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Now showing items 21-30 of 62
Preprint
Lagrangian approximations and weak solutions of the Navier-Stokes equations
(2007)
The motion of a viscous incompressible fluid flow in bounded domains with a smooth boundary can be described by the nonlinear Navier-Stokes equations. This description corresponds to the so-called Eulerian approach. We develop a new approximation method for the Navier-Stokes equations in both the stationary and the non-stationary case by a suitable coupling of the Eulerian and the Lagrangian representation of the flow, where the latter is defined by the trajectories of the particles of the fluid. The method leads to ...
Preprint
Parity of the Number of Irreducible Factors for Composite Polynomials
(2008)
Various results on parity of the number of irreducible factors of given polynomials over finite fields have been obtained in the recent literature. Those are mainly based on Swan’s theorem in which discriminants of polynomials over a finite field or the integral ring Z play an important role. In this paper we consider discriminants of the composition of some polynomials over finite fields. The relation between the discriminants of composed polynomial and the original ones will be established. We apply this to obtain ...
Preprint
On the Gap-Complexity of Simple RL-Automata
(2006)
Analysis by reduction is a method used in linguistics for checking the correctness of sentences of natural languages. This method is modelled by restarting automata. All types of restarting automata considered in the literature up to now accept at least the deterministic context-free languages. Here we introduce and study a new type of restarting automaton, the so-called t-RL-automaton, which is an RL-automaton that is rather restricted in that it has a window of size one only, and that it works under a minimal ...
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 potentials, ...
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 system ...
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.
Preprint
Restarting automata with restricted utilization of auxiliary symbols
(Universität Kassel, FB 17, Mathematik/Informatik, 2005)
The restarting automaton is a restricted model of computation that was introduced by Jancar et al. to model the so-called analysis by reduction, which is a technique used in linguistics to analyze sentences of natural languages. The most general models of restarting automata make use of auxiliary symbols in their rewrite operations, although this ability does not directly correspond to any aspect of the analysis by reduction. Here we put restrictions on the way in which restarting automata use auxiliary symbols, and ...
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 ...