• 제목/요약/키워드: restricted linear equation

검색결과 15건 처리시간 0.027초

CONDENSED CRAMER RULE FOR COMPUTING A KIND OF RESTRICTED MATRIX EQUATION

  • Gu, Chao;Xu, Zhaoliang
    • Journal of applied mathematics & informatics
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    • 제26권5_6호
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    • pp.1011-1020
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    • 2008
  • The problem of finding Cramer rule for solutions of some restricted linear equation Ax = b has been widely discussed. Recently Wang and Qiao consider the following more general problem AXB = D, $R(X){\subset}T$, $N(X){\supset}\tilde{S}$. They present the solution of above general restricted matrix equation by using generalized inverses and give an explicit expression for the elements of the solution matrix for the matrix equation. In this paper we re-consider the restricted matrix equation and give an equivalent matrix equation to it. Through the equivalent matrix equation, we derive condensed Cramer rule for above restricted matrix equation. As an application, condensed determinantal expressions for $A_{T,S}^{(2)}$ A and $AA_{T,S}^{(2)}$ are established. Based on above results, we present a method for computing the solution of a kind of restricted matrix equation.

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LINEAR STABILITY OF TRIANGULAR EQUILIBRIUM POINTS IN THE PHOTOGRAVITATIONAL RESTRICTED THREE BODY PROBLEM WITH TRIAXIAL RIGID BODIES, WITH THE BIGGER ONE AN OBLATE SPHEROID AND SOURCE OF RADIATION

  • KUMAR, AVDHESH;ISHWAR, B.
    • 천문학논총
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    • 제30권2호
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    • pp.297-299
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    • 2015
  • In this paper we have examined the linear stability of triangular equilibrium points in the photogravitational restricted three body problem when both primaries are triaxial rigid bodies, the bigger one an oblate spheroid and source of radiation. The orbits about the Lagrangian equilibrium points are important for scientific investigation. A number of space missions have been completed and some are being proposed by various space agencies. We analyze the periodic motion in the neighbourhood of the Lagrangian equilibrium points as a function of the value of the mass parameter. Periodic orbits of an infinitesimal mass in the vicinity of the equilibrium points are studied analytically and numerically. The linear stability of triangular equilibrium points in the photogravitational restricted three body problem with Poynting-Robertson drag when both primaries are oblate spheroids has been examined by A. Kumar (2007). We have found the equations of motion and triangular equilibrium points for our problem. With the help of the characteristic equation we have discussed stability conditions. Finally, triangular equilibrium points are stable in the linear sense. It is further seen that the triangular points have long or short periodic elliptical orbits in the same range of ${\mu}$.

일반역행열(一般逆行列)을 이용(利用)한 케이블네트 구조물(構造物)의 형상결정에 관한 연구 (A Study on the Shape Finding of Cable-Net Structures Introducing General Inverse Matrix)

  • 서삼열;이장복
    • 한국공간구조학회논문집
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    • 제2권1호
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    • pp.75-84
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    • 2002
  • In this study, the 'force density method' for shape finding of cable net structures is presented. This concept is based on the force-length ratios or force densities which are defined for each branch of the net structures. This method renders a simple linear 'analytical form finding' possible. If the free choice of the force densities is restricted by further condition, the linear method is extended to a nonlinear one. The nonlinear one can be applied to the detailed computation of networks. In this paper, the general inverse matrix is introduced to solve the nonlinear equilibrium equation including Jacobian matrix which is rectangular matrix. Several examples for linear and nonlinear analysis applied additional constraints are presented. It is shown that the force density method is suitable for form finding of cable net and the general inverse matrix can be applied to solve the nonlinear equation without Lagrangian factors.

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Using real time data with rigorous models to optimize plant performance

  • Clemmons, Josh
    • 제어로봇시스템학회:학술대회논문집
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    • 제어로봇시스템학회 1989년도 한국자동제어학술회의논문집; Seoul, Korea; 27-28 Oct. 1989
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    • pp.828-834
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    • 1989
  • On-Line optimization of process units has heretofore been restricted to the individual equipment level using linear approximate models. The advent of the low cost, high speed micro-computer coupled with the speed and robustness of an equation based exact simulator is making real-time optimization of entire process units a reality. The resultant implications for a decision system applied to day-to-day operations, point to a significant change in the way process plants will be managed in the future.

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Parametric roll of container ships in head waves

  • Moideen, Hisham;Falzarano, Jeffrey M.;Sharma, S.Abhilash
    • Ocean Systems Engineering
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    • 제2권4호
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    • pp.239-255
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    • 2012
  • Analysis of ship parametric roll has generally been restricted to simple analytical models and sophisticated time domain simulations. Simple analytical models do not capture all the critical dynamics while time-domain simulations are often time consuming to implement. The model presented in this paper captures the essential dynamics of the system without over simplification. This work incorporates various important aspects of the system and assesses the significance of including or ignoring these aspects. Special consideration is given to the fact that a hull form asymmetric about the design waterline would not lead to a perfectly harmonic variation in metacentric height. Many of the previous works on parametric roll make the assumption of linearized and harmonic behaviour of the time-varying restoring arm or metacentric height. This assumption enables modelling the roll motion as a Mathieu equation. This paper provides a critical assessment of this assumption and suggests modelling the roll motion as a Hills equation. Also the effects of non-linear damping are included to evaluate its effect on the bounded parametric roll amplitude in a simplified manner.

병원 환자 운반 업무의 작업 부하 분석에 NIOSH 들기 작업 공식의 적용 가능성 (Applicability of NIOSH Lifting Equation to analysis of Workload for Patients Transferring)

  • 기도형
    • 대한인간공학회지
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    • 제25권2호
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    • pp.43-50
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    • 2006
  • The purpose of this study was to investigate applicability of NIOSH lifting equation(NLE) to analysis of workload for patient transferring. In principle, the NLE is not applied to analyzing workload of patient transferring, because 1) the task is generally performed by two or more persons; 2) unlike ordinary objects, human body of patients is basically unstable load with their location of the center of mass significantly varying during lifting activity; and 3) the task is done in a restricted work space. This study was conducted through comparison of NIOSH lifting indexes(LIs) and L5/S1 compressive forces by 3DSSPP for patient transferring tasks performed by 2~6 persons. The results showed that LIs are linearly correlated with L5/S1 compressive forces with correlation coefficient of 0.92, which resulted in a significant simple linear regression equation for LIs and L5/S1 compressive forces. Consequently, it was concluded that the NLE is applicable to transferring patient only with slight modification. Based on the results, instead of 1.0 originally used by NIOSH, the LI of 1.5 was proposed as a gauge to estimate whether or not the task needs corrective action to reduce risk for developing lifting-related low back pain.

CFD/Kirchhoff 적분 방법을 이용한 자동차 타이어의 Air-Pumping 소음 예측 (CFD/Kirchhoff Integral Method for the Prediction of the Air-Pumping Noise by a Car Tyre)

  • 김성태;이수갑
    • 한국소음진동공학회:학술대회논문집
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    • 한국소음진동공학회 2004년도 추계학술대회논문집
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    • pp.916-919
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    • 2004
  • The monopole theory has long been used to model air-pumped effect from the elastic cavities in car tire. This approach models the change of an air as a piston moving backward and forward on a spring and equates local air movements exactly with the volume changes of the system. Thus, the monopole theory has a restricted domain of applicability due to the usual assumption of a small amplitude acoustic wave equation and acoustic monopole theory. This paper describes an approach to predict the air-pumping noise of a car ave with CFD/Kirchhoff integral method. The type groove is simply modeled as piston-cavity-sliding door geometry and with the aid of CFD technique flow properties in the groove of rolling car tyre are acquired. And these unsteady flow data are used as a air-pumping source in the next Cm calculation of full tyre-road geometry. Acoustic far field is predicted from Kirchhoff integral method by using unsteady flow data in space and time, which is provided by the CFD calculation of full tyre-road domain. This approach can cover the non-linearity of acoustic monopole theory with the aid of using Non-linear governing equation in CFD calculation. The method proposed in this paper is applied to the prediction of air-pumping noise of modeled car tyre and the predicted results are qualitatively compared with the experimental data.

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Restricted Bayesian Optimal Designs in Turning Point Problem

  • Seo, Han-Son
    • Journal of the Korean Statistical Society
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    • 제30권1호
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    • pp.163-178
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    • 2001
  • We consider the experimental design problem of selecting values of design variables x for observation of a response y that depends on x and on model parameters $\theta$. The form of the dependence may be quite general, including all linear and nonlinear modeling situations. The goal of the design selection is to efficiently estimate functions of $\theta$. Three new criteria for selecting design points x are presented. The criteria generalized the usual Bayesian optimal design criteria to situations n which the prior distribution for $\theta$ amy be uncertain. We assume that there are several possible prior distributions,. The new criteria are applied to the nonlinear problem of designing to estimate the turning point of a quadratic equation. We give both analytic and computational results illustrating the robustness of the optimal designs based on the new criteria.

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MAX-MIN CONTROLLABILITY OF DELAY-DIFFERENTIAL GAMES IN HILBERT SPACES

  • Kang, Yong-Han;Jeong, Jin-Mun;Park, Jong-Yeoul
    • 대한수학회지
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    • 제38권1호
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    • pp.177-191
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    • 2001
  • We consider a linear differential game described by the delay-differential equation in a Hilbert space H; (※Equations, See Full-text) U and V are Hilbert spaces, and B(t) and C(t) are families of bounded operators on U and V to H, respectively. A(sub)0 generates an analytic semigroup T(t) = e(sup)tA(sub)0 in H. The control variables g, and u and v are supposed to be restricted in the norm bounded sets (※Equations, See Full-text). For given x(sup)0 ∈ H and a given time t > 0, we study $\xi$-approximate controllability to determine x($.$) for a given g and v($.$) such that the corresponding solution x(t) satisfies ∥x(t) - x(sup)0∥ $\leq$ $\xi$($\xi$ > 0 : a given error).

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