we obtain an asymptotic formula for the mean value of $L(1,{\chi}_{\gamma}{\small{D}})$ and calculate the average value of the ideal class number $h_{\gamma}\small{D}$ when the average is taken over $D{\in}\mathcal{H}_{2g+2}$.

• The Journal of Korean Physical Therapy
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• v.25 no.6
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• pp.374-378
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• 2013

Purpose: Human body have biological rhythmic pattern in a day, which is affected by internal and external environmental factors. We investigated whether respiratory function was fluctuated according to the influence of time-of-day (around at 9 am, 1 pm, and 6 pm) in health subjects, using pulmonary function test (PFT). Methods: Eighteen healthy volunteers (8 men, mean ages; $22.4{\pm}1.6$, mean heights; $166.61{\pm}9.60$, mean weight; $59.3{\pm}10.3$) were recruited. Pulmonary function test (PFT) was measured at three time points in day, around 9 am, 1 pm, and 6 pm in calm research room with condition of under 55dB noise level, using a spirometer (Vmax 229, SensorMecis, USA). Forced vital capacity (FVC), forced expiratory volume at one second (FEV1), FVC/FEV1, and peak expiratory flow (PEF) were acquired. Results: In comparison of raw value of PFT among three time points, subjects showed generally better respiratory function at 9 am, than at other points, although no significance was found. In comparison of distribution of ranking for respiratory function in each individual, only PEF showed significant difference. In general, distributional ratio of subjects who showed best performance of respiratory function in a day was high. Conclusion: These findings showed that circadian rhythm by diurnal pattern was not detected on respiratory function throughout all day. But, best performance on respiratory function was observed mostly in the morning, although statistical significance did not exist.

• Transactions on Electrical and Electronic Materials
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• v.13 no.1
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• pp.10-15
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• 2012

In conventional, skin detection methods using for skin color definitions is based on prior knowledge. By experimentation, the threshold value for dividing the background from the skin region is determined subjectively. A drawback of such techniques is that their performance is dependent on a threshold value which is estimated from repeated experiments. To overcome this, the present paper introduces a skin region detection method. This method uses a histogram approximation based on the mean shift algorithm. This proposed method applies the mean shift procedure to a histogram of a skin map of the input image. It is generated by comparing with the standard skin colors in the $C_bC_r$ color space. It divides the background from the skin region by selecting the maximum value according to the brightness level. As the histogram has the form of a discontinuous function. It is accumulated according to the brightness values of the pixels. It is then, approximated by a Gaussian mixture model (GMM) using the Bezier curve technique. Thus, the proposed method detects the skin region using the mean shift procedure to determine a maximum value. Rather than using a manually selected threshold value, as in existing techniques this becomes the dividing point. Experiments confirm that the new procedure effectively detects the skin region.

• Journal of the Korean Statistical Society
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• v.33 no.3
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• pp.323-337
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• 2004

This article coined a general class of estimators for various measures in normal population when some' a priori' or guessed value of standard deviation a is available in addition to sample information. The class of estimators is primarily defined for a function of standard deviation. An unbiased estimator and the minimum mean squared error estimator are worked out and the suggested class of estimators is compared with these classical estimators. Numerical computations in terms of percent relative efficiency and absolute relative bias established the merits of the proposed class of estimators especially for small samples. Simulation study confirms the excellence of the proposed class of estimators. The beauty of this article lies in estimation of various measures like standard deviation, variance, Fisher information, precision of sample mean, process capability index $C_{p}$, fourth moment about mean, mean deviation about mean etc. as particular cases of the proposed class of estimators.