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In an undirected graph G we associate costs and weights to each edge. The weight-constrained minimum spanning tree problem is to find a spanning tree of total edge weight at most a given value W and minimum total costs under this restriction. In this thesis a literature overview on this NP-hard problem, theoretical properties concerning the convex hull and the Lagrangian relaxation are given. We present also some in- and exclusion-test for this problem. We apply a ranking algorithm and the method of approximation through decomposition to our problem and design also a new branch and bound scheme. The numerical results show that this new solution approach performs better than the existing algorithms.
* naive examples which show drawbacks of discrete wavelet transform and windowed Fourier transform; * adaptive partition (with a 'best basis' approach) of speech-like signals by means of local trigonometric bases with orthonormal windows. * extraction of formant-like features from the cosine transform; * further proceedingings for classification of vowels or voiced speech are suggested at the end.
The understanding of the many fields of control theory can be supported using demonstrators, as
influencing a system to achieve a desired behaviour is the main purpose of control theory. This
thesis covers the setup, implementation and controlling of an inverse multi-pendulum on a cart.
Construction design and brief dimensioning will be described. In addition, a drive to move the
cart and influence the system will be chosen, which will be controlled using industrial automation
technology components. The state feedback controller introduced requires state measurement that
is made available by a radio sensor designed in this thesis. A web user interface is designed and
in addition the data processing structure involving the industrial automation technology and the
custom radio sensor is implemented. The pendulum is then controlled and stabilized by an optimal
controller. Furthermore, an upswing control approach is pointed out using numerical optimal
control.
Hamiltonian daemons allow the transfer of energy from systems with very fast degrees
of freedom to systems with slower ones across several orders of magnitude. They act on
small scales and can be regarded as micro-engines.
Such daemons were previously described in the classical as well as the quantum me-
chanical regime. In this thesis the semi-classical regime is examined, where quantum
phenomena occur as corrections to classical systems. Here, the focus is on numerical
simulations.
First some introductory models are examined. They are concerned with quantum
tunneling, since it occurs as an important quantum correction, as well as with the
capture and decay of bound states, since this represents the transition between the
dynamical phases of a daemon: adiabatic decoupling and downconversion.
The examinations are carried out using wave functions, as solutions to the Schrödinger
equation, and by means of Wigner functions in a quantum mechanical phase-space in
the framework of the Weyl-Wigner-Groenewold-Moyal formalism. For one these Wigner
functions are computed from the wave functions, but they are also obtained from a
numerical method based on the Moyal equation, which will be introduced here.
After developing this methodology, it is employed in the study of a daemon system
with a tilted washboard potential. The daemon behavior is studied with regards to
quantum corrections, especially in phase-space and concerning Kruskal’s theorem, which
describes the capture of phase-space flow via a time-dependent separatrix.
Lastly the semi-classically quantized phase-space will be discussed as a basis for a
combined description of both classical and quantum daemons. The behavior of the
energy spectrum in the deep quantum regime is explained by dynamical tunneling pro-
cesses.
Satellite-to-satellite tracking (SST) and satellite gravity gradiometry (SGG), respectively, are two measurement principles in modern satellite geodesy which yield knowledge of the first and second order radial derivative of the earth's gravitational potential at satellite altitude, respectively. A numerical method to compute the gravitational potential on the earth's surface from those observations should be capable of processing huge amounts of observational data. Moreover, it should yield a reconstruction of the gravitational potential at different levels of detail, and it should be possible to reconstruct the gravitational potential from only locally given data. SST and SGG are modeled as ill-posed linear pseudodifferential operator equations with an injective but non-surjective compact operator, which operates between Sobolev spaces of harmonic functions and such ones consisting of their first and second order radial derivatives, respectively. An immediate discretization of the operator equation is obtained by replacing the signal on its right-hand-side either by an interpolating or a smoothing spline which approximates the observational data. Here the noise level and the spatial distribution of the data determine whether spline-interpolation or spline-smoothing is appropriate. The large full linear equation system with positive definite matrix which occurs in the spline-interplation and spline-smoothing problem, respectively, is efficiently solved with the help of the Schwarz alternating algorithm, a domain decomposition method which allows it to split the large linear equation system into several smaller ones which are then solved alernatingly in an iterative procedure. Strongly space-localizing regularization scaling functions and wavelets are used to obtain a multiscale reconstruction of the gravitational potential on the earth's surface. In a numerical experiment the advocated method is successfully applied to reconstruct the earth's gravitational potential from simulated 'exact' and 'error-affected' SGG data on a spherical orbit, using Tikhonov regularization. The applicability of the numerical method is, however, not restricted to data given on a closed orbit but it can also cope with realistic satellite data.
A hub location problem consists of locating p hubs in a network in order to collect and consolidate flow between node pairs. This thesis deals with the uncapacitated single allocation p-hub center problem (USApHCP) as a special type of hub location problem with min max objective function. Using the so-called radius formulation of the problem, the dimension of the polyhedron of USApHCP is derived. The formulation constraints are investigated to find out which of these define facets. Then, three new classes of facet-defining inequalities are derived. Finally, efficient procedures to separate facets in a branch-and-cut algorithm are proposed. The polyhedral analysis of USApHCP is based on a tight relation to the uncapacitated facility location problem (UFL). Hence, many results stated in this thesis also hold for UFL.
The flow of a liquid into an empty channel is simulated. The simulation is based on a recently published model for general fluid/liquid/solid systems which eliminates the shear stress singularity at the moving contact line between the liquid/fluid interface and the solid. This model is carefully analyzed for low Reynolds and Capillary numbers, adapted to the channel inflow problem, and implemented. Very convincing numerical results are presented.