• Title, Summary, Keyword: quadratic form

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Stochastic along-wind response of nonlinear structures to quadratic wind pressure

  • Floris, Claudio;de Iseppi, Luca
    • Wind and Structures
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    • v.5 no.5
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    • pp.423-440
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    • 2002
  • The effects of the nonlinear (quadratic) term in wind pressure have been analyzed in many papers with reference to linear structural models. The present paper addresses the problem of the response of nonlinear structures to stochastic nonlinear wind pressure. Adopting a single-degree-of-freedom structural model with polynomial nonlinearity, the solution is obtained by means of the moment equation approach in the context of It$\hat{o}$'s stochastic differential calculus. To do so, wind turbulence is idealized as the output of a linear filter excited by a Gaussian white noise. Response statistical moments are computed for both the equivalent linear system and the actual nonlinear one. In the second case, since the moment equations form an infinite hierarchy, a suitable iterative procedure is used to close it. The numerical analyses regard a Duffing oscillator, and the results compare well with Monte Carlo simulation.

A control allocation sterategy based on multi-parametric quadratic programming algorithm

  • Jeong, Tae-Yeong;Ji, Sang-Won;Kim, Young-Bok
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.49 no.2
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    • pp.153-160
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    • 2013
  • Control allocation is an important part of a system. It implements the function that map the desired command forces from the controller into the commands of the different actuators. In this paper, the authors present an approach for solving constrained control allocation problem in vessel system by using multi-parametric quadratic programming (mp-QP) algorithm. The goal of mp-QP algorithm applied in this study is to compute a solution to minimize a quadratic performance index subject to linear equality and inequality constraints. The solution can be pre-computed off-line in the explicit form of a piecewise linear (PWL) function of the generalized forces and constrains. The efficiency of mp-QP approach is evaluated through a dynamic positioning simulation for a vessel by using four tugboats with constraints about limited pushing forces and found to work well.

ON STABILITY OF A GENERALIZED QUADRATIC FUNCTIONAL EQUATION WITH n-VARIABLES AND m-COMBINATIONS IN QUASI-𝛽-NORMED SPACES

  • Koh, Heejeong;Lee, Yonghoon
    • Journal of the Chungcheong Mathematical Society
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    • v.33 no.3
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    • pp.319-326
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    • 2020
  • In this paper, we establish a general solution of the following functional equation $$mf\({\sum\limits_{k=1}^{n}}x_k\)+{\sum\limits_{t=1}^{m}}f\({\sum\limits_{k=1}^{n-i_t}}x_k-{\sum\limits_{k=n-i_t+1}^{n}}x_k\)=2{\sum\limits_{t=1}^{m}}\(f\({\sum\limits_{k=1}^{n-i_t}}x_k\)+f\({\sum\limits_{k=n-i_t+1}^{n}}x_k\)\)$$ where m, n, t, it ∈ ℕ such that 1 ≤ t ≤ m < n. Also, we study Hyers-Ulam-Rassias stability for the generalized quadratic functional equation with n-variables and m-combinations form in quasi-𝛽-normed spaces and then we investigate its application.

Development of an Optimal Hull Form with Minimum Resistance in Still Water

  • Choi Hee-Jong;Kim Mun-Chan;Chun Ho-Hwan
    • Journal of Ship and Ocean Technology
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    • v.9 no.3
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    • pp.1-13
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    • 2005
  • A design procedure for a ship with minimum total resistance has been developed using a numerical optimization method called SQP (Sequential Quadratic Programming) to search for optimized hull form and CFD(Computational Fluid Dynamics) technique. The friction resistance is estimated using the ITTC 1957 model-ship correlation line formula and the wave making resistance is evaluated using a potential-flow panel method based on Rankine sources with nonlinear free surface boundary conditions. The geometry of hull surface is represented and modified using B-spline surface patches during the optimization process. Using the Series 60 hull ($C_B$ =0.60) as a base hull, the optimization procedure is applied to obtain an optimal hull that produces the minimum total resistance for the given constraints. To verify the validity of the result, the original model and the optimized model obtained by the optimization process have been built and tested in a towing tank. It is shown that the optimal hull obtained around $13\%$ reduction in the total resistance and around $40\%$ reduction in the residual resistance at a speed tested compared with that of the original one, demonstrating that the present optimization tool can be effectively used for efficient hull form designs.

A student's conceiving a pattern of change between two varying quantities in a quadratic functional situation and its representations: The case of Min-Seon (이차함수에서 두 변량사이의 관계 인식 및 표현의 발달 과정 분석: 민선의 경우를 중심으로)

  • Lee, Dong Gun;Moon, Min Joung;Shin, Jaehong
    • The Mathematical Education
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    • v.54 no.4
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    • pp.299-315
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    • 2015
  • The aim of this qualitative case study is twofold: 1) to analyze how an eleventh-grader, Min-Seon, conceive and represent a pattern of change between two varying quantities in a quadratic functional situation, and 2) further to help her form a concept of 'derivative' as a tool to express the relationship with employing a concept of 'rate of change.' The result indicates that Min-Seon was able to construct graphs of piecewise functions that take average rates of change as range of the functions, and managed to conjecture the derivative of a quadratic function, $y=x^2$. In conclusion, we argue that covariational approach could not only facilitate students' construction of an initial function concept, but also support their understanding of the concept of 'derivative.'

A Study on the Development of Computer Assisted Instruction for the Middle School Mathematics Education - Focused on the graph of quadratic function - (중학교 수학과 CAI 프로그램 개발 연구 -이차함수의 그래프를 중심으로-)

  • 장세민
    • Journal of the Korean School Mathematics Society
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    • v.1 no.1
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    • pp.151-163
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    • 1998
  • In mathematics education, teaching-learning activity can be divided largely into the understanding the mathematical concepts, derivation of principles and laws, acquirement of the mathematical abilities. We utilize various media, teaching tools, audio-visual materials, manufacturing materials for understanding mathematical concepts. But sometimes we cannot define or explain correctly the concepts as well as the derivation of principles and laws by these materials. In order to solve the problem we can use the computer. In this paper, character and movement state of various quadratic function graph types can be used. Using the computers is more visible than other educational instruments like blackboards, O.H.Ps., etc. Then, students understand the mathematical concepts and the correct quadratic function graph correctly. Consquently more effective teaching-learning activity can be done. Usage of computers is the best method for improving the mathematical abilities because computers have functions of the immediate reaction, operation, reference and deduction. One of the important characters of mathematics is accuracy, so we use computers for improving mathematical abilities. This paper is about the program focused on the part of "the quadratic function graph", which exists in mathematical curriculum the middle school. When this program is used for students, it is expected the following educational effect. 1, Students will have positive thought by arousing interests of learning because this program is composed of pictures, animations with effectiveness of sound. 2. This program will cause students to form the mathematical concepts correctly. 3. By visualizing the process of drawing the quadratic function graph, students understand the quadratic function graph structually. 4. Through the feedback, the recognition ability of the trigonometric function can be improved. 5. It is possible to change the teacher-centered instruction into the student-centered instruction. For the purpose of increasing the efficiencies and qualities of mathmatics education, we have to seek the various learning-teaching methods. But considering that no computer can replace the teacher′s role, tearchers have to use the CIA program carefully.

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Closed-loop predictive control using periodic gain

  • Lee, Young-Il
    • 제어로봇시스템학회:학술대회논문집
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    • pp.173-176
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    • 1994
  • In this paper a closed-form predictive control which takes the intervalwise receding horizon strategy is presented and its stability properties are investigated. A slate-space form output predictor is derived which is composed of the one-step ahead optimal output prediction, input and output data of the system. A set of feedback gains are obtained using the dynamic programming algorithm so that they minimize a multi-stage quadratic cost function and they are used periodically.

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Study for the Development of an Optimum Hull Form using SQP (SQP법을 이용한 최적선형개발에 대한 연구)

  • Choi, Hee-Jong;Lee, Gyoung-Woo;Kim, Sang-Hoon;Kim, Ho
    • Proceedings of the Korean Institute of Navigation and Port Research Conference
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    • v.29 no.1
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    • pp.47-53
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    • 2005
  • 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 NURBS(Non-Uniform Rational B-Spline) surface patches. To verity the validity of the developed program the numerical calculations for Wigley hull and Series 60(C${_B}$=0.6) hull had been performed and the results obtained after the numerical calculations had been compared with the original hulls.

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Study for the Development of an Optimum Hull Form using SQP (SQP법을 이용한 최적선형개발에 대한 연구)

  • Choi, Hee-Jong;Lee, Gyoung-Woo;Yun, Soon-Dong
    • Journal of Navigation and Port Research
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    • v.30 no.10
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    • pp.869-875
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    • 2006
  • 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 NURBS(Non-Uniform Rational B-Spline) surface patches. To verity the validity of the developed program the numerical calculations for Wigley hull and Series 60( $C_B=0.6$) hull have been performed and the results obtained by the numerical calculations have been compared with the original hulls.