• Title/Summary/Keyword: Quadratic equation

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Sectional Forming Analysis of Stamping Processes for Luminum Alloy Sheet metals (알루미늄 합금 박판 스탬핑 공정의 단면 성형 해석)

  • 이광병;이승열;금영탁
    • Transactions of Materials Processing
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    • v.6 no.4
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    • pp.279-290
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    • 1997
  • The sectional forming analysis of stamping pocesses for aluminum alloy sheet metals was investigated. For the modeling of the anomalous behavior of aluminum alloy sheet. the Barlat's strain rate potential and Hill's 1990 non-quadratic yield theory with an isotropic hardening rule were employed. The rigid-viscoplastic FEM formulation which solves equilibrium equation for plane-strain stage with mesh-normal geometric constraints was derived. A new method to determine the Barlat's anisotropic coefficients was also suggested. To verify the validity of the formulation, the stretch and draw forming processes of a square cup were simulated.

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Correlation, Regression, and Path Analysis between Yield and its Components in Tobacco (Nicotiana tabacum L.) (담배의 수량과 수량구성요소의 상관, 회귀 및 경로분석)

  • 김용암;유점호
    • Journal of the Korean Society of Tobacco Science
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    • v.3 no.2
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    • pp.115-122
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    • 1981
  • Data for this study were obtained from Burley 21 (Nicotiana tabacum L.) grown under various densities on the field in 1978 and 1979 at the Jeonju Experiment Station, Korea Ginseng & Tobacco Research Institute. Interrelations between yield and its components were statistically studied by correlation, regression, and pathway analysis. Correlation of yield with plant population was significant and positive. Quadratic functions for yield vs. plant population and the length of the largest leaf were fitted to the data. Multiple recession equation between yield and its components (leaf number ($X_1$), a leaf area ($X_5$), weight per unit leaf area ($X_9$), plant population ($X_14$)), was significant at the 5% level. Measuring the relative importance of its components on yield, plant population was 49.5%, weight per unit leaf area 25.3%, a leaf 15.6%, and leaf number 9.8%.

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Variable Structure Control with Optimized Sliding Surface for Spacecraft Slewing Maneuver

  • Cho, Sang-Bum;Moon, Gwan-Young;Kim, You-Dan
    • International Journal of Aeronautical and Space Sciences
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    • v.7 no.1
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    • pp.65-72
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    • 2006
  • A variable structure controller with an optimized sliding surface is proposed for slew maneuver of a rigid spacecraft. Rodrigues parameters are chosen to represent the spacecraft attitude. The quadratic type of performance index is used to design the sling surface. For optimization of the sliding surface, a Hamilton- Jacobi-Bellman equation is formulated and it is solved through the numerical algorithm using Galerkin approximation. The solution denotes a nonlinear sliding surface, on which the trajectory of the system satisfies the optimality condition approximately. Simulation result demonstrates that the proposed controller is effectively applied to the slew maneuver of a rigid spacecraft.

Robust $H_{\infty}$ Control for Bilinear Systems via State Feedback (상태 피드백에 의한 쌍일차 계통의 강인 $H_{\infty}$ 제어)

  • Kim, Young-Joong;Kim, Beom-Soo;Lim, Myo-Taeg
    • Proceedings of the KIEE Conference
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    • 2002.07d
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    • pp.2037-2039
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    • 2002
  • This paper focuses on robust $H_{\infty}$ control for bilinear systems with time-varying parameter uncertainties via state feedback. The suitable robustly stabilizing feedback control law can be constructed in term of solution to a state variable x-dependent quadratic Riccati equation using successive approximation technique. Also, the state feedback control law robustly stabilizes the plant and guarantees a robust $H_{\infty}$ performance for the closed-loop bilinear system with parameter uncertainties and exogenous disturbance.

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Statistical Analysis of Random Ship Rolling Using Equivalent Linearization Method (등가선형화방법을 이용한 선체의 불규칙 횡동요 운동의 통계적 해석)

  • Dong-Soo Kim;Won-Kyoung Lee
    • Journal of the Society of Naval Architects of Korea
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    • v.30 no.4
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    • pp.39-45
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    • 1993
  • In order to analyze the rolling motion of a ship in random beam waves we have used the equivalent linearization method. The quadratic nonlinear damping, the cubic and quintic nonlinear restoring moments were added to a single degree of freedom linear equation of roll motion. The irregular excitation moment was assumed to be the Gaussian white noise. The statistical characteristic of the response by the equivalent linearization method was compared with the simulation result.

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Optimal Design of Fuzzy Hybrid Multilayer Perceptron Structure (퍼지 하이브리드 다층 퍼셉트론구조의 최적설계)

  • Kim, Dong-Won;Park, Byoung-Jun;Oh, Sung-Kwun
    • Proceedings of the KIEE Conference
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    • 2000.07d
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    • pp.2977-2979
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    • 2000
  • A Fuzzy Hybrid-Multilayer Perceptron (FH-MLP) Structure is proposed in this paper. proposed FH-MLP is not a fixed architecture. that is to say. the number of layers and the number of nodes in each layer of FH-MLP can be generated to adapt to the changing environment. FH-MLP consists of two parts. one is fuzzy nodes which each node is operated as a small fuzzy system with fuzzy implication rules. and its fuzzy system operates with Gaussian or Triangular membership functions in premise part and constants or regression polynomial equation in consequence part. the other is polynomial nodes which several types of high-order polynomial such as linear. quadratic. and cubic form are used and is connected as various kinds of multi-variable inputs. To demonstrate the effectiveness of the proposed method. time series data for gas furnace process has been applied.

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A New Numerical Method for Solving Differential Equation by Quadratic Approximation (포물선 근사법에 의한 상태방정식의 새로운 수치해석적 접근법에 관한 연구)

  • Lee, Jong-Gi;Kwon, Yong-Jun;Choi, Byoung-Kon;Moon, Young-Hyun
    • Proceedings of the KIEE Conference
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    • 2003.07a
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    • pp.107-109
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    • 2003
  • 전력계통의 과도 안정도 해석의 접근방법에는 SI(Simultaneous Implicit)법과 PE(Partitioned Explicit)법 두 가지방법을 사용해오고 있다. SI법에는 Trapezoidal법 등이 있고, PE법에는 Runge-Kutta법, Euler법등이 사용되고 있다. SI법인 Trapezoidal법은 PE법의 Runge-Kutta법 또는 Euler법에 비해 시간간격을 크게 해서 계산속도를 줄일 수 있다는 장점이 있지만, 정화도면에서는 신뢰한 수 없는 단점이 있다. 이 논문에서는 포물선 사법을 이용하여 Trapezoidal법의 정확도를 개선학 수 있는 방법을 제시하고 명확한 수학적 증명을 통해 타당성을 보여준다. 연속함수와 불연속함수에 대해서 Runge-Kutta법과 Trapezoidal법과 제안한 방법을 적용시켜서 제안한 방법의 정화함을 보여준다.

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FUNCTIONAL EQUATIONS IN THREE VARIABLES

  • Boo, Deok-Hoon;Park, Chun-Gil;Wee, Hee-Jung
    • Journal of the Chungcheong Mathematical Society
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    • v.17 no.2
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    • pp.169-190
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    • 2004
  • Let r, s be nonzero real numbers. Let X, Y be vector spaces. It is shown that if a mapping f : $X{\rightarrow}Y$ satisfies f(0) = 0, and $$sf(\frac{x+y{\pm}z}{r})+f(x)+f(y){\pm}f(z)=sf(\frac{x+y}{r})+sf(\frac{y{\pm}z}{r})+sf(\frac{x{\pm}z}{r})$$, or $$sf(\frac{x+y{\pm}y}{r})+f(x)+f(y){\pm}f(z)=f(x+y)+f(y{\pm}z)+f(x{\pm}z)$$ for all x, y, $z{\in}X$, then there exist an additive mapping A : $X{\rightarrow}Y$ and a quadratic mapping Q : $X{\rightarrow}Y$ such that f(x) = A(x) + Q(x) for all $x{\in}X$. Furthermore, we prove the Cauchy-Rassias stability of the functional equations as given above.

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AN IMPROVED EXPONENTIAL REGULA FALSI METHODS WITH CUBIC CONVERGENCE FOR SOLVING NONLINEAR EQUATIONS

  • Ibrahim, S.A. Hoda
    • Journal of applied mathematics & informatics
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    • v.28 no.5_6
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    • pp.1467-1476
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    • 2010
  • The aim of this paper is to propose a cubic convergent regula falsi iterative method for solving the nonlinear equation f(x) = 0, where f : [a,b] $\subset$ R $\rightarrow$ R is a continuously differentiable. In [3,6] a quadratically convergent regula falsi iterative methods for solving this nonlinear equations is proposed. It is shown there that both the sequences of diameters and iterative points sequence converge to zero simultaneously. So The aim of this paper is to accelerate further the convergence of these methods from quadratic to cubic. This is done by replacing the parameter p in the iteration of [3,5,6] by a function p(x) defined suitably. The convergence analysis is carried out for the method. The method is tested on number of numerical examples and results obtained shows that our methods are better and more effective and comparable to well-known methods.

Effect of Temperature on the Growth of the Water Strider, Gerris paludum insularis (Gerridae, Heteroptera)

  • Park, Sang-Ock
    • The Korean Journal of Ecology
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    • v.27 no.6 s.122
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    • pp.369-373
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    • 2004
  • The water strider, Gerris paludum insularis, was reared in a growth cabinet at two constant temperatures and ${\approx}20^{\circ}C$ under a 16:8 (L:D) photoperiod. Differences in head width among three temperatures of ${\approx}20^{\circ}C,\;25^{\circ}C\;and\;30^{\circ}C$ in G. paludum insularis, were compared. Temperature affected growth of head width of G. paludum insularis. There were highly significant differences among head width for three temperature regimes and the immature stages. It was found that head width is greater in $30^{\circ}C$ than $25^{\circ}C\;and\;{\approx}20^{\circ}C$. The growth quantity of the head width in ${\approx}20^{\circ}C$ shows the slowest increase, and $25^{\circ}C\;and\;30^{\circ}C$ were gradually increased in that order. The maximum ratio of growth quantity by each stage is in the first instar in all regimes. The growth rates of all regimes show an increase pattern.