Suche
Anzeige der Dokumente 21-30 von 42
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 ...
Preprint
Error estimates for approximate approximations on compact intervals
(2005)
The aim of this paper is the investigation of the error which results from the method of approximate approximations applied to functions defined on compact in-tervals, only. This method, which is based on an approximate partition of unity, was introduced by V. Mazya in 1991 and has mainly been used for functions defied on the whole space up to now. For the treatment of differential equations and boundary integral equations, however, an efficient approximation procedure on compact intervals is needed.
In the present ...
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 ...
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.
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 ...
Preprint
On Oseen Resolvent Estimates: A Negative Result
(2009)
We consider the resolvent problem for the scalar Oseen equation in the whole space R^3. We show that for small values of the resolvent parameter it is impossible to obtain an L^2-estimate analogous to
the one which is valid for the Stokes resolvent, even if the resolvent parameter has positive real part.
Preprint
Computations in Relative Algebraic K-Groups
(2007)
Let G be finite group and K a number field or a p-adic field with ring of integers O_K. In the first part of the manuscript we present an algorithm that computes the relative algebraic K-group K_0(O_K[G],K) as an abstract abelian group. We solve the discrete logarithm problem, both in K_0(O_K[G],K) and the locally free class group cl(O_K[G]). All algorithms have been implemented in MAGMA for the case K = \IQ. In the second part of the manuscript we prove formulae for the torsion subgroup of K_0(\IZ[G],\IQ) for large ...
Preprint
Approximate approximations for the Poisson and the Stokes equations
(2006)
The method of approximate approximations is based on generating functions representing an approximate partition of the unity, only. In the present paper this method is used for the numerical solution of the Poisson equation and the Stokes system in R^n (n = 2, 3). The corresponding approximate volume potentials will be computed explicitly in these cases, containing a one-dimensional integral, only. Numerical simulations show the efficiency of the method and confirm the expected convergence of essentially second order, ...
Preprint
The Navier-Stokes Equations with Time Delay
(2007)
In the present paper we use a time delay epsilon > 0 for an energy conserving approximation of the nonlinear term of the non-stationary Navier-Stokes equations. We prove that the corresponding initial value problem (N_epsilon)in smoothly bounded domains G \subseteq R^3 is well-posed. Passing to the limit epsilon \rightarrow 0 we show that the sequence of stabilized solutions has an accumulation point such that it solves the Navier-Stokes problem (N_0) in a weak sense (Hopf).
Preprint
Approximate Approximations and a Boundary Point Method for the Linearized Stokes System
(2007)
The method of approximate approximations, introduced by Maz'ya [1], can also be used for the numerical solution of boundary integral equations. In this case, the matrix
of the resulting algebraic system to compute an approximate source density depends only on the position of a finite number of boundary points and on the direction of the normal vector in these points (Boundary Point Method). We investigate this approach for the Stokes problem in the whole space and for the Stokes boundary value problem in a bounded ...