Dual-Petrov-Galerkin approximations to linear third-order equations and the Korteweg-de Vries equation on semi-infinite intervals are considered. It is shown that by choosing appropriate trial and test basis functions the Dual-Petrov-Galerkin method using Laguerre functions leads to strongly coercive linear systems which are easily invertible and enjoy optimal convergence rates. A novel multi-d...

We consider determinants of Wronskian type whose entries are multiple orthogonal polynomials associated with a path connecting two multi-indices. By assuming that the weight functions form an algebraic Chebyshev (AT) system, we show that the polynomials represented by the Wronskians keep a constant sign in some cases, while in some other cases oscillatory behavior appears, which generalizes cla...

Ever since Kaplansky and Riordan [9-l I] developed their elegant theory of permutations with restricted position, a great variety of combinatorial problems have been explicitly solved, for example, see Dillon and, Roselle [l], Goldman, Joichi, and White [4-S], and Foata, Schutzenberger [2; 31. Spurred by the oft-noted analogy between the case of finite boolean algebras and that of lattices of v...

Fractional differentiation systems are characterized by the presence of non-exponential aperiodic multimodes. Although rational orthogonal bases can be used to model any L2[0,∞[ system, they fail to quickly capture the aperiodic multimode behavior with a limited number of terms. Hence, fractional orthogonal bases are expected to better approximate fractional models with fewer parameters. Intuit...

Optimal transport from the volume measure to a convex combination of Dirac measures yields a tessellation of a Riemannian manifold into pieces of arbitrary relative size. This tessellation is studied for the cost functions cp(z, y) = 1 p d(z, y) and 1 ≤ p < ∞. Geometric descriptions of the tessellations for all p is obtained for compact subsets of the Euclidean space and the sphere. For p = 1 t...

We propose long-time convergent numerical integration processes for delay differential equations. We first construct an integration process based on modified Laguerre functions. Then we establish its global convergence in certain weighted Sobolev space. The proposed numerical integration processes can also be used for systems of delay differential equations. We also developed a technique for re...

Linear operators which (1) preserve the reality of zeros of polynomials having only real zeros and (2) map stable polynomials into stable polynomials are investigated using recently established results concerning the zeros of certain Fox–Wright functions and generalized Mittag-Leffler functions. The paper includes several open problems and questions.  2005 Elsevier Inc. All rights reserved.

We present the exact solution for a set of nonlinear algebraic equations 1 zl = πd + 2d n ∑ m6=l 1 zl−zm . These were encountered by us in a recent study of the low energy spectrum of the Heisenberg ferromagnetic chain [1]. These equations are low d (density) “degenerations” of more complicated transcendental equation of Bethe’s Ansatz for a ferromagnet, but are interesting in themselves. They ...

An important chapter in the theory of distribution of zeros of polynomials and transcendental entire functions pertains to the study of linear operators acting on entire functions. This article surveys some recent developments (as well as some classical results) involving some specific classes of linear operators called multiplier sequences and complex zero decreasing sequences. This expository...

An efficient algorithm and a Fortran 90 module (LaguerrePol) for computing Laguerre polynomials L (α) n (z) are presented. The standard threeterm recurrence relation satisfied by the polynomials and different types of asymptotic expansions valid for n large and α small, are used depending on the parameter region. Based on tests of contiguous relations in the parameter α and the degree n satisfi...