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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.
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
Divisibility of Trinomials by Irreducible Polynomials over F_2
(2008)
Irreducible trinomials of given degree n over F_2 do not always exist and in the cases that there is no irreducible trinomial of degree n it may be effective to use trinomials with an irreducible factor of degree n. In this paper we consider some conditions under which irreducible polynomials divide trinomials over F_2. A condition for divisibility of self-reciprocal trinomials by irreducible polynomials over F_2 is established. And we extend Welch's criterion for testing if an irreducible polynomial divides trinomials ...
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
Network properties of folksonomies
(2007)
Social resource sharing systems like YouTube and del.icio.us have acquired a large number of users within the last few years. They provide rich resources for data analysis, information retrieval, and knowledge discovery applications. A first step towards this end is to gain better insights into content and structure of these systems. In this paper, we will analyse the main network characteristics of two of these systems. We consider their underlying data structures â so-called folksonomies â as tri-partite ...
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
Semantic web mining and the representation, analysis, and evolution of web space
(2005)
Semantic Web Mining aims at combining the two fast-developing research areas Semantic Web and Web Mining. This survey analyzes the convergence of trends from both areas: Growing numbers of researchers work on improving the results of Web Mining by exploiting semantic structures in the Web, and they use Web Mining techniques for building the Semantic Web. Last but not least, these techniques can be used for mining the Semantic Web itself. The second aim of this paper is to use these concepts to circumscribe what Web ...
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
Creation and merging of ontology top-levels
(2003)
We provide a new method for systematically structuring the top-down level of ontologies. It is based on an interactive, top-down knowledge acquisition process, which assures that the knowledge engineer considers all possible cases while avoiding redundant acquisition. The method is suited especially for creating/merging the top part(s) of the ontologies, where high accuracy is required, and for supporting the merging of two (or more) ontologies on that level.
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.