• 대한수학회보
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• 제48권6호
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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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• 제22권1_2호
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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].

• 한국해양공학회지
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• 제19권5호
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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.

• 대한인간공학회지
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• 제29권6호
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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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• 제17권1호
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• pp.21-30
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• 1992

KCCH cyclotron neutron(30cCy/min) 및 $^{60}Co\;{\gamma}-ray(210cGy/min)$를 시험관내의 정상인체 말초혈액임파구에 조사하여 염색체이상(dicentric 및 centric ring)을 관찰하고 이의 선량-반응관계식을 linear model$(Y=K_1D+a)$, power-law model$(Y=K_2D^n)$, quadratic model$(Y=K_3D^2)$ 및 linear-quadratic model$(Y={\alpha}D+{\beta}D^2)$을 사용하여 구하고 이들 model중 염색체이상의 측정치와 가장 일치하는 관계식을 근거로 하여 ${\gamma}-ray$에 대한 neutron의 relative biological effectiveness (RBE)를 산출하였다. 염색체 이상(dicentric plus centric ring)의 발생분포는 ${\gamma}-ray$의 경우 linear model(P=0.067)을 제외한 power-law model$[Y=(5.81{\pm}1.96){\times}10^6D^{1.93+0.06},\;P=0.931]$, quadratic model$[Y=(3.91{\pm}0.09){\times}10^{-6}D^2,\;P=0.972]$ 및 linear-quadratic model $[Y=(6.55{\pm}6.83){\times}10^{-5}D+(3.72{\pm}0.22){\times}10^{-6}D^2$ P=0.922]에 적합하였다 neutron의 경우 linear model $(Y=(6.12{\pm}0.17){\times}10^{-3}\;D-0.22,\;P=0.987]$에 가장 일치하였고 quadratic model (P<0.005)을 제외한 power-law model $[Y=(5.36{\pm}3.02) {\times}10^{-4}D^{1.42+0.11},\;P=0.601]$ 및 linear-quadratic model $[Y=(2.43{\pm}0.70){\times}10^{-3}D+(1.21{\pm}0.39){\times}10^{-7}D^2,\;P=0.415]$에 비교적 적합하였다. 세포당 0.1-1.5개의 염색체이상을 나타내는 neutron의 ${\gamma}-ray$에 대한 RBE는 $2.714{\pm}0.408$이었다.

• 대한방사선기술학회지:방사선기술과학
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• 제43권6호
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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.

• 항공우주정책ㆍ법학회지
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• 제spc호
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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

• 대한수학회논문집
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• 제13권2호
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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.

• 대한수학회지
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• 제45권4호
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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 $EX^2={\sigma}^2<{\infty}$.

• 한국전산구조공학회논문집
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• 제28권5호
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• pp.553-561
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• 2015

지수 함수 및 멱 법칙 함수를 이용한 점진기능재료(FGM) 판의 전단 및 두께 방향 변형을 고려한 이론을 정식화하여 동적 평형방정식을 유도하였다. 지수 함수 및 멱 법칙 함수는 두께 방향으로 재료의 변화를 고려할 수 있고 3차원 해석방법은 전단 및 두께 방향 변형을 고려함으로써 점진기능재료의 정확한 구조적 특성을 고려할 수 있다. Pasternak탄성지반 위에 놓인 4변이 단순 지지되고 전단 및 두께 방향 변형이 고려된 점진기능재료 판의 지배방정식을 풀기 위해 Navier 방법을 사용하였다. 거듭제곱 지수와 3차원 해석의 효과를 나타내기 위한 지수 및 멱 법칙 점진기능재료 판의 동적 해석결과를 제시하였다. 기존의 2차원 고차전단변형 이론 및 3차원 이론과의 관계를 수치해석 결과를 통하여 고찰하였다. 또한 (i) 거듭제곱 지수, (ii) 폭-두께 비, 그리고 (iii) 탄성지반 계수, 등이 점진기능재료 판의 자유진동수에 미치는 효과에 대하여 관찰하였다. 본 연구의 결과를 검증하기 위해 참고문헌의 결과들과 비교 분석하였다.