Numerical splitting methods for nonsmooth convex optimization problems

In this thesis, we develop and investigate numerical methods for solving nonsmooth convex optimization problems in real Hilbert spaces. We construct algorithms, such that they handle the terms in the objective function and constraints of the minimization problems separately, which makes these methods simpler to compute. In the first part of the thesis, we extend the well known AMA method from Tseng to the Proximal AMA algorithm by introducing variable metrics in the subproblems of the primal-dual algorithm. For a special choice of metrics, the subproblems become proximal steps. Thus, for objectives in a lot of important applications, such as signal and image processing, machine learning or statistics, the iteration process consists of expressions in closed form that are easy to calculate. In the further course of the thesis, we intensify the investigation on this algorithm by considering and studying a dynamical system. Through explicit time discretization of this system, we obtain Proximal AMA. We show the existence and uniqueness of strong global solutions of the dynamical system and prove that its trajectories converge to the primal-dual solution of the considered optimization problem. In the last part of this thesis, we minimize a sum of finitely many nonsmooth convex functions (each can be composed by a linear operator) over a nonempty, closed and convex set by smoothing these functions. We consider a stochastic algorithm in which we take gradient steps of the smoothed functions (which are proximal steps if we smooth by Moreau envelope), and use a mirror map to 'mirror'' the iterates onto the feasible set. In applications, we compare them to similar methods and discuss the advantages and practical usability of these new algorithms

Formation of stored heat by means of bled steam during times of load reduction and its use in peak load times

Technical possibilities and economic advantages of integrating hot water storage systems into power plants fired with fossil fuels are discussed. The systems can be charged during times of load reduction and then used for back-up during peak load periods. Investment costs are higher for such systems than for gas turbine power plants fired with natural gas or light oil installed to meet peak load demand. However, by improving specific heat consumption by about 1,000 kcal/k ohm, which thus reduces the related costs, investment costs will be compensated for, so that power production costs will not increase

08451 Abstracts Collection -- Representation, Analysis and Visualization of Moving Objects

From 02.11. to 07.11.2008, the Dagstuhl Seminar 08451 ``Representation, Analysis and Visualization of Moving Objects \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

New catalyst for the epoxidation of olefins

This thesis describes the development of inexpensive and practical iron catalysts for the environmentally benign epoxidation of olefins with hydrogen peroxide as terminal oxidant. Investigations on ruthenium complexes derived from N,N,N-tridentate ligands together with the co-ligand pyridine-2,6-dicarboxylic acid (H2pydic) showed high catalytic activity in the epoxidation of various olefins. In order to develop an improved, environmentally benign and more economical procedure, these ruthenium catalysts were replaced by iron catalytic systems. By systematic variation of ligands, metal sources and reaction conditions, it was discovered that FeCl3-6H2O in combination with H2pydic and various amines as bases and co-ligands shows high reactivity and good to excellent selectivity towards epoxidation of aromatic and aliphatic olefins. Excellent results were achieved in asymmetric epoxidation by the use of chiral diphenylethylene diamine derivatives.Die vorliegende Dissertation beschäftigt sich mit der Entwicklung von kosten-günstigen und praktischen Eisenkatalysatoren für die umweltfreundliche Epoxidation von Olefinen mithilfe von Wasserstoffperoxid als Oxidationsmittel. Bei Untersuchungen zu Rutheniumkomplexen mit N,N,N-tridentaten Liganden und Pyridin-2,6-dicarbonsäure (H2pydic) als Coliganden wurde hohe katalytische Aktivität für die Epoxidation von verschiedenartigen Olefinen gefunden. Für die Entwicklung eines verbesserten, umweltfreundlicheren und ökonomischeren Verfahrens konnten diese Rutheniumkatalysatoren durch katalytische Eisen-Systeme ersetzt werden. Durch systematische Änderung der Liganden, Metallquellen und Reaktionsbedingungen wurde festgestellt, dass FeCl3-6H2O in Kombination mit H2pydic und verschiedenen Aminen als Basen und Coliganden hohe Aktivität und exzellente Selektivität gegenüber der Epoxidation von aromatischen und aliphatischen Olefinen zeigt. Des Weiteren zeigte der Einsatz von chiralen Diphenylethylendiamin-Derivaten sehr gute Ergebnisse bei der asymmetrischen Epoxidation

Solution to the Henckell--Rhodes problem: finite FF-inverse covers do exist

For a finite connected graph $\mathcal{E}$ with set of edges $E$, a finite $E$-generated group $G$ is constructed such that the set of relations $p=1$ satisfied by $G$ (with $p$ a word over $E\cup E^{-1}$) is closed under deletion of generators (i.e.~edges). As a consequence, every element $g\in G$ admits a unique minimal set $\mathrm{C}(g)$ of edges (the \emph{content} of $g$) needed to represent $g$ as a word over $\mathrm{C}(g)\cup\mathrm{C}(g)^{-1}$. The crucial property of the group $G$ is that connectivity in the graph $\mathcal{E}$ is encoded in $G$ in the following sense: if a word $p$ forms a path $u\longrightarrow v$ in $\mathcal{E}$ then there exists a $G$-equivalent word $q$ which also forms a path $u\longrightarrow v$ and uses only edges from their content; in particular, the content of the corresponding group element $[p]_G=[q]_G$ spans a connected subgraph of $\mathcal{E}$ containing the vertices $u$ and $v$. As an application it is shown that every finite inverse monoid admits a finite $F$-inverse cover. This solves a long-standing problem of Henckell and Rhodes.Comment: 46 pages, 14 figures, new result Cor. 2.7 included, several inaccuracies removed, more details include

“In school you notice the performance gap and how different it is between the students” – Student teachers’ collective orientations about the learners’ heterogeneity in mathematics

International audienceCollective orientations about the heterogeneity of the learners emerge on the basis of experiences that are unique to the individual, but in many ways structurally similar. Guided by the assumption that collective orientations significantly influence the practice of (student) teachers, our goal is to reconstruct (student) teachers’ ways of thinking in the context of heterogeneous learning groups in mathematics education using the documentary method. In the data of the project HeLeA , it became apparent that one main focus of the group discussions was the variety of student performance. The differences in the achievement of the students, especially in mathematics, seem to be a great challenge for student teachers. Furthermore, there are discontinuities between the everyday discourse of student teachers and the academic discourse on the topic of heterogeneity

Flashix: modular verification of a concurrent and crash-safe flash file system

The Flashix project has developed the first realistic verified file system for Flash memory. This paper gives an overview over the project and the theory used. Specification is based on modular components and subcomponents, which may have concurrent implementations connected via refinement. Functional correctness and crash-safety of each component is verified separately. We highlight some components that were recently added to improve efficiency, such as file caches and concurrent garbage collection. The project generates 18K of C code that runs under Linux. We evaluate how efficiency has improved and compare to UBIFS, the most recent flash file system implementation available for the Linux kernel