## Search

Now showing items 31-40 of 42

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Preprint
A crack on the interface of piezo-electric bodies

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

Singularities of elastic and electric fields are investigated at the tip of a crack on the interface of two anisotropic piezo-electric media under various boundary conditions on the crack surfaces. The Griffith formulae are obtained for increments of energy functionals due to growth of the crack and the notion of the energy release matrix is introduced. Normalization conditions for bases of singular solution are proposed to adapt them to the energy, stress, and deformation fracture criteria. Connections between these ...

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Preprint
A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it

(2005)

In this work, we present a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type s(x)y"n(x) + t(x)y'n(x) - lnyn(x) = 0 and show that all the three classical orthogonal polynomial families as well as three finite orthogonal polynomial families, extracted from this equation, can be identified as special cases of this derived polynomial sequence. Some general properties of this sequence are also given.

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Preprint
Modellierung und numerische Simulation der Thermoregulation von Früh- und Neugeborenen

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

Bei frühgeborenen Säuglingen spielt die Thermoregulation zur Aufrechterhaltung einer überlebenswichtigen Körpertemperatur durch Wärmeproduktion, -abgabe bzw. -aufnahme eine entscheidende Rolle. Der Einsatz moderner Inkubatoren soll die körpereigenen Thermoregulatoren unterstützen, und es ist im Hinblick auf verschiedene medizinische Fragestellungen wünschenswert, diesen Prozess modellieren zu können. Wir stellen ein einfaches Modell auf der Basis von partiellen Differentialgleichungen vor und beschreiben detailliert ...

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Preprint
Asymptotics of number fields and the Cohen-Lenstra heuristics

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

We study the asymptotics conjecture of Malle for dihedral groups Dl of order 2l, where l is an odd prime. We prove the expected lower bound for those groups. For the upper bounds we show that there is a connection to class groups of quadratic number fields. The asymptotic behavior of those class groups is predicted by the Cohen-Lenstra heuristics. Under the assumption of this heuristic we are able to prove the expected upper bounds.

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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 ...

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Preprint
A generalization of Student’s t-distribution from the viewpoint of special functions

(2005)

Student’s t-distribution has found various applications in mathematical statistics. One of the main properties of the t-distribution is to converge to the normal distribution as the number of samples tends to infinity. In this paper, by using a Cauchy integral we introduce a generalization of the t-distribution function with four free parameters and show that it converges to the normal distribution again. We provide a comprehensive treatment of mathematical properties of this new distribution. Moreover, since the ...

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Preprint
Artificial boundary conditions for the Stokes and Navier-Stokes equations in domains that are layer-like at infinity

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

Artificial boundary conditions are presented to approximate solutions to Stokes- and Navier-Stokes problems in domains that are layer-like at infinity. Based on results about existence and asymptotics of the solutions v^infinity, p^infinity to the problems in the unbounded domain Omega the error v^infinity - v^R, p^infinity - p^R is estimated in H^1(Omega_R) and L^2(Omega_R), respectively. Here v^R, p^R are the approximating solutions on the truncated domain Omega_R, the parameter R controls the exhausting of Omega. ...

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Preprint
Anisotropic adaptive resolution of boundary layers for heat conduction problems

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

We deal with the numerical solution of heat conduction problems featuring steep gradients. In order to solve the associated partial differential equation a finite volume technique is used and unstructured grids are employed. A discrete maximum principle for triangulations of a Delaunay type is developed. To capture thin boundary layers incorporating steep gradients an anisotropic mesh adaptation technique is implemented. Computational tests are performed for an academic problem where the exact solution is known as ...

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Preprint
An approximation method using approximate approximations

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

The aim of this paper is to 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 Laplace equation in two dimensions using approximate approximations. The procedure is based on potential ...

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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 ...