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Published in Philip A. Laplante, Comprehensive Dictionary of Electrical Engineering, 2018
The parameter represents the parasitic elements such as small masses, inertias, capacitances, inductances, etc. The system properties undergo a discontinuous change when the perturbation parameter is set to zero since the second differential equations becomes an algebraic, or a transcendental equation 0 = g(t, x, z, 0). The singular perturbation methods are used in the analyses of high-gain nonlinear control systems as well as variable structure sliding mode control systems. singular value decomposition (SVD) useful decomposition method for matrix inverse and pseudoinverse problems, including the leastsquared solution of overdetermined systems. SVD 1 represents the matrix A in the form A = U 2 V , where is a diagonal matrix whose entries are the singular values of A, and U and V are the row and column eigenvector systems of A. Any matrix can be represented in this way. In image processing, SVD has been applied to coding, to image filtering, and to the approximation of non-separable 2-D point spread functions by two orthogonal 1-D impulse responses. singularity a location in the workspace of the manipulator at which the robot loses one or more DOF in Cartesian space, i.e., there is some direction (or directions) in Cartesian space along which it is impossible to move the robot end effector no matter which robot joints are moved. singularity function a function-like operation that is not a proper function in the analytic sense. This is because it has a point at which the function or its derivative is infinite or is undefined. In particular, the Dirac delta function is defined as: (t) = , m = 0 0, otherwise
A compositional demand/supply framework to quantify the resilience of civil infrastructure systems (Re-CoDeS)
Published in Sustainable and Resilient Infrastructure, 2018
Max Didier, Marco Broccardo, Simona Esposito, Bozidar Stojadinovic
where is the singularity function that returns 0 for negative arguments, or the argument otherwise. The start and the end time of the resilience assessment are denoted as t0 and tf, respectively. Equation (2) is valid as long as the available supply at element i at time t is known and can be strictly delimited, i.e. effects of other system elements are accounted for, negligible, or the available supply is independent of and not influenced by other parts of the system. The demand/supply concept at the component level is qualitatively shown in Figure 1. SRi(t) is the supply reserve margin at component i at time t, defined as the difference between the available supply and the demand at element i at time t (i.e. ). SRi(t) can be integrated over a given time period to obtain SRi, as shown in Figure 1. is the component resilience time, defined as the duration of time during which a supply deficit is observed.
Flexural response of beams on viscoelastic foundations with predictions beyond the loading area
Published in International Journal of Geotechnical Engineering, 2020
Parvathi Geetha Sreekantan, Prabir Kumar Basudhar
For all the nodes in the imaginary parts of the beam, EI is considered to be zero as in fact there is no beam. The equations can be written in a generalized form using singularity function as follows. The Equation (10) for the section at a distance x is considered from the right-hand side of the real beam is given in Equation (11).