## Search

Now showing items 11-20 of 53

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Preprint
Characterization theorem for classical orthogonal polynomials on non-uniform lattices: The functional approach

(2010)

Using the functional approach, we state and prove a characterization theorem for classical orthogonal polynomials on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable) including the Askey-Wilson polynomials. This theorem proves the equivalence between seven characterization properties, namely the Pearson equation for the linear functional, the second-order divided-difference equation, the orthogonality of the derivatives, the Rodrigues formula, two types of structure relations,and the ...

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Preprint
On Solutions of Holonomic Divided-Difference Equations on Non-Uniform Lattices

(2010)

The main aim of this paper is the development of suitable bases (replacing the power basis x^n (n\in\IN_\le 0) which enable the direct series representation of orthogonal polynomial systems on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable). We present two bases of this type,
the first of which allows to write solutions of arbitrary divided-difference equations in terms of series representations extending results given in [16] for the q-case. Furthermore it enables the representation ...

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Preprint
Stability of preconditioned finite volume schemes at low Mach numbers

(Universität Kassel, FB 17, Mathematik/Informatik, 2004)

In [4], Guillard and Viozat propose a finite volume method for the simulation of inviscid steady as well as unsteady flows at low Mach numbers, based on a preconditioning technique. The scheme satisfies the results of a single scale asymptotic analysis in a discrete sense and comprises the advantage that this can be derived by a slight modification of the dissipation term within the numerical flux function. Unfortunately, it can be observed by numerical experiments that the preconditioned approach combined with an ...

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Preprint
An algebraic proof of Iitaka's conjecture C2,1

(Universität Kassel, FB 17, Mathematik/Informatik, 2002)

We give a proof of Iitaka's conjecture C2,1 using only elementary methods from algebraic geometry.

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Preprint
Computation of locally free class groups

(2006)

We show that the locally free class group of an order in a semisimple algebra over a number field is isomorphic to a certain ray class group. This description is then used to present an algorithm that computes the
locally free class group. The algorithm is implemented in MAGMA for the case where the algebra is a group ring over the rational numbers.

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Preprint
Duplication coefficients via generating functions

(2006)

In this paper, we solve the duplication problem
P_n(ax) = sum_{m=0}^{n}C_m(n,a)P_m(x) where {P_n}_{n>=0} belongs to a wide class of polynomials, including the classical orthogonal polynomials (Hermite, Laguerre, Jacobi) as well as the classical discrete orthogonal polynomials
(Charlier, Meixner, Krawtchouk) for the specific case a = −1. We give closed-form expressions
as well as recurrence relations satisfied by the duplication coefficients.

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Preprint
On the equivariant Tamagawa number conjecture for abelian extensions of a quadratic imaginary field

(Universität Kassel, FB 17, Mathematik/Informatik, 2005)

Let k be a quadratic imaginary field, p a prime which splits in k/Q and does not divide the class number hk of k. Let L denote a finite abelian extention of k and let K be a subextention of L/k. In this article we prove the p-part of the Equivariant Tamagawa Number Conjecture for the pair (h0(Spec(L)),Z[Gal(L/K)]).

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Preprint
A generic formula for the values at the boundary points of monic classical orthogonal polynomials

(2005)

In a previous paper we have determined a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type σ(x)y"n(x)+τ(x)y'n(x)-λnyn(x)=0. In this paper, we give another such formula which enables us to present a generic formula for the values of monic classical orthogonal polynomials at their boundary points of definition.

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Preprint
Spacelike maximal surfaces in 3D Lorentz-Minkowski space

(2006)

We investigate spacelike maximal surfaces in 3-dimensional Lorentz-Minkowski space,
give an Enneper-Weierstrass representation of such surfaces and classify those with a Lorentzian or Euclidian rotation symmetry.

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Preprint
Orthogonal polynomials and recurrence equations, operator equations and factorization

(Universität Kassel, FB 17, Mathematik/Informatik, 2005)

This article surveys the classical orthogonal polynomial systems of the Hahn class, which are solutions of second-order differential, difference or q-difference equations. Orthogonal families satisfy three-term recurrence equations. Example applications of an algorithm to determine whether a three-term recurrence equation has solutions in the Hahn class - implemented in the computer algebra system Maple - are given. Modifications of these families, in particular associated orthogonal systems, satisfy fourth-order ...