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We consider a highly-qualified individual with respect to her choice between two distinct career paths. She can choose between a mid-level management position in a large company and an executive position within a smaller listed company with the possibility to directly affect the company’s share price. She invests in the financial market includ- ing the share of the smaller listed company. The utility maximizing strategy from consumption, investment, and work effort is derived in closed form for logarithmic utility. The power utility case is discussed as well. Conditions for the individual to pursue her career with the smaller listed company are obtained. The participation constraint is formulated in terms of the salary differential between the two posi- tions. The smaller listed company can offer less salary. The salary shortfall is offset by the possibility to benefit from her work effort by acquiring own-company shares. This gives insight into aspects of optimal contract design. Our framework is applicable to the pharma- ceutical and financial industry, and the IT sector.

We introduce a class of models for time series of counts which include INGARCH-type models as well as log linear models for conditionally Poisson distributed data. For those processes, we formulate simple conditions for stationarity and weak dependence with a geometric rate. The coupling argument used in the proof serves as a role model for a similar treatment of integer-valued time series models based on other types of thinning operations.

We present a two-scale finite element method for solving Brinkman’s and Darcy’s equations. These systems of equations model fluid flows in highly porous and porous media, respectively. The method uses a recently proposed discontinuous Galerkin FEM for Stokes’ equations byWang and Ye and the concept of subgrid approximation developed by Arbogast for Darcy’s equations. In order to reduce the “resonance error” and to ensure convergence to the global fine solution the algorithm is put in the framework of alternating Schwarz iterations using subdomains around the coarse-grid boundaries. The discussed algorithms are implemented using the Deal.II finite element library and are tested on a number of model problems.

Universal Shortest Paths
(2010)

We introduce the universal shortest path problem (Univ-SPP) which generalizes both - classical and new - shortest path problems. Starting with the definition of the even more general universal combinatorial optimization problem (Univ-COP), we show that a variety of objective functions for general combinatorial problems can be modeled if all feasible solutions have the same cardinality. Since this assumption is, in general, not satisfied when considering shortest paths, we give two alternative definitions for Univ-SPP, one based on a sequence of cardinality contrained subproblems, the other using an auxiliary construction to establish uniform length for all paths between source and sink. Both alternatives are shown to be (strongly) NP-hard and they can be formulated as quadratic integer or mixed integer linear programs. On graphs with specific assumptions on edge costs and path lengths, the second version of Univ-SPP can be solved as classical sum shortest path problem.

Tropical intersection theory
(2010)

This thesis consists of five chapters: Chapter 1 contains the basics of the theory and is essential for the rest of the thesis. Chapters 2-5 are to a large extent independent of each other and can be read separately. - Chapter 1: Foundations of tropical intersection theory In this first chapter we set up the foundations of a tropical intersection theory covering many concepts and tools of its counterpart in algebraic geometry such as affine tropical cycles, Cartier divisors, morphisms of tropical cycles, pull-backs of Cartier divisors, push-forwards of cycles and an intersection product of Cartier divisors and cycles. Afterwards, we generalize these concepts to abstract tropical cycles and introduce a concept of rational equivalence. Finally, we set up an intersection product of cycles and prove that every cycle is rationally equivalent to some affine cycle in the special case that our ambient cycle is R^n. We use this result to show that rational and numerical equivalence agree in this case and prove a tropical Bézout's theorem. - Chapter 2: Tropical cycles with real slopes and numerical equivalence In this chapter we generalize our definitions of tropical cycles to polyhedral complexes with non-rational slopes. We use this new definition to show that if our ambient cycle is a fan then every subcycle is numerically equivalent to some affine cycle. Finally, we restrict ourselves to cycles in R^n that are "generic" in some sense and study the concept of numerical equivalence in more detail. - Chapter 3: Tropical intersection products on smooth varieties We define an intersection product of tropical cycles on tropical linear spaces L^n_k and on other, related fans. Then, we use this result to obtain an intersection product of cycles on any "smooth" tropical variety. Finally, we use the intersection product to introduce a concept of pull-backs of cycles along morphisms of smooth tropical varieties and prove that this pull-back has all expected properties. - Chapter 4: Weil and Cartier divisors under tropical modifications First, we introduce "modifications" and "contractions" and study their basic properties. After that, we prove that under some further assumptions a one-to-one correspondence of Weil and Cartier divisors is preserved by modifications. In particular we can prove that on any smooth tropical variety we have a one-to-one correspondence of Weil and Cartier divisors. - Chapter 5: Chern classes of tropical vector bundles We give definitions of tropical vector bundles and rational sections of tropical vector bundles. We use these rational sections to define the Chern classes of such a tropical vector bundle. Moreover, we prove that these Chern classes have all expected properties. Finally, we classify all tropical vector bundles on an elliptic curve up to isomorphisms.

The Train Marshalling Problem consists of rearranging an incoming train in a marshalling yard in such a way that cars with the same destinations appear consecutively in the final train and the number of needed sorting tracks is minimized. Besides an initial roll-in operation, just one pull-out operation is allowed. This problem was introduced by Dahlhaus et al. who also showed that the problem is NP-complete. In this paper, we provide a new lower bound on the optimal objective value by partitioning an appropriate interval graph. Furthermore, we consider the corresponding online problem, for which we provide upper and lower bounds on the competitiveness and a corresponding optimal deterministic online algorithm. We provide an experimental evaluation of our lower bound and algorithm which shows the practical tightness of the results.

The purpose of Exploration in Oil Industry is to "discover" an oil-containing geological formation from exploration data. In the context of this PhD project this oil-containing geological formation plays the role of a geometrical object, which may have any shape. The exploration data may be viewed as a "cloud of points", that is a finite set of points, related to the geological formation surveyed in the exploration experiment. Extensions of topological methodologies, such as homology, to point clouds are helpful in studying them qualitatively and capable of resolving the underlying structure of a data set. Estimation of topological invariants of the data space is a good basis for asserting the global features of the simplicial model of the data. For instance the basic statistical idea, clustering, are correspond to dimension of the zero homology group of the data. A statistics of Betti numbers can provide us with another connectivity information. In this work represented a method for topological feature analysis of exploration data on the base of so called persistent homology. Loosely, this is the homology of a growing space that captures the lifetimes of topological attributes in a multiset of intervals called a barcode. Constructions from algebraic topology empowers to transform the data, to distillate it into some persistent features, and to understand then how it is organized on a large scale or at least to obtain a low-dimensional information which can point to areas of interest. The algorithm for computing of the persistent Betti numbers via barcode is realized in the computer algebra system "Singular" in the scope of the work.

We will present a rigorous derivation of the equations and interface conditions for ion, charge and heat transport in Li-ion insertion batteries. The derivation is based exclusively on universally accepted principles of nonequilibrium thermodynamics and the assumption of a one step intercalation reaction at the interface of electrolyte and active particles. Without loss of generality the transport in the active particle is assumed to be isotropic. The electrolyte is described as a fully dissociated salt in a neutral solvent. The presented theory is valid for transport on a spatial scale for which local charge neutrality holds i.e. beyond the scale of the diffuse double layer. Charge neutrality is explicitely used to determine the correct set of thermodynamically independent variables. The theory guarantees strictly positive entropy production. The various contributions to the Peltier coeficients for the interface between the active particles and the electrolyte as well as the contributions to the heat of mixing are obtained as a result of the theory.

The main focus of this dissertation is the synthesis and characterization of more recent zeolites with different pore architectures. The unique shape-selective properties of the zeolites are important in various chemical processes and the new zeolites containing novel internal pore architectures are of high interest, since they could lead to further improvement of existing processes or open the way to new applications. This dissertation is organized in the following way: The first part is focused on the synthesis of selected recent zeolites with different pore architectures and their modification to the acidic and bifunctional forms. The second part comprises the characterization of the physicochemical properties of the prepared zeolites by selected physicochemical methods, viz. powder X-ray diffractometry (XRD), N2 adsorption, thermogravimetric analysis (TGA/DTA/MS), ultraviolet-visible (UV-Vis) spectroscopy, atomic absorption spectroscopy (AAS), infrared (IR) spectroscopy, scanning electron microscopy (SEM), 27Al and 29Si magic angle spinning nuclear magnetic resonance (MAS NMR) spectroscopy, temperature-programmed reduction (TPR), temperature-programmed desorption of pyridine (pyridine TPD) and adsorption experiments with hydrocarbon adsorptives. The third part of this work is devoted to the application of test reactions, i.e., the acid catalyzed disproportionation of ethylbenzene and the bifunctional hydroconversion of n-decane, to characterize the pore size and architecture of the prepared zeolites. They are known to be valuable tools for exploring the pore structure of zeolites. Finally, an additional test, viz. the competitive hydrogenation of 1-hexene and 2,4,4-trimethyl-1-pentene, has been applied to probe the location of noble metals in medium pore zeolite. The synthesis of the following zeolite molecular sieves was successfully performed in the frame of this thesis (they are ranked according to the largest window size in the respective structure): • 14-MR pores: UTD-1, CIT-5, SSZ-53 and IM-12 • 12-MR pores: ITQ-21 and MCM-68 • 10-MR pores: SSZ-35 and MCM-71 All of them were obtained as pure phase (except zeolite MCM-71 with a minor impurity phase that is hardly to avoid and also present in samples shown in the patent literature). The synthesis conditions are very critical with respect to the formation of the zeolite with a given structure. In this work, the recommended synthesis recipes are included. Among the 14-MR zeolites, the aluminosilicates UTD-1 (nSi/nAl = 28), CIT-5 (nSi/nAl = 116) and SSZ-53 (nSi/nAl = 55) with unidimensional extra-large pore opening formed from 14-MR rings exhibit promising catalytic properties with high thermal stability and they possess strong Brønsted-acid sites. By contrast, the germanosilicate IM-12 with a structure containing 14-MR channels intersecting with 12-MR channels is unstable toward moisture. It was found that UTD-1 and SSZ-53 zeolites are highly active catalysts for the acid catalyzed disproportionation of ethylbenzene and n-decane hydroconversion due to their high Brønsted acidity. To explore their pore structures, the applied two test reactions suggest that UTD-1, CIT-5 and SSZ-53 zeolites contain a very open pore system (12-MR or larger pore systems) because the product distributions are not hampered by too small pores. ITQ-21, a germanoaluminosilicate zeolite with a three-dimensional pore system and large spherical cages accessible through six 12-MR windows, can be synthesized with nSi/nAl ratios between 27 and >200. It possesses a large amount of Brønsted-acid sites. The aluminosilicate zeolite MCM-68 (nSi/nAl = 9) is an extremely active catalyst in the disproportionation of ethylbenzene and in the n-decane hydroconversion. This is due to the presence of a high density of strong Brønsted-acid sites in its structure. The disproportionation of ethylbenzene suggests that MCM-68 is a large pore (i.e., at least 12-MR) zeolite, in agreement with its crystallographic structure. In the hydroconversion of n-decane, the presence of tribranched and ethylbranched isomers and a high isopentane yield of 58 % in the hydrocracked products suggest the presence of large (12-MR) pores in its structure. By contrast, a relatively high value for CI* (modified constraint index) of 2.9 suggests the presence of medium (10-MR) pores in its structure. As a whole, the results are in-line with the crystallographic structure of MCM-68. SSZ-35, a 10-MR zeolite, can be synthesized in a broad range of nSi/nAl ratios between 11 and >500. This zeolite is interesting in terms of shape selectivity resulting from its unusual pore system having unidimensional channels alternating between 10-MR windows and large 18-MR cages. This thermally very stable zeolite contains both, strong Brønsted- and strong Lewis-acid sites. The disproportionation of ethylbenzene classifies SSZ-35 as a large pore zeolite. In the hydroconversion of n-decane, the suppression of bulky ethyloctanes and propylheptane clearly suggests the presence of 10-MR sections in the pore system. By contrast, the low CI* values of 1.2-2.3 and the high isopentane yields of 56-60 % in the hydrocracked products suggest that SSZ-35 also possesses larger intracystalline voids, i.e., the 18-MR cages. The results from the catalytic characterization are in good agreement with the crystallographic structure of zeolite SSZ-35. It was also found that the nSi/nAl ratio influences the crystallite size and therefore the external surface area. As a consequence, product selectivities are also influenced: The lowest nSi/nAl ratio or the smallest crystallite size sample produces larger amounts of the relatively bulky products. The formation of these products probably results from the higher conversion or they are preferentially formed on the external surface area of the catalyst. Zeolite MCM-71 (nSi/nAl = 8) possesses an extremely thermally stable structure and contains a high concentration of Brønsted-acid sites. Its structure allows for the separation of n-alkanes from branched alkanes by selective adsorption. MCM-71 exhibits unique shape-selective properties towards the product distribution in ethylbenzene disproportionation, which is different to those obtained in the medium pore SSZ-35 zeolite. All reaction parameters are fulfilled to classify MCM-71 as medium pore zeolite and this is in good agreement with its reported structure consisting of two-dimensional network of elliptical 10-MR channels and an orthogonal sinusoidal 8-MR channels. The competitive hydrogenation of 1-hexene and 2,4,4-trimethyl-1-pentene was exploited to probe that the major part of the noble metal is located inside the intracrystalline void volume of the medium pore zeolite SSZ-35.

We tackle the problem of obtaining statistics on content and structure of XML documents by using summaries which may provide cardinality estimations for XML query expressions. Our focus is a data-centric processing scenario in which we use a query engine to process such query expressions. We provide three new summary structures called LESS (Leaf-Element-in-Subtree), LWES (Level-Wide Element Summarization), and EXsum (Element-centered XML Summarization) which are targeted to base an estimation process in an XML query optimizer. Each of these collects structural statistical information of XML documents, and the latter (EXsum) gathers, in addition, statistics on document content. Estimation procedures and/or heuristics for specic types of query expressions of each proposed approach are developed. We have incorporated and implemented our proposals in XTC, a native XML database management system (XDBMS). With this common implementation base, we present an empirical and comparative study in which our proposals are stressed against others published in the literature, which are also incorporated into the XTC. Furthermore, an analysis is made based on criteria pertinent to a query optimizer process.