• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1137-1146
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• 2011

Let {$X_i$, $i{\geq}1$} be a sequence of i.i.d. nondegenerate random variables which is in the domain of attraction of the normal law with mean zero and possibly infinite variance. Denote $S_n={\sum}_{i=1}^n\;X_i$, $M_n=max_{1{\leq}i{\leq}n}\;{\mid}S_i{\mid}$ and $V_n^2={\sum}_{i=1}^n\;X_i^2$. Then for d > -1, we showed that under some regularity conditions, $$\lim_{{\varepsilon}{\searrow}0}{\varepsilon}^2^{d+1}\sum_{n=1}^{\infty}\frac{(loglogn)^d}{nlogn}I\{M_n/V_n{\geq}\sqrt{2loglogn}({\varepsilon}+{\alpha}_n)\}=\frac{2}{\sqrt{\pi}(1+d)}{\Gamma}(d+3/2)\sum_{k=0}^{\infty}\frac{(-1)^k}{(2k+1)^{2d+2}}\;a.s.$$ holds in this paper, where If g denotes the indicator function.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.331-338
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• 2006

The Paley-type inequalities for the complete convergence and lower and upper bounds in the Baum-Katz law of large numbers for i.i.d. random variables sequence are obtained. The results obtained generalize the result of Pruss [8].

• Journal of Ocean Engineering and Technology
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• v.19 no.5 s.66
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• pp.58-64
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• 2005

In this paper, a feedback linearizing anti-sway control law, using a 2-D model for container cranes, is investigated. The equations of motion are first derived from Lagrange's equation. Then, by substituting the sway dynamics into the trolley dynamics, a reduction of variables from three (trolley, hoist, sway) to two (trolley, hoist) is pursued. The anti-sway control law is designed based on the Lyapunov stability theorem. The proposed control law guarantees the uniform asymptotic stability of the closed-loop system. The simulation results of the derived control law, using MATLAB/Simulink, are compared with those of the sliding mode control law, noted in previous literature. Also, experimental results using a 3-D pilot crane are provided.

• Journal of the Ergonomics Society of Korea
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• v.29 no.6
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• pp.861-868
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• 2010

This study explored an extended three-dimensional Fitts' law that is more suited for the pointing task than the conventional Fitts' law. The experiments were conducted under the manipulation of the distance to the target, size of the target, and direction of the target's location that can be described by two angles, $\theta1$ and $\theta2$. Considering the starting point as the center of coordinates, $\theta1$ is the angle between the positive z-axis and the target location and $\theta2$ is the angle between the positive y-axis and the projected target location on the x-y plane. From the experimental results, we confirmed that all four variables significantly affect the movement time. As we extended the index of difficulty of the conventional Fitts' model by incorporating $\theta1$ and $\theta2$, we established an extended Fitts' model that showed better accordance with the empirical data than the conventional Fitts' model and 3D Fitts' law of Murata and Iwase, in terms of the $r^2$ and the standard error of the residual between the measured movement time and the predicted value.

• Journal of Radiation Protection and Research
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• v.17 no.1
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• pp.21-30
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• 1992

The frequencies of KCCH cyclotron neutron (30 cGy/min) or $^{60}Co\;{\gamma}-rays$ (210 cGy/min)-induced asymmetrical interchanges (dicentrics and centric rings) and acentric fragments (deletion) at several doses were measured in the normal human peripheral blood lymphocytes Chromosome aberrations were scored at the first nitosis after stimulation with phytohemagglutinin. The neutron and y-ray data were analysed on linear, power-law, quadratic and linear-quadratic model . When the dicentrics and centric rings of ${\gamma}-rays$ datas were pooled and fitted to these model, good fits were obtained to power-law $[Y=(5.81{\pm}1.96){\times}10^6D^{1.93+0.06},\; P=0.931]$, quadratic $[Y=(3.91{\pm}0.09){\times}10^{-6}D^2,\;P=0.972]$ an linear-Quadrati model $[Y=(6.55{\pm}6.83){\times}10^{-5}D+(3.72{\pm}0.22){\times}10^{-6}D^2\; P=0.922]$, except for linear model (P=0.067) As in the case of neutron data, the best fit was obtained to the linear model $(Y=(6.12{\pm}0.17){\times}10^{-3}\;D-0.22,\;P=0.987]$ and good fits were obtained to power-law$[Y=(5.36{\pm}3.02) {\times}10^{-4}D^{1.42+0.11},\; P=0.601]$ and linear-quadratic model$[Y=(2.43{\pm}0.70){\times}10^{-3}D+(1.21{\pm}0.39){\times}10^{-7}D^2$, \;P=0.415], except for quadratic model (P<0.005). The relative biological effectiveness (RBE) of neutron compared with y-ray was estimated by best fitting model. In the asymmetrical interchanges range between 0.1 and 1.5 per cell, the RBE was found to be $2.714{\pm}0.408$.

• Journal of radiological science and technology
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• v.43 no.6
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• pp.489-494
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• 2020

The Law method is observing the temporal bone. There are two types of methods: the double angle method, which manipulates the center ray angle of the tube twice, and the single angle method, which manipulates once. The purpose is to increase the reproducibility of the image by making vertical incidence by making an assistive device using a 3D printer. Two assistive devices with a wedge-shaped 8.5 × 10 × 2.3 cm, an inclined surface of 7.5 cm, and an inclination angle of 15° were fabricated. Assistive devices can be combined with each other in the form of grooves, and PLA (Poly Lactic Acid) is used as a material. In the first experiment, 10 examiners operated the tube 15° in the caudad direction and 15° in the anterior direction, and measured it with a protractor to conduct a reproducibility experiment. Second, two examiners acquired vertically incidence images using the existing law method and assistive devices, and measured the distance between each measurement point to evaluate the reproducibility. The tube center ray angle reproducibility experiment was not statistically significant, but the angle difference was up to 9° between examiners. The reproducibility experiment of radiographic images was not statistically significant with the conventional method, and the method using an assistive device was statistically significant. Therefore, regardless of skill level, an image capable of securing reproducibility, which is the advantage of vertical incidence, could be obtained.

• The Korean Journal of Air & Space Law and Policy
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• no.spc
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• pp.225-246
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• 2007

This article is dedicated to my colleague and friend Professor Soon-Kil Hong, Ph.D, who is the famous President of the Korean Association of Air and Space Law and distinguished teacher at the prestigious Hankuk Aviation University. I had the honour and pleasure to teach there a few years ago - upon his gracious invitation. Professor Soon-Kil Hong has made a long, outstanding and impressive career in aviation and space activities, both from a practitioners and academic perspective. That is why I have tried to find a subject which addresses these facets of his personality although this humble article cannot do justice to the great merits of Professor Soon-Kil Hong. This article discusses the liability aspects for damages and injuries to passengers on suborbital flights, by examining: 1. Recent developments regarding space tourism 2. Suborbital flights in relation to the Chicago Convention 3. The application of space law treaties to space tourism 4. Potential candidates for liability regimes applying to space tourism 4.1 Introduction 4.2 Liability under international space law 4.2.1 The Outer Space Treaty (1969) 4.2.2 The Liability Convention (1972) 4.2.3 Conclusions 4.3 Liability under international private air law 4.3.1 Introduction 4.3.2 The Warsaw Convention (1929), as variously amended 4.3.3 The Montreal Agreement (1999) 4.3.4 Conclusions 5. Final observations

• Communications of the Korean Mathematical Society
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• v.13 no.2
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• pp.385-391
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• 1998

In this note, we study a weak law of large numbers for sequences of exchangeable random variables. As a special case, we have an extension of Kolmogorov's generalization of Khintchine's weak law of large numbers to i.i.d. random variables.

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.993-1005
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• 2008

Let {$X,\;X_n;n{\geq}1$} be a sequence of i.i.d. random variables. Set $S_n=X_1+X_2+{\cdots}+X_n,\;M_n=\max_{k{\leq}n}|S_k|,\;n{\geq}1$. Then we obtain that for any -1$\lim\limits_{{\varepsilon}{\searrow}0}\;{\varepsilon}^{2b+2}\sum\limits_{n=1}^\infty\;{\frac {(log\;n)^b}{n^{3/2}}\;E\{M_n-{\varepsilon}{\sigma}\sqrt{n\;log\;n\}+=\frac{2\sigma}{(b+1)(2b+3)}\;E|N|^{2b+3}\sum\limits_{k=0}^\infty\;{\frac{(-1)^k}{(2k+1)^{2b+3}$ if and only if EX=0 and $EX^2={\sigma}^2<{\infty}$.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.28 no.5
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• pp.553-561
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• 2015

The exponential and power law functionally graded material(FGM) theory is reformulated considering the refined shear and normal deformation theory. This theory has ability to capture the both normal deformation effect and exponential and power law function in terms of the volume fraction of the constituents for material properties through the plate thickness. Navier's method has been used to solve the governing equations for all edges simply supported plates on Pasternak elastic foundation. Numerical solutions of vibration analysis of FGM plates are presented using this theory to illustrate the effects of power law index and 3-D theory of exponential and power law function on natural frequency. The relations between 3-D and 2-D higher-order shear deformation theory are discussed by numerical results. Further, effects of (i) power law index, (ii) side-to-thickness ratio, and (iii) elastic foundation parameter on nondimensional natural frequency are studied. To validate the present solutions, the reference solutions are discussed.