• 산업공학
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• 제13권4호
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• pp.738-744
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• 2000

This Paper presents a method for unfinished work transition probability distribution of modulated $n^*D/D/l$ queue with overload period. The Modulated $n^*D/D/l$ queue is well known as a performance analysis model of ATM multiplexer with superposition of homogeneous periodic on-off traffic sources. Theory of probability by conditioning and results of $N^*D/D/l$ queue are used for analytic methodology. The results from this paper are expected to be applied to general modulated $n^*D/D/l$ queue.

• Journal of the Korean Statistical Society
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• 제19권2호
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• pp.122-127
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• 1990

Consider the following problem in the large deviation theory. For constants $a_1, \cdots, a_p$ the tail probability $P(M_1 > a_1, \cdots, M_p > a_p)$ of the sample medians $(M_1, \cdots, M_p)$ is supposed to converge to zero as sample size increases. This paper shows that this probability converges to zero exponentially fast and estimates the convergence rates of the above tail probability of the sample medians. Also compare with the rates about the sample means.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.257-273
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• 2010

One can construct a theory of probability of fractional order in which the exponential function is replaced by the Mittag-Leffler function. In this framework, it seems of interest to generalize some useful classical mathematical tools, so that they are more suitable in fractional calculus. After a short background on fractional calculus based on modified Riemann Liouville derivative, one summarizes some definitions on probability density of fractional order (for the motive), and then one introduces successively fractional Euler's integrals (first and second kind) and fractional Hermite polynomials. Some properties of the Gaussian density of fractional order are exhibited. The fractional probability so introduced exhibits some relations with quantum probability.

• Structural Engineering and Mechanics
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• 제45권2호
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• pp.201-209
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• 2013

A new dynamic reliability analysis of structure under repeated random loads is proposed in this paper. The proposed method is developed based on the idea that the probability density of several times random loads can be derived from the probability density of single-time random load. The reliability prediction models of structure based on time responses under several times random loads with and without strength degradation are obtained by using the stress-strength interference theory and probability density evolution method. The resulting differential equations in the prediction models can be solved by using the forward finite difference method. Then, the probability density functions of strength redundancy of the structures can be obtained. Finally, the structural dynamic reliability can be calculated using integral method. The efficiency of the proposed method is demonstrated numerically through a speed reducer. The results have shown that the proposed method is practicable, feasible and gives reasonably accurate prediction.

• 대한수학회지
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• 제55권2호
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• pp.447-469
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• 2018

Types (over parameters) in the theory of atomless random variable structures correspond precisely to (conditional) distributions in probability theory. Moreover, the logic (resp. metric) topology on the type space corresponds to the topology of weak (resp. strong) convergence of distributions. In this paper, we study metrics between types. We show that type spaces under $d^{\ast}-metric$ are isometric to Wasserstein spaces. Using optimal transport theory, two formulas for the metrics between types are given. Then, we give a new proof of an integral formula for the Wasserstein distance, and generalize some results in optimal transport theory.

• 한국해양공학회:학술대회논문집
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• 한국해양공학회 2006년 창립20주년기념 정기학술대회 및 국제워크샵
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• pp.127-134
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• 2006

Based on a weakly non-Gaussian theory the occurrence probability of freak waves is formulated in terms of the number of waves in a time series and the surface elevation kurtosis. Finite kurtosis gives rise to a significant enhancement of freak wave generation in comparison with the linear narrow banded wave theory. For fixed number of waves, the estimated amplification ratio of freak wave occurrence due to the deviation from the Gaussian theory is 50% - 300%. The results of the theory are compared with laboratory and field data.

• 한국수학사학회지
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• 제14권2호
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• pp.93-100
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• 2001

The problem of vagueness has been investigated for a long time by philosophers and mathematicians. There are there approaches in mathematics to the problem, which are probability theory, fuzzy logic, and rough set theory. In this paper I introduce these theories and their meanings.

• 한국정보시스템학회지:정보시스템연구
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• 제29권2호
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• pp.131-147
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• 2020

Purpose The purpose of this study is to develop intelligent vehicle parking distribution system based on LoRa network at the circumstance of traffic congestion during cultural festival in a local city. This paper proposes a parking dispatch and distribution system using a Q-learning algorithm to rapidly disperse traffics that increases suddenly because of in-bound traffics from the outside of a city in the real-time base as well as to increase parking probability in a parking lot which is widely located in a city. Design/methodology/approach The system get information on realtime-base from the sensor network of IoT (LoRa network). It will contribute to solve the sudden increase in traffic and parking bottlenecks during local cultural festival. We applied the simulation system with Queuing model to the Yudeung Festival in Jinju, Korea. We proposed a Q-learning algorithm that could change the learning policy by setting the acceptability value of each parking lot as a threshold from the Jinju highway IC (Interchange) to the 7 parking lots. LoRa Network platform supports to browse parking resource information to each vehicle in realtime. The system updates Q-table periodically using Q-learning algorithm as soon as get information from parking lots. The Queuing Theory with Poisson arrival distribution is used to get probability distribution function. The Dijkstra algorithm is used to find the shortest distance. Findings This paper suggest a simulation test to verify the efficiency of Q-learning algorithm at the circumstance of high traffic jam in a city during local festival. As a result of the simulation, the proposed algorithm performed well even when each parking lot was somewhat saturated. When an intelligent learning system such as an O-learning algorithm is applied, it is possible to more effectively distribute the vehicle to a lot with a high parking probability when the vehicle inflow from the outside rapidly increases at a specific time, such as a local city cultural festival.

• 예술인문사회 융합 멀티미디어 논문지
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• 제6권12호
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• pp.587-594
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• 2016

주요 인공지능 기술 선진국에서는 인공지능으로 운행하는 자율주행 자동차가 이미 실험 단계의 수준을 넘어섰다. 운전자가 없이 운행하는 자율주행 자동차에서 가장 큰 문제 가운데 하나는, 사고 발생과 그 사고에 대한 책임 문제이다. 운전자와 보행자 모두를 함께 고려해야 하는 사고 상황에서 자율주행 자동차는 윤리적 딜레마에 부딪힐 수 있다. 이런 딜레마를 해결할 최선의 판단이 자율자동차의 인공지능에 어떻게 설계되어야 하는지 물을 수 있다. 책임의 주체로서 자율주행 자동차에 대해 법적 책임을 어떻게 부여할 수 있는지는 어려운 문제이다. 필자는 우선, 사고 상황에서 자율자동차의 윤리적 딜레마가 무엇인지 소개한다. 다음으로, 사고에 대한 책임의 주체로서 자율주행 자동차에 법적 책임을 부여할 방법을 찾는다. 특별히 인과적 책임에 대한 상당성 개념으로 자율주행 자동차 사고의 법적 책임을 해명할 방법을 모색한다. 상당성은 법적 판단에서 인과적 책임을 해명하는 데에 가장 일반적으로 수용하는 개념이다. 그러나 여전히 해명이 필요한 모호한 개념이다. 필자는 사건 수준의 인과에 대한 확률 이론으로 보다 명료한 인과적 책임에 대한 상당성 개념을 제시한다. 이처럼 해명된 상당성은 자율주행 자동차뿐 아니라 일반적인 영역의 법적 판단에서 요구되는 인과적 책임을 설명하는 데에 기여할 수 있다.

• Earthquakes and Structures
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• 제22권6호
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• pp.609-623
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• 2022

To study the empirical seismic fragility of a reinforced concrete girder bridge, based on the theory of numerical analysis and probability modelling, a regression fragility method of a rapid fragility prediction model (Gaussian first-order regression probability model) considering empirical seismic damage is proposed. A total of 1,069 reinforced concrete girder bridges of 22 highways were used to verify the model, and the vulnerability function, plane, surface and curve model of reinforced concrete girder bridges (simple supported girder bridges and continuous girder bridges) considering the number of samples in multiple intensity regions were established. The new empirical seismic damage probability matrix and curve models of observation frequency and damage exceeding probability are developed in multiple intensity regions. A comparative vulnerability analysis between simple supported girder bridges and continuous girder bridges is provided. Depending on the theory of the regional mean seismic damage index matrix model, the empirical seismic damage prediction probability matrix is embedded in the multidimensional mean seismic damage index matrix model, and the regional rapid prediction matrix and curve of reinforced concrete girder bridges, simple supported girder bridges and continuous girder bridges in multiple intensity regions based on mean seismic damage index parameters are developed. The established multidimensional group bridge vulnerability model can be used to quantify and predict the fragility of bridges in multiple intensity regions and the fragility assessment of regional group reinforced concrete girder bridges in the future.