laguerre function has many advantages such as good approximation capability for different systems, low computational complexity and the facility of on-line parameter identification. therefore, it is widely adopted for complex industrial process control. in this work, laguerre function based adaptive model predictive control algorithm (ampc) was implemented to control continuous stirred tank rea...

In this paper, we establish a result concerning eigenvector for the product of two operators C and D defined on a Lie algebra of endomorphisms of a vector space. Further, A new method has been devised to define some properties viz. differential recurrence relations and differential equations of 2-variables generalized Hermite matrix polynomials and 2variables matrix Laguerre polynomials to deri...

We show that the use of operational methods and of multi-index Bessel functions allow the derivation of generating functions, involving the product of an arbitrary number of Laguerre polynomials. ∗2000 Mathematics Subject Classification. 33C45, 44A45. †E-mail:[email protected] ‡E-mail:[email protected] §E-mail:[email protected] ¶E-mail:[email protected] 270 G. Dattol...

We introduce the so-called Clifford–Hermite polynomials in the framework of Dunkl operators, based on the theory of Clifford analysis. Several properties of these polynomials are obtained, such as a Rodrigues formula, a differential equation and an explicit relation connecting them with the generalized Laguerre polynomials. A link is established with the generalized Hermite polynomials related ...

A Laguerre polynomial sequence of parameter ε/2 was previously characterized in a recent work [Ana F. Loureiro and P. Maroni (2008) [28]] as an orthogonal Fε-Appell sequence, where Fε represents a lowering (or annihilating) operator depending on the complex parameter ε ≠ −2n for any integer n ⩾ 0. Here, we proceed to the quadratic decomposition of anFε-Appell sequence, and we conclude that the ...

Abstract. The spectral order on Rn induces a natural partial ordering on the manifold Hn of monic hyperbolic polynomials of degree n. We show that all differential operators of Laguerre-Pólya type preserve the spectral order. We also establish a global monotony property for infinite families of deformations of these operators parametrized by the space l of real bounded sequences. As a consequen...

In this paper we propose, a collocation method for solving nonlinear singular Lane-Emden equation which is a nonlinear ordinary differential equation on semi-infnite interval. This approach is based on a generalized Laguerre polynomial collocation method. This method reduces the solution of this problem to the solution of a system of algebraic equations.We also present the comparison of this wo...

Let x1 and xk be the least and the largest zeros of the Laguerre or Jacobi polynomial of degree k. We shall establish sharp inequalities of the form x1 < A, xk > B, which are uniform in all the parameters involved. Together with inequalities in the opposite direction, recently obtained by the author, this locates the extreme zeros of classical orthogonal polynomials with the relative precision,...

Visual information of videos is based on spatial and temporal extents. However, most of video indexing techniques work in the spatial extent. Thus, spatial features are extracted from individual frames and then temporal information is introduced by their temporal evolution or tracking in order to construct motion vectors that serve as temporal features. In this paper we present a novel approach...

Abstract. The distribution function for the first eigenvalue spacing in the Laguerre unitary ensemble of finite rank random matrices is found in terms of a Painlevé V system, and the solution of its associated linear isomonodromic system. In particular it is characterised by the polynomial solutions to the isomonodromic equations which are also orthogonal with respect to a deformation of the La...