During the mode transition from the pure electric propulsion mode to the hybrid propulsion mode, clutch-based pre-transmission parallel hybrid electric vehicles are subject to drivability issues. These issues originate from the fact that in the clutch-based pre-transmission parallel hybrid powertrain (CPPHP) configuration, the clutch connects the engine and the motor. Without a carefully design...

The main object of this paper is to give a di erent approach to proof of generating matrix functions for Laguerre matrix polynomials. We also obtain the hypergeometric matrix representations, addition theorem, nite summation formula and an integral representation for Laguerre matrix polynomials. We get the relations between Laguerre, Legendre and Hermite matrix polynomials. We get the generatin...

We discuss numerical solution of Altarelli-Parisi equations in a Laguerre-polynomial method and in a brute-force method. In the Laguerre method, we get good accuracy by taking about twenty Laguerre polynomials in the flavor-nonsinglet case. Excellent evolution results are obtained in the singlet case by taking only ten Laguerre polynomials. The accuracy becomes slightly worse in the small and l...

The notion of using orthonormal Laguerre sequences to represent discrete-time signals (sequences) 1.],,2.] was recently used for the representation of electromagnetic pulse (EMP) data 3.]. This formulations resulted in an error function that needed to be minimized with respect to a Laguerre parameter. The objective of this paper is to introduce some suucient conditions for this error function t...

In this study, a new and efficient approach is presented for numerical solution of Fredholm integro-differential equations (FIDEs) of the second kind on unbounded domain with degenerate kernel based on operational matrices with respect to generalized Laguerre polynomials(GLPs). Properties of these polynomials and operational matrices of integration, differentiation are introduced and are ultili...

The notion of representing discrete-time electromagnetic pulse (EMP) signals using or-thonormal Laguerre sequences is introduced. The motivation for doing so is that EMP signals and Laguerre sequences are both characterized by decaying exponentials. It is shown that very eecient Laguerre representation of EMP signals is possible using this approach. Given a sequence x(n), its Laguerre expansion...

The Laguerre method for numerically inverting Laplace transforms is an old established method based on the 1935 Tricomi-Widder theorem, which shows (under suitable regularity conditions) that the desired function can be represented as a weighted sum of Laguerre functions, where the weights are coefficients of a generating function constructed from the Laplace transform using a bilinear transfor...

From this definition it readily follows that a Laguerre plane of order n has n + 1 generators, that every circle contains exactly n + 1 points and that there are n3 circles. All known models of finite Laguerre planes are of the following form. Let O be an oval in the Desarguesian projective plane P2 = PG(2, pm), p a prime. Embed P2 into threedimensional projective space P3 = PG(3, pm) and let v...

Based on the method of the vectorial angular spectrum, an analytical expression of the electric field of an elegant LaguerreGaussian beam in free space is derived beyond the paraxial approximation, and the corresponding magnetic field is obtained by taking the curl of the electric field. By using the expressions for the electromagnetic fields, the expression of the orbital angular momentum dens...

a new ARX-Laguerre representation is recently built to model the dynamics of complex processes [1, 2]. The ARX-Laguerre models have proven their ability to accurately suit the behavior of systems. In this work, the model is exploited to diagnose the system by detecting its defaults. In this paper we build a proportional observer based on the ARX-Laguerre model. Therefore, the designed observer ...