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Preprint
On the Gap-Complexity of Simple RL-Automata
(2006)
Analysis by reduction is a method used in linguistics for checking the correctness of sentences of natural languages. This method is modelled by restarting automata. All types of restarting automata considered in the literature up to now accept at least the deterministic context-free languages. Here we introduce and study a new type of restarting automaton, the so-called t-RL-automaton, which is an RL-automaton that is rather restricted in that it has a window of size one only, and that it works under a minimal ...
Preprint
Approximate solutions and error estimates for a Stokes boundary value problem
(2009)
The aim of this paper is the numerical treatment of a boundary value problem for the system of Stokes' equations. For this we 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 system ...
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 present ...
Dissertation
Some New Classes of Orthogonal Polynomials and Special Functions
(2006-11-01)
In dieser Dissertation präsentieren wir zunächst eine Verallgemeinerung der üblichen Sturm-Liouville-Probleme mit symmetrischen Lösungen und erklären eine umfassendere Klasse. Dann führen wir einige neue Klassen orthogonaler Polynome und spezieller Funktionen ein, welche sich aus dieser symmetrischen Verallgemeinerung ableiten lassen. Als eine spezielle Konsequenz dieser Verallgemeinerung führen wir ein Polynomsystem mit vier freien Parametern ein und zeigen, dass in diesem System fast alle klassischen symmetrischen ...
Dissertation
Structural characterization and distribution of zebrafish germ plasm during interphase and mitosis
(2007-06-21)
In zebrafish, germ cells are responsible for transmitting the genetic information from one generation to the next. During the first cleavages of zebrafish embryonic development, a specialized part of the cytoplasm known as germ plasm, is responsible of committing four blastomeres to become the progenitors of all germ cells in the forming embryo.
Much is known about how the germ plasm is spatially distributed in early stages of primordial germ cell development, a process described to be dependant on microtubules and ...
Aufsatz
Tomographic imaging of molecular orbitals in length and velocity form
(American Institute of Physics, 2007-11-29)
Recently Itatani et al. [Nature 432, 876 (2004)] introduced the new concept of molecular orbital tomography, where high harmonic generation (HHG) is used to image electronic wave functions. We describe an alternative reconstruction form, using momentum instead of dipole matrix elements for the electron recombination step in HHG. We show that using this velocity-form reconstruction, one obtains better results than using the original length-form reconstruction. We provide numerical evidence for our claim that one has ...
Preprint
Church-Rosser groups and growing context-sensitive groups
(2006)
A finitely generated group is called a Church-Rosser group (growing context-sensitive group) if it admits a finitely generated presentation for which the word problem is a Church-Rosser (growing context-sensitive) language. Although the Church-Rosser languages are incomparable to the context-free languages under set inclusion, they strictly contain the class of deterministic context-free languages. As each context-free group language is actually deterministic context-free, it follows that all context-free groups are ...
Preprint
Functions satisfying holonomic q-differential equations
(2007-05-21)
In a similar manner as in some previous papers, where explicit algorithms for finding the differential equations satisfied by holonomic functions were given, in this paper we deal with the space of the q-holonomic functions which are the solutions of linear q-differential equations with polynomial coefficients. The sum, product and the composition with power functions of q-holonomic functions are also q-holonomic and the resulting q-differential equations can be computed algorithmically.
Preprint
On the Computation of Fourier Coefficients
(2006-11-16)
In this paper we derive an identity for the Fourier coefficients of a differentiable function f(t) in terms of the Fourier coefficients of its derivative f'(t). This yields an algorithm to compute the Fourier coefficients of f(t) whenever the Fourier coefficients of f'(t) are known, and vice versa. Furthermore this generates an iterative scheme for N times differentiable functions complementing the direct computation of Fourier coefficients via the defining integrals which can be also treated automatically in certain cases.
Dissertation
A semi-phenomenological approach to the structure and transport properties of macromolecules in solution
(2006-08-03)
Motiviert durch die Lebenswissenschaften (Life sciences) haben sich Untersuchungen zur Dynamik von Makromolekülen in Lösungen in den vergangenen Jahren zu einem zukunftsweisenden Forschungsgebiet etabliert, dessen Anwendungen von der Biophysik über die physikalische Chemie bis hin zu den Materialwissenschaften reichen. Neben zahlreichen experimentellen Forschungsprogrammen zur räumlichen Struktur und den Transporteigenschaften grosser MolekÄule, wie sie heute praktisch an allen (Synchrotron-) Strahlungsquellen ...