• Kyungpook Mathematical Journal
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• 제64권1호
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• pp.69-94
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• 2024

In this paper, we introduce an inertial self-adaptive projection method using Bregman distance techniques for solving pseudomonotone equilibrium problems in reflexive Banach spaces. The algorithm requires only one projection onto the feasible set without any Lipschitz-like condition on the bifunction. Using this method, a strong convergence theorem is proved under some mild conditions. Furthermore, we include numerical experiments to illustrate the behaviour of the new algorithm with respect to the Bregman function and other algorithms in the literature.

• 대한교통학회지
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• 제26권2호
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• pp.89-100
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• 2008

교통신호와 개별 통행자의 경로선택은 서로 상호작용하는 관계이다. 통행자의 경로 선택은 교통신호에 따라 결정될 수 있으며 또한 최적의 교통신호 역시 이동류별 교통량에 따라 달라지게된다. 본 연구는 양방향 링크를 포함하는 4현시 교차로로 구성된 네트워크에서 모든 이동류에 대하여 교통신호의 영향을 반영할 수 있는 통행배정 모형을 구축하고 이를 신호최적화 문제와 결합하여 네트워크의 총 지체를 최소화하는 신호제어변수와 통행배정 결과를 산출하는 모형을 bi-level problem으로 구축하였다. 본 연구에서 사용된 경로기반 통행배정 모형은 M.H. Xu 등이 제한한 Column Generation 방법의 일종인 heuristic Equilibrium Assignment 기법을 기반으로 하여 교차로의 이동류별 통행비용을 고려할 수 있도록 수정하여 구성하였으며 지체최소화를 목적함수로하는 신호최적화 방법론으로는 Genetic Algorithm을 사용하였다. 본 모형을 모의네트워크에 적용하여 실험한 결과 네트워크의 통행비용함수를 최소화하는 신호변수와 통행자의 경로선택 결과를 산출하였다.

• 대한교통학회지
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• 제24권2호
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• pp.169-178
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• 2006

통행배정 (traffic assignment)은 장래 통행수요를 예측할 뿐 아니라. 교통혼잡을 완화시키는 각종 교통정책들을 사전에 평가하는 도구로 그 활용범위가 넓어지고 있다. 현재 대표적인 통행배정방법은 Wardrop(1952)이 제시한 사용자 균형원리 (user equilibrium principle)에 따라 통행자를 교통망에 배정하는 방법으로 동등 수리최소화모형 (equivalent mathematical minimization model), 변동부등식 (Variational inequality), 비선형상보문제 (Nonlinear Complementary Problem), 고정점 모형(fixed point method) 등이 있다. 그런데, 최근 Jin(2005a)은 동적과정(dynamic process)에 기초하여 사용자 균형해를 구할 수 있는 새로운 모형을 제시하였다. 본 연구는 Jin이 제시한 모형에 대한 효과적인 알고리듬을 개발하고 이를 평가하는 데 연구의 목적이 있다. 개발된 알고리듬은 통행배정모형을 풀기 위하여 현재 널리 사용되는 Frank-Wolfe방법보다 쉽게 프로그램화 할 수 있는데, 목적함수를 평가(evaluation)하는 단계가 불필요하며 축차적인 계산과정을 통하여 해를 구하기 때문이다. 제시된 알고리듬을 예제 교통망을 대상으로 분석한 결과, 사용자 균형해(user equilibrium)를 도출함을 확인할 수 있었다.

• 산업경영시스템학회지
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• 제41권3호
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• pp.162-169
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• 2018

Net neutrality, which has not been a problem, has recently become a problem for ISPs (Internet Service Providers), and their complaints have been paid by domestic platform companies, but overseas global IT companies such as Google and YouTube, generate huge revenues from domestic markets. In this situation, domestic IT companies claim that it is natural to impose more expensive charges or restrict speed on users who generate huge traffic. On the other side, however, the telecommunication network has become an essential public good that is essential to our everyday life, and because it has been given a monopoly position by a private company to efficiently respond to the explosive demand for telecommunication services, It is necessary to provide equal and universal service and fulfill public duty. In this paper, we deal with the network neutrality problem, focusing on the price elasticity between the CP (Contents Provider) and the ISP, rather than the user who is one side of the two-sided market for the already saturated satellites communication market. We present a game model that determines the optimal price for each platform by Nash equilibrium and analyze how the net neutrality affects CP according to the change of exogenous variables through the proposed game model.

• 천문학논총
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• 제30권2호
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• pp.295-296
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• 2015

This study deals with the generalization of the Elliptic Restricted Three-Body Problem (ER3BP) by considering the effects of radiation and oblate spheroid primaries. This may illustrate a gas giant exoplanet orbiting its host star with eccentric orbit. In the three dimensional case, this generalization may possess two additional equilibrium points ($L_{6,7}$, out-of-plane). We determine the existence of $L_{6,7}$ in ER3BP under the effects of radiation (bigger primary) and oblateness (small primary). We analytically derive the locations of $L_{6,7}$ and assume initial approximations of (${\mu}-1$, ${\pm}\sqrt{3A_2}$), where ${\mu}$ and $A_2$ are the mass parameter and oblateness factor, respectively. The fixed locations are then determined. Our results show that the locations of $L_{6,7}$ are periodic and affected by $A_2$ and the radiation factor ($q_1$).

• 천문학논총
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• 제30권2호
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• pp.293-294
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• 2015

This work considers the elliptic restricted three-body problem under effects of radiation of the bigger primary, and an oblate spheroid for the smaller primary to mimic an exoplanetary system with a gas giant planet. Under the influences of both effects we look for the existence of the triangular equilibrium points and the influences of the radiation and oblateness on the locations and motion of the points. We set the system in a normalized rotating coordinate system and derive equations of motion for the third infinitesimal object. Our study shows that the effects modify the equilateral/isosceles triangle shape with respect to the primaries. The triangular points also have non-planar motion with period depending on the value of the planet oblateness.

• Journal of applied mathematics & informatics
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• 제30권3_4호
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• pp.365-380
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• 2012

Non-negative matrix factorization (NMF) is a very efficient method to explain the relationship between functions for finding basis information of multivariate nonnegative data. The multiplicative update (MU) algorithm is a popular approach to solve the NMF problem, but it fails to approach a stationary point and has inner iteration and zero divisor. So the elementwisely alternating projected gradient (eAPG) algorithm was proposed to overcome the defects. In this paper, we use the fact that the equilibrium point is stable to prove the convergence of the eAPG algorithm. By using a classic model, the equilibrium point is obtained and the invariant sets are constructed to guarantee the integrity of the stability. Finally, the convergence conditions of the eAPG algorithm are obtained, which can accelerate the convergence. In addition, the conditions, which satisfy that the non-zero equilibrium point exists and is stable, can cause that the algorithm converges to different values. Both of them are confirmed in the experiments. And we give the mathematical proof that the eAPG algorithm can reach the appointed precision at the least iterations compared to the MU algorithm. Thus, we theoretically illustrate the advantages of the eAPG algorithm.

• 한국ITS학회 논문지
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• 제7권5호
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• pp.180-183
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• 2008

본 논문은 교통망에서 관측 링크 교통량, 미관측 링크의 이용자평형 정보를 이용하여 O-D행렬을 수학적으로 생성하는 모형을 제시하고 있다. 교통량이 관측되지 않은 링크로부터 이용자 평형 상태에서 추출 가능한 정보를 바탕으로 일련의 논리적 연산을 거쳐 실제교통량에 근접하는 서브알고리듬을 유추하여 O-D행렬 추정의 정확도와 연산의 일관성을 제고하였다. 이를 위해 이용자평형상태에서 새로운 정리(Theorem)와 보조정리(Lemma)를 유도하여 적용하였다. 모형의 시험은 3개의 초기 O-D 행렬과 3개의 미관측 링크 교통량 시나리오를 각각의 모형에 적용하여 그 결과를 비교하였다. 적용 결과 본 논문에서 제시된 모형은 기존의 이용자균형 접근방식의 모형emf에 비해 추정된 O-D값의 실제 값과의 차이(O-D Trip RMSE)가 현저히 감소되는 것을 확인하였다.

• Advances in aircraft and spacecraft science
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• 제8권1호
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• pp.1-15
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• 2021

Mars exploration demands aerodynamic computations for a proper design of missions of spacecraft carrying instruments and astronauts to Mars. Both Computational Fluid Dynamics (CFD) and Direct Simulation Monte Carlo (DSMC) method play a key role for this purpose. To the author's knowledge, the altitude separating the fields of applicability of CFD and DSMC in Mars atmosphere entry is not yet clearly defined. The limitations in using DSMC at low altitudes are due to technical limitations of the computer. The limitations in using CFD at high altitudes are due to thermodynamic non-equilibrium. Here, this problem is studied in Mars atmosphere entry, considering the Mars Pathfinder capsule in the altitude interval 40-80 km, by means of a DSMC code. Non-equilibrium is quantified by the relative differences between translational temperature and: rotational (θt-r), vibrational (θt-v), overall (θt-ov) temperatures, anisotropy is quantified by the relative difference between the translational temperature component along x and those along y (θx-y) and along z (θx-z). The results showed that θt-r, θt-v, θx-y, θx-z are almost equivalent. The altitude of 45 km should be the limit altitude for a proper use of a CFD code and the altitude of 40 km should be the limit altitude for a reasonable use of a DSMC code.

• 한국환경과학회지
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• 제22권1호
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• pp.119-129
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• 2013

We compared equilibrium evaporation($E_{equili}$) eddy-covariance($E_{eddy}$) with soil moisture data($E_{SMseries}$) which were measured with a 2 hours sampling interval at three points for a humid forest hillslope from May 5th to May 31th in 2009. Accumulations of $E_{eddy}$, $E_{equili}$ for the study period were estimated as 2.52, 3.28 mm and those of $E_{SMseries}$ were ranged from 1.91 to 2.88 mm. It suggested that the eddy-covariance method considering the spatial heterogeneity of soil evaporation is useful to evaluate the soil evaporation. Method A, B and C were proposed using mean meterological data and daily moisture variation and the computations were compared to eddy-covariance method and equilibrium evaporation. The methods using soil moisture data can describe the variations of soil evaporation from eddy-covariance through simple moving average analysis. Method B showed a good matched with eddy-covariance method. This indicated that Dry Surface Layer (DSL) at 14:00 which was used for method B is important variable for the evaluation of soil evaporation. The total equilibrium evaporation was not significantly different to those of the others. However, equilibrium evaporation showed a problem in estimating soil evaporation because the temporal tendency of $E_{equili}$ was not related with the those of the other methods. The improved understanding of the soil evaporation presented in this study will contribute to the understandings of water cycles in a forest hillslope.