The formulation and methodology of curve fitting polynomials by discounted least squares can be simplified through the use of the discrete Laguerre polynomials, which are mutually orthogonal with respect to an
Let the cumulative distribution function of TPρ be denoted by Fρ,Λ and its p-value by pρ, whose limiting distribution is a Uniform, U0,1. Hansen and Timmermann (2012) make several contributions. The first is to show that the limiting distribution in (30) can be simplified to: (31...
The response of an LTI system to a complex exponential is a complex exponential with the same frequency and a possible change in its magnitude and/or phase. With H(f) as the LTI system transfer function, the response to the exponential exp(j2πf0t) is exp(j2πf0t)H(f0). Note that...
We shall abbreviate 'exponential generating function' by egf, and 'or- dinary generating function' by ogf. Most of the (ordinary or exponential) generating functions of sets of combinatorial classes are exponentials of power series with nonnegative coef- ficients, the object of interest of this...
)zn is the exponential generating function (egf) of a labeled combinatorial class G (no object of size 0), then f(z)=eg(z)=∑n=0∞(an/n!)zn is the egf of the labeled class of sets formed with the objects of G, termed assemblies in [1]. Next, we consider first sets of the...
Suppose that x(s, t) = 5s^2 -3t^2,y a function of (s, t) with y(1, 1) = 1 and \frac{\partial y}{\partial t} (1, 1) = -4. Suppose that u = xy, v a function of x, y with \frac{\partial v}{\partial y} ...
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[19] presented a computational investigation of nanofluid flow (Oldroyd-B Model) with mass and heat transport, gyrotactic microbes past a rotating disc using the MATLAB built-in function bvp4c. Uddin et al. [20] first described the blowing effect on bio-convection flow across a dynamic stretch...
together with Sp(1)=SU(2). For all these compact Lie groups the analytical evaluation of the matrix exponential function has been studied in this work. Actually, the obtained formula can be evaluated most straightforwardly for the symplectic group Sp(2), whereas in the other cases one has ...
gene interaction network with 424 genes (Schuldiner et al.2005; Wang et al.2019). The model included geometrically weighted in-degree and out-degree terms, but not any triangular terms; the interest is rather in the clusters it finds, which may be used to predict function (Wang et al....