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Now showing items 41-50 of 56
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 ...
Preprint
Numerical simulation of tunnel fires using preconditioned finite volume schemes
(2006)
This article is concerned with the numerical simulation of flows at low Mach numbers which are subject to the gravitational force and strong heat sources. As a specific example for such flows, a fire event in a car tunnel will be considered in detail. The low Mach flow is treated with a preconditioning technique allowing the computation of unsteady flows, while the source terms for gravitation and heat are incorporated via operator splitting. It is shown that a first order discretization in space is not able to compute ...
Preprint
Mathematical problem solving, modelling, applications, and links to other subjects
(1989)
The paper will consist of three parts. In part I we shall present some background considerations which are necessary as a basis for what follows. We shall try to clarify some basic concepts and notions, and we shall collect the most important arguments (and related goals) in favour of problem solving, modelling and applications to other subjects in mathematics instruction. In the main part II we shall review the present state, recent trends, and prospective lines of development, both in empirical or theoretical ...
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.
Preprint
On the equivariant Tamagawa number conjecture for abelian extensions of a quadratic imaginary field
(Universität Kassel, FB 17, Mathematik/Informatik, 2005)
Let k be a quadratic imaginary field, p a prime which splits in k/Q and does not divide the class number hk of k. Let L denote a finite abelian extention of k and let K be a subextention of L/k. In this article we prove the p-part of the Equivariant Tamagawa Number Conjecture for the pair (h0(Spec(L)),Z[Gal(L/K)]).
Preprint
Construction of recurrent fractal interpolation surfaces(RFISs) on rectangular grids
(2008)
A recurrent iterated function system (RIFS) is a genaralization of an IFS and provides
nonself-affine fractal sets which are closer to natural objects. In general, it's attractor
is not a continuous surface in R3. A recurrent fractal interpolation surface (RFIS) is an
attractor of RIFS which is a graph of bivariate continuous interpolation function. We
introduce a general method of generating recurrent interpolation surface which are at-
tractors of RIFSs about any data set on a grid.
Preprint
Construction of fractal interpolation surfaces on rectangular grids
(2008)
We present a general method of generating continuous fractal interpolation surfaces
by iterated function systems on an arbitrary data set over rectangular grids and estimate
their Box-counting dimension.
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.
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.