Das Handlungsreisendenproblem ist eines der bekanntesten NP-vollständigen kombinatorischen Optimierungsprobleme. Algorithmen mit unterschiedlichen Konzepten und Strategien wurden entwickelt, die sich in Lösungsqualität und Laufzeit unterscheiden. Ein vergleichsweise neuer Ansatz stellt jedoch das Kombinieren vorhandener Lösungen dar. Hier werden die Kantenmengen gegebener Handlungsreisendertouren als Ausgangsbasis für weitere Optimierungen verwendet. Erste Veröffentlichungen zu diesem Gebiet stellen bereits vielversprechende Ergebnisse vor, die nachfolgend vertieft evaluiert werden.
Channel estimation is of great importance in many wireless communication systems, since it influences the overall performance of a system significantly. Especially in multi-user and/or multi-antenna systems, i.e. generally in multi-branch systems, the requirements on channel estimation are very high, since the training signals or so called pilots that are used for channel estimation suffer from multiple access interference. Recently, in the context with such systems more and more attention is paid to concepts for joint channel estimation (JCE) which have the capability to eliminate the multiple access interference and also the interference between the channel coefficients. The performance of JCE can be evaluated in noise limited systems by the SNR degradation and in interference limited systems by the variation coefficient. Theoretical analysis carried out in this thesis verifies that both performance criteria are closely related to the patterns of the pilots used for JCE, no matter the signals are represented in the time domain or in the frequency domain. Optimum pilots like disjoint pilots, Walsh code based pilots or CAZAC code based pilots, whose constructions are described in this thesis, do not show any SNR degradation when being applied to multi-branch systems. It is shown that optimum pilots constructed in the time domain become optimum pilots in the frequency domain after a discrete Fourier transformation. Correspondingly, optimum pilots in the frequency domain become optimum pilots in the time domain after an inverse discrete Fourier transformation. However, even for optimum pilots different variation coefficients are obtained in interference limited systems. Furthermore, especially for OFDM-based transmission schemes the peak-to-average power ratio (PAPR) of the transmit signal is an important decision criteria for choosing the most suitable pilots. CAZAC code based pilots are the only pilots among the regarded pilot constructions that result in a PAPR of 0 dB for the transmit signal that origins in the transmitted pilots. When summarizing the analysis regarding the SNR degradation, the variation coefficient and the PAPR with respect to one single service area and considering the impact due to interference from other adjacent service areas that occur due to a certain choice of the pilots, one can conclude that CAZAC codes are the most suitable pilots for the application in JCE of multi-carrier multi-branch systems, especially in the case if CAZAC codes that origin in different mother codes are assigned to different adjacent service areas. The theoretical results of the thesis are verified by simulation results. The choice of the parameters for the frequency domain or time domain JCE is oriented towards the evaluated implementation complexity. According to the chosen parameterization of the regarded OFDM-based and FMT-based systems it is shown that a frequency domain JCE is the best choice for OFDM and a time domain JCE is the best choice for FMT applying CAZAC codes as pilots. The results of this thesis can be used as a basis for further theoretical research and also for future JCE implementation in wireless systems.
This Essay considers the motives and the formation of European New Towns, in particular German ones. For this reason it studies basically the development of German New towns, further defines the German classification of this urban term. This essay suggests additionally for this sense a kind of classification in Germany – considering to periodical as well as formal progress of German New towns. All suggested classes are specifically and individually recognized and introduced, for each one is also given specific examples. Each case is furthermore introduced and it’s motive of formation and development are considered as well, e.g. cities like Ludwigshafen, Hellerau, Wolfsburg, Wulfen. Regarding to the development of German New Towns and up to the given facts in the essay, the current and the expected situation of German New towns are finally considered, also the sense of German experiences for Iranian New towns, and it’s possible significance for them.
This thesis contains the mathematical treatment of a special class of analog microelectronic circuits called translinear circuits. The goal is to provide foundations of a new coherent synthesis approach for this class of circuits. The mathematical methods of the suggested synthesis approach come from graph theory, combinatorics, and from algebraic geometry, in particular symbolic methods from computer algebra. Translinear circuits form a very special class of analog circuits, because they rely on nonlinear device models, but still allow a very structured approach to network analysis and synthesis. Thus, translinear circuits play the role of a bridge between the "unknown space" of nonlinear circuit theory and the very well exploited domain of linear circuit theory. The nonlinear equations describing the behavior of translinear circuits possess a strong algebraic structure that is nonetheless flexible enough for a wide range of nonlinear functionality. Furthermore, translinear circuits offer several technical advantages like high functional density, low supply voltage and insensitivity to temperature. This unique profile is the reason that several authors consider translinear networks as the key to systematic synthesis methods for nonlinear circuits. The thesis proposes the usage of a computer-generated catalog of translinear network topologies as a synthesis tool. The idea to compile such a catalog has grown from the observation that on the one hand, the topology of a translinear network must satisfy strong constraints which severely limit the number of "admissible" topologies, in particular for networks with few transistors, and on the other hand, the topology of a translinear network already fixes its essential behavior, at least for static networks, because the so-called translinear principle requires the continuous parameters of all transistors to be the same. Even though the admissible topologies are heavily restricted, it is a highly nontrivial task to compile such a catalog. Combinatorial techniques have been adapted to undertake this task. In a catalog of translinear network topologies, prototype network equations can be stored along with each topology. When a circuit with a specified behavior is to be designed, one can search the catalog for a network whose equations can be matched with the desired behavior. In this context, two algebraic problems arise: To set up a meaningful equation for a network in the catalog, an elimination of variables must be performed, and to test whether a prototype equation from the catalog and a specified equation of desired behavior can be "matched", a complex system of polynomial equations must be solved, where the solutions are restricted to a finite set of integers. Sophisticated algorithms from computer algebra are applied in both cases to perform the symbolic computations. All mentioned algorithms have been implemented using C++, Singular, and Mathematica, and are successfully applied to actual design problems of humidity sensor circuitry at Analog Microelectronics GmbH, Mainz. As result of the research conducted, an exhaustive catalog of all static formal translinear networks with at most eight transistors is available. The application for the humidity sensor system proves the applicability of the developed synthesis approach. The details and implementations of the algorithms are worked out only for static networks, but can easily be adopted for dynamic networks as well. While the implementation of the combinatorial algorithms is stand-alone software written "from scratch" in C++, the implementation of the algebraic algorithms, namely the symbolic treatment of the network equations and the match finding, heavily rely on the sophisticated Gröbner basis engine of Singular and thus on more than a decade of experience contained in a special-purpose computer algebra system. It should be pointed out that the thesis contains the new observation that the translinear loop equations of a translinear network are precisely represented by the toric ideal of the network's translinear digraph. Altogether, this thesis confirms and strengthenes the key role of translinear circuits as systematically designable nonlinear circuits.
This document introduces the extension of Katja to support position structures and explains the subtleties of their application as well as the design decisions made and problems solved with respect to their implementation. The Katja system was first introduced by Jan Schäfer in the context of his project work and is based on the MAX system developed by Arnd Poetzsch-Heffter.