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A NEW KIND OF THE LAW OF THE ITERATED LOGARITHM FOR PRODUCT OF A CERTAIN PARTIAL SUMS

  • Zang, Qing-Pei
    • Bulletin of the Korean Mathematical Society
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    • v.48 no.5
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    • pp.1041-1046
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    • 2011
  • Let {X, $X_{i};\;i{\geq}1$} be a sequence of independent and identically distributed positive random variables. Denote $S_n= \sum\array\\_{i=1}^nX_i$ and $S\array\\_n^{(k)}=S_n-X_k$ for n ${\geq}$1, $1{\leq}k{\leq}n$. Under the assumption of the finiteness of the second moments, we derive a type of the law of the iterated logarithm for $S\array\\_n^{(k)}$ and the limit point set for its certain normalization.

UCP600: An Exercise in International Private Sector Self Regulation (UCP 600: 국제 사적 부문 자체 규제의 일례)

  • Byrne, James E.
    • THE INTERNATIONAL COMMERCE & LAW REVIEW
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    • v.36
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    • pp.47-84
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    • 2007
  • The Uniform Customs and Practice for Documentary Credits ("UCP") may be treated as a useful laboratory for studying the scope and limitations of self regulation. This is due to its almost universal success on a global stage which provides it a perspective rarely available for self regulatory provisions and due to extensive experience of judicial review of it. In this sense, it is worthwhile to examine in brief the latest iteration of the UCP, Publication No. 600 ("UCP600"). This article describes and analyze some of core provisions of the UCP600 from the perspective of their adequacy as an exercise in self regulation. It is attempted first in view of several categories of private rulemaking; definitional rulemaking, default rules, procedural rules, and remedies. After that, it is examined second in view of sound rulemaking which is related to the relative role of law and practice. It points out rich and varied insights into the possibilities and problems associated with private rulemaking in connection with commercial transactions.

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PI-type Variable Structure Control with High Speed Reaching Mode (빠른 도달 속도를 가지는 PI형 가변구조 제어)

  • Shin, Seung-Min;Jun, Kyung-Han;Jun, Hae-Jin;Choi, Bong-Yeol
    • Proceedings of the KIEE Conference
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    • 2001.11c
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    • pp.236-239
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    • 2001
  • In this paper, we present the new PI-type VSC(variable structure control). In general, conventional VSCs with a discontinuous reaching law have a chattering problem, and with a PI-type reaching law have a slow reaching speed characteristic. To solve this problem, we propose the reaching law consists of a discontinuous and a PI-type reaching law to obtain a high speed reaching mode and a non-chattering characteristic at the same time. Simulation results show the effectiveness of a proposed scheme.

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Application of the Scaling Law for Swept Shock/Boundary-Layer Interactions

  • Lee, Yeol
    • Journal of Mechanical Science and Technology
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    • v.17 no.12
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    • pp.2116-2124
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    • 2003
  • An experimental study providing additional knowledge of quasi-conical symmetry in swept shock wave/turbulent boundary-layer interactions is described. When a turbulent boundary layer on the flat plate is subjected to interact with a swept planar shock wave, the interaction flowfield far from fin leading edge has a nature of conical symmetry, which topological features of the interaction flow appear to emanate from a virtual conical origin. Surface streakline patterns obtained from the kerosene-lampblack tracings have been utilized to obtain representative surface features of the flow, including the location of the virtual conical origin. The scaling law for the sharp-fin interactions suggested by previous investigators has been reexamined for different freestream Mach numbers. It is noticed that the scaling law reasonably agrees with the present experimental data, however, that the law is not appropriate to estimate the location of the virtual conical origin. Further knowledge of the correlation for the virtual conical origin has thus been proposed.

The Constitutionality of Individual Mandate under the U.S. Patient Protection and Affordable Care Act of 2010 (미국 의료개혁법의 의료보험 의무가입 제도에 대한 연방대법원의 합헌결정)

  • Lee, Won Bok
    • The Korean Society of Law and Medicine
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    • v.14 no.1
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    • pp.275-302
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    • 2013
  • The Unites States has been plagued with soaring health care costs and an alarmingly large number of uninsured population. The Patient Protection and Affordable Care Act of 2010 ushered in the most sweeping health care reform in the United States since the introduction of Medicare and Medicaid in 1965 to address these issues. The law's requirement for individuals to purchase health insurance (the so-called "individual mandate"), however, not only caused a political stir but also prompted constitutional challenges. Some questioned whether the federal government, lacking general police power, could require its citizens to buy unwanted insurance based on its enumerated powers under the U.S. Constitution. This paper summarizes the decision of the U.S. Supreme Court on the constitutionality of individual mandate, and explores how the decision relates to Korea's own universal health care.

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An Art of Arbitration:Dispute Resolutions in Shakespeare's The Merchant of Venice

  • Yeon, Jeom-Suk
    • International Commerce and Information Review
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    • v.7 no.4
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    • pp.457-466
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    • 2005
  • The main narrative of Shakespeare's The Merchant of Venice deals with a dispute over the matter of bond in regard to moneylending, and its consequences upon the eventual default. Only the clever interference of a lawyer or judge brings the crisis to an end. In solving his dispute over the bond between Antonio, the merchant of Venice, and Shylock, the money lender and a Jew, Shakespeare offers one of the most famous trial scenes in literature. This trial scene presents the art of arbitration by Portia who was disguised as a Doctor of Law and sheds light on the nature of law, justice, equity, and divine law. What one cannot overlook in this trial scene is the importance of reading ability. After all, interpretation is the next stage of reading. Drawing just verdicts and wise arbitration while at the same time deconstructing the implicit violence and incongruity in law is based on ceaseless effort of analytic and creative act of reading.

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Comparison Study of Nonlinear CSAS Flight Control Law Design Using Dynamic Model Inversion and Classical Gain Scheduling (항공기 CSAS 설계를 위한 고전적 Gain Scheduling 기법과 Dynamic Model Inversion 비선형 기법의 비교 연구)

  • Ha, Cheol-Geun;Im, Sang-Su;Kim, Byeong-Su
    • Journal of Institute of Control, Robotics and Systems
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    • v.7 no.7
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    • pp.574-581
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    • 2001
  • In this paper we design and evaluate the longitudinal nonlinear N(aub)z-CSAS(Command and Stability Augmentation System) flight control law in \"DMI(Dynamic Model Inversion)-method\" and classical \"Gain Scheduling-method\", respectively, to meet the handling quality requirements associated with push-over pull-up maneuver. It is told that the flight control law designed in \"DM-method\" is adequate to the full flight regime without gain scheduling and is efficient to produce the time response shape desired to the handling quality requirements. On the contrary, the flight control law designed in \"Gain Scheduling-method\" is easy to be implemented in flight control computer and insensitive to variation of the actuator model characteristics.n of the actuator model characteristics.

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Response of the Adolescents to the School Uniform Regulations according to Personal Character and Clothing Needs (청소년의 성격특성과 의복욕구에 따른 교복복장규제에 대한 반응)

  • Bak, Yeong-Eun;Oh, Kyung-Wha
    • Fashion & Textile Research Journal
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    • v.13 no.4
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    • pp.499-510
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    • 2011
  • The response of the adolescents toward school uniform regulations according to personal character and clothing needs was studied. To carry out this experiment, questionnaires were administered to 514 students in middle and high schools in Seoul and Gyeonggi-do. The collected data were analyzed with Factor analysis(Varimax rotation), Cronbach's ${\alpha}$, Frequencies Statistics, t-test, ANOVA, and multiple regression analysis using the SPSS WIN 15.0. By surveying on actual condition of uniform regulation in school, it was found that the existing uniform regulation was unnecessarily strict and caused stress leading a negative educational effect. Based on the relationship among the degree of regulation, stress, and student attitude toward school uniform regulation, stress and negative attitude to uniform regulation increased as the degree of regulation increased, resulting in an decrease in observance behavior of students. Since the stress from the school uniform regulation can be reduced by establishing rational law, which induced voluntary conduct of student to obey, it is important for student to participate in establishment of adoptable and reasonable school uniform regulation law.

An Analysis of Middle School Student's Eye Movements in the Law of Large Numbers Simulation Activity (큰 수의 법칙 시뮬레이션에서 중학생의 안구 운동 분석)

  • Choi, In Yong;Cho, Han Hyuk
    • The Mathematical Education
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    • v.56 no.3
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    • pp.281-300
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    • 2017
  • This study analyzed the difficulties of middle school students in computer simulation of the law of large numbers through eye movement analysis. Some students did not attend to the simulation results and could not make meaningful inferences. It is observed that students keep the existing concept even though they observe the simulation results which are inconsistent with the misconceptions they have. Since probabilistic intuition influence student's thinking very strongly, it is necessary to design a task that allows students to clearly recognize the difference between their erroneous intuitions and simulation results. In addition, we could confirm through eye movements analysis that students could not make meaningful observations and inferences if too much reasoning was needed even though the simulation included a rich context. It is necessary to use visual representations such as graphs to provide immediate feedback to students, to encourage students to attend to the results in a certain intentional way to discover the underlying mathematical structure rather than simply presenting experimental data. Some students focused their attention on the visually salient feature of the experimental results and have made incorrect conclusion. The simulation should be designed so that the patterns of the experimental results that the student must discover are not visually distorted and allow the students to perform a sufficient number of simulations. Based on the results of this study, we suggested that cumulative relative frequency graph showing multiple results at the same time, and the term 'generally tends to get closer' should be used in learning of the law of large numbers. In addition, it was confirmed that eye-tracking method is a useful tool for analyzing interaction in technology-based probabilistic learning.

Determining minimum analysis conditions of scale ratio change to evaluate modal damping ratio in long-span bridge

  • Oh, Seungtaek;Lee, Hoyeop;Yhim, Sung-Soon;Lee, Hak-Eun;Chun, Nakhyun
    • Smart Structures and Systems
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    • v.22 no.1
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    • pp.41-55
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    • 2018
  • Damping ratio and frequency have influence on dynamic serviceability or instability such as vortex-induced vibration and displacement amplification due to earthquake and critical flutter velocity, and it is thus important to make determination of damping ratio and frequency accurate. As bridges are getting longer, small scale model test considering similitude law must be conducted to evaluate damping ratio and frequency. Analysis conditions modified by similitude law are applied to experimental test considering different scale ratios. Generally, Nyquist frequency condition based on natural frequency modified by similitude law has been used to determine sampling rate for different scale ratios, and total time length has been determined by users arbitrarily or by considering similitude law with respect to time for different scale ratios. However, Nyquist frequency condition is not suitable for multimode system with noisy signals. In addition, there is no specified criteria for determination of total time length. Those analysis conditions severely affect accuracy of damping ratio. The focus of this study is made on the determination of minimum analysis conditions for different scale ratios. Influence of signal to noise ratio is studied according to the level of noise level. Free initial value problem is proposed to resolve the condition that is difficult to know original initial value for free vibration. Ambient and free vibration tests were used to analyze the dynamic properties of a system using data collected from tests with a two degree-of-freedom section model and performed on full bridge 3D models of cable stayed bridges. The free decay is estimated with the stochastic subspace identification method that uses displacement data to measure damping ratios under noisy conditions, and the iterative least squares method that adopts low pass filtering and fourth order central differencing. Reasonable results were yielded in numerical and experimental tests.