## Search

Now showing items 31-40 of 42

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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 ...

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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
Solution properties of the de Branges differential recurrence equation

(2005)

In this 1984 proof of the Bieberbach and Milin conjectures de Branges used a positivity result of special functions which follows from an identity about Jacobi polynomial sums thas was published by Askey and Gasper in 1976. The de Branges functions Tn/k(t) are defined as the solutions of a system of differential recurrence equations with suitably given initial values. The essential fact used in the proof of the Bieberbach and Milin conjectures is the statement Tn/k(t)<=0. In 1991 Weinstein presented another proof of ...

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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
Numerical Methods for Non-Stationary Stokes Flow

(2008)

We consider a first order implicit time stepping procedure (Euler scheme)
for the non-stationary Stokes equations in smoothly bounded domains of R3. Using
energy estimates we can prove optimal convergence properties in the Sobolev
spaces Hm(G) (m = 0;1;2) uniformly in time, provided that the solution of the
Stokes equations has a certain degree of regularity. For the solution of the resulting
Stokes resolvent boundary value problems we use a representation in form of
hydrodynamical volume and boundary layer ...

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Preprint
The Parity of the Number of Irreducible Factors for Some Pentanomials

(2008)

It is well known that Stickelberger-Swan theorem is very important for determining reducibility of polynomials over a binary field. Using this theorem it was determined the parity of the number of irreducible factors for some kinds of polynomials over a binary field, for instance, trinomials,
tetranomials, self-reciprocal polynomials and so on. We discuss this problem for type II pentanomials namely x^m +x^{n+2} +x^{n+1} +x^n +1 \in\ IF_2 [x].
Such pentanomials can be used for efficient implementing multiplication ...

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Preprint
Statistical Analysis of Diabetes Mellitus

(2009)

Diabetes mellitus is a disease where the glucosis-content of the blood does not automatically
decrease to a ”normal” value between 70 mg/dl and 120 mg/dl (3,89 mmol/l and
6,67 mmol/l) between perhaps one hour (or two hours) after eating. Several instruments
can be used to arrive at a relative low increase of the glucosis-content. Besides drugs (oral
antidiabetica, insulin) the blood-sugar content can mainly be influenced by
(i) eating, i.e., consumption of the right amount of food at the right time
(ii) physical ...

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Preprint
Approximate solutions and error estimates for a Stokes boundary value problem

(2009)

The aim of this paper is the numerical treatment of a boundary value
problem for the system of Stokes' equations. For this we extend the method
of approximate approximations to boundary value problems. This method
was introduced by V. Maz'ya in 1991 and has been used until now for the
approximation of smooth functions defined on the whole space and for the
approximation of volume potentials.
In the present paper we develop an approximation procedure for the solution
of the interior Dirichlet problem for the ...

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Preprint
Image compression predicated on recurrent iterated function systems

(2008)

Recurrent iterated function systems (RIFSs) are improvements of
iterated function systems (IFSs) using elements of the theory of Marcovian
stochastic processes which can produce more natural looking images. We
construct new RIFSs consisting substantially of a vertical contraction factor
function and nonlinear transformations. These RIFSs are applied to image
compression.

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Preprint
On Nonlinear Preconditioners in Newton-Krylov-Methods for Unsteady Flows

(2008)

The application of nonlinear schemes like dual time stepping as preconditioners in matrix-free Newton-Krylov-solvers is considered and analyzed. We provide a novel formulation of the left preconditioned operator that says it is in fact linear in the matrix-free sense, but changes the Newton scheme. This allows to get some insight in the convergence properties of these schemes which are demonstrated through numerical results.