## Search

Now showing items 21-30 of 61

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Preprint
Learning analysis by reduction from positive data

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

Analysis by reduction is a linguistically motivated method for checking correctness of a sentence. It can be modelled by restarting automata. In this paper we propose a method for learning restarting automata which are strictly locally testable (SLT-R-automata). The method is based on the concept of identification in the limit from positive examples only. Also we characterize the class of languages accepted by SLT-R-automata with respect to the Chomsky hierarchy.

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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 ...

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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 ...

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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).

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Preprint
The Navier-Stokes Equations with Particle Methods

(2007)

The non-stationary nonlinear Navier-Stokes equations describe the motion of a viscous incompressible fluid flow for 0<t≤T in some bounded three-dimensional domain.
Up to now it is not known wether these equations are well-posed or not. Therefore we use a particle method to develop a system of approximate equations. We show that this system can be solved uniquely and globally in time and that its solution has a high degree of spatial regularity. Moreover we prove that the system of approximate solutions has an ...

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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 ...

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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 ...

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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 ...