• Title/Summary/Keyword: problem space

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초등수학 기하문제해결에서의 시각화 과정 분석

  • Yun, Yea-Joo;Kim, Sung-Joon
    • East Asian mathematical journal
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    • v.26 no.4
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    • pp.553-579
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    • 2010
  • Geometric education emphasize reasoning ability and spatial sense through development of logical thinking and intuitions in space. Researches about space understanding go along with investigations of space perception ability which is composed of space relationship, space visualization, space direction etc. Especially space visualization is one of the factors which try conclusion with geometric problem solving. But studies about space visualization are limited to middle school geometric education, studies in elementary level haven't been done until now. Namely, discussions about elementary students' space visualization process and ability in plane or space figures is deficient in relation to geometric problem solving. This paper examines these aspects, especially in relation to plane and space problem solving in elementary levels. Firstly we propose the analysis frame to investigate a visualization process for plane problem solving and a visualization ability for space problem solving. Nextly we select 13 elementary students, and observe closely how a visualization process is progress and how a visualization ability is played role in geometric problem solving. Together with these analyses, we propose concrete examples of visualization ability which make a road to geometric problem solving. Through these analysis, this paper aims at deriving various discussions about visualization in geometric problem solving of the elementary mathematics.

LINEAR PROGRAMMING SOLUTIONS OF GENERALIZED LINEAR IMPULSIVE CORRECTION FOR GEOSTATIONARY STATIONKEEPING

  • Park, Jae-Woo
    • Journal of Astronomy and Space Sciences
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    • v.13 no.1
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    • pp.48-54
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    • 1996
  • The generalized linear impulsive correction problem is applied to make a linear programming problem for optimizing trajectory of an orbiting spacecraft. Numerical application for the stationkeeping maneuver problem of geostationary satellite shows that this problem can efficiently find the optimal solution of the stationkeeping parameters, such as velocity changes, and the points of impulse by using the revised simplex method.

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Analyzing Problem Instance Space Based on Difficulty-distance Correlation (난이도-거리 상관관계 기반의 문제 인스턴스 공간 분석)

  • Jeon, So-Yeong;Kim, Yong-Hyuk
    • Journal of the Korean Institute of Intelligent Systems
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    • v.22 no.4
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    • pp.414-424
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    • 2012
  • Finding or automatically generating problem instance is useful for algorithm analysis/test. The topic has been of interest in the field of hardware/software engineering and theory of computation. We apply objective value-distance correlation analysis to problem spaces, as previous researchers applied it to solution spaces. According to problems, we define the objective function by (1) execution time of tested algorithm or (2) its optimality; this definition is interpreted as difficulty of the problem instance being solved. Our correlation analysis is based on the following aspects: (1) change of correlation when we use different algorithms or different distance functions for the same problem, (2) change of that when we improve the tested algorithm, (3) relation between a problem instance space and the solution space for the same problem. Our research demonstrates the way of problem instance space analysis and will accelerate the problem instance space analysis as an initiative research.

A Study on Modeling of Search Space with GA Sampling

  • Banno, Yoshifumi;Ohsaki, Miho;Yoshikawa, Tomohiro;Shinogi, Tsuyoshi;Tsuruoka, Shinji
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 2003.09a
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    • pp.86-89
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    • 2003
  • To model a numerical problem space under the limitation of available data, we need to extract sparse but key points from the space and to efficiently approximate the space with them. This study proposes a sampling method based on the search process of genetic algorithm and a space modeling method based on least-squares approximation using the summation of Gaussian functions. We conducted simulations to evaluate them for several kinds of problem spaces: DeJong's, Schaffer's, and our original one. We then compared the performance between our sampling method and sampling at regular intervals and that between our modeling method and modeling using a polynomial. The results showed that the error between a problem space and its model was the smallest for the combination of our sampling and modeling methods for many problem spaces when the number of samples was considerably small.

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A Study on the Current Status and Analysis on the Problem of Unfloored space and Floor Repair in Rural House (농촌주택의 봉당·마루 개보수 현황 및 문제점 분석)

  • Park, Gil-Beom;Park, Jun-Mo;Kim, Ok-Kyue
    • Proceedings of the Korean Institute of Building Construction Conference
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    • 2014.11a
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    • pp.117-118
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    • 2014
  • The unfloored space and floor is one of characteristic of traditional house in Korea. This space is used to connecting passage between room or entrance of house. Currently, according to decline of heat insulation property thereby becoming decrepit house, native is repairing it for block external environment such as rain, wind and so on. But, variety problem is happening from wrong repair. This object of this study is current status and analysis on problem of unfloored space and floor repair. As a result, current status of repair is classified repair type, installation position and using form. And position of problem is confirmed connection between original house and extend space.

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An Influence of Visualization on Geometric Problem Solving in the Elementary Mathematics (시각화가 초등기하문제해결에 미치는 영향)

  • Yun, Yea-Joo;Kang, Sin-Po;Kim, Sung-Joon
    • Journal of the Korean School Mathematics Society
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    • v.13 no.4
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    • pp.655-678
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    • 2010
  • In the elementary mathematics, geometric education emphasize spatial sense and understandings of figures through development of intuitions in space. Especially space visualization is one of the factors which try conclusion with geometric problem solving. But studies about space visualization are limited to middle school geometric education, studies in elementary level haven't been done until now. Namely, discussions about elementary students' space visualization process and methods in plane or space figures is deficient in relation to geometric problem solving. This paper examines these aspects, especially in relation to plane and space problem solving in elementary levels. First, we investigate visualization methods for plane problem solving and space problem solving respectively, and analyse in diagram form how progress understanding of figures and visualization process. Next, we derive constituent factor on visualization process, and make a check errors which represented by difficulties in visualization process. Through these analysis, this paper aims at deriving an influence of visualization on geometric problem solving in the elementary mathematics.

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DIFFERENTIAL EQUATIONS ON CLOSED SUBSETS OF A PROBABILISTIC NORMED SPACE

  • Kim, Jong-Kyu;Jin, Byoung-Jae
    • Journal of applied mathematics & informatics
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    • v.5 no.1
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    • pp.223-233
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    • 1998
  • This paper is concerned with the problem of existence of solutions to the initial value problem u'(t) = A(t, u(t)), u(a) = z in a probabilistic normed space where $A : [a,b)\;{\times}\;D->E$ is continuous, D is a closed subset of a probabilistic normed space E, and $z\;{\in}\;D$. With a dissipative type condition on A, we estabilish sufficient conditions for this initial value problem to have a solution.

TOPOLOGICAL APPROACH FOR THE MULTIPLE SOLUTIONS OF THE NONLINEAR PARABOLIC PROBLEM WITH VARIABLE COEFFICIENT JUMPING NONLINEARITY

  • Jung, Tacksun;Choi, Q-Heung
    • Korean Journal of Mathematics
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    • v.19 no.1
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    • pp.101-109
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    • 2011
  • We get a theorem which shows that there exist at least two or three nontrivial weak solutions for the nonlinear parabolic boundary value problem with the variable coefficient jumping nonlinearity. We prove this theorem by restricting ourselves to the real Hilbert space. We obtain this result by approaching the topological method. We use the Leray-Schauder degree theory on the real Hilbert space.

An Inventory Problem with Lead Time Proportional to Lot Size and Space Constraint (로트크기에 비례하는 리드타임과 공간 제약을 고려한 재고관리 정책)

  • Lee, Dongju
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.38 no.4
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    • pp.109-116
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    • 2015
  • This paper is concerned with the single vendor single buyer integrated production inventory problem. To make this problem more practical, space restriction and lead time proportional to lot size are considered. Since the space for the inventory is limited in most practical inventory system, the space restriction for the inventory of a vendor and a buyer is considered. As product's quantity to be manufactured by the vendor is increased, the lead time for the order is usually increased. Therefore, lead time for the product is proportional to the order quantity by the buyer. Demand is assumed to be stochastic and the continuous review inventory policy is used by the buyer. If the buyer places an order, then the vendor will start to manufacture products and the products will be transferred to the buyer with equal shipments many times. The mathematical formulation with space restriction for the inventory of a vendor and a buyer is suggested in this paper. This problem is constrained nonlinear integer programming problem. Order quantity, reorder points for the buyer, and the number of shipments are required to be determined. A Lagrangian relaxation approach, a popular solution method for constrained problem, is developed to find lower bound of this problem. Since a Lagrangian relaxation approach cannot guarantee the feasible solution, the solution method based on the Lagrangian relaxation approach is proposed to provide with a good feasible solution. Total costs by the proposed method are pretty close to those by the Lagrangian relaxation approach. Sensitivity analysis for space restriction for the vendor and the buyer is done to figure out the relationships between parameters.

A Heuristic for Efficient Scheduling of Ship Engine Assembly Shop with Space Limit (공간제약을 갖는 선박용 엔진 조립공장의 효율적인 일정계획을 위한 발견적 기법)

  • Lee, Dong-Hyun;Lee, Kyung-Keun;Kim, Jae-Gyun;Park, Chang-Kwon;Jang, Gil-Sang
    • IE interfaces
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    • v.12 no.4
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    • pp.617-624
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    • 1999
  • In order to maximize an availability of machine and utilization of space, the parallel machines scheduling problem with space limit is frequently discussed in the industrial field. In this paper, we consider a scheduling problem for assembly machine in ship engine assembly shop. This paper considers the parallel machine scheduling problem in which n jobs having different release times, due dates and space limits are to be scheduled on m parallel machines. The objective function is to minimize the sum of earliness and tardiness. To solve this problem, a heuristic is developed. The proposed heuristic is divided into three modules hierarchically: job selection, machine selection and job sequencing, solution improvement. To illustrate its effectiveness, a proposed heuristic is evaluated with a large number of randomly generated test problems based on the field situation. Through the computational experiment, we determine the job selection rule that is suitable to the problem situation considered in this paper and show the effectiveness of our heuristic.

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