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In this thesis a new family of codes for the use in optical high bit rate transmission systems with a direct sequence code division multiple access scheme component was developed and its performance examined. These codes were then used as orthogonal sequences for the coding of the different wavelength channels in a hybrid OCDMA/WDMA system. The overall performance was finally compared to a pure WDMA system. The common codes known up to date have the problem of needing very long sequence lengths in order to accommodate an adequate number of users. Thus, code sequence lengths of 1000 or more were necessary to reach bit error ratios of with only about 10 simultaneous users. However, these sequence lengths are unacceptable if signals with data rates higher than 100 MBit/s are to be transmitted, not to speak about the number of simultaneous users. Starting from the well known optical orthogonal codes (OOC) and under the assumption of synchronization among the participating transmitters - justified for high bit rate WDM transmission systems -, a new code family called ?modified optical orthogonal codes? (MOOC) was developed by minimizing the crosscorrelation products of each two sequences. By this, the number of simultaneous users could be increased by several orders of magnitude compared to the known codes so far. The obtained code sequences were then introduced in numerical simulations of a 80 GBit/s DWDM transmission system with 8 channels, each carrying a 10 GBit/s payload. Usual DWDM systems are featured by enormous efforts to minimize the spectral spacing between the various wavelength channels. These small spacings in combination with the high bit rates lead to very strict demands on the system components like laser diode, filters, multiplexers etc. Continuous channel monitoring and temperature regulations of sensitive components are inevitable, but often cannot prevent drop downs of the bit error ratio due to aging effects or outer influences like mechanical stress. The obtained results show that - very different to the pure WDM system - by orthogonally coding adjacent wavelength channels with the proposed MOOC, the overall system performance gets widely independent from system parameters like input powers, channel spacings and link lengths. Nonlinear effects like XPM that insert interchannel crosstalk are effectively fought. Furthermore, one can entirely dispense with the bandpass filters, thus simplifying the receiver structure, which is especially interesting for broadcast networks. A DWDM system upgraded with the OCDMA subsystem shows a very robust behavior against a variety of influences.
This paper deals with the handling of deformable linear objects (DLOs), such as hoses, wires or leaf springs. It investigates the a priori knowledge about the 6-dimensional force/torque signal for a changing contact situation between a DLO and a rigid polyhedral obstacle. The result is a complete list, containing for each contact change the most significant combination of force/torque signal components together with a description of the expected signal curve. This knowledge enables the reliable detection of changes in the DLO contact situation and with it the implementation of sensor-based manipulation skills for all possible contact changes.
This article presents contributions in the field of path planning for industrial robots with 6 degrees of freedom. This work presents the results of our research in the last 4 years at the Institute for Process Control and Robotics at the University of Karlsruhe. The path planning approach we present works in an implicit and discretized C-space. Collisions are detected in the Cartesian workspace by a hierarchical distance computation. The method is based on the A* search algorithm and needs no essential off-line computation. A new optimal discretization method leads to smaller search spaces, thus speeding up the planning. For a further acceleration, the search was parallelized. With a static load distribution good speedups can be achieved. By extending the algorithm to a bidirectional search, the planner is able to automatically select the easier search direction. The new dynamic switching of start and goal leads finally to the multi-goal path planning, which is able to compute a collision-free path between a set of goal poses (e.g., spot welding points) while minimizing the total path length.
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.
Abstract
The main theme of this thesis is about Graph Coloring Applications and Defining Sets in Graph Theory.
As in the case of block designs, finding defining sets seems to be difficult problem, and there is not a general conclusion. Hence we confine us here to some special types of graphs like bipartite graphs, complete graphs, etc.
In this work, four new concepts of defining sets are introduced:
• Defining sets for perfect (maximum) matchings
• Defining sets for independent sets
• Defining sets for edge colorings
• Defining set for maximal (maximum) clique
Furthermore, some algorithms to find and construct the defining sets are introduced. A review on some known kinds of defining sets in graph theory is also incorporated, in chapter 2 the basic definitions and some relevant notations used in this work are introduced.
chapter 3 discusses the maximum and perfect matchings and a new concept for a defining set for perfect matching.
Different kinds of graph colorings and their applications are the subject of chapter 4.
Chapter 5 deals with defining sets in graph coloring. New results are discussed along with already existing research results, an algorithm is introduced, which enables to determine a defining set of a graph coloring.
In chapter 6, cliques are discussed. An algorithm for the determination of cliques using their defining sets. Several examples are included.
We survey old and new results about optimal algorithms for summation of finite sequences and for integration of functions from Hölder or Sobolev spaces. First we discuss optimal deterministic and randornized algorithms. Then we add a new aspect, which has not been covered before on conferences
about (quasi-) Monte Carlo methods: quantum computation. We give a short introduction into this setting and present recent results of the authors on optimal quantum algorithms for summation and integration. We discuss comparisons between the three settings. The most interesting case for Monte
Carlo and quantum integration is that of moderate smoothness \(k\) and large dimension \(d\) which, in fact, occurs in a number of important applied problems. In that case the deterministic exponent is negligible, so the \(n^{-1/2}\) Monte Carlo and the \(n^{-1}\) quantum speedup essentially constitute the entire convergence rate.
The purpose of satellite-to-satellite tracking (SST) and/or satellite gravity gradiometry (SGG) is to determine the gravitational field on and outside the Earth's surface from given gradients of the gravitational potential and/or the gravitational field at satellite altitude. In this paper both satellite techniques are analysed and characterized from mathematical point of view. Uniqueness results are formulated. The justification is given for approximating the external gravitational field by finite linear combination of certain gradient fields (for example, gradient fields of single-poles or multi-poles) consistent to a given set of SGG and/or SST data. A strategy of modelling the gravitational field from satellite data within a multiscale concept is described; illustrations based on the EGM96 model are given.
The anchored hyperplane location problem is to locate a hyperplane passing through some given points P IR^n and minimizing either the sum of weighted distances (median problem), or the maximum weighted distance (center problem) to some other points Q IR^n . If the distances are measured by a norm, it will be shown that in the median case there exists an optimal hyperplane that passes through at least n - k affinely independent points of Q, if k is the maximum number of affinely independent points of P. In the center case, there exists an optimal hyperplane which isatmaximum distance to at least n - k + 1 affinely independent points of Q. Furthermore, if the norm is a smooth norm, all optimal hyperplanes satisfy these criteria. These new results generalize known results about unrestricted hyperplane location problems.