FACULTY OF

MATHEMATICS

Research Interests

• theoretical and numerical investigations for systems of hyperbolic conservation laws
• kinetic theory of gases, classical and relativistic theory
• micro-macro transitions and continuum mechanics
• Electromagnetic diffraction theory; scalar and vectorial pseudodifferential operators on Sobolev spaces:
• Number theory
• formal languages and mathematical logic

Selected Papers

• • Electromagnetic diffraction theory; scalar and vectorial pseudodifferential operators on Sobolev spaces:
    "On energy conditions for electromagnetic diffraction by apertures'' (PDF file), with N. Gorenflo, ISRN Mathematical Physics (2011).
  • Number theory:
    Lehrbuch mit Y. Abramchuk and A. Bondarava : `"Elementare Zahlentheorie" (2018)
    (PDF-File, im arXiv unter https://arxiv.org/pdf/1809.09710 frei verfübar).
    Lehr- und Übungsmaterial zur Kettenbruchentwicklung,
    "Charakterisierung der Riemannschen Hypothese mit Hilfe eines Hilbertschen Folgenraumes'' (PDF file),
    (Preprint Nr. 20/2011, Otto-von-Guericke-Universität Magdeburg).
    "Farey-Sequenzen'' (PDF file), (Preprint Nr. 1/2012, Otto-von-Guericke-Universität Magdeburg).
    "On the formulas for pi(x) and psi(x) of Riemann and von-Mangoldt'' (PDF file), (Preprint Nr. 09/2005, Otto-von-Guericke-Universität Magdeburg).
  • Lehrbuch mit Piotr Skrzypacz: "Höhere Analysis durch Anwendungen lernen''. Errata zu diesem Lehrbuch: errata.pdf (PDF file).
  • ''Habilitationsschrift im Rahmen des DFG-Schwerpunkt-Programms ANumE mit dem Titel "Selected initial and boundary value problems for hyperbolic systems and kinetic equations'' (PDF file) (Preprint Nr. 23/2004, Otto-von-Guericke-Universität Magdeburg).
  • formal languages and mathematical logic
    Formal mathematical systems including a structural induction principle,
    Preprint arXiv:2005.04951
    Further results and examples for formal mathematical systems with structural induction
    Preprint arXiv:2008.07385
    "Manuskript zum Vollständigkeitssatz und zum Satz von Löwenheim/Skolem für formale mathematische Systeme" (PDF file)

   

Publications

2024

Radially symmetric solutions of the ultra-relativistic Euler equations in several space dimensions.
with A. Kolb, S. Müller, F. Thein
https://doi.org/10.1016/j.jcp.2024.113330

On the downward Löwenheim-Skolem Theorem for elementary submodels.
http://dx.doi.org/10.25673/115368
Typos. Section 3, first lines in 6.3 and 6.4 for the definition of a model: Replace in both cases the membership symbol with the word "of".
Update Version is also available on https://arxiv.org/abs/2406.03860

2023

Reduced Set Theory.
Preprint arXiv:2311.18551
https://doi.org/10.48550/arXiv.2311.18551

2021

Radially symmetric solutions of the ultra-relativistic Euler equations.
mit H. Liu, G. Warnecke: Methods and Applications of Analysis Volume 28 (4), 401-422 (2021).
Dedicated to Professor Hsiao Ling on the occasion of her 80th birthday.

2020

New insight into results of Ostrowski and Lang on sums of remainders using Farey sequences.
Online Journal of Analytic Combinatorics, Issue 15, #11 (2020). (PDF file)

Further results and examples for formal mathematical systems with structural induction
Preprint arXiv:2008.07385 (2020).

2018

Lehrbuch: "Elementare Zahlentheorie"
mit Y. Abramchuk, A. Bondarava, Preprint arXiv:1809.09710 (2018).

A scaling property of Farey Fractions. Part IV: mean value formulas.
Eur. J. Math. 4(4), 1549-1559 (2018).

2017

A scaling property of Farey Fractions. Part III: representation formulas.
Eur. J. Math. 3(2), 363-378 (2017).

Revisiting energy dissipation due to elastic waves at impact of spheres on large thick plates.
with R. Böttcher, S. Eichmann, A. Russell, P. Müller ,International journal of impact engineering - Amsterdam [u.a.]: Elsevier Science, Bd. 104, 45-54 (2017).

2016

A scaling property of Farey Fractions. Part II: convergence at rational points.
Eur. J. Math. 2(3), 886-896 (2016).

A scaling property of Farey Fractions.
Eur. J. Math. 2(2), 383-417 (2016).

2014

Lehrbuch "Höhere Analysis durch Anwendungen lernen''
with Piotr Skrzypacz, Springer Sektrum, ISBN 978-3-658-02265-5, (2014).

The ultra-relativistic Euler equations
with Mahmoud A.E. Abdelrahman, Math. Meth. Appl. Sci..doi:10.1002/mma.3141, (2014).

The interaction of waves for the ultra-relativistic Euler equations
with Mahmoud A.E. Abdelrahman, Journal of Mathematical Analysis and Applications 2014|409|2|1140-1158, (2014).

A new front tracking scheme for the ultra-relativistic Euler equations
with Mahmoud A.E. Abdelrahman, Journal of Computational Physics, pages 213-235 (2014).

2012

On energy conditions for electromagnetic diffraction by apertures
with N. Gorenflo, ISRN Mathematical Physics, Vol. 2012 (2012), (PDF-file).

Power series with the von Mangoldt function
with Lutz G. Lucht, Functiones et Approximatio 47.1, pages 15-33, (2012).

A new and self-contained presentation of the theory of boundary operators for slit diffraction and their logarithmic approximations
mit N. Gorenflo, Mathematische Nachrichten, Vol. 285, Issue 1, pages 74-102, (2012).

2010

Explicit solution formulas for the acoustic diffraction problem with a slit in a hard and a soft screen: Continuous Media with Microstructure, dedicated to Prof. Dr. Krzysztof Wilmanski,
Editor: B.Albers, Springer Verlag, doi:10.1007/978-3-642-11445-8, 221-231 (2010).

2009

Logarithmic Fourier integrals for the Riemann zeta function, New Directions in value-distribution theory of Zeta- and L-functions,
Proceedings of the Würzburg Conference, October 2008. Editors: J.Steuding, R.Steuding, Shaker Publishing, 131-147 (2009).

2008

A generalized kinetic model of sedimentation of polydisperse suspensions with a continuous particle size distribution
mit Raimund Bürger and Antonio Garcia: Mathematical Models and Methods in Applied Sciences 18, no. 10, 1741-1785 (2008).

Diffraction of light revisited
mit Piotr Skrzypacz: doi:10.1002/mma.945, Mathematical Methods in the Applied Sciences 31, 793-820 (2008).

The analytical solution of two interesting hyperbolic problems as a test case for a finite volume method with a new grid refinement technique
mit Wolfram Heineken: doi:10.1016/j.cam.2007.03.008, J. Comp. Appl. Math. 214 , no. 2, 509-532 (2008).

2005

A reduction of the Boltzmann-Peierls equation
mit S. Qamar and G. Warnecke: International Journal of Computational Methods 2 , 213-229 (2005).

Kinetic schemes for selected initial and boundary value problems
mit W. Dreyer and M. Herrmann and S. Qamar: Editor G. Warnecke, Springer Verlag Berlin, Heidelberg, New York, 203-232 (2005).

2004

"Selected initial and boundary value problems for hyperbolic systems and kinetic equations", Habilitationsschrift
Otto-von-Guericke-Universität Magdeburg, Preprint 04-23 der Fakultät für Mathematik (2004).

Kinetic schemes for the relativistic gas dynamics
mit S. Qamar and G. Warnecke: Numer. Math. No. 97 159-191 (2004).

BGK-type kinetic flux vector splitting schemes for the ultra-relativistic Euler equations, with S. Qamar and G. Warnecke, J. Sci. Comput., 26, pp. 196-223, (2004).

2003

Second order accurate kinetic schemes for the ultra-relativistic Euler aquations
mit S. Qamar and G. Warnecke: Journal of Computational Physics 192, 695-726 (2003).

Kinetic schemes for the ultra-relativistic Euler equations
mit S. Qamar and G. Warnecke: Journal of Computational Physics 187, 572-596 (2003).

2001

On the approximation of the Fokker-Planck equation by moment systems
mit W. Dreyer and M. Junk: Nonlinearity 14, 881-906 (2001).

A critical look at the kinematic-wave theory for sedimentation-consolidation processes in closed vessels
mit R. Bürger: Mathematical Methods in the Applied Sciences 24, 1257-1273 (2001).

Kinetic solutions of the Boltzmann-Peierls-Equation and its moment systems
mit W. Dreyer and M. Herrmann: Berlin, WIAS Preprint, No. 709 (2001).

2000

On the approximation of kinetic equations by moment systems
mit W.Dreyer and M. Junk: Berlin, WIAS Preprint, No. 592 (2000).

Cold, thermal and oscillator closure of the atomic chain
mit W.Dreyer: Journal of Physics A: Math. Gen. , No. 33, 2097-2129 (2000).

The scaling of time and space in micro-macro transitions: Contributions to Continuum Theories, (collected by B. Albers)
Continuum Mechanics and Thermodynamics, WIAS Report No. 18, 146-154 (2000).

Hyperbolic heat conduction
mit W.Dreyer: Trends in applications of Mathematics to Mechanics, Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics, Vol. 106 (2000).

1999

Initial and boundary value problem of hyperbolic heat conduction
mit W.Dreyer: Continuum Mechanics and Thermodynamics, Vol. 11, No. 4, 227-245 (1999).

1998

Iterative procedure for multidimensional Euler equations
mit W. Dreyer, K. Sabelfeld, N. Simonov, K. Wilmanski: Monte Carlo Methods and Applications, Vol. 4, No. 3, 253-271 (1998).

Reflections of Eulerian shock waves at moving adiabatic boundaries
mit W.Dreyer: Monte Carlo Methods and Applications, Vol. 4, No. 3, 231-252 (1998).

Maximum entropy principle revisited
mit W.Dreyer: Continuum Mechanics and Thermodynamics, Vol. 10, 331-347 (1998).

1993

A solution formula for a non-convex scalar conservation law with monotone initial data
Mathematical Methods in the Applied Sciences, Vol. 16, 895-902 (1993).

1992

A numerical method for some initial value problems of one scalar hyperbolic conservation law
Mathematical Methods in the Applied Sciences, Vol. 15, 495-509 (1992).