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 ...
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 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 exponential weighting function. One advantage of this formulation is that the first k+ 1 ...
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Its sole purpose is to present some concepts of the disclosed subject matter in a simplified form as a prelude to the more detailed description that is presented later. Various aspects described herein relate to an exponential (e.g., 2n) voltage converter based on an area efficient switched ...
We show, how these expansions can be reconstructed from function samples using generalized shift operators. We derive an ESPRIT-like algorithm for the generalized recovery method and illustrate, how the method can be simplified if some frequency parameters are known beforehand. Furthermore, we present...
In a recent work [2] the solution of the matrix exponential function has been extended to the 𝑆𝑈(3) group with eight real parameters. By employing the Cayley–Hamilton relation the required matrix powers could be reduced to the zeroth, first and second. The resulting analytical formula ...
However, it is important to highlight that the phase inductance curve with respect to current (i) is a continuous function, as shown in [27]. Therefore, the inductance for a specific position (𝜃θ) can be represented by a polynomial function, as stated in [18]: 𝐿(𝜃,𝑖)=∑...
In a recent work [2] the solution of the matrix exponential function has been extended to the 𝑆𝑈(3) group with eight real parameters. By employing the Cayley–Hamilton relation the required matrix powers could be reduced to the zeroth, first and second. The resulting analytical formula ...
When α = β = 1 , the function τ ( v ) can be simplified as τ ( v ) = λ 1 / [ 2 λ 1 v + ( λ 2 2 + 2 λ 1 λ 3 ) ] − 1 . Then, lim v → ∞ τ ( v ) = − 1 and lim v → 0 τ ( v ) = λ 1 λ 2 2 + 2 λ 1 λ 3 − 1 . Henc...