• Title/Summary/Keyword: solution set

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An Analytic Analysis for a Two-Dimensional Floating and Fluid-Filled Membrane Structure (부유식 유체저장용 2차원 막구조물의 이론적 해석)

  • Choi, Yoon-Rak
    • Journal of Ocean Engineering and Technology
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    • v.23 no.4
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    • pp.32-37
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    • 2009
  • An analytic similarity shape solution was studied for a two-dimensional floating and fluid-filled membrane structure. The static shape of a membrane structure can be expressed as a set of nonlinear ordinary differential equations. The integration of curvature leads to an analytic solution for the shape, which contains unknown boundary values. Matching the upper and lower shapes at the free surface incorporated with their buoyancy allowed the unknowns to be determined. Some characteristic values of similarity shapes were evaluated and shapes are illustrated for various density ratios and volume efficiency ratios.

An Inverse Kinematics of Redundant Manipulators (여유 자유도 로봇의 역기구학에 관한 연구)

  • Cho, Dong-Kwon;Sung, Young-Hwee;Chung, Myung-Jin
    • Proceedings of the KIEE Conference
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    • 1993.07a
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    • pp.399-402
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    • 1993
  • In this paper, an inverse kinematics of redundant manipulators is proposed. Optimality-constraint based inverse kinematic algorithms have some problems because those algorithms are based on necessary conditions for optimality. Among the problems, switching from a maximum value to a minimum value may occur and make an inverse kinematic solution unstable while performing a given task. An inverse kinematic solution for protecting from the switchings is suggested. By sufficient conditions for optimality, the configuration space is defined as a set of regions, potentially good configuration region and potentially bad configuration region. Inverse kinematics solution within potentially good configuration region can provide joint trajectories without both singularities and switchings. Through a simulation of tracing a circle, we show the effectiveness of this inverse kinematics.

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Improvement of the Degreasing Performance of Surface Treating Steel Sheet by the Automatic Control of Alkaline Degreasing Process (알칼리탈지공정 자동화관리에 의한 표면처리용 강판의 탈지능 향상)

  • 박노범;박대수;박정렬;유민수
    • Journal of the Korean institute of surface engineering
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    • v.29 no.2
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    • pp.132-139
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    • 1996
  • Experiments on the automatic control of NaOH concentration and on the spraying condition of NaOH solution in the alkaline degreasing process of a continuous hot-dip galvanizing line have been carried out in order to improve degreasing performance of a galvanizing sheet steel using laboratory degreasing and galvanizing simulators. The concentration of NaOH for the good degreasing has been determined to be 6.0% and more and this concentration has been able to be automatically well controlled within $\pm$0.1% by employing a solution electrical conductivity meter under a flow injection analysis condition rather than by employing a sodium ion selective electrode in the degreasing simulator. Frequent blocking of the spraying nozzles of the solution has been reduced considerably by the set-up and periodical operation of an automatic valve system in the nozzle system. By applying this automatic valve system and by automatic controlling the NaOH concentration and other ordinary variables in the degreasing process, the degreasing performance has been increased from the conventional 76% to the new 85%.

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EXISTENCE OF GLOBAL SOLUTIONS TO SOME NONLINEAR EQUATIONS ON LOCALLY FINITE GRAPHS

  • Chang, Yanxun;Zhang, Xiaoxiao
    • Journal of the Korean Mathematical Society
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    • v.58 no.3
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    • pp.703-722
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    • 2021
  • Let G = (V, E) be a connected locally finite and weighted graph, ∆p be the p-th graph Laplacian. Consider the p-th nonlinear equation -∆pu + h|u|p-2u = f(x, u) on G, where p > 2, h, f satisfy certain assumptions. Grigor'yan-Lin-Yang [24] proved the existence of the solution to the above nonlinear equation in a bounded domain Ω ⊂ V. In this paper, we show that there exists a strictly positive solution on the infinite set V to the above nonlinear equation by modifying some conditions in [24]. To the m-order differential operator 𝓛m,p, we also prove the existence of the nontrivial solution to the analogous nonlinear equation.

Generalized Inverses and Solutions to Equations in Rings with Involution

  • Yue Sui;Junchao Wei
    • Kyungpook Mathematical Journal
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    • v.64 no.1
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    • pp.15-30
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    • 2024
  • In this paper, we focus on partial isometry elements and strongly EP elements on a ring. We construct characterizing equations such that an element which is both group invertible and MP-invertible, is a partial isometry element, or is strongly EP, exactly when these equations have a solution in a given set. In particular, an element a ∈ R# ∩ R is a partial isometry element if and only if the equation x = x(a)*a has at least one solution in {a, a#, a, a*, (a#)*, (a)*}. An element a ∈ R#∩R is a strongly EP element if and only if the equation (a)*xa = xaa has at least one solution in {a, a#, a, a*, (a#)*, (a)*}. These characterizations extend many well-known results.

A Study of New Evolutionary Approach for Multiobjective Optimization (다목적함수 최적화를 위한 새로운 진화적 방법 연구)

  • Shim, Mun-Bo;Suh, Myung-Won
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.26 no.6
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    • pp.987-992
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    • 2002
  • In an attempt to solve multiobjective optimization problems, many traditional methods scalarize the objective vector into a single objective. In those cases, the obtained solution is highly sensitive to the weight vector used in the scalarization process and demands the user to have knowledge about the underlying problem. Moreover, in solving multiobjective problems, designers may be interested in a set of Pareto-optimal points, instead of a single point. In this paper, pareto-based Continuous Evolutionary Algorithms for Multiobjective Optimization problems having continuous search space are introduced. This algorithm is based on Continuous Evolutionary Algorithms to solve single objective optimization problems with a continuous function and continuous search space efficiently. For multiobjective optimization, a progressive reproduction operator and a niche-formation method fur fitness sharing and a storing process for elitism are implemented in the algorithm. The operator and the niche formulation allow the solution set to be distributed widely over the Pareto-optimal tradeoff surface. Finally, the validity of this method has been demonstrated through a numerical example.

An Approximate Analytical Solution to the Ideal Adiabatic Model of Stirling Engines (스터링기관의 이상적인 단열모델에 대한 해석적 근사해)

  • 유호선
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.14 no.1
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    • pp.172-178
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    • 1990
  • To predict the qualitative performance characteristics of Stirling Engines, an analytical approach to the Ideal Adiabatic Model set up by Urieli et al. has been treated. First, volume variations of both the expansion and the compression cylinders are approximated to piecewise linear function of the crank angle, which make it possible to specify the mass flow direction of each cylinder a priori to solve a set of basic equation. In consequences, an engine cycle can be considered as a combination of 4-type fundamental process. For each process, pressure is obtained as a solution of the algebraic equation. Application of the cyclic steady condition to the whole cycle completes the analysis. Further investigations result in analytical expressions for cyclic heat and work in terms of dependent variables determined from the pressure. The results are expected useful in establishing the preliminary design conditions of Stirling Engines.

Structural Design Optimization of a High-Precision Grinding Machine for Minimum Compliance and Lightweight Using Genetic Algorithm (가변 벌점함수 유전알고리즘을 이용한 고정밀 양면 연삭기 구조물의 경량 고강성화 최적설계)

  • Hong Jin-Hyun;Park Jong-Kweon;Choi Young-Hyu
    • Journal of the Korean Society for Precision Engineering
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    • v.22 no.3 s.168
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    • pp.146-153
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    • 2005
  • In this paper, a multi-step optimization using genetic algorithm with variable penalty function is introduced to the structural design optimization of a grinding machine. The design problem, in this study, is to find out the optimum configuration and dimensions of structural members which minimize the static compliance, the dynamic compliance, and the weight of the machine structure simultaneously under several design constraints such as dimensional constraints, maximum deflection limit, safety criterion, and maximum vibration amplitude limit. The first step is shape optimization, in which the best structural configuration is found by getting rid of structural members that have no contributions to the design objectives from the given initial design configuration. The second and third steps are sizing optimization. The second design step gives a set of good design solutions having higher fitness for lightweight and minimum static compliance. Finally the best solution, which has minimum dynamic compliance and weight, is extracted from the good solution set. The proposed design optimization method was successfully applied to the structural design optimization of a grinding machine. After optimization, both static and dynamic compliances are reduced more than 58.4% compared with the initial design, which was designed empirically by experienced engineers. Moreover the weight of the optimized structure are also slightly reduced than before.

Multi-Objective Short-Term Fixed Head Hydrothermal Scheduling Using Augmented Lagrange Hopfield Network

  • Nguyen, Thang Trung;Vo, Dieu Ngoc
    • Journal of Electrical Engineering and Technology
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    • v.9 no.6
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    • pp.1882-1890
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    • 2014
  • This paper proposes an augmented Lagrange Hopfield network (ALHN) based method for solving multi-objective short term fixed head hydrothermal scheduling problem. The main objective of the problem is to minimize both total power generation cost and emissions of $NO_x$, $SO_2$, and $CO_2$ over a scheduling period of one day while satisfying power balance, hydraulic, and generator operating limits constraints. The ALHN method is a combination of augmented Lagrange relaxation and continuous Hopfield neural network where the augmented Lagrange function is directly used as the energy function of the network. For implementation of the ALHN based method for solving the problem, ALHN is implemented for obtaining non-dominated solutions and fuzzy set theory is applied for obtaining the best compromise solution. The proposed method has been tested on different systems with different analyses and the obtained results have been compared to those from other methods available in the literature. The result comparisons have indicated that the proposed method is very efficient for solving the problem with good optimal solution and fast computational time. Therefore, the proposed ALHN can be a very favorable method for solving the multi-objective short term fixed head hydrothermal scheduling problems.

A Study on the optimal text corpus for company names (한국어최적상호명코퍼스설계에관한연구)

  • Lee, Sun-Jung
    • Journal of the Korea Computer Industry Society
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    • v.5 no.5
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    • pp.747-754
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    • 2004
  • In this paper, we obtain an optimal corpus that can represent its characteristics very well from the baseline corpus which consists of unique 1,566,943 names among company names in a directory assistance serve (114). Two kinds of optimal solutions ared considered to obtain the optimal corpus. The first solution is to find phonetically balanced corpus (PBC), which are the minimum set including all possible triphones in the baseline corpus. The second solution is to find the phonetically distributed corpus (PDC), which is a minimum set representing the frequency characteristics of triphones in the baseline corpus. We can obtain 8,699 words as the PBC and 16,783 words (similarity measure R = 0.92) as PDC, respectively. These corpora can be used for the development of speech recognition and speech synthesis.

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