• Title/Summary/Keyword: Upper-lower solutions

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The Flash Points of the Butylacetate+2-Propanol System Measured By Air Blowing Tester

  • Ha, Dong Myeong;Lee, Sung Jin;Mok, Yun Soo;Choi, Jae Wook
    • International Journal of Safety
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    • v.2 no.1
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    • pp.34-38
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    • 2003
  • The lower and upper flash points of the flammable binary system, butylacetate+2-propanol were measured by air blowing tester. The shape of the concentration-temperature region of flash depended on the components of the mixture in solution. The experimental data were compared with the values calculated by the reduced model under an ideal solution assumption and the flash point-prediction models based on Van Laar equation. Good qualitative agreement was obtained with these models. The prediction results of these models can thus be applied to incorporate inherently safer design for chemical process, such as the determination of the safe storage conditions for flammable solutions.

A Study on the Optimal Routing Problem for a Transfer Crane (컨테이너 터미널에서의 트랜스퍼 크레인의 최적 운영 방안에 관한 연구)

  • Kim, Hu-Gan;Kim, Chul-Han
    • Journal of the Korean Operations Research and Management Science Society
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    • v.33 no.1
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    • pp.35-49
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    • 2008
  • To load a container in a yard block onto a ship, a Transfer Crane (TC) moves to a target yard bay, then its hoist picks up a selected container and loads it onto a waiting Yard Truck (YT). An optimal routing problem of Transfer Crane is a decision problem which determines a given TC's the visiting sequence of yard-bays and the number of containers to transfer from each yard-bay. The objective is to minimize the travel time of the TC between yard-bays and setup time for the TC in a visiting yard. In this paper, we shows that the problem is NP-complete, and suggests a new formulation for it. Using the new formulation for the problem, we investigate some characteristics of solutions, a lower and upper bounds for it. Moreover, our lower and upper bound is very efficient to applying some instances suggested in a previous work.

Hydrodynamic performance of a composite breakwater with an upper horizontal porous plate and a lower rubble mound

  • Liu, Yong;Li, Hua-Jun
    • Ocean Systems Engineering
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    • v.3 no.1
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    • pp.55-70
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    • 2013
  • A composite breakwater with an upper horizontal porous plate and a lower rubble mound is proposed and studied in this work. By means of matched eigenfunction expansions, a semi-analytical solution is developed for analyzing the hydrodynamic performance of the breakwater. The semi-analytical solution is verified by known solutions for special cases and an independently developed multi-domain boundary element method solution. Numerical examples are given to examine the reflection, transmission and energy loss coefficients of the breakwater and the wave force acting on the horizontal porous plate. Some useful results are presented for engineering applications.

Sensitivity Analysis on the Degenerate Tree Solution of the Minimum Cost Flow Problem (최소비용문제의 퇴화 정점 최적해에 대한 감도분석)

  • Chung, Ho-Yeon;Park, Soon-Dal
    • IE interfaces
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    • v.7 no.3
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    • pp.193-199
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    • 1994
  • The purpose of this paper is to develop a method of the sensitivity analysis that can be applicable to a degenerate tree solution of the minimum cost flow problem. First, we introduce two types of sensitivity analysis. A sensitivity analysis of Type 1 is the well known method applicable to a spanning tree solution. However, this method have some difficulties in case of being applied to a degenerate tree solution. So we propose a sensitivity analysis of Type 2 that keeps solutions of upper bounds remaining at upper bounds, those of lower bounds at lower bounds, and those of intermediate values at intermediate values. For the cost coefficient, we present a method that the sensitivity analysis of Type 2 is solved by using the method of a sensitivity analysis of Type 1. Besides we also show that the results of sensitivity analysis of Type 2 are union set of those of Type 1 sensitivity analysis. For the right-hand side constant or the capacity, we present a simple method for the sensitivity analysis of Type 2 which uses arcs with intermediate values.

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Flow Characteristics in Spin-Up of a Three-Layer Fluid

  • Sviridov Evgeny;Hyun Jae Min
    • Journal of Mechanical Science and Technology
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    • v.20 no.2
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    • pp.271-277
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    • 2006
  • A numerical study is made of the spin-up from rest of a three-layer fluid in a closed, vertically-mounted cylinder. The densities in the upper layer $\rho_1$, middle layer $\rho_2$ and lower layer $\rho_3\;are\;\rho_3\;>\;\rho_2\;>\;\rho_1$, and the kinematic viscosities are left arbitrary. The representative system Ekman number is small. Numerical solutions are obtained to the time-dependent axisymmetric Navier-Stokes equations, and the treatment of the interfaces is modeled by use of the Height of Liquid method. Complete three-component velocity fields, together with the evolution of the interface deformations, are depicted. At small times, when the kinematic viscosity in the upper layer is smaller than in the middle layer, the top interface rises (sinks) in the central axis (peripheral) region. When the kinematic viscosity in the lower layer is smaller than in the middle layer, the bottom interface rises (sinks) in the periphery (axis) region. Detailed shapes of interfaces are illustrated for several cases of exemplary viscosity ratios.

A Study on The Construction of Desirable Model of the National Spatial Data Infrastructure Policy Promotion System (국가공간정보정책 추진체계의 바람직한 모형구축에 대한 연구)

  • Kim, Tae Jin
    • Spatial Information Research
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    • v.20 no.6
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    • pp.91-98
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    • 2012
  • In order to efficiently promote a nation's National Spatial Data Infrastructure (NSDI) vision, it is important that a rational NSDI promotion system should be established. For such a NSDI promotion system, cooperation among the related organizations and the consistency of policies are crucial. In these regards, the main purpose of this research is to suggest a desirable model for the NSDI promotion system. Also, this study attempts to demonstrate problems and provide solutions in Korea NSDI promotion system. To accomplish this purpose, the literature reviews and content analysis were used. Following are the major findings of this research. First, a desirable NSDI promotion system should be consisted of the upper system (at the planning level) and the lower system (at the executive or implementing level). Second, the upper and lower system in NSDI promotion system should both be vertically connected and be horizontally connected. Third, the upper system should consist of the NSDI promotion committee, civil advisory committee, and sub-committee. Fourth, the lower system for the execution purposes of NSDI projects should consist of the NSDI top manager, in each central/local government, and professional support institute.

Linear Analysis of Water Surface Waves Generated by Submerged Wave Board Whose Upper and Lower Ends Oscillate Horizontally Freely (상하단이 자유롭게 수평동요하는 수중 조파판에 의해 생성된 수면파의 근사해석)

  • Kim, Hyochul;Oh, Jungkeun;Kwon, Jongoh;Lew, Jae-Moon
    • Journal of the Society of Naval Architects of Korea
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    • v.56 no.5
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    • pp.418-426
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    • 2019
  • To derive a simplified analytic solution which can be utilized as a fundamental solution for the wave maker design, a segment of the wave board has been idealized as a submerged line segment in a two dimensional domain of a wave flume. The lower end of the line segment could be located at arbitrary depth of the wave flume and the upper end of the board could be also submerged to any depth from the free surface. The freely oscillating motion of the wave board is assumed to be defined by determining the condition of horizontal oscillation on both ends differently. The submerged wave board oscillating in horizontal direction could be specified by selecting the amplitude, frequency and the phase lag differently on lower and upper ends of the board. The simplified two dimensional wave generated by the wave board segment has been obtained by the first order perturbation method. It is found that the general solution of the freely oscillating wave board in two dimensional domain could be decomposed into the solution of flap motion with lower end hinge and swing motion with upper end hinge. The case study of the analytic solutions has been carried out to evaluate the effect on the wave height due to the difference of oscillation frequency, phase difference and variation of stroke between for the motion of both ends. It is found that the solution of the freely oscillating wave board could be utilized for the development of high performance wavemaker especially for irregular waves.

Bending of a rectangular plate resting on a fractionalized Zener foundation

  • Zhang, Cheng-Cheng;Zhu, Hong-Hu;Shi, Bin;Mei, Guo-Xiong
    • Structural Engineering and Mechanics
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    • v.52 no.6
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    • pp.1069-1084
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    • 2014
  • The long-term performance of plates resting on viscoelastic foundations is a major concern in the analysis of soil-structure interaction. As a powerful mathematical tool, fractional calculus may address these plate-on-foundation problems. In this paper, a fractionalized Zener model is proposed to study the time-dependent behavior of a uniformly loaded rectangular thin foundation plate. By use of the viscoelastic-elastic correspondence principle and the Laplace transforms, the analytical solutions were obtained in terms of the Mittag-Leffler function. Through the analysis of a numerical example, the calculated plate deflection, bending moment and foundation reaction were compared to those from ideal elastic and standard viscoelastic models. It is found that the upper and lower bound solutions of the plate response estimated by the proposed model can be determined using the elastic model. Based on a parametric study, the impacts of model parameters on the long-term performance of a foundation plate were systematically investigated. The results show that the two spring stiffnesses govern the upper and lower bound solutions of the plate response. By varying the values of the fractional differential order and the coefficient of viscosity, the time-dependent behavior of a foundation plate can be accurately captured. The fractional differential order seems to be dependent on the mechanical properties of the ground soil. A sandy foundation will have a small fractional differential order while in order to simulate the creeping of clay foundation, a larger fractional differential order value is needed. The fractionalized Zener model is capable of accounting for the primary and secondary consolidation processes of the foundation soil and can be used to predict the plate performance over many decades of time.

BLOW-UP AND GLOBAL SOLUTIONS FOR SOME PARABOLIC SYSTEMS UNDER NONLINEAR BOUNDARY CONDITIONS

  • Guo, Limin;Liu, Lishan;Wu, Yonghong;Zou, Yumei
    • Journal of the Korean Mathematical Society
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    • v.56 no.4
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    • pp.1017-1029
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    • 2019
  • In this paper, blows-up and global solutions for a class of nonlinear divergence form parabolic equations with the abstract form of $({\varrho}(u))_t$ and time dependent coefficients are considered. The conditions are established for the existence of a solution globally and also the conditions are established for the blow up of the solution at some finite time. Moreover, the lower bound and upper bound of the blow-up time are derived if blow-up occurs.

A Branch-and-Bound Algorithm to Minimize the Makespan in a Fire Scheduling Problem (최소 종료시간 사격 스케줄을 위한 분지계획법 알고리즘 연구)

  • Cha, Young-Ho;Bang, June-Young
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.38 no.4
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    • pp.132-141
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    • 2015
  • We focus on the fire scheduling problem (FSP), the problem of determining the sequence of targets to be fired at, for the objective of minimizing makespan to achieve tactical goals. In this paper, we assume that there are m available weapons to fire at n targets (> m) and the weapons are already allocated to targets. One weapon or multiple weapons can fire at one target and these fire operations should start simultaneously while the finish time of them may be different. We develop several dominance properties and a lower bound for the problem, and suggest a branch and bound algorithm implementing them. Also, In addition, heuristic algorithms that can be used for obtaining an initial upper bound in the B&B algorithm and for obtaining good solutions in a short time were developed. Computational experiments are performed on randomly generated test problems and results show that the suggested algorithm solves problems of a medium size in a reasonable amount of computation time. The proposed lower bound, the dominance properties, and the heuristics for upper bound are tested in B&B respectively, and the result showed that lower bound is effective to fathoming nodes and the dominance properties and heuristics also worked well. Also, it is showed that the CPU time required by this algorithm increases rapidly as the problem size increases. Therefore, the suggested B&B algorithm would be limited to solve large size problems. However, the employed heuristic algorithms can be effectively used in the B&B algorithm and can give good solutions for large problems within a few seconds.