We give some easy to use criteria for deciding whether a MM obius plane, Laguerre plane or Minkowski plane, given in some normal form, is 2-dimensional. As an application of our results we prove that a Laguerre plane or Minkowski plane with a given topology on the point set is a (topological) 2-dimensional plane if and only if each derived aane plane at points of at least one parallel class is ...

and Applied Analysis 3 2.5. Laguerre Surface. LetΦ be a Laguerre surface inR. Any regular pointP onΦ is thus represented as in (16). Denote the corresponding isotropic surface by Φ with P given by (16). By duality, their corresponding curvatures are related by H ∗ = H K , K ∗ = 1 K . (17) Blaschke [6] defined the middle tangent sphere to be the tangent to the tangent plane P with radius

In this paper we present a Maple library (MOPs) for computing Jack, Hermite, Laguerre, and Jacobi multivariate polynomials, as well as eigenvalue statistics for the Hermite, Laguerre, and Jacobi ensembles of Random Matrix theory. We also compute multivariate hypergeometric functions, and offer both symbolic and numerical evaluations for all these quantities. We prove that all algorithms are wel...

The paper presents a model predictive control method for continuous-time systems based on subspace identification. It’s developed by reformulating the continuous-time systems using Laguerre filters to obtain the subspace prediction output. Then, the subspace predictors are derived by QR decomposition from input-output and Laguerre matrices. The subspace predictive controller is designed with th...

In this paper we examine the zero and first order eigenvalue fluctuations for the β-Hermite and β-Laguerre ensembles, using the matrix models we described in [5], in the limit as β → ∞. We find that the fluctuations are described by Gaussians of variance O(1/β), centered at the roots of a corresponding Hermite (Laguerre) polynomial. We also show that the approximation is very good, even for sma...

We address the problem of computing the fitting line of a set of circles in the Laguerre metric, that minimizes the distance to the farthest circle. To solve the fitting line problem we introduce a generalization of the concept of the width of a set of points using the Laguerre metric. We also present an efficient algorithm for finding the fitting line of a set of circles using minimization dia...

The distribution function for the first eigenvalue spacing in the Laguerre unitary ensemble of finite size may be expressed in terms of a solution of the fifth Painlevé transcendent. The generating function of a certain discontinuous linear statistic of the Laguerre unitary ensemble can similarly be expressed in terms of a solution of the fifth Painlevé equation. The methodology used to derive ...

We derive the interaction Hamiltonian of a Laguerre-Gaussian beam with a simple atomic system, under the assumption of a small spread of the center of mass wave function in comparison with the waist of the Laguerre-Gaussian beam. The center of mass motion of the atomic system is taken into account. Using the properties of regular spherical harmonics the internal and center of mass coordinates a...

It is known that the generalized Laguerre polynomials can enjoy subexponential growth for large primary index. In particular, for certain fixed parameter pairs (a, z) one has the large-n asymptotic behavior L(−a) n (−z) ∼ C(a, z)n−a/2−1/4e2 √ . We introduce a computationally motivated contour integral that allows efficient numerical Laguerre evaluations, yet also leads to the complete asymptoti...

The object of this paper is to prove combinatorially several (13 of them) limit formulas relating different families of hypergeometric orthogonal polynomials in Askey’s chart classifying them. We first find a combinatorial model for Hahn polynomials which, as pointed out by Foata at the ICM (1983), “contains” models for Jacobi, Meixner, Krawtchouk, Laguerre and Charlier polynomials. Seven limit...