In 2009, Gómez-Ullate, Kamran, and Milson characterized all sequences of polynomials {pn}n=1, with deg pn = n ≥ 1, that are eigenfunctions of a secondorder differential equation and are orthogonal with respect to a positive Borel measure on the real line having finite moments of all orders. Up to a complex linear change of variable, the only such sequences are theX1-Laguerre and theX1-Jacobi po...

For α = n− 1, n ∈ N\{0}, the operator D2 is the radial part of the sub-Laplacian on the Heisenberg groupHn (see [2, 4]). These operators have gained considerable interest in various fields of mathematics (see [1, 4]). They give rise to generalizations of many two-variable analytic structures like the Laguerre-Fourier transform L, the Laguerre-convolution product, the dispersion and the Gaussian...

A coupled Legendre-Laguerre spectral element method is proposed for the Stokes and Navier-Stokes equations in unbounded domains. The method combines advantages of the high accuracy of the Laguerre-spectral method for unbounded domains and the geometric flexibility of the spectral-element method. Rigorous stability and error analysis for the Stokes problem is carried out. Numerical results indic...

In 2009, Gómez–Ullate, Kamran, and Milson characterized all sequences of polynomials {pn}n=1, with deg pn = n ≥ 1, that are eigenfunctions of a second– order differential equation and are orthogonal with respect to a positive Borel measure on the real line having finite moments of all orders. Up to a complex linear change of variable, the only such sequences are the X1-Laguerre and the X1-Jacob...

We construct flat Laguerre planes that admit the universal covering group of SL2R, extended by a factor R, as a group of automorphisms. These planes contain the affine Moulton planes as derived planes, and they are constructed by gluing together two copies of a Moulton plane, folded up along their fixed lines. The action of the Moulton group carries over (modulo Z2) to the Laguerre planes, and ...

The radial part of the wave function of an electron in a Coulomb potential is the product of a Laguerre polynomial and an exponential with the variable scaled by a factor depending on the degree. This note presents an elementary proof of the orthogonality of wave functions with differing energy levels. It is also shown that this is the only other natural orthogonality for Laguerre polynomials. ...

For many products, it is not uncommon to see that a unit with a higher degradation rate has a more volatile degradation path. Motivated by this observation, we propose a new class of random effects model for the Wiener process model. We express the Wiener process in a special form and allow one of the parameters to be random across the product population so that a unit with a high degradation r...

DE algorithm is a population-based heuristic global search technology. The algorithm has simple principle, fewer control parameters, but has strong robustness, and good optimization performance. This paper uses differential evolution algorithm for parameters identification of Wiener model. Firstly, we analyze the influence of mutation rate F on global parallel search ability and convergence in ...

Dendritic macromolecules’ have attracted much attention as organic examples of well-defined nanostructures. These molecules are ideal model systems for studying how physical properties depend on molecular size and architecture. In this paper using a simple result, some GAP programs are prepared to compute Wiener and hyper Wiener indices of dendrimers.

While there exists a substantial literature on the identification of Hammerstein and Wiener models, the identification of WienerHammerstein models has received considerably less attention yet this is a model class of very great practical importance. This paper proposes an elegant approach to estimating Wiener-Hammerstein systems from measured data.