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This thesis investigates the constrained form of the spherical Minimax location problem and the spherical Weber location problem. Specifically, we consider the problem of locating a new facility on the surface of the unit sphere in the presence of convex spherical polygonal restricted regions and forbidden regions such that the maximum weighted distance from the new facility on the surface of the unit sphere to m existing facilities is minimized and the sum of the weighted distance from the new facility on the surface of the unit sphere to m existing facilities is minimized. It is assumed that a forbidden region is an area on the surface of the unit sphere where travel and facility location are not permitted and that distance is measured using the great circle arc distance. We represent a polynomial time algorithm for the spherical Minimax location problem for the special case where all the existing facilities are located on the surface of a hemisphere. Further, we have developed algorithms for spherical Weber location problem using barrier distance on a hemisphere as well as on the unit sphere.
In modern textile manufacturing industries, the function of human eyes to detect disturbances in the production processes which yield defective products is switched to cameras. The camera images are analyzed with various methods to detect these disturbances automatically. There are, however, still problems with in particular semi-regular textures which are typical for weaving patterns. We study three parts of that problem of automatic texture analysis: image smoothing, texture synthesis and defect detection. In image smoothing, we develop a two dimensional kernel smoothing method with locally and directionally adaptive bandwidths allowing correlation in the errors. Two approaches are used in synthesising texture. The first is based on constructing a generalized Ising energy function in the Markov Random Field setup, and for the second, we use two-dimensional periodic bootstrap methods for semi-regular texture synthesis. We treat defect detection as multihypothesis testing problem with the null hypothesis representing the absence of defects and the other hypotheses representing various types of defects. We develop a test based on a nonparametric regression setup, and we use the bootstrap for approximating the distribution of our test statistic.
An autoregressive-ARCH model with possible exogeneous variables is treated. We estimate the conditional volatility of the model by applying feedforward networks to the residuals and prove consistency and asymptotic normality for the estimates under the rate of feedforward networks complexity. Recurrent neural networks estimates of GARCH and value-at-risk is studied. We prove consistency and asymptotic normality for the recurrent neural networks ARMA estimator under the rate of recurrent networks complexity. We also overcome the estimation problem in stochastic variance models in discrete time by feedforward networks and the introduction of a new distributions on the innovations. We use the method to calculate market risk such as expected shortfall and Value-at risk. We tested this distribution together with other new distributions on the GARCH family models against other common distributions on the financial market such as Normal Inverse Gaussian, normal and the Student's t- distributions. As an application of the models, some German stocks are studied and the different approaches are compared together with the most common method of GARCH(1,1) fit.
This thesis deals with the development of thermoplastic polyolefin elastomers using recycled polyolefins and ground tyre rubber (GTR). The disposal of worn tyres and their economic recycling mean a great challenge nowadays. Material recycling is a preferred way in Europa owing to legislative actions and ecological arguments. This first step with worn tyres is already done in this direc-tion as GTR is available in different fractions in guaranteed quality. As the traditional applications of GTR are saturated, there is a great demand for new, value-added products containing GTR. So, the objective of this work was to convert GTR by reac-tive blending with polyolefins into thermoplastic elastomers (TPE) of suitable me-chanical and rheological properties. It has been established that bituminous reclamation of GTR prior to extrusion melt compounding with polyolefins is a promising way of TPE production. By this way the sol-content (acetone soluble fraction) of the GTR increases and the GTR particles can be better incorporated in the corresponding polyolefin matrix. The adhesion be-tween GTR and matrix is given by molecular intermingling in the resulting interphase. GTR particles of various production and mean particle size were involved in this study. As polyolefins recycled low-density polyethylene (LDPE), recycled high-density polyethylene (HDPE) and polypropylene (PP) were selected. First, the opti-mum conditions for the GTR reclamation in bitumen were established (160 °C < T < 180 °C; time ca. 4 hours). Polyolefin based TPEs were produced after GTR reclamation in extrusion compounding. Their mechanical (tensile behaviour, set properties), thermal (dynamic-mechanical thermal analysis, differential scanning calorimetry) and rheological properties (both in low- and high-shear rates ) were determined. The PE-based blends contained an ethylene/propylene/diene (EPDM) rubber as compatibilizer and their composition was as follows: PE/EPDM/GTR:bitumen = 50/25/25:25. The selected TPEs met the most important criterion, i.e. elongation at break > 100 %; compression set < 50%. The LDPE-based TPE (TPE(LDPE)) showed better me-chanical performance compared to the TPE(HDPE). This was assigned to the higher crystallinity of the HDPE. The PP-based blends of the compositions PP/(GTR-bitumen) 50/50 and 25/75, whereby the ratio of GTR/bitumen was 60/40, outperformed those containing non-reclaimed GTR. The related blends showed also a better compatibility with a PP-based commercial thermoplastic dynamic vulcanizate (TDV). Surprisingly, the mean particle size of the GTR, varied between < 0.2 and 0.4-0.7 mm, had a small effect on the mechanical properties, however somewhat larger for the rheological behaviour of the TPEs produced.
In der vorliegenden Arbeit wurden mittels ab initio Methoden die Strukturen und Eigenschaften sowie das Reaktionsverhalten der kationischen Zwischenstufen einer nucleophilen und einer elektrophilen Substitution untersucht. Geometrieoptimierungen wurden unter Verwendung des B3LYP-Dichtefunktionals durchgeführt, Energien und Enthalpien aus Coupled-Cluster (CCSD(T))-Rechnungen gewonnen. Standardmäßig wurde der Basissatz 6-31++G(d,p) benutzt. Im ersten Teil der Arbeit stand die Frage im Mittelpunkt, welchen Einfluss eine Aminosubstitution am Bicyclo[3.1.0]hex-3-ylium-Kation auf dessen Reaktionsverhalten im Vergleich zum Grundkörper hat und ob sich die experimentell beobachteten Produktbilder der nucleophilen Substitution mit der Annahme dieser Zwischenstufe vereinbaren lassen. Die Reaktions- und Aktivierungsenergien der beiden Teilschritte einer nucleophilen S(N)1-Reaktion an chlor-substituierten Amino-Bicyclo[3.1.0]hexanen unter Gegenwart von Methanol und Methanolat-Anionen sowie der Isomerisierungswege des intermediären Amino-Bicyclo[3.1.0]hex-3-ylium-Kations wurden in CCSD(T)-Rechnungen ermittelt. Der Einfluss des Lösungsmittels Methanol auf die Energien wurde unter Verwendung des C-PCM-Modells bestimmt. Es konnte gezeigt werden, dass die Anwesenheit eines NH2- oder Morpholin-Substituenten zwar wenig an den elektronischen Eigenschaften des Bicyclo[3.1.0]hex-3-ylium-Kations ändert, jedoch neue Reaktionswege, insbesondere Möglichkeiten zur Isomerisierung eröffnet. Die Energiebarrieren dieser Prozesse liegen jedoch durchweg über denen eines nucleophilen Angriffs, so dass die Bildung eines thermodynamisch stabilen, methoxy-substituierten Produktes die vorherrschende Reaktion bleibt und keine isomeren Kationen zu erwarten sind. Der Aminorest erzeugt aus sterischen Gründen und durch die von ihm bewirkte Erhöhung des Dipolmomentes im Trishomocyclopropenylium-Kation eine hohe Regioselektivität zugunsten eines nucleophilen Angriffs an Ringposition beta-C(3), was die aus Sicht der Experimentatoren dringendste Frage nach den Ursachen des regio- und stereochemischen Verlauf der Substitution beantwortet. Im zweiten Teil der vorliegenden Dissertation wurden die Strukturen der sigma- und pi-Komplexe der protonierten Aromaten Benzol, Toluol und Mesitylen bestimmt sowie die Energieprofile der in diesen Verbindungen ablaufenden 1,2-Hydridverschiebungen berechnet. Darüber hinaus wurden für Benzol und Mesitylen die Strukturen von Arenium-Aren-Komplexen und Arenium-Tetrachloroaluminat-Verbindungen ermittelt und die Energetik von Protonentransfers innerhalb dieser Spezies untersucht. Als Ergebnis liegt eine umfassende Datenbasis zur Energetik von intra- und intermolekularen Wasserstoffverschiebungen vor. Die von allen aufgeführten Spezies unter Verwendung der SQM-Methode simulierten Schwingungsspektren erlauben es, bestimmte Verbindungen und Zwischenstufen in Zukunft zuverlässiger und schneller zu identifizieren. Es zeigten sich durchweg sehr gute Übereinstimmungen mit Daten aus IR-, NMR-, MS- und Röntgenstruktur-Experimenten. Einige offene Fragen, wie etwa Auffälligkeiten in den Kristallstrukturen, konnten beantwortet werden. Viele bisher nur qualitativ bekannte Fakten können anhand der erarbeiteten Daten in einem neuen Licht betrachtet werden. Die vorliegenden quantenchemischen Daten bestätigen in den untersuchten Fällen die Beobachtungen der Experimentatoren und liefern darüber hinaus eine fundierte Basis für detaillierte Modellvorstellungen über den Mechanismus von Substitutionsreaktionen, die über substituierte Trishomocyclopropenylium-Kationen oder protonierte Alkylbenzole verlaufen.
Metallocenes containing diarylethene type photochromic switches are synthesized, characterized and tested in polyolefin catalysts. Propylene polymerizations using unbridged bis(2,3-dibenzo[b]thiophen-3-yl)cyclopenta[b]thien-3-yl)zirconium dichloride/MAO (80) treated with 254nm UV irradiation produced bimodal polymer distributions by GPC. This was due to an increase in the low molecular weight fractions when the closed form of the catalyst/photoswitch was made. Comparison with similarly structured catalyst without photoisomerization properties did not produce bimodal polymer under identical conditions. Propylene polymerizations made with dimethylsilyl[(1,5-dimethyl-3-phenylcyclopenta[b]thien-6-yl)][(2,3-dibenzothien-3-yl)cyclopenta[b]thien-6-yl)]zirconium dichloride/MAO (86) with 254nm UV irradiation caused a 3 fold increase in the polymer molecular weight. Polymers made with ethylene and ethylene/hexene using (80) after UV irradiation did not show differences in measured polymer properties. Polymerizations with ethylene/ hexene mixtures using (86) had increased activity and co-monomer (hexene) incorporation with UV irradiation.
Im Rahmen der Arbeit wurden neue monosubstituierte, optisch aktive Cyclopentadienylliganden mit [2.2.1]-bicyclischen Substituenten synthetisiert. Als Startmaterialien dienten Verbindungen aus dem chiral pool wie beispielsweise Campher, Borneol oder auch Fenchon. Mit den neuen Liganden wurden optisch aktive Komplexe des Zirkoniums und des Titans hergestellt. Ein erstes Katalyseexperiment (katalytische Hydrierung) wurde durchgeführt.
It is considered an analytical model of defaultable bond portfolio in terms of its face value process. The face value process dynamically evolves with time and incorporates changes caused by recovery payment on default followed by purchasing of new bonds. The further studies involve properties, distribution and control of the face value process.
The aim of the thesis is the numerical investigation of saturated, stationary, incompressible Newtonian flow in porous media when inertia is not negligible. We focus our attention to the Navier-Stokes system with two pressures derived by two-scale homogenization. The thesis is subdivided into five Chapters. After the introductory remarks on porous media, filtration laws and upscaling methods, the first chapter is closed by stating the basic terminology and mathematical fundamentals. In Chapter 2, we start by formulating the Navier-Stokes equations on a periodic porous medium. By two-scale expansions of the velocity and pressure, we formally derive the Navier-Stokes system with two pressures. For the sake of completeness, known existence and uniqueness results are repeated and a convergence proof is given. Finally, we consider Stokes and Navier-Stokes systems with two pressures with respect to their relation to Darcy's law. Chapter 3 and Chapter 4 are devoted to the numerical solution of the nonlinear two pressure system. Therefore, we follow two approaches. The first approach which is developed in Chapter 3 is based on a splitting of the Navier-Stokes system with two pressures into micro and macro problems. The splitting is achieved by Taylor expanding the permeability function or by discretely computing the permeability function. The problems to be solved are a series of Stokes and Navier-Stokes problems on the periodicity cell. The Stokes problems are solved by an Uzawa conjugate gradient method. The Navier-Stokes equations are linearized by a least-squares conjugate gradient method, which leads to the solution of a sequence of Stokes problems. The macro problem consists of solving a nonlinear uniformly elliptic equation of second order. The least-squares linearization is applied to the macro problem leading to a sequence of Poisson problems. All equations will be discretized by finite elements. Numerical results are presented at the end of Chapter 3. The second approach presented in Chapter 4 relies on the variational formulation in a certain Hilbert space setting of the Navier-Stokes system with two pressures. The nonlinear problem is again linearized by the least-squares conjugate gradient method. We obtain a sequence of Stokes systems with two pressures. For the latter systems, we propose a fast solution method which relies on pre-computing Stokes systems on the periodicity cell for finite element basis functions acting as right hand sides. Finally, numerical results are discussed. In Chapter 5 we are concerned with modeling and simulation of the pressing section of a paper machine. We state a two-dimensional model of a press nip which takes into account elasticity and flow phenomena. Nonlinear filtration laws are incorporated into the flow model. We present a numerical solution algorithm and the chapter is closed by a numerical investigation of the model with special focus on inertia effects.
The present thesis deals with a novel approach to increase the resource usage in digital communications. In digital communication systems, each information bearing data symbol is associated to a waveform which is transmitted over a physical medium. The time or frequency separations among the waveforms associated to the information data have always been chosen to avoid or limit the interference among them. By doing so, n the presence of a distortionless ideal channel, a single receive waveform is affected as little as possible by the presence of the other waveforms. The conditions necessary to meet the absence of any interference among the waveforms are well known and consist of a relationship between the minimum time separation among the waveforms and their bandwidth occupation or, equivalently, the minimum frequency separation and their time occupation. These conditions are referred to as Nyquist assumptions. The key idea of this work is to relax the Nyquist assumptions and to transmit with a time and/or frequency separation between the waveforms smaller than the minimum required to avoid interference. The reduction of the time and/or frequency separation generates not only an increment of the resource usage, but also a degradation in the quality of the received data. Therefore, to maintain a certain quality in the received signal, we have to increase the amount of transmitted power. We investigate the trade-off between the increment of the resource usage and the correspondent performance degradation in three different cases. The first case is the single carrier case in which all waveforms have the same spectrum, but have different temporal locations. The second one is the multi carrier case in which each waveform has its distinct spectrum and occupies all the available time. Finally, the hybrid case when each waveform has its unique time and frequency location. These different cases are framed within the general system modelling developed in the thesis so that they can be easily compared. We evaluate the potential of the key idea of the thesis by choosing a set of four possible waveforms with different characteristics. By doing so, we study the influence of the waveform characteristics in the three system configurations. We propose an interpretation of the results by modifying the well-known Shannon capacity formula and by explicitly expressing its dependency on the increment of resource usage and on the performance degradation. The results are very promising. We show that both in the case of a single carrier system with a time limited waveform and in the case of a multi-carrier system with a frequency limited waveform, the reduction of the time or frequency separation, respectively, has a positive effect on the channel capacity. The latter, depending on the actual SNR, can double or increase even more significantly.