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Full-Text Articles in Physical Sciences and Mathematics
A Generalized Univariate Change-Of-Variable Transformation Technique, Andrew G. Glen, Lawrence Leemis, John H. Drew
A Generalized Univariate Change-Of-Variable Transformation Technique, Andrew G. Glen, Lawrence Leemis, John H. Drew
Arts & Sciences Articles
We present a generalized version of the univariate change-of-variable technique for transforming continuous random variables. Extending a theorem from Casella and Berger [1990. Statistical Inference, Wadsworth and Brooks/Cole, Inc., Pacific Grove, CA] for many-to-1 transformations, we consider more general univariate transformations. Specifically, the transformation can range from 1-to-1 to many-to-1 on various subsets of the support of the random variable of interest. We also present an implementation of the theorem in a computer algebra system that automates the technique. Some examples demonstrate the theorem's application.
Discrete-Time Linear And Nonlinear Aerodynamic Impulse Responses For Efficient Cfd Analyses, Walter A. Silva
Discrete-Time Linear And Nonlinear Aerodynamic Impulse Responses For Efficient Cfd Analyses, Walter A. Silva
Dissertations, Theses, and Masters Projects
This dissertation discusses the mathematical existence and the numerical identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Theodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. …