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Next we consider a matrix-polynomial extension of the concept of a common factor of two scalar polynomials. Since one of the polynomial matrices is always square in our application to transfer function representation, attention is restricted to that situation. ...
It is shown that the Laplace transform of a continuous lifetime random variable with a polynomial failure rate function satisfies a certain differential equation. This generates a set of differential equations which can be used to express the polynomial coefficients in terms of the derivatives of ...
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4.2. The relationship between the shape parameters and the shape of the curves The properties of the basis function described above makes the shape of these Bézier curves remarkably simple to alter. The shape of the extension curves can be adjusted by changing the shape parameter, with every ...
Using all this information, we can sketch the function described by Eq. (I.1.16); see Fig. I.1.4. Example I.1.3 (Physical Application ). To motivate things more, let's look at a physical example of a rational function (and where we'll also use a polynomial function): the van der ...
A separate row is provided for the model with a linear function of weight because it is often the default when including a predictor in the model. The fractional powers of the models are shown in the Powers column. An estimate of the residual standard error is given in the Residual std. ...
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Assuming that has finite variance, PCE represents the output variable as a function of another random variable, ξ, called the germ with a known distribution as and Physically constrained polynomial chaos expansion (PC2)– deterministic formulation In this section, we propose a novel approach to ...