• 제목/요약/키워드: quadratic form

검색결과 273건 처리시간 0.03초

Hull-form optimization of a container ship based on bell-shaped modification function

  • Choi, Hee Jong
    • International Journal of Naval Architecture and Ocean Engineering
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    • 제7권3호
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    • pp.478-489
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    • 2015
  • In the present study, a hydrodynamic hull-form optimization algorithm for a container ship was presented in terms of the minimum wave-making resistance. Bell-shaped modification functions were developed to modify the original hull-form and a sequential quadratic programming algorithm was used as an optimizer. The wave-making resistance as an objective function was obtained by the Rankine source panel method in which non-linear free surface conditions and the trim and sinkage of the ship were fully taken into account. Numerical computation was performed to investigate the validity and effectiveness of the proposed hull-form modification algorithm for the container carrier. The computational results were validated by comparing them with the experimental data.

A LOWER BOUND FOR THE NUMBER OF SQUARES WHOSE SUM REPRESENTS INTEGRAL QUADRATIC FORMS

  • Kim, Myung-Hwan;Oh, Byeong-Kweon
    • 대한수학회지
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    • 제33권3호
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    • pp.651-655
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    • 1996
  • Lagrange's famous Four Square Theorem [L] says that every positive integer can be represented by the sum of four squares. This marvelous theorem was generalized by Mordell [M1] and Ko [K1] as follows : every positive definite integral quadratic form of two, three, four, and five variables is represented by the sum of five, six, seven, and eight squares, respectively. And they tried to extend this to positive definite integral quadratic forms of six or more variables.

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SOLUTIONS OF NONCONVEX QUADRATIC OPTIMIZATION PROBLEMS VIA DIAGONALIZATION

  • YU, MOONSOOK;KIM, SUNYOUNG
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • 제5권2호
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    • pp.137-147
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    • 2001
  • Nonconvex Quadratic Optimization Problems (QOP) are solved approximately by SDP (semidefinite programming) relaxation and SOCP (second order cone programmming) relaxation. Nonconvex QOPs with special structures can be solved exactly by SDP and SOCP. We propose a method to formulate general nonconvex QOPs into the special form of the QOP, which can provide a way to find more accurate solutions. Numerical results are shown to illustrate advantages of the proposed method.

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AN EXPLICIT FORM OF POWERS OF A $2{\times}2$ MATRIX USING A RECURSIVE SEQUENCE

  • Kim, Daniel;Ryoo, Sangwoo;Kim, Taesoo;SunWoo, Hasik
    • 충청수학회지
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    • 제25권1호
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    • pp.19-25
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    • 2012
  • The purpose of this paper is to derive powers $A^{n}$ using a system of recursive sequences for a given $2{\times}2$ matrix A. Introducing a recursive sequence we have a quadratic equation. Solutions to this quadratic equation are related with eigenvalues of A. By solving this quadratic equation we can easily obtain an explicit form of $A^{n}$. Our method holds when A is defined not only on the real field but also on the complex field.

최소 조파저항을 가지는 컨테이너선의 선형최적화 기법에 대한 연구 (Development of an Optimum Hull Form for a Container Ship with Minimum Wave Resistance)

  • 최희종;서광철;김방은;전호환
    • 대한조선학회논문집
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    • 제40권4호
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    • pp.8-15
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    • 2003
  • This paper presents the method for developing an optimum hull form with minimum wave resistance using SQP(sequential quadratic programming) as an optimization technique. The wave resistance is evaluated by a Rankine source panel method with non-linear free surface conditions and the ITTC 1957 friction line is used to predict the frictional resistance coefficient. The geometry of the hull surface is represented and modified using B-spline surface patches. The optimization method is applied to Series 60 hull and KCS(KRISO 3600 TEU Container Ship). The obtained results prove that the method is appropriate for preliminary hull form design.

다항식 관점에 의한 이차함수의 성질 탐구와 지도방안 탐색 (A Study about the Properties of Quadratic Functions and Classroom Implications from a Polynomial Perspective)

  • 조정수
    • 한국학교수학회논문집
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    • 제9권2호
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    • pp.121-139
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    • 2006
  • 본 논문은 현행 중등수학과 교육과정에서 제시하고 있는 이차함수 관련 내용이 학생 들이 이미 배워서 알고 있는 다항식의 관점이 아니라 새로운 개념인 평행이동과 완전 제곱에 의한 꼭지점 형식의 변형으로 지도함으로써 지도내용 사이의 연계성 상실과 학생들의 개념적 이해를 저해하고 있다는 문제점을 인식했다. 이를 해소하기 위하여 본 연구는 다항식 접근을 통한 이차함수의 성질 탐구와 지도방안을 살펴보며 이 접근의 이점을 몇 가지 구체적인 예를 사용하여 논의하고자 한다.

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고속 Ro-Pax선형의 조파저항성능 향상을 위한 최적 선형설계에 관한 연구 (Study for Optimal Hull Form Design of a High Speed Ro-Pax Ship on Wave-making Resistance Performance)

  • 박동우;최희종
    • 한국항해항만학회지
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    • 제36권10호
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    • pp.787-793
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    • 2012
  • 최적화기법과 선형변환 자동화기법을 도입하여 고속 중형 Ro-Pax선박의 조파저항성능을 향상시킬 수 있는 선형설계방법에 대하여 연구하였다. 최적화기법으로는 SQP(sequential quadratic programming)을 적용하였으며, 선형변환 자동화기법으로는 NURBS(Non-Uniform Rational B-Spline)기법을 적용하였다. 목적함수인 선박의 조파저항성능을 예측하기 위하여 비선형 자유수면 경계조건과 선체의 침하량을 고려한 비점성 유동 해석 기법인 패널법을 적용하였다. 기준선형에 대하여 선형최적화를 수행하였으며 그 결과로 도출된 최적선형에 대하여 모형선을 제작하여 모형시험을 수행하였다. 기준선형과 최적선형에 대한 수치해석을 수행하여 얻은 결과와 최적선형에 대한 모형시험을 수행하여 얻은 결과를 서로 비교하였다.