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  • 1
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    Barrier methods for a control problem from hyperthermia treatment planning (2009)
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    Publikationsdatum: 2019-01-29
    Beschreibung: We consider an optimal control problem from hyperthermia treatment planning and its barrier regularization. We derive basic results, which lay the groundwork for the computation of optimal solutions via an interior point path-following method. Further, we report on a numerical implementation of such a method and its performance at an example problem.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 2
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    Transparent boundary conditions for Maxwell's equations: Numerical concepts beyond the PML method (2009)
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    Publikationsdatum: 2016-06-09
    Beschreibung: Optical technologies are ubiquitously used in hi-tech devices. As a common feature of such devices one finds structures with dimensions in the order of the wavelength of the used light. To design and produce such devices, the wave nature of light must be taken into account. Accordingly, robust simulation tools are required which are based on rigorously solving Maxwell's equations, the governing equations of light propagation within macroscopic media. This thesis contributes to the modeling and the numerical computation of light scattering problems: Light scattering problems are typically posed on the entire space. The Perfectly-Matched -Layer method (PML) is widely used to restrict the simulation problem onto a bounded computational domain. We propose an adaptive PML method which exhibits a good convergence even for critical problems where standard PML implementations fail. Besides the computation of the near field, that is the electromagnetic field within the computational domain, it is of major interest to evaluate the electromagnetic field in the exterior domain and to compute the far field. So far, this was numerically only possible for simple geometries such as homogeneous exterior domains or layered media. To deal with more complicated devices, for example with waveguide inhomogeneities, we develop an evaluation formula based on the PML solution which allows for an exterior domain field evaluation in a half space above the device. Finally, we generalize the PML method to problems with multiply structured exterior domains. The term “multiply structured exterior domain” is defined in this thesis and means that the exterior domain exhibits several half-infinite structures. Mathematically, this gives rise to various complications. For example, no analytical solutions to Maxwell's equations for standard light sources are available in the exterior domain, which are needed to describe the incoming field in a light scattering problem. To tackle this we propose a new light scattering problem formulation which fits well into the PML method framework and which may be regarded as an extension of classical contributions by Sommerfeld, Wiener and Hopf. An exterior domain evaluation formula for multiply structured exterior domains with an extended illumination is derived as well.
    Schlagwort(e): ddc:510
    Sprache: Englisch
    Materialart: doctoralthesis , doc-type:doctoralThesis
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  • 3
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    The Coolest Path Problem (2009)
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    Publikationsdatum: 2020-08-05
    Beschreibung: We introduce the coolest path problem, which is a mixture of two well-known problems from distinct mathematical fields. One of them is the shortest path problem from combinatorial optimization. The other is the heat conduction problem from the field of partial differential equations. Together, they make up a control problem, where some geometrical object traverses a digraph in an optimal way, with constraints on intermediate or the final state. We discuss some properties of the problem and present numerical solution techniques. We demonstrate that the problem can be formulated as a linear mixed-integer program. Numerical solutions can thus be achieved within one hour for instances with up to 70 nodes in the graph.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 4
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    The MCF-Separator -- Detecting and Exploiting Multi-Commodity Flow Structures in MIPs (2009)
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    Publikationsdatum: 2021-08-05
    Beschreibung: Given a general mixed integer program (MIP), we automatically detect block structures in the constraint matrix together with the coupling by capacity constraints arising from multi-commodity-flow formulations. We identify the underlying graph and generate cutting planes based on cuts in the detected network. Our implementation adds a separator to the branch-and-cut libraries of SCIP and CPLEX. We make use of the complemented mixed integer rounding framework (cMIR) but provide a special purpose aggregation heuristic that exploits the network structure. Our separation scheme speeds-up the computation for a large set of MIPs coming from network design problems by a factor of two on average.
    Schlagwort(e): ddc:510
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
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  • 5
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    Nonlinear pseudo-Boolean optimization: relaxation or propagation? (2009)
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    Publikationsdatum: 2022-03-14
    Beschreibung: Pseudo-Boolean problems lie on the border between satisfiability problems, constraint programming, and integer programming. In particular, nonlinear constraints in pseudo-Boolean optimization can be handled by methods arising in these different fields: One can either linearize them and work on a linear programming relaxation or one can treat them directly by propagation. In this paper, we investigate the individual strengths of these approaches and compare their computational performance. Furthermore, we integrate these techniques into a branch-and-cut-and-propagate framework, resulting in an efficient nonlinear pseudo-Boolean solver.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 6
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    Planning Problems in Public Transit (2009)
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    Publikationsdatum: 2020-08-05
    Beschreibung: Every day, millions of people are transported by buses, trains, and airplanes in Germany. Public transit (PT) is of major importance for the quality of life of individuals as well as the productivity of entire regions. Quality and efficiency of PT systems depend on the political framework (state-run, market oriented) and the suitability of the infrastructure (railway tracks, airport locations), the existing level of service (timetable, flight schedule), the use of adequate technologies (information, control, and booking systems), and the best possible deployment of equipment and resources (energy, vehicles, crews). The decision, planning, and optimization problems arising in this context are often gigantic and “scream” for mathematical support because of their complexity. This article sketches the state and the relevance of mathematics in planning and operating public transit, describes today’s challenges, and suggests a number of innovative actions. The current contribution of mathematics to public transit is — depending on the transportation mode — of varying depth. Air traffic is already well supported by mathematics. Bus traffic made significant advances in recent years, while rail traffic still bears significant opportunities for improvements. In all areas of public transit, the existing potentials are far from being exhausted. For some PT problems, such as vehicle and crew scheduling in bus and air traffic, excellent mathematical tools are not only available, but used in many places. In other areas, such as rolling stock rostering in rail traffic, the performance of the existing mathematical algorithms is not yet sufficient. Some topics are essentially untouched from a mathematical point of view; e.g., there are (except for air traffic) no network design or fare planning models of practical relevance. PT infrastructure construction is essentially devoid of mathematics, even though enormous capital investments are made in this area. These problems lead to questions that can only be tackled by engineers, economists, politicians, and mathematicians in a joint effort. Among other things, the authors propose to investigate two specific topics, which can be addressed at short notice, are of fundamental importance not only for the area of traffic planning, should lead to a significant improvement in the collaboration of all involved parties, and, if successful, will be of real value for companies and customers: • discrete optimal control: real-time re-planning of traffic systems in case of disruptions, • model integration: service design in bus and rail traffic. Work on these topics in interdisciplinary research projects could be funded by the German ministry of research and education (BMBF), the German ministry of economics (BMWi), or the German science foundation (DFG).
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 7
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    Solving Steel Mill Slab Problems with Branch and Price (2009)
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    Publikationsdatum: 2020-08-05
    Beschreibung: The steel mill slab design problem from the CSPLib is a binpacking problem that is motivated by an application of the steel industry and that has been widely studied in the constraint programming community. Recently, several people proposed new models and methods to solve this problem. A steel mill slab library was created which contains 380 instances. A closely related binpacking problem called multiple knapsack problem with color constraints, originated from the same industrial problem, were discussed in the integer programming community. In particular, a simple integer programming for this problem has been given by Forrest et al. [3]. The aim of this paper is to bring these different studies together. Moreover, we adopt the model of [3] for the steel mill slab problem. Using a state of the art integer program solver, this model is capable to solve all instances of the steel mill slab library, mostly in less than one second, to optimality. We improved, thereby, the solution value of 76 instances.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 8
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    On the Hardness of Finding Small Shortest Path Routing Conflicts (2009)
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    Publikationsdatum: 2020-08-05
    Beschreibung: Nowadays most data networks use shortest path protocols such as OSPF or IS-IS to route traffic. Given administrative routing lengths for the links of a network, all data packets are sent along shortest paths with respect to these lengths from their source to their destination. One of the most fundamental problems in planning shortest path networks is to decide whether a given set of routing paths forms a valid routing and, if this is not the case, to find a small subset of the given paths that cannot be shortest paths simultaneously for any routing lengths. In this paper we show that it is NP-hard to approximate the size of the smallest shortest path conflict by a factor less than 7/6.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 9
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    A Binary Quadratic Programming Approach to the Vehicle Positioning Problem (2009)
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    Publikationsdatum: 2020-08-05
    Beschreibung: The Vehicle Positioning Problem (VPP) consists of the assignment of vehicles (buses, trams or trains) of a public transport or railway company to parking positions in a depot and to timetabled trips. Such companies have many different types of vehicles, and each trip can be performed only by vehicles of some of these types. These assignments are non-trivial due to the topology of depots. The parking positions are organized in tracks, which work as one- or two-sided stacks or queues. If a required type of vehicle is not available in the front of any track, shunting movements must be performed in order to change vehicles' positions, which is undesirable and should be avoided. In this text we present integer linear and non-linear programming formulations for some versions of the problem and compare them from a theoretical and a computational point of view.
    Schlagwort(e): ddc:510
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
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  • 10
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    Statistical Error Estimation and Grid-free Hierarchical Refinement in Conformation Dynamics (2009)
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    Publikationsdatum: 2020-03-11
    Beschreibung: The understanding of geometric structures and dynamical properties of molecular conformations gives insight into molecular long-term behavior. The identification of metastable conformations together with their life times and transition patterns is the intention of conformation dynamics. Conformation dynamics is a multi-scale approach that leads to a reduced description of the dynamical system in terms of a stochastic transition probability matrix. The present thesis deals with the error analysis of computed matrices and the resulting matrix functions. Since conformational membership vectors, as they are computed by the Robust Perron Cluster Analysis (PCCA+), form an invariant subspace of the transition matrix, subspace-based error estimators are of particular interest. The decomposition of the state space into basis functions and the approximation of integrals by Monte-Carlo quadrature give rise to row-wise correlated random matrices, for which stochastic norms are computed. Together with an appropriate statistical model for the distribution of matrix rows, this allows for the calculation of error bounds and error distributions of the invariant subspace and other variables of interest. Equilibration of errors among the basis functions can be achieved by enhanced sampling in regions where the trajectories are mixing slowly. Hierarchical refinement of such basis functions systematically improves the clustering into metastable conformations by reducing the error in the corresponding invariant subspace. These techniques allow for an evaluation of simulation results and pave the way for the analysis of larger molecules. Moreover, the extension of PCCA+ to non-reversible Markov chains, verified by the corresponding perturbation theory, and the modification of the objective function for the case of soft membership vectors represent a further generalization of the clustering method, thus continuing the development from PCCA over PCCA+ to PCCA++. The methods developed in this thesis are useful for but not limited to conformation dynamics. In fact, they are applicable to a broader class of problems which combine domain decomposition with Monte-Carlo quadrature. Possible application areas may include the chemical master equation or quantum dynamical systems.
    Beschreibung: Das Verständnis von geometrischen Strukturen und dynamischen Eigenschaften molekularer Konformationen ist essentiell für die Vorhersage des Langzeitverhaltens von Molekülen. Die Identifikation metastabiler Konformationen sowie die Bestimmung von Übergangswahrscheinlichkeiten und Haltezeiten sind Bestandteil der Konformationdynamik. Dabei handelt es sich um eine Mehrskalenmethode, die auf eine reduzierte Beschreibung des Systems mittels einer stochastischen Übergangsmatrix führt. In der vorliegenden Dissertation wurde untersucht, wie man die Genauigkeit der Matrizen sowie der daraus berechneten Größen quantifizieren kann. Im Mittelpunkt stehen dabei Fehlerschätzer für den invarianten Unterraum, da die rechten Eigenvektoren als Grundlage der Robusten Perron Cluster Analyse (PCCA+) zur Identifizierung der metastabilen Konformationen dienen. Die Zerlegung des Zustandsraumes in Basisfunktionen sowie die Approximation der Matrixeinträge mittels Monte-Carlo-Quadratur führen zu zeilenweise korrelierten Zufallsmatrizen. Mit Hilfe einer stochastischen Norm sowie einem geeigneten statistischen Modell für die Verteilung der Matrixzeilen können u.a. Fehlerschranken und -verteilungen für den invarianten Unterraum brechnet werden. Eine Equilibrierung des Fehlers zwischen den Basisfunktionen kann durch erweitertes Sampling in solchen Regionen erreicht werden, in denen die Trajektorien nur langsam mischen.Eine hierarchische Zerlegung dieser Basisfunktionen verbessert systematisch die Zerlegung in metastabile Konformationen, indem sie den Fehler im invarianten Unterraum reduziert. Diese Techniken gestatten eine Evaluierung der Simulationsergebnisse und ebnen den Weg zur Behandlung komplexerer Moleküle. Desweiteren wurden Verallgemeinerungen der PCCA+ untersucht. Die Erweiterung der PCCA+ auf nicht-reversible Markov-Ketten sowie die Modifizierung der Zielfunktion für den Fall der weichen Clusterung setzen die Entwicklung von der PCCA über PCCA+ zu PCCA++ fort. Somit können neue Anwendungsfelder für dieses Cluster-Verfahren erschlossen werden. Die Methoden wurden zwar in Rahmen der Konformationsdynamik entwickelt, jedoch lassen sie sich auf eine weite Problemklasse anwenden, in der Gebietszerlegungsverfahren mit Monte-Carlo-Quadratur kombiniert werden. Mögliche Anwendungsgebiete umfassen die chemische Master-Gleichung oder quantenchemische Systeme.
    Schlagwort(e): ddc:510
    Sprache: Englisch
    Materialart: doctoralthesis , doc-type:doctoralThesis
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  • 11
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    A Set Partitioning Approach to Shunting (2009)
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    Publikationsdatum: 2020-08-05
    Beschreibung: The Vehicle Positioning Problem (VPP) is a classical combinatorial optimization problem in public transport planning. A number of models and approaches have been suggested in the literature, which work for small problems, but not for large ones. We propose in this article a novel set partitioning model and an associated column generation solution approach for the VPP. The model provides a tight linear description of the problem. The pricing problem, and hence the LP relaxation itself, can be solved in polynomial resp. pseudo-polynomial time for some versions of the problems.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 12
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    Solving Large-scale Open Pit Mining Production Scheduling Problems by Integer Programming (2009)
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    Publikationsdatum: 2020-08-05
    Beschreibung: Since the initial application of mathematical optimisation methods to mine planning in 1965, the Lerchs-Grossmann algorithm for computing the ultimate pit limit, operations researchers have worked on a variety of challenging problems in the area of open pit mining. This thesis focuses on the open pit mining production scheduling problem: Given the discretisation of an orebody as a block model, determine the sequence in which the blocks should be removed from the pit, over the lifespan of the mine, such that the net present value of the mining operation is maximised. In practise, when some material has been removed from the pit, it must be processed further in order to extract the valuable elements contained therein. If the concentration of valuable elements is not sufficiently high, the material is discarded as waste or stockpiled. Realistically-sized block models can contain hundreds of thousands of blocks. A common approach to render these problem instances computationally tractable is the aggregation of blocks to larger scheduling units. The thrust of this thesis is the investigation of a new mixed-integer programming formulation for the open pit mining production scheduling problem, which allows for processing decisions to be made at block level, while the actual mining schedule is still computed at aggregate level. A drawback of this model in its full form is the large number of additional variables needed to model the processing decisions. One main result of this thesis shows how these processing variables can be aggregated efficiently to reduce the problem size significantly, while practically incurring no loss in net present value. The second focus is on the application of lagrangean relaxation to the resource constraints. Using a result of Möhring et al. (2003) for project scheduling, the lagrangean relaxation can be solved efficiently via minimum cut computations in a weighted digraph. Experiments with a bundle algorithm implementation by Helmberg showed how the lagrangean dual can be solved within a small fraction of the time required by standard linear programming algorithms, while yielding practically the same dual bound. Finally, several problem-specific heuristics are presented together with computational results: two greedy sub-MIP start heuristics and a large neighbourhood search heuristic. A combination of a lagrangean-based start heuristic followed by a large neighbourhood search proved to be effective in generating solutions with objective values within a 0.05% gap of the optimum.
    Schlagwort(e): ddc:510
    Sprache: Englisch
    Materialart: masterthesis , doc-type:masterThesis
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  • 13
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    1D-Reduktion thermal signifikanter Aderstränge in der Hyperthermie-Modellierung (2009)
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    Publikationsdatum: 2019-01-29
    Beschreibung: In dieser Arbeit wird ein neuer Ansatz zur Modellierung von thermal signifikanten Gefäßsträngen im Hyperthermie-Kontext betrachtet. Ausgehend von einer Konvektions-Diffusions-Gleichung wird durch Reskalierung des Massenflussterms eine Reduktion des Adergebietes auf eine 1D-Struktur erreicht. Nach numerischen Vorbetrachtungen wird die Grenzgleichung innerhalb einer verallgemeinerten Sobolev-Algebra formuliert. Die Untersuchung der Lösungsfamilie in klassischen Funktionenräumen zeigt, dass deren schwacher Grenzwert die Lösung der korrespondierenden Diffusions-Gleichung ist. Die Diskretisierung einer formalen Grenzgleichung mit Linienstromanteil stellt jedoch eine gute Approximation an die Diskretisierung des ursprünglichen Problems dar, wenn man die lokale Maschenweite an die Gefäßradien koppelt und bei erhöhtem Genauigkeitsbedarf auf ein vollständiges 3D-Modell umschaltet.
    Schlagwort(e): ddc:510
    Sprache: Deutsch
    Materialart: masterthesis , doc-type:masterThesis
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  • 14
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    Undercover – a primal heuristic for MINLP based on sub-MIPs generated by set covering (2009)
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    Publikationsdatum: 2022-03-14
    Beschreibung: We present Undercover, a primal heuristic for mixed-integer nonlinear programming (MINLP). The heuristic constructs a mixed-integer linear subproblem (sub-MIP) of a given MINLP by fixing a subset of the variables. We solve a set covering problem to identify a minimal set of variables which need to be fixed in order to linearise each constraint. Subsequently, these variables are fixed to approximate values, e.g. obtained from a linear outer approximation. The resulting sub-MIP is solved by a mixed-integer linear programming solver. Each feasible solution of the sub-MIP corresponds to a feasible solution of the original problem. Although general in nature, the heuristic seems most promising for mixed-integer quadratically constrained programmes (MIQCPs). We present computational results on a general test set of MIQCPs selected from the MINLPLib.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 15
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    On sojourn times in M/GI systems under state-dependent processor sharing (2009)
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    Publikationsdatum: 2020-08-05
    Beschreibung: We consider a system with Poisson arrivals and i.i.d. service times. The requests are served according to the state-dependent processor sharing discipline, where each request receives a service capacity which depends on the actual number of requests in the system. The linear systems of PDEs describing the residual and attained sojourn times coincide for this system, which provides time reversibility including sojourn times for this system, and their minimal non negative solution gives the LST of the sojourn time $V(\tau)$ of a request with required service time $\tau$. For the case that the service time distribution is exponential in a neighborhood of zero, we derive a linear system of ODEs, whose minimal non negative solution gives the LST of $V(\tau)$, and which yields linear systems of ODEs for the moments of $V(\tau)$ in the considered neighborhood of zero. Numerical results are presented for the variance of $V(\tau)$. In case of an M/GI/2-PS system, the LST of $V(\tau)$ is given in terms of the solution of a convolution equation in the considered neighborhood of zero. For bounded from below service times, surprisingly simple expressions for the LST and variance of $V(\tau)$ in this neighborhood of zero are derived, which yield in particular the LST and variance of $V(\tau)$ in M/D/2-PS.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 16
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    E-Learning and the Working Mathematician (2009)
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    Publikationsdatum: 2020-12-11
    Beschreibung: Eigentlich war der erste Autor nur zu einem Grußwort zur Tagung „GML² 2009 - Grundfragen Multi¬medialen Lehrens und Lernens“ eingeladen. Daraus wurde ein E-Learning-bezogener Vortrag, der – basierend auf Erfahrungen im Fach Mathematik – einen kritischen Blick auf die E-Learning-Szene in Deutschland wirft und diese mit entsprechenden Aktivitäten weltweit vergleicht. Dies ist die in seinen mathematischen Teilen gekürzte, in den E-Learning-Anteilen ein wenig erweiterte schriftliche Fassung des Vortrags. Der Artikel stammt nicht von E-Learning-Spezialisten sondern von Personen, die sich seit fast zwanzig Jahren mit elektronischer Information und Kommunikation (kurz: IuK) – insbesondere in der Mathematik – beschäftigen. Nach einer Definition von Michael Kerres kennzeichnet der Begriff E-Learning (electronic learning – elektronisch unterstütztes Lernen) alle Formen von Lernen, bei denen digitale Medien für die Präsentation und Distribution von Lernmaterialien und/oder zur Unterstützung zwischenmenschlicher Kommunikation zum Einsatz kommen, siehe z.B. http://de.wikipedia.org/wiki/E-Learning. IuK und E-Learning haben nach dieser Begriffsbildung viele Berührungspunkte. Deswegen wagen wir es, unsere positiven und negativen Erfahrungen im Bereich IuK in diesem Eröffnungsvortrag zu berichten, einige Entwicklungslinien zu vergleichen und eine eigene Kurzversion der Definition von E-Learning (besser E-Teaching and -Learning) voranzustellen: „Lehren und Lernen mit Unterstützung elektronischer Hilfsmittel“.
    Schlagwort(e): ddc:510
    Sprache: Deutsch
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  • 17
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    Optimal Design of Survivable Multi-layer Telecommunication Networks (2009)
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    Publikationsdatum: 2020-08-05
    Beschreibung: Telecommunication transport networks consist of a stack of technologically different subnetworks, so-called layers, which are strongly interdependent. For example, one layer may correspond to an Internet (IP) backbone network whose links are realized by lightpath connections in an underlying optical fiber layer. To ensure that the network can fulfill its task of routing all communication requests, the inter-layer dependencies have to be taken into account already in the planning phase of the network. This is particularly important with survivability constraints, where connections in one layer have to be protected against cable cuts or equipment failures in another layer. The traditional sequential planning approach where one layer is optimized after the other cannot properly take care of the inter-layer dependencies; this can only be achieved with an integrated planning of several network layers at the same time. This thesis provides mathematical models and algorithmic techniques for the integrated optimization of two network layers with survivability constraints. We describe a multi-layer network design problem which occurs in various technologies, and model it mathematically using mixed-integer programming (MIP) formulations. The presented models cover many important practical side constraints from different technological contexts. In contrast to previous models from the literature, they can be used to design large two-layer networks with survivability requirements. We discuss modeling alternatives for various aspects of a multi-layer network and compare different routing formulations under multi-layer survivability constraints. We solve our models using a branch-and-cut-and-price approach with various problemspecific enhancements. This includes a presolving technique based on linear programming to reduce the problem size, combinatorial and sub-MIP-based primal heuristics to compute feasible network configurations, cutting planes which take the multi-layer survivability constraints into account to improve the lower bound on the optimal network cost, and column generation to generate flow variables dynamically during the algorithm. We develop techniques to speed up computations in a Benders decomposition approach and compare this approach to the standard formulation with a single MIP. We use the developed techniques to design large survivable two-layer networks by means of linear and integer programming methods. On realistic test instances with up to 67 network nodes and survivability constraints, we investigate the algorithmic impact of our techniques and show how to use them to compute good network configurations with quality guarantees. Most of the smaller test instances with up to 17 nodes can be solved to near-optimality. Moreover, we can compute feasible solutions and dual bounds even for large networks with survivability constraints, which has not been possible before.
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    Sprache: Englisch
    Materialart: doctoralthesis , doc-type:doctoralThesis
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  • 18
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    On the Factorization of Simplex Basis Matrices (2009)
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    Publikationsdatum: 2020-08-05
    Beschreibung: In the simplex algorithm, solving linear systems with the basis matrix and its transpose accounts for a large part of the total computation time. We investigate various methods from modern numerical linear algebra to improve the computation speed of the basis updates arising in LPs. The experiments are executed on a large real-world test set. The most widely used solution technique is sparse LU factorization, paired with an updating scheme that allows to use the factors over several iterations. Clearly, small number of fill-in elements in the LU factors is critical for the overall performance. Using a wide range of LPs we show numerically that after a simple permutation the non-triangular part of the basis matrix is so small, that the whole matrix can be factorized with (relative) fill-in close to the optimum. This permutation has been exploited by simplex practitioners for many years. But to our knowledge no systematic numerical study has been published that demonstrates the effective reduction to a surprisingly small non-triangular problem, even for large scale LPs. For the factorization of the non-triangular part most existing simplex codes use some variant of dynamic Markowitz pivoting, which originated in the late 1950s. We also show numerically that, in terms of fill-in and in the simplex context, dynamic Markowitz is quite consistently superior to other, more recently developed techniques.
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    Sprache: Englisch
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  • 19
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    Computing expectation values for molecular quantum dynamics (2009)
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    Publikationsdatum: 2020-03-11
    Beschreibung: We compute expectation values for the solution of the nuclear Schrödinger equation. The proposed particle method consists of three steps: sampling of the initial Wigner function, classical transport of the sampling points, weighted phase space summation for the final computation of the expectation values. The Egorov theorem guarantees that the algorithm is second order accurate with respect to the semiclassical parameter. We present numerical experiments for a two-dimensional torsional potential with three different sets of initial data and for a six-dimensional Henon-Heiles potential. By construction, the computing times scale linearly with the number of initial sampling points and range between three seconds and one hour.
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    Sprache: Englisch
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  • 20
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    Extending a CIP framework to solve MIQCPs (2009)
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    Publikationsdatum: 2022-03-14
    Beschreibung: This paper discusses how to build a solver for mixed integer quadratically constrained programs (MIQCPs) by extending a framework for constraint integer programming (CIP). The advantage of this approach is that we can utilize the full power of advanced MIP and CP technologies. In particular, this addresses the linear relaxation and the discrete components of the problem. For relaxation, we use an outer approximation generated by linearization of convex constraints and linear underestimation of nonconvex constraints. Further, we give an overview of the reformulation, separation, and propagation techniques that are used to handle the quadratic constraints efficiently. We implemented these methods in the branch-cut-and-price framework SCIP. Computational experiments indicates the potential of the approach.
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    Sprache: Englisch
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  • 21
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    A Subspace Approach to Molecular Markov State Models via an Infinitesimal Generator (2009)
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    Publikationsdatum: 2016-06-09
    Beschreibung: Supercomputers can simulate complex molecular systems. However, there is a very large gap between the fastest oscillations of covalent bonds of a molecule and the time-scale of the dominant processes. In order to extract the dominant time-scales and to identify the dominant processes, a clustering of information is needed. This thesis shows that only the subspace-based Robust Perron Cluster Analysis (PCCA+) can solve this problem correctly by the construction of a Markov State Model. PCCA+ allows for time-extrapolation in molecular kinetics. This thesis shows the difference between molecular dynamics and molecular kinetics. Only in the molecular kinetics framework a definition of transition rates is possible. In this context, the existence of an infinitesimal generator of the dynamical processes is discussed. If the existence is assumed, the Theorem of Gauß can be applied in order to compute transition rates efficiently. Molecular dynamics, however, is not able to provide a suitable statistical basis for the determination of the transition pattern.
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    Sprache: Englisch
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  • 22
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    Approximations for the second moments of sojourn times in M/GI systems under state-dependent processor sharing (2009)
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    Publikationsdatum: 2020-08-05
    Beschreibung: We consider a system with Poisson arrivals and general service times, where the requests are served according to the State-Dependent Processor Sharing (SDPS) discipline (Cohen's generalized processor sharing discipline), where each request receives a service capacity which depends on the actual number of requests in the system. For this system, denoted by $M/GI/SDPS$, we derive approximations for the squared coefficients of variation of the conditional sojourn time of a request given its service time and of the unconditional sojourn time by means of two-moment fittings of the service times. The approximations are given in terms of the squared coefficients of variation of the conditional and unconditional sojourn time in related $M/D/SDPS$ and $M/M/SDPS$ systems, respectively. The numerical results presented for $M/GI/m-PS$ systems illustrate that the proposed approximations work well.
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    Sprache: Englisch
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  • 23
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    Insensitivity bounds for the moments of the sojourn times in M/GI systems under state-dependent processor sharing (2009)
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    Publikationsdatum: 2020-08-05
    Beschreibung: We consider a system with Poisson arrivals and i.i.d. service times and where the requests are served according to the state-dependent (Cohen's generalized) processor sharing discipline, where each request in the system receives a service capacity which depends on the actual number of requests in the system. For this system we derive asymptotically tight upper bounds for the moments of the conditional sojourn time of a request with given required service time. The bounds generalize corresponding results, recently given for the single-server processor sharing system by Cheung et al. and for the state-dependent processor sharing system with exponential service times by the authors. Analogous results hold for the waiting times.
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    Sprache: Englisch
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  • 24
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    Randomized Online Algorithms for Dynamic Multi-Period Routing Problems (2009)
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    Publikationsdatum: 2020-11-13
    Beschreibung: The Dynamic Multi-Period Routing Problem DMPRP introduced by Angelelli et al. gives a model for a two-stage online-offline routing problem. At the beginning of each time period a set of customers becomes known. The customers need to be served either in the current time period or in the following. Postponed customers have to be served in the next time period. The decision whether to postpone a customer has to be done online. At the end of each time period, an optimal tour for the customers assigned to this period has to be computed and this computation can be done offline. The objective of the problem is to minimize the distance traveled over all planning periods assuming optimal routes for the customers selected in each period. We provide the first randomized online algorithms for the DMPRP which beat the known lower bounds for deterministic algorithms. For the special case of two planning periods we provide lower bounds on the competitive ratio of any randomized online algorithm against the oblivious adversary. We identify a randomized algorithm that achieves the optimal competitive ratio of $\frac{1+\sqrt{2}}{2}$ for two time periods on the real line. For three time periods, we give a randomized algorithm that is strictly better than any deterministic algorithm.
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    Sprache: Englisch
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  • 25
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    Constraint Integer Programming (2009)
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    Publikationsdatum: 2021-08-05
    Beschreibung: This thesis introduces the novel paradigm of "constraint integer programming" (CIP), which integrates constraint programming (CP) and mixed integer programming (MIP) modeling and solving techniques. It is supplemented by the software SCIP, which is a solver and framework for constraint integer programming that also features SAT solving techniques. SCIP is freely available in source code for academic and non-commercial purposes. Our constraint integer programming approach is a generalization of MIP that allows for the inclusion of arbitrary constraints, as long as they turn into linear constraints on the continuous variables after all integer variables have been fixed. The constraints, may they be linear or more complex, are treated by any combination of CP and MIP techniques: the propagation of the domains by constraint specific algorithms, the generation of a linear relaxation and its solving by LP methods, and the strengthening of the LP by cutting plane separation. The current version of SCIP comes with all of the necessary components to solve mixed integer programs. In the thesis, we cover most of these ingredients and present extensive computational results to compare different variants for the individual building blocks of a MIP solver. We focus on the algorithms and their impact on the overall performance of the solver. In addition to mixed integer programming, the thesis deals with chip design verification, which is an important topic of electronic design automation. Chip manufacturers have to make sure that the logic design of a circuit conforms to the specification of the chip. Otherwise, the chip would show an erroneous behavior that may cause failures in the device where it is employed. An important subproblem of chip design verification is the property checking problem, which is to verify whether a circuit satisfies a specified property. We show how this problem can be modeled as constraint integer program and provide a number of problem-specific algorithms that exploit the structure of the individual constraints and the circuit as a whole. Another set of extensive computational benchmarks compares our CIP approach to the current state-of-the-art SAT methodology and documents the success of our method.
    Beschreibung: Diese Arbeit stellt einen integrierten Ansatz aus "Constraint Programming" (CP) und Gemischt-Ganzzahliger Programmierung ("Mixed Integer Programming", MIP) vor, den wir "Constraint Integer Programming" (CIP) nennen. Sowohl Modellierungs- als auch Lösungstechniken beider Felder fließen in den neuen integrierten Ansatz ein, um die unterschiedlichen Stärken der beiden Gebiete zu kombinieren. Als weiteren Beitrag stellen wir der wissenschaftlichen Gemeinschaft die Software SCIP zur Verfügung, die ein Framework für Constraint Integer Programming darstellt und zusätzlich Techniken des SAT-Lösens beinhaltet. SCIP ist im Source Code für akademische und nicht-kommerzielle Zwecke frei erhältlich. Unser Ansatz des Constraint Integer Programming ist eine Verallgemeinerung von MIP, die zusätzlich die Verwendung beliebiger Constraints erlaubt, solange sich diese durch lineare Bedingungen ausdrücken lassen falls alle ganzzahligen Variablen auf feste Werte eingestellt sind. Die Constraints werden von einer beliebigen Kombination aus CP- und MIP-Techniken behandelt. Dies beinhaltet insbesondere die "Domain Propagation", die Relaxierung der Constraints durch lineare Ungleichungen, sowie die Verstärkung der Relaxierung durch dynamisch generierte Schnittebenen. Die derzeitige Version von SCIP enthält alle Komponenten, die für das effiziente Lösen von Gemischt-Ganzzahligen Programmen benötigt werden. Die vorliegende Arbeit liefert eine ausführliche Beschreibung dieser Komponenten und bewertet verschiedene Varianten in Hinblick auf ihren Einfluß auf das Gesamt-Lösungsverhalten anhand von aufwendigen praktischen Experimenten. Dabei wird besonders auf die algorithmischen Aspekte eingegangen. Ein weiterer Hauptteil der Arbeit befasst sich mit der Chip-Design-Verifikation, die ein wichtiges Thema innerhalb des Fachgebiets der "Electronic Design Automation" darstellt. Chip-Hersteller müssen sicherstellen, dass der logische Entwurf einer Schaltung der gegebenen Spezifikation entspricht. Andernfalls würde der Chip fehlerhaftes Verhalten aufweisen, dass zu Fehlfunktionen innerhalb des Gerätes führen kann, in dem der Chip verwendet wird. Ein wichtiges Teilproblem in diesem Feld ist das Eigenschafts-Verifikations-Problem, bei dem geprüft wird, ob der gegebene Schaltkreisentwurf eine gewünschte Eigenschaft aufweist. Wir zeigen, wie dieses Problem als Constraint Integer Program modelliert werden kann und geben eine Reihe von problemspezifischen Algorithmen an, die die Struktur der einzelnen Constraints und der Gesamtschaltung ausnutzen. Testrechnungen auf Industrie-Beispielen vergleichen unseren Ansatz mit den bisher verwendeten SAT-Techniken und belegen den Erfolg unserer Methode.
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    Sprache: Englisch
    Materialart: doctoralthesis , doc-type:doctoralThesis
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  • 26
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    Fare Planning for Public Transport (2009)
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    Publikationsdatum: 2020-08-05
    Beschreibung: In this paper we investigate the fare planning model for public transport, which consists in designing a system of fares maximizing the revenue. We discuss a discrete choice model in which passengers choose between different travel alternatives to express the demand as a function of fares. Furthermore, we give a computational example for the city of Potsdam and discuss some theoretical aspects.
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  • 27
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    Improving the performance of elevator systems using exact reoptimization algorithms (2009)
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    Publikationsdatum: 2020-08-05
    Beschreibung: This extended abstract is about algorithms for controlling elevator systems employing destination hall calls, i.e. the passenger provides his destination floor when calling an elevator. We present the first exact algorithm for controlling a group of elevators and report on simulation results indicating that destination hall call systems outperform conventional systems.
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    Sprache: Englisch
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  • 28
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    On goal-oriented adaptivity for elliptic optimal control problems (2009)
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    Publikationsdatum: 2019-01-29
    Beschreibung: The paper proposes goal-oriented error estimation and mesh refinement for optimal control problems with elliptic PDE constraints using the value of the reduced cost functional as quantity of interest. Error representation, hierarchical error estimators, and greedy-style error indicators are derived and compared to their counterparts when using the all-at-once cost functional as quantity of interest. Finally, the efficiency of the error estimator and generated meshes are demonstrated on numerical examples.
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    Sprache: Englisch
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  • 29
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    Consistency Results for the Contact-Stabilized Newmark Method (2009)
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    Publikationsdatum: 2016-06-09
    Beschreibung: The paper considers the time integration of frictionless dynamical contact problems between viscoelastic bodies in the frame of the Signorini condition. Among the numerical integrators, interest focuses on the contact-stabilized Newmark method recently suggested by Deuflhard et al., which is compared to the classical Newmark method and an improved energy dissipative version due to Kane et al. In the absence of contact, any such variant is equivalent to the Störmer-Verlet scheme, which is well-known to have consistency order 2. In the presence of contact, however, the classical approach to discretization errors would not show consistency at all because of the discontinuity at the contact. Surprisingly, the question of consistency in the constrained situation has not been solved yet. The present paper fills this gap by means of a novel proof technique using specific norms based on earlier perturbation results due to the authors. The corresponding estimation of the local discretization error requires the bounded total variation of the solution. The results have consequences for the construction of an adaptive timestep control, which will be worked out subsequently in a forthcoming paper.
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  • 30
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    Discrete Optimization in Public Transportation (2009)
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    Publikationsdatum: 2020-08-05
    Beschreibung: The mathematical treatment of planning problems in public transit has made significant advances in the last decade. Among others, the classical problems of vehicle and crew scheduling can nowadays be solved on a routine basis using combinatorial optimization methods. This is not yet the case for problems that pertain to the design of public transit networks, and for the problems of operations control that address the implementation of a schedule in the presence of disturbances. The article gives a sketch of the state and important developments in these areas, and it addresses important challenges. The vision is that mathematical tools of computer aided scheduling (CAS) will soon play a similar role in the design and operation of public transport systems as CAD systems in manufacturing.
    Beschreibung: Die mathematische Behandlung von Planungsproblemen im öffentlichen Verkehr hat im letzten Jahrzehnt große Fortschritte gemacht. Klassische Probleme wie die Umlauf- und die Dienstplanung können heutzutage routinemäßig mit kombinatorischen Optimierungsmethoden gelöst werden. Die Behandlung von Problemen der Angebotsplanung und der Betriebssteuerung sind dagegen noch nicht ganz auf diesem Stand. Dieser Artikel gibt einen Überblick über den Stand der Forschung, über wichtige Entwicklungen und einige Herausforderungen in diesem Gebiet. Die Vision ist, dass mathematische Planungswerkzeuge im öffentlichen Verkehr (Computer Aided Scheduling, CAS) in Zukunft eine ähnliche Rolle spielen werden wie CAD-Systeme in der industriellen Fertigung.
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    Sprache: Englisch
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  • 31
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    Variational and statistical shape modeling for 3D geometry reconstruction (2009)
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    Publikationsdatum: 2022-07-19
    Beschreibung: The reconstruction of geometric shapes plays an important role in many biomedical applications. One example is the patient-specific, computer-aided planning of complex interventions, which requires the generation of explicitly represented geometric models of anatomical structures from medical image data. Only solutions that require minimal interaction by medical personnel are likely to enter clinical routine. Another example is the planning of surgical corrections of deformities where the target shape is unknown. Surgeons are often forced to resort to subjective criteria. These applications still pose highly challenging reconstruction problems, which are addressed in this thesis. The fundamental hypothesis, pursued in this thesis, is that the problems can be solved by incorporating a-priori knowledge about shape and other application-specific characteristics. Here, we focus mainly on the aspect of geometric shape analysis. The basic idea is to capture the most essential variations of a certain class of geometric objects via statistical shape models, which model typical features contained in a given population, and restrict the outcome of a reconstruction algorithm (more or less) to the space spanned by such models. A fundamental prerequisite for performing statistical shape analysis on a set of different objects is the identification of corresponding points on their associated surfaces. This problem is particularly difficult to solve if the shapes stem from different individuals. The reason lies in the basic difficulty of defining suitable measures of similarity. In this thesis, we divide the correspondence problem into feature and non-feature matching. The feature part depends on the application, while the non-feature part can be characterized by a purely geometric description. We propose two different approaches. The first approach has proved useful in many applications. Yet, it suffers from some practical limitations and does not yield a measure of similarity. Our second, variational, approach is designed to overcome these limitations. In it, we propose to minimize an invariant stretching measure, constrained by previously computed features. An important property, which sets our method apart from previous work, is that it does not require the computation of a global surface parameterization.
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    Sprache: Englisch
    Materialart: doctoralthesis , doc-type:doctoralThesis
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  • 32
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    Diskrete Mathematik und ihre Anwendungen: Auf dem Weg zu authentischem Mathematikunterricht (2008)
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    Publikationsdatum: 2020-08-05
    Beschreibung: Das heutige Leben ist durchdrungen von komplexen Technologien. Ohne Kommunikationsnetze, Internet, Mobilfunk, Logistik, Verkehrstechnik, medizinische Apparate, etc. könnte die moderne Gesellschaft nicht funktionieren. Fast alle dieser Technologien haben einen hohen Mathematikanteil. Der "normale Bürger"' weiss davon nichts, der Schulunterricht könnte dem ein wenig abhelfen. Einige mathematische Aspekte dieser Technologien sind einfach und sogar spielerisch intuitiv zugänglich. Solche Anwendungen, die zusätzlich noch der Lebensumwelt der Schüler zugehören, können dazu genutzt werden, die mathematische Modellierung, also die mathematische Herangehensweise an die Lösung praktischer Fragen, anschaulich zu erläutern. Gerade in der diskreten Mathematik können hier, quasi "nebenbei" mathematische Theorien erarbeitet und Teilaspekte (Definitionen, Fragestellungen, einfache Sachverhalte) durch eigenständiges Entdecken der Schüler entwickelt werden. Wir beginnen mit einigen Beispielen.
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  • 33
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    Wegeprobleme der Graphentheorie (2008)
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    Publikationsdatum: 2020-08-05
    Beschreibung: Den kürzesten Weg in einem Graphen zu finden ist ein klassisches Problem der Graphentheorie. Über einen Vortrag zu diesem Thema beim Tag der Mathematik 2007 von R. Borndörfer kam ich in Kontakt mit dem Konrad-Zuse-Zentrum (ZIB), das sich u.a. mit Wegeoptimierung beschäftigt. Ein Forschungsschwerpunkt dort ist im Rahmen eines Projekts zur Chipverifikation das Zählen von Lösungen, das, wie wir sehen werden, eng mit dem Zählen von Wegen zusammenhängt. Anhand von zwei Fragen aus der Graphentheorie soll diese Facharbeit unterschiedliche Lösungsmethoden untersuchen. Wie bestimmt man den kürzesten Weg zwischen zwei Knoten in einem Graphen und wie findet man alle möglichen Wege? Nach einer Einführung in die Graphentheorie und einer Konkretisierung der Probleme wird zunächst für beide eine Lösung mit auf Graphen basierenden Algorithmen vorgestellt. Während der Algorithmus von Dijkstra sehr bekannt ist, habe ich für das Zählen von Wegen einen eigenen Algorithmus auf der Basis der Tiefensuche entwickelt. Im zweiten Teil der Arbeit wird das Konzept der ganzzahligen Programmierung vorgestellt und die Lösungsmöglichkeiten für Wegeprobleme, die sich darüber ergeben. Schließlich wurden die vorgestellten Algorithmen am Beispiel des S- und U-Bahnnetzes von Berlin implementiert und mit Programmen, die die gleichen Fragen über ganzzahlige Programmierung lösen, verglichen.
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  • 34
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    A Perturbation Result for Dynamical Contact Problems (2008)
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    Publikationsdatum: 2016-06-09
    Beschreibung: This paper is intended to be a first step towards the continuous dependence of dynamical contact problems on the initial data as well as the uniqueness of a solution. Moreover, it provides the basis for a proof of the convergence of popular time integration schemes as the Newmark method. We study a frictionless dynamical contact problem between both linearly elastic and viscoelastic bodies which is formulated via the Signorini contact conditions. For viscoelastic materials fulfilling the Kelvin-Voigt constitutive law, we find a characterization of the class of problems which satisfy a perturbation result in a non-trivial mix of norms in function space. This characterization is given in the form of a stability condition on the contact stresses at the contact boundaries. Furthermore, we present perturbation results for two well-established approximations of the classical Signorini condition: The Signorini condition formulated in velocities and the model of normal compliance, both satisfying even a sharper version of our stability condition.
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    Sprache: Englisch
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  • 35
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    An Integer Programming Algorithm for Routing Optimization in IP Networks (2008)
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    Publikationsdatum: 2020-08-05
    Beschreibung: Most data networks nowadays use shortest path protocols to route the traffic. Given administrative routing lengths for the links of the network, all data packets are sent along shortest paths with respect to these lengths from their source to their destination. In this paper, we present an integer programming algorithm for the minimum congestion unsplittable shortest path routing problem, which arises in the operational planning of such networks. Given a capacitated directed graph and a set of communication demands, the goal is to find routing lengths that define a unique shortest path for each demand and minimize the maximum congestion over all links in the resulting routing. We illustrate the general decomposition approach our algorithm is based on, present the integer and linear programming models used to solve the master and the client problem, and discuss the most important implementational aspects. Finally, we report computational results for various benchmark problems, which demonstrate the efficiency of our algorithm.
    Schlagwort(e): ddc:510
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    The Line Connectivity Problem (2008)
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    Publikationsdatum: 2020-12-15
    Beschreibung: This paper introduces the "line connectivity problem", a generalization of the Steiner tree problem and a special case of the line planning problem. We study its complexity and give an IP formulation in terms of an exponential number of constraints associated with "line cut constraints". These inequalities can be separated in polynomial time. We also generalize the Steiner partition inequalities.
    Schlagwort(e): ddc:510
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    Using Model Counting to Find Optimal Distinguishing Tests (2008)
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    Publikationsdatum: 2020-08-05
    Beschreibung: Testing is the process of stimulating a system with inputs in order to reveal hidden parts of the system state. In the case of non-deterministic systems, the difficulty arises that an input pattern can generate several possible outcomes. Some of these outcomes allow to distinguish between different hypotheses about the system state, while others do~not. In this paper, we present a novel approach to find, for non-deterministic systems modeled as constraints over variables, tests that allow to distinguish among the hypotheses as good as possible. The idea is to assess the quality of a test by determining the ratio of distinguishing (good) and not distinguishing (bad) outcomes. This measure refines previous notions proposed in the literature on model-based testing and can be computed using model counting techniques. We propose and analyze a greedy-type algorithm to solve this test optimization problem, using existing model counters as a building block. We give preliminary experimental results of our method, and discuss possible improvements.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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    On the Effects of Minor Changes in Model Formulations (2008)
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    Publikationsdatum: 2021-08-05
    Beschreibung: Starting with the description of the Traveling Salesmen Problem formulation as given by van Vyve and Wolsey in the article Approximate extended formulations'', we investigate the effects of small variations onto the performance of contemporary mixed integer programming solvers. We will show that even minor changes in the formulation of the model can result in performance difference of more than a factor of 1000. As the results show it is not obvious which changes will result in performance improvements and which not.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 39
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    Detecting Orbitopal Symmetries (2008)
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    Publikationsdatum: 2022-03-14
    Beschreibung: Orbitopes can be used to handle symmetries which arise in integer programming formulations with an inherent assignment structure. We investigate the detection of symmetries appearing in this approach. We show that detecting so-called orbitopal symmetries is graph-isomorphism hard in general, but can be performed in linear time if the assignment structure is known.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 40
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    Optimization and Identification in Regional Hyperthermia (2008)
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    Publikationsdatum: 2019-01-29
    Beschreibung: Regional hyperthermia is a cancer therapy aiming at heating tumors using phased array applicators. This article provides an overview over current mathematical challenges of delivering individually optimal treatments. The focus is on therapy planning and identification of technical as well as physiological quantities from MR thermometry measurements.
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    Sprache: Englisch
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  • 41
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    On Efficiency and Accuracy in Cardioelectric Simulation (2008)
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    Publikationsdatum: 2019-05-10
    Beschreibung: Reasons for the failure of adaptive methods to deliver improved efficiency when integrating monodomain models for myocardiac excitation are discussed. Two closely related techniques for reducing the computational complexity of linearly implicit integrators, deliberate sparsing and splitting, are investigated with respect to their impact on computing time and accuracy.
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    Sprache: Englisch
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  • 42
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    Models for Periodic Timetabling (2008)
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    Publikationsdatum: 2020-08-05
    Beschreibung: We investigate the computation of periodic timetables for public transport by mixed integer programming. After introducing the problem, we describe two mathematical models for periodic timetabling, the PERIODIC EVENT SCHEDULING PROBLEM (PESP) and the QUADRATIC SEMI-ASSIGNMENT PROBLEM. Specifically, we give an overview of existing integer programming (IP) formulations for both models. An important contribution of our work are new IP formulations for the PESP based on time discretization. We provide an analytical comparison of these formulations and describe different techniques that allow a more efficient solution by mixed integer programming. In a preliminary computational study, on the basis of standard IP solvers, we compare different formulations for computing periodic timetables. Our results justify a further investigation of the time discretization approach. Typically the timetable is optimized for the current traffic situation. The main difficulty with this approach is that after introducing the new timetable the passengers’ travel behavior may differ from that assumed for the computation. Motivated by this problem, we examine an iterative timetabling procedure that is a combination of timetable computation and passenger routing. We discuss the algorithmic issues of the passenger routing and study properties of the computed timetables. Finally, we confirm our theoretical results on the basis of an own implementation.
    Beschreibung: Wir untersuchen die Berechnung von Taktfahrplänen für den öffentlichen Verkehr mit gemischt-ganzzahliger Programmierung (MIP). Im Anschluss an die Problembeschreibung, stellen wir zwei mathematische Modellierungen vor, das PERIODIC EVENT SCHEDULING PROBLEM (PESP) und das QUADRATIC SEMI-ASSIGNMENT PROBLEM. Wichtiger Bestandteil ist ein Überblick über existierende ganzzahlige Formulierungen beider Modelle. Wir entwickeln neue ganzzahlige Formulierungen für das PESP auf der Basis von Zeitdiskretisierung. Diese werden analytisch miteinander verglichen und wir beschreiben verschiedene Techniken, die eine effizientere Lösung der Formulierungen mit gemischt-ganzzahliger Programmierung ermöglichen. In einer ersten Rechenstudie, unter Verwendung gängiger MIP-Löser, vergleichen wir verschiedene ganzzahlige Formulierungen zur Berechnung von Taktfahrplänen. Unsere Ergebnisse rechtfertigen eine weitere Untersuchung des Zeitdiskretisierungsansatzes. In der Regel werden Fahrpläne mit Bezug auf die gegenwärtige Verkehrssituation optimiert. Dies birgt jedoch folgendes Problem. Wenn der neue Fahrplan eingeführt wird, ist es möglich, dass die Passagiere ein anderes Fahrverhalten zu Tage legen, als für die Berechnung des Fahrplans angenommen wurde. Vor diesem Hintergrund behandeln wir ein iteratives Verfahren zur Berechnung von Taktfahrplänen. Dieses ist eine Kombination aus Fahrplanberechnung und Passagierrouting. Neben den algorithmischen Details des Passagierroutings untersuchen wir Eigenschaften der berechneten Fahrpläne. Abschließend bestätigen wir unsere theoretischen Ergebnisse auf Grundlage einer eigenen Implementierung des Verfahrens.
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    Sprache: Englisch
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    Experiments with nonlinear extensions to SCIP (2008)
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    Publikationsdatum: 2020-08-05
    Beschreibung: This paper describes several experiments to explore the options for solving a class of mixed integer nonlinear programming problems that stem from a real-world mine production planning project. The only type of nonlinear constraints in these problems are bilinear equalities involving continuous variables, which enforce the ratios between elements in mixed material streams. A branch-and-bound algorithm to handle the integer variables has been tried in another project. However, this branch-and-bound algorithm is not effective for handling the nonlinear constraints. Therefore state-of-the-art nonlinear solvers are utilized to solve the resulting nonlinear subproblems in this work. The experiments were carried out using the NEOS server for optimization. After finding that current nonlinear programming solvers seem to lack suitable preprocessing capabilities, we preprocess the instances beforehand and use an heuristic approach to solve the nonlinear subproblems. In the appendix, we explain how to add a polynomial constraint handler that uses IPOPT as embedded nonlinear programming solver for the constraint programming framework SCIP. This is one of the crucial steps for implementing our algorithm in SCIP. We briefly described our approach and give an idea of the work involved.
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  • 44
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    Tiefensuche: Bemerkungen zur Algorithmengeschichte (2008)
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    Publikationsdatum: 2020-08-05
    Beschreibung: Dieser kurze Aufsatz zur Algorithmengeschichte ist Eberhard Knobloch, meinem Lieblings-Mathematikhistoriker, zum 65. Geburtstag gewidmet. Eberhard Knobloch hat immer, wenn ich ihm eine historische Frage zur Mathematik stellte, eine Antwort gewusst – fast immer auch sofort. Erst als ich mich selbst ein wenig und dazu amateurhaft mit Mathematikgeschichte beschäftigte, wurde mir bewusst, wie schwierig dieses „Geschäft“ ist. Man muss nicht nur mehrere (alte) Sprachen beherrschen, sondern auch die wissenschaftliche Bedeutung von Begriffen und Symbolen in früheren Zeiten kennen. Man muss zusätzlich herausfinden, was zur Zeit der Entstehung der Texte „allgemeines Wissen“ war, insbesondere, was seinerzeit gültige Beweisideen und -schritte waren, und daher damals keiner präzisen Definition oder Einführung bedurfte. Es gibt aber noch eine Steigerung des historischen Schwierigkeitsgrades: Algorithmengeschichte. Dies möchte ich in diesem Artikel kurz darlegen in der Hoffnung, dass sich Wissenschaftshistoriker dieses Themas noch intensiver annehmen, als sie das bisher tun. Der Grund ist, dass heute Algorithmen viele Bereiche unserer Alltagswelt steuern und unser tägliches Leben oft von funktionierenden Algorithmen abhängt. Daher wäre eine bessere Kenntnis der Algorithmengeschichte von großem Interesse.
    Schlagwort(e): ddc:510
    Sprache: Deutsch
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    State constrained optimal control problems with states of low regularity (2008)
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    Publikationsdatum: 2016-06-09
    Beschreibung: We consider first order optimality conditions for state constrained optimal control problems. In particular we study the case where the state equation has not enough regularity to admit existence of a Slater point in function space. We overcome this difficulty by a special transformation. Under a density condition we show existence of Lagrange multipliers, which have a representation via measures and additional regularity properties.
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    Properties of Reduced Reversible Markov Chains (2008)
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    Publikationsdatum: 2016-06-09
    Beschreibung: The enormous time lag between fast atomic motion and complex pro- tein folding events makes it almost impossible to compute molecular dy- namics on a high resolution. A common way to tackle this problem is to model the system dynamics as a Markov process. Yet for large molec- ular systems the resulting Markov chains can hardly be handled due to the curse of dimensionality. Coarse graining methods can be used to re- duce the dimension of a Markov chain, but it is still unclear how far the coarse grained Markov chain resembles the original system. In order to answer this question, two different coarse-graining methods were analysed and compared: a classical set-based reduction method and an alternative subspace-based approach, which is based on membership vectors instead of sets. On the basis of a small toy system, it could be shown, that in con- trast to the subset-based approach, the subspace-based reduction method preserves the Markov property as well as the essential dynamics of the original system.
    Schlagwort(e): ddc:510
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    Line Planning on Paths and Tree Networks with Applications to the Quito Trolebus System (2008)
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    Publikationsdatum: 2021-02-19
    Beschreibung: Line planning is an important step in the strategic planning process of a public transportation system. In this paper, we discuss an optimization model for this problem in order to minimize operation costs while guaranteeing a certain level of quality of service, in terms of available transport capacity. We analyze the problem for path and tree network topologies as well as several categories of line operation that are important for the Quito Trolebus system. It turns out that, from a computational complexity worst case point of view, the problem is hard in all but the most simple variants. In practice, however, instances based on real data from the Trolebus System in Quito can be solved quite well, and significant optimization potentials can be demonstrated.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 48
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    On the optimality of Least Recently Used (2008)
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    Publikationsdatum: 2020-08-05
    Beschreibung: It is well known that competitive analysis yields too pessimistic results when applied to the paging problem and it also cannot make a distinction between many paging strategies. Many deterministic paging algorithms achieve the same competitive ratio, ranging from inefficient strategies as flush-when-full to the good performing least-recently-used (LRU). In this paper, we study this fundamental online problem from the viewpoint of stochastic dominance. We show that when sequences are drawn from distributions modelling locality of reference, LRU is stochastically better than any other online paging algorithm.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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    Angebotsplanung im öffentlichen Nahverkehr (2008)
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    Publikationsdatum: 2020-12-15
    Beschreibung: Die Angebotsplanung im öffentlichen Nahverkehr umfasst die Aufgaben der Netz-, Linien-,Fahr- und Preisplanung. Wir stellen zwei mathematische Optimierungsmodelle zur Linien- und Preisplanung vor. Wir zeigen anhand von Berechnungen für die Verkehrsbetriebe in Potsdam(ViP), dass sich damit komplexe Zusammenhänge quantitativ analysieren lassen. Auf diese Weise untersuchen wir die Auswirkungen von Freiheitsgraden auf die Konstruktion von Linien und die Wahl von Reisewegen der Passagiere, Abhängigkeiten zwischen Kosten und Reisezeiten sowie den Einfluss verschiedener Preissysteme auf Nachfrage und Kostendeckung.
    Schlagwort(e): ddc:510
    Sprache: Deutsch
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    Constraint Integer Programming: a New Approach to Integrate CP and MIP (2008)
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    Publikationsdatum: 2022-03-14
    Beschreibung: This article introduces constraint integer programming (CIP), which is a novel way to combine constraint programming (CP) and mixed integer programming (MIP) methodologies. CIP is a generalization of MIP that supports the notion of general constraints as in CP. This approach is supported by the CIP framework SCIP, which also integrates techniques from SAT solving. SCIP is available in source code and free for non-commercial use. We demonstrate the usefulness of CIP on two tasks. First, we apply the constraint integer programming approach to pure mixed integer programs. Computational experiments show that SCIP is almost competitive to current state-of-the-art commercial MIP solvers. Second, we employ the CIP framework to solve chip design verification problems, which involve some highly non-linear constraint types that are very hard to handle by pure MIP solvers. The CIP approach is very effective here: it can apply the full sophisticated MIP machinery to the linear part of the problem, while dealing with the non-linear constraints by employing constraint programming techniques.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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    An Extended Mathematical Framework for Barrier Methods in Function Space (2008)
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    Publikationsdatum: 2016-06-09
    Beschreibung: An extended mathematical framework for barrier methods for state constrained optimal control compared to [Schiela, ZIB-Report 07-07] is considered. This allows to apply the results derived there to more general classes of optimal control problems, in particular to boundary control and finite dimensional control.
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    Counting solutions of integer programs using unrestricted subtree detection (2008)
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    Publikationsdatum: 2021-08-05
    Beschreibung: In the recent years there has been tremendous progress in the development of algorithms to find optimal solutions for integer programs. In many applications it is, however, desirable (or even necessary) to generate all feasible solutions. Examples arise in the areas of hardware and software verification and discrete geometry. In this paper, we investigate how to extend branch-and-cut integer programming frameworks to support the generation of all solutions. We propose a method to detect so-called unrestricted subtrees, which allows us to prune the integer program search tree and to collect several solutions simultaneously. We present computational results of this branch-and-count paradigm which show the potential of the unrestricted subtree detection.
    Schlagwort(e): ddc:510
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    On the cardinality constrained matroid polytope (2008)
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    Publikationsdatum: 2020-08-05
    Beschreibung: Edmonds showed that the so-called rank inequalities and the nonnegativity constraints provide a complete linear description of the matroid polytope. By essentially adding Grötschel's cardinality forcing inequalities, we obtain a complete linear description of the cardinality constrained matroid polytope which is the convex hull of the incidence vectors of those independent sets that have a feasible cardinality. Moreover, we show how the separation problem for the cardinality forcing inequalities can be reduced to that for the rank inequalities. We also give necessary and sufficient conditions for a cardinality forcing inequality to be facet defining.
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    On solving large systems of polynomial equations appearing in Discrete Differential Geometry (2008)
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    Publikationsdatum: 2020-08-05
    Beschreibung: The paper describes a method for solution of very large overdetermined algebraic polynomial systems on an example that appears from a classification of all integrable 3-dimensional scalar discrete quasilinear equations $Q_3=0$ on an elementary cubic cell of the lattice ${\mathbb Z}^3$. The overdetermined polynomial algebraic system that has to be solved is far too large to be formulated. A probing' technique which replaces independent variables by random integers or zero allows to formulate subsets of this system. An automatic alteration of equation formulating steps and equation solving steps leads to an iteration process that solves the computational problem.
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    Sprache: Englisch
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    Invertible Mappings of Nonlinear PDEs to Linear PDEs Through Admitted Conservation Laws (2008)
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    Publikationsdatum: 2020-08-05
    Beschreibung: An algorithmic method using conservation law multipliers is introduced that yields necessary and sufficient conditions to find invertible mappings of a given nonlinear PDE to some linear PDE and to construct such a mapping when it exists. Previous methods yielded such conditions from admitted point or contact symmetries of the nonlinear PDE. Through examples, these two linearization approaches are contrasted.
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    Classification of 3-dimensional integrable scalar discrete equations (2008)
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    Publikationsdatum: 2021-02-26
    Beschreibung: We classify all integrable 3-dimensional scalar discrete affine linear equations $Q_3=0$ on an elementary cubic cell of the lattice ${\mathbb Z}^3$. An equation $Q_3=0$ %of such form is called integrable if it may be consistently imposed on all $3$-dimensional elementary faces of the lattice ${\mathbb Z}^4$. Under the natural requirement of invariance of the equation under the action of the complete group of symmetries of the cube we prove that the only ontrivial(non-linearizable) integrable equation from this class is the well-known dBKP-system.
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    About a Computer Algebra based online Mathtest (2008)
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    Publikationsdatum: 2020-12-11
    Beschreibung: The article describes the online mathematics test {\tt http://lie.math.brocku.ca/mathtest}, its typical applications and experiences gathered.
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    TTPLIB 2008 - A Library for Train Timetabling Problems (2008)
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    Publikationsdatum: 2020-08-05
    Beschreibung: We introduce (TTPlib), a data library for train timetabling problems that can be accessed at http://ttplib.zib.de. In version 1.0, the library contains data related to 50 scenarios. Most instances result from the combination of macroscopic railway networks and several train request sets for the German long distance area containing Hannover, Kassel and Fulda, short denoted by Ha-Ka-Fu. In this paper, we introduce the data concepts of TTPlib, describe the scenarios included in the library and provide a free visualization tool TraVis.
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    The Parametric Solution of Underdetermined linear ODEs (2008)
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    Publikationsdatum: 2020-08-05
    Beschreibung: The purpose of this paper is twofold. An immediate practical use of the presented algorithm is its applicability to the parametric solution of underdetermined linear ordinary differential equations (ODEs) with coefficients that are arbitrary analytic functions in the independent variable. A second conceptual aim is to present an algorithm that is in some sense dual to the fundamental Euclids algorithm, and thus an alternative to the special case of a Gr\"{o}bner basis algorithm as it is used for solving linear ODE-systems. In the paper Euclids algorithm and the new dual version' are compared and their complementary strengths are analysed on the task of solving underdetermined ODEs. An implementation of the described algorithm is interactively accessible at http://lie.math.brocku.ca/crack/uode.
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    Probabilistic analysis of Online Bin Coloring algorithms via Stochastic Comparison (2008)
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    Publikationsdatum: 2020-08-05
    Beschreibung: This paper proposes a new method for probabilistic analysis of online algorithms that is based on the notion of stochastic dominance. We develop the method for the Online Bin Coloring problem introduced by Krumke et al. Using methods for the stochastic comparison of Markov chains we establish the strong result that the performance of the online algorithm GreedyFit is stochastically dominated by the performance of the algorithm OneBin for any number of items processed. This result gives a more realistic picture than competitive analysis and explains the behavior observed in simulations.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 61
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    Models for Fare Planning in Public Transport (2008)
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    Publikationsdatum: 2020-12-15
    Beschreibung: The optimization of fare systems in public transit allows to pursue objectives such as the maximization of demand, revenue, profit, or social welfare. We propose a non-linear optimization approach to fare planning that is based on a detailed discrete choice model of user behavior. The approach allows to analyze different fare structures, optimization objectives, and operational scenarios involving, e.g., subsidies. We use the resulting models to compute optimized fare systems for the city of Potsdam, Germany.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 62
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    Solving Pseudo-Boolean Problems with SCIP (2008)
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    Publikationsdatum: 2022-03-14
    Beschreibung: Pseudo-Boolean problems generalize SAT problems by allowing linear constraints and a linear objective function. Different solvers, mainly having their roots in the SAT domain, have been proposed and compared,for instance, in Pseudo-Boolean evaluations. One can also formulate Pseudo-Boolean models as integer programming models. That is,Pseudo-Boolean problems lie on the border between the SAT domain and the integer programming field. In this paper, we approach Pseudo-Boolean problems from the integer programming side. We introduce the framework SCIP that implements constraint integer programming techniques. It integrates methods from constraint programming, integer programming, and SAT-solving: the solution of linear programming relaxations, propagation of linear as well as nonlinear constraints, and conflict analysis. We argue that this approach is suitable for Pseudo-Boolean instances containing general linear constraints, while it is less efficient for pure SAT problems. We present extensive computational experiments on the test set used for the Pseudo-Boolean evaluation 2007. We show that our approach is very efficient for optimization instances and competitive for feasibility problems. For the nonlinear parts, we also investigate the influence of linear programming relaxations and propagation methods on the performance. It turns out that both techniques are helpful for obtaining an efficient solution method.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 63
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    Planung von öffentlichem Personenverkehr (2008)
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    Publikationsdatum: 2020-08-05
    Beschreibung: Millionen von Menschen werden allein in Deutschland täglich von Bussen, Bahnen und Flugzeugen transportiert. Der öffentliche Personenverkehr (ÖV) ist von großer Bedeutung für die Lebensqualität einzelner aber auch für die Leistungsfähigkeit ganzer Regionen. Qualität und Effizienz von ÖV-Systemen hängen ab von politischen Rahmenbedingungen (staatlich geplant, wettbewerblich organisiert) und der Eignung der Infrastruktur (Schienensysteme, Flughafenstandorte), vom vorhandenen Verkehrsangebot (Fahr- und Flugplan), von der Verwendung angemessener Technologien (Informations-, Kontroll- und Buchungssysteme) und dem bestmöglichen Einsatz der Betriebsmittel (Energie, Fahrzeuge und Personal). Die hierbei auftretenden Entscheidungs-, Planungs- und Optimierungsprobleme sind z.T. gigantisch und "schreien" aufgrund ihrer hohen Komplexität nach Unterstützung durch Mathematik. Dieser Artikel skizziert den Stand und die Bedeutung des Einsatzes von Mathematik bei der Planung und Durchführung von öffentlichem Personenverkehr, beschreibt die bestehenden Herausforderungen und regt zukunftsweisende Maßnahmen an.
    Schlagwort(e): ddc:510
    Sprache: Deutsch
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  • 64
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    Development and test of a numerical model for pulse thermography in civil engineering (2008)
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    Publikationsdatum: 2019-05-10
    Beschreibung: Pulse thermography of concrete structures is used in civil engineering for detecting voids, honeycombing and delamination. The physical situation is readily modeled by Fourier's law. Despite the simplicity of the PDE structure, quantitatively realistic numerical 3D simulation faces two major obstacles. First, the short heating pulse induces a thin boundary layer at the heated surface which encapsulates all information and therefore has to be resolved faithfully. Even with adaptive mesh refinement techniques, obtaining useful accuracies requires an unsatisfactorily fine discretization. Second, bulk material parameters and boundary conditions are barely known exactly. We address both issues by a semi-analytic reformulation of the heat transport problem and by parameter identification. Numerical results are compared with measurements of test specimens.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 65
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    Barrier Methods for Optimal Control Problems with Convex Nonlinear Gradient Constraints (2008)
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    Publikationsdatum: 2016-06-09
    Beschreibung: In this paper we are concerned with the application of interior point methods in function space to gradient constrained optimal control problems, governed by partial differential equations. We will derive existence of solutions together with first order optimality conditions. Afterwards we show continuity of the central path, together with convergence rates depending on the interior point parameter.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 66
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    Interior Point Methods in Function Space for State Constraints - Inexact Newton and Adaptivity (2008)
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    Publikationsdatum: 2016-06-09
    Beschreibung: We consider an interior point method in function space for PDE constrained optimal control problems with state constraints. Our emphasis is on the construction and analysis of an algorithm that integrates a Newton path-following method with adaptive grid refinement. This is done in the framework of inexact Newton methods in function space, where the discretization error of each Newton step is controlled by adaptive grid refinement in the innermost loop. This allows to perform most of the required Newton steps on coarse grids, such that the overall computational time is dominated by the last few steps. For this purpose we propose an a-posteriori error estimator for a problem suited norm.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 67
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    Fair Ticket Prices in Public Transport (2008)
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    Publikationsdatum: 2020-08-05
    Beschreibung: Ticket pricing in public transport usually takes a welfare or mnemonics maximization point of view. These approaches do not consider fairness in the sense that users of a shared infrastructure should pay for the costs that they generate. We propose an ansatz to determine fair ticket prices that combines concepts from cooperative game theory and integer programming. An application to pricing railway tickets for the intercity network of the Netherlands demonstrates that, in this sense, prices that are much fairer than standard ones can be computed in this way.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 68
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    A sharp interface finite volume method for elliptic equations on Cartesian grids (2008)
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    Publikationsdatum: 2014-02-26
    Beschreibung: We present a second order sharp interface finite volume method for the solution of the three-dimensional poisson equation with variable coefficients on Cartesian grids. In particular, we focus on interface problems with discontinuities in the coefficient, the source term, the solution, and the fluxes across the interface. The method uses standard piecewiese trilinear finite elements for normal cells and a double piecewise trilinear ansatz for the solution on cells intersected by the interface resulting always in a compact 27-point stencil. Singularities associated with vanishing partial volumes of intersected grid cells are removed by a two-term asymptotic approach. In contrast to the 2D method presented by two of the authors in [M.~Oevermann, R.~Klein: A Cartesian grid finite volume method for elliptic equations with variable coefficients and embedded interfaces, J.~Comp.~Phys.~219 (2006)] we use a minimization technique to determine the unknown coefficients of the double trilinear ansatz. This simplifies the treatment of the different cut-cell types and avoids additional special operations for degenerated interface topologies. The resulting set of linear equations has been solved with a BiCGSTAB solver preconditioned with an algebraic multigrid. In various testcases -- including large coefficient ratios and non-smooth interfaces -- the method achieves second order of accuracy in the L_inf and L_2 norm.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 69
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    Cardinality Constrained Combinatorial Optimization: Complexity and Polyhedra (2008)
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    Publikationsdatum: 2020-08-05
    Beschreibung: Given a combinatorial optimization problem and a subset $N$ of natural numbers, we obtain a cardinality constrained version of this problem by permitting only those feasible solutions whose cardinalities are elements of $N$. In this paper we briefly touch on questions that addresses common grounds and differences of the complexity of a combinatorial optimization problem and its cardinality constrained version. Afterwards we focus on polytopes associated with cardinality constrained combinatorial optimization problems. Given an integer programming formulation for a combinatorial optimization problem, by essentially adding Grötschel's cardinality forcing inequalities, we obtain an integer programming formulation for its cardinality restricted version. Since the cardinality forcing inequalities in their original form are mostly not facet defining for the associated polyhedra, we discuss possibilities to strengthen them.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 70
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    On the complexity of column generation in survivable network design with path-based survivability mechanisms (2008)
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    Publikationsdatum: 2020-08-05
    Beschreibung: This survey concerns optimization problems arising in the design of survivable communication networks. It turns out that such problems can be modeled in a natural way as non-compact linear programming formulations based on multicommodity flow network models. These non-compact formulations involve an exponential number of path flow variables, and therefore require column generation to be solved to optimality. We consider several path-based survivability mechanisms and present results, both known and new, on the complexity of the corresponding column generation problems (called the pricing problems). We discuss results for the case of the single link (or node) failures scenarios, and extend the considerations to multiple link failures. Further, we classify the design problems corresponding to different survivability mechanisms according to the structure of their pricing problem. Finally, we show that almost all encountered pricing problems are hard to solve for scenarios admitting multiple failures.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 71
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    On the Line Planning Problem in Tree Networks (2008)
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    Publikationsdatum: 2021-02-19
    Beschreibung: We introduce an optimization model for the line planning problem in a public transportation system that aims at minimizing operational costs while ensuring a given level of quality of service in terms of available transport capacity. We discuss the computational complexity of the model for tree network topologies and line structures that arise in a real-world application at the Trolebus Integrated System in Quito. Computational results for this system are reported.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 72
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    Line Planning on Paths and Tree Networks with Applications to the Quito Trolebus System (Extended Abstract) (2008)
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    Publikationsdatum: 2021-02-19
    Beschreibung: Line planning is an important step in the strategic planning process of a public transportation system. In this paper, we discuss an optimization model for this problem in order to minimize operation costs while guaranteeing a certain level of quality of service, in terms of available transport capacity. We analyze the problem for path and tree network topologies as well as several categories of line operation that are important for the Quito Trolebus system. It turns out that, from a computational complexity worst case point of view, the problem is hard in all but the most simple variants. In practice, however, instances based on real data from the Trolebus System in Quito can be solved quite well, and significant optimization potentials can be demonstrated.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 73
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    Meshless Methods in Confirmation Dynamics (2006)
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    Publikationsdatum: 2016-06-09
    Schlagwort(e): ddc:510
    Sprache: Englisch
    Materialart: doctoralthesis , doc-type:doctoralThesis
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  • 74
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    Kombinatorische Optimierung –Inhalte und Methoden für einen authentischen Mathematikunterricht (2006)
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    Publikationsdatum: 2020-08-05
    Beschreibung: wird nachgereicht
    Schlagwort(e): ddc:510
    Sprache: Englisch
    Materialart: doctoralthesis , doc-type:doctoralThesis
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  • 75
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    Digitale Medien
    Incremental modification of styrene-butadiene rubber with tert-dodecyl mercaptan (1961)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 5 (1961), S. 116-123 
    Details
    ISSN: 0021-8995
    Schlagwort(e): Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Maschinenbau , Physik
    Notizen: The molecular weights and molecular weight distribution of a styrene-butadiene rubber produced at 5°C. according to an incrementally modified recipe with tert-dodecyl mercaptan modifier, do not differ significantly from those of similar conventionally modified rubbers. The limiting effect of diffusion upon the mass transfer of mercaptan in the system provides a consistent explanation of this finding.
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/app.1961.070051318
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  • 76
    Digitale Medien
    Digitale Medien
    Glass transitions in polymers (1961)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 5 (1961), S. S1 
    Details
    ISSN: 0021-8995
    Schlagwort(e): Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Maschinenbau , Physik
    Zusätzliches Material: 1 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/app.1961.070051319
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  • 77
    Digitale Medien
    Digitale Medien
    Polymer news (1961)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 5 (1961), S. S4 
    Details
    ISSN: 0021-8995
    Schlagwort(e): Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Maschinenbau , Physik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/app.1961.070051321
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  • 78
    Digitale Medien
    Digitale Medien
    Use of the HLB system in selecting emulsifiers for emulsion polymerization (1961)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 5 (1961), S. 135-148 
    Details
    ISSN: 0021-8995
    Schlagwort(e): Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Maschinenbau , Physik
    Notizen: In the present work a wide variety of nonionic emulsifiers and anionic/nonionic blends of emulsifiers were evaluated in the emulsion polymerization of vinyl acetate and styrene. It was found that the emulsion stability and other polymer emulsion properties are often dependent upon a certain property of the emulsifier known as the HLB value. It has been shown elsewhere that the HLB value can be correlated with a fundamental physical property of the system oil-water-emulsifier, namely, the spreading coefficient of the internal phase liquid on the surface of a 1% solution of the emulsifier in the external phase. In the emulsion polymerization of styrene, good emulsion stability coupled with adequate conversion rate was obtained in an emulsifier HLB range of 13 to 16. For certain emulsifier blends it was found that emulsion viscosity and emulsion particle size were strongly dependent on the HLB of the emulsifier. Similar comments apply to vinyl acetate polymerization, except that the most stable emulsions were obtained with emulsifiers in an HLB range from 14.5 to 17.5. These observations on preferred HLB range apply only to nonionic emulsifiers and anionic/nonionic emulsifier blends, which were the emulsifier types screened in the present investigation. For both styrene and vinyl acetate the most generally satisfactory emulsion properties were obtained in the present work by the use of an anionic/nonionic emulsifier blend (G-3300/G-3920).
    Zusätzliches Material: 13 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/app.1961.070051402
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  • 79
    Digitale Medien
    Digitale Medien
    Influence of the initiator on the grafting of polyvinyl polymers (1961)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 5 (1961), S. 149-152 
    Details
    ISSN: 0021-8995
    Schlagwort(e): Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Maschinenbau , Physik
    Notizen: The dependence of grafting on the type of initiator has been examined in the case of three polymer-monomer systems: polystyrene-methyl methacrylate, polymethyl methacrylate-vinyl acetate, and polyethyl α-chloroacrylate-vinyl acetate. The different initiators used in these experiments were benzoyl peroxide (Bz2O2), azobisisobutyronitrile (AIBN), di-tert-butyl peroxide (DTBP), and tert-butyl hydroperoxide (TBHP). In each case the graft copolymers were separated from the homopolymers by fractional precipitation or by extraction. In the case of the system polystyrene-methyl methacrylate, an appreciable degree of grafting as well as formation of graft copolymer occur in the presence of Bz2O2; in contrast, the grafting is low with DTBP and doubtful with AIBN. For the other two systems no noticeable differences occurred as function of the initiator. In the case of polyethyl α-chloroacrylate the amount of graft copolymer is exceptionally high owing to the sensitivity of this polymer to a radical attack; this sensitivity results in the partial insolubility of the graft copolymers in the presence of TBHP and DTBP, but not in the presence of AIBN.
    Zusätzliches Material: 1 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/app.1961.070051403
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  • 80
    Digitale Medien
    Digitale Medien
    A new synthetic elastomer based on a chlorophosphonated polyolefin (1961)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 5 (1961), S. 157-162 
    Details
    ISSN: 0021-8995
    Schlagwort(e): Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Maschinenbau , Physik
    Notizen: A new synthetic elastomer has been obtained based on an ethylene-propylene copolymer prepared using an organometallic catalyst system. Reactive sites (phosphonyl dichloride groups) are placed on the copolymer chain by treating the polymer with phosphorus trichloride and oxygen. After hydrolysis or alcoholysis of the phosphonyl dichloride groups to phosphonic acid or phosphonic acid esters, vulcanization may be carried out by reaction with metallic oxides, particularly lead oxide. Vulcanizates of the polyolefin elastomer have outstanding resistance to heat, ozone, and oxygen, and have excellent electrical properties. This combination suggests the use of this material in high temperature electrical applications.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/app.1961.070051405
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  • 81
    Digitale Medien
    Digitale Medien
    Changes in fine structure and mechanical properties induced by cyanoethylation of cotton yarns. II. Reacted without longitudinal shrinkagePaper presented before the 138th Meeting of the American Chemical Society, New York, September 11-16, 1960. (1961)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 5 (1961), S. 163-170 
    Details
    ISSN: 0021-8995
    Schlagwort(e): Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Maschinenbau , Physik
    Notizen: The cellulose of cotton yarns was reacted with acrylonitrile under conditions preventing their longitudinal contraction. Changes taking place in the fine structure of the fiber were studied by means of optical microscopy, density measurements, x-ray diffraction, and thermal stress behavior measurements. The results indicate that in spite of the strong tensions developed in the yarns, the reaction proceeds in both the accessible and the crystalline regions with considerable volume expansion and eventual disappearance of crystalline structure. Suggestions of a glass transition temperature appear at substitutions slightly above D.S. = 1. Annealing becomes possible at substitutions above D.S. = 2 with the development of the cyanoethyl cellulose crystal structure and over 40% increase in tensile strength. Changes in tenacity, ultimate elongation, energy of rupture, and immediate elastic recovery were also observed.
    Zusätzliches Material: 6 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/app.1961.070051406
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  • 82
    Digitale Medien
    Digitale Medien
    Poly(4-methyl-1-pentene) and some soluble crystalline copolymers (1961)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 5 (1961), S. 184-190 
    Details
    ISSN: 0021-8995
    Schlagwort(e): Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Maschinenbau , Physik
    Notizen: Poly(4-methyl-1-pentene) has been prepared by polymerizing the monomer over a catalyst made from titanium tetrachloride and lithium aluminum tetradecyl. The molecular weight of the crystalline polymer was invariably too high for fiber preparation, even when polymerization variables were varied drastically, so a technique for thermal cracking was developed. By heating grease-free, crystalline poly(4-methyl-1-pentene) in a vacuum at about 280°, it was possible to lower smoothly the molecular weight of the polymer to any desired value, without undesirable crosslinking or by-product formation. The polymer was melt-spun by conventional techniques to highly oriented, tough fibers. Copolymerization of 10-25% 1-hexene and other linear 1-olefins with 4-methyl-1-pentene gives products which are still high-melting, but which are readily soluble in such solvents as cyclohexane or chloroform, in contrast to the homopolymer which is only slightly soluble. Polymerization in solvents for the copolymer gave solutions which were converted to fibers and film without intermediate isolation of polymer or removal of the catalyst. An interesting terpolymer in which divinylbenzene was the third component was found to be initially soluble, but was readily crosslinked at elevated temperature.
    Zusätzliches Material: 2 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/app.1961.070051409
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  • 83
    Digitale Medien
    Digitale Medien
    Structural characterization of vulcanizates. Part II. Use of triphenylphosphine to determine the structures of sulfur linkages in unaccelerated natural rubber-sulfur vulcanizate networks (1961)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 5 (1961), S. 299-302 
    Details
    ISSN: 0021-8995
    Schlagwort(e): Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Maschinenbau , Physik
    Notizen: Treatment of unaccelerated natural rubber-sulfur vulcanizate networks with triphenylphosphine in benzene at 80°C. effects the removal of part of the combined sulfur, the proportion removed decreasing with increasing cure time. This partial desulfurization of the network is attributed, on the basis of the mode of interaction of simple organic di- and polysulfides with triphenylphosphine, to the conversion of polysulfide linkages in the network into either mono- or disulfide groups. Knowledge of the amount of sulfur removed by the reagent, and of the chemical degree of crosslinking and combined sulfur content of the untreated networks permits the following semiquantitative conclusions to be reached concerning the structures of the sulfur linkages in the networks: (1) long polysulfidic crosslinks (—S11— to —S12—) are initially formed, which on continued cure progressively decrease in length to a limiting value of —S2— to —S4—; and (2) a very high proportion to the combined sulfur (ca. 77% for short cure times, increasing to ca. 95% on extended cure) is present in cyclic monosulfide groups situated along the polyisoprene chains.
    Zusätzliches Material: 2 Tab.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/app.1961.070051508
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  • 84
    Digitale Medien
    Digitale Medien
    The relationship between glass temperature, molar cohesion, and polymer structurePresented before the Division of Polymer Chemistry at the 138th meeting of the American Chemical Society, New York, September 1960. (1961)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 5 (1961), S. 318-321 
    Details
    ISSN: 0021-8995
    Schlagwort(e): Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Maschinenbau , Physik
    Notizen: An empirical equation relating glass temperature, molar cohesion, and polymer structure has been developed from data found in the literature. A fairly extensive list of group cohesion values has been obtained from this relationship and glass temperatures which are in good agreement with reported values have been calculated. The equation is $$ H_c = 0.5nRT_g - 25n $$ where Hc is the molar cohesion and n is an empirical number obtained from the polymer structure.
    Zusätzliches Material: 1 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/app.1961.070051511
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  • 85
    Digitale Medien
    Digitale Medien
    Isobutylene copolymers of vinylbenzyl chloride and isopropenylbenzyl chloride (1961)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 5 (1961), S. 452-459 
    Details
    ISSN: 0021-8995
    Schlagwort(e): Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Maschinenbau , Physik
    Notizen: The styrene derivatives vinylbenzyl chloride and isopropenylbenzyl chloride were prepared and copolymerized with isobutylene and propylene in order to produce polymers with reactive halogens. Vinylbenzyl chloride and isobutylene have relative reactivities such that the copolymer is much richer in isobutylene than the starting mixture, while with isopropenylbenzyl chloride and isobutylene the difference in reactivities is less and is in the opposite direction. Copolymers containing small amounts of the reactive benzylic chlorine were vulcanized, either with amines or with a conventional butyl rubber cure. Permselective membranes were prepared from copolymers rich in benzylic chlorine.
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/app.1961.070051611
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  • 86
    Digitale Medien
    Digitale Medien
    The mechanism of post cure of viton ARegistered trademark of E. I. du Pont de Nemours & Co., Inc. Fluorocarbon elastomerBased on a lecture delivered at the 2nd International Synthetic Rubber Symposium, London, October 1960, by arrangement with Rubber and Plastics World. (1961)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 5 (1961), S. 460-467 
    Details
    ISSN: 0021-8995
    Schlagwort(e): Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Maschinenbau , Physik
    Notizen: The necessity for oven post-curing Viton A vulcanizates is explained in the following way: The formation of crosslinks is accompanied by the elimination of HF from the polymer. In the subsequent reaction of HF with the magnesium oxide present as acid acceptor water is formed which acts to inhibit the full development of cure unless it is removed from the vicinity of the polymer by post-curing in an open system. Measurement of the rate of elimination of water from the polymer serves as a method of following the development of crosslinking during cure. Approximately two moles of water, derived from four moles of hydrogen fluoride, are associated with the use of one mole of diamine curing agent. This ratio is confirmed by independent estimates of the relationship of crosslinking density to curing agent level based on measurements of swollen compression moduli.
    Zusätzliches Material: 11 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/app.1961.070051612
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  • 87
    Digitale Medien
    Digitale Medien
    Room temperature sulfur and nonsulfur vulcanization of natural rubber: With sulfur and piperidinium n-pentamethylenedithiocarbamate and with quinone dioxime (GMF) and yellow mercuric oxide (1961)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 5 (1961), S. 349-353 
    Details
    ISSN: 0021-8995
    Schlagwort(e): Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Maschinenbau , Physik
    Notizen: Calendered sheets of pale crepe rubber containing an ultra-accelerator, piperidinium N-pentamethylenedithiocarbamate, and zinc oxide were embedded in powdered sulfur and kept at room temperature. Tensile strengths up to 294.2 kg./cm.2 (4185 psi) and elongations up to 530% were attained; the combined sulfur in 115 weeks was 3.60%. Calendered pale crepe rubber containing 10 parts of yellow mercuric oxide to 100 parts of rubber allowed to stand covered with quinone dioxime (GMF) powder at room temperature slowly vulcanizes, reaching a tensile strength of 53.1 kg./cm.2 (754 psi) in 405 days, and retaining this condition for at least twice this same period of time. The elongation reached 740%, and the set was 0.16. The tensile strength obtained is almost as high as that obtained in a press cure with quinone dioxime alone. The untreated sample containing yellow mercuric oxide alone showed a tensile strength of only 5.3 kg./cm.2 (75 psi). Calendered pale crepe with no mercuric oxide set in quinone dioxime and calendered pale crepe containing 2 parts of quinone dioxime, when allowed to stand at room temperature, showed no signs of vulcanization.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/app.1961.070051515
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  • 88
    Digitale Medien
    Digitale Medien
    Uniformity of substitution during the emulsion xanthation of celluloseA portion of a thesis submitted in partial fulfillment of the requirements of The Institute of Paper Chemistry for the degree of Doctor of Philosophy from Lawrence College, Appleton, Wis., June, 1960. This work was carried out under the direction of Kyle Ward, Jr. (1961)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 5 (1961), S. 364-369 
    Details
    ISSN: 0021-8995
    Schlagwort(e): Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Maschinenbau , Physik
    Notizen: Viscose-grade cotton linters (DPw = 1135) were converted to viscose by the emulsion xanthation technique. Two variables - namely, substitution level and xanthation time - were considered insofar as their influence on the uniformity of substitution with regard to chain length was concerned. The stable diethylacetamide derivatives were prepared by reaction with diethylchloroacetamide and fractionally precipitated from aqueous 2-chloroethanol. The DPw and degree of substitution (DS) of the individual fractions were determined. The results in each case indicated that the longer chains were more highly substituted than the shorter chains. For a constant xanthation time (6 hr.), uniformity in substitution improved with increasing substitution level. For a constant CS2:cellulose ratio (1.48), uniformity increased with xanthation time. A mechanism is suggested which accounts for these phenomena.
    Zusätzliches Material: 2 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/app.1961.070051517
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  • 89
    Digitale Medien
    Digitale Medien
    A comparison of the thermal gradient and elution methods of polymer fractionation (1961)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 5 (1961), S. 354-363 
    Details
    ISSN: 0021-8995
    Schlagwort(e): Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Maschinenbau , Physik
    Notizen: The elution method is essentially a single-stage process, whereas the thermal gradient method is a multistage process which depends upon a thermal gradient to bring about reprecipitation of polymer in the fractions. As a test of the effectiveness of the thermal gradient, comparisons have been made of fractionation by these two column methods on high molecular weight polystyrene samples. It was found that the thermal gradient method definitely provides superior resolution and reproducibility, as expected. However, the degree of fractionation obtained by the elution method was surprising, accounting for at least 80% of the sample under the usual conditions and giving complete fractionation with certain modifications of conditions. These results indicate the difference in performance of the two methods is less than expected from an elementary consideration of the operation of the columns, and fractionation by the elution method, as conducted here, exceeds that expected for a single-stage extraction process. Although the reasons for the observed behavior are not clear, the following conclusions have been reached about certain factors which influence fractionation. Alternative methods of controlling the concentration of polymer in the fractions give almost equivalent results but enhanced resolution of the high molecular weight portion of the sample is obtained with extended solvent gradients. The inhibitor, tert-butyl catechol, which it was necessary to add to the solvents to limit degradation of the very high molecular weight sample, plays a specific role in the fractionation due to a reaction with the polystyrene which alters the fractionation behavior without affecting the molecular weight. Also, trace amounts of chemical heterogeneity in the polymers, presumably hydroxyl groups, have a marked adverse effect on fractionation by the elution method and probably account for molecular weight reversals observed in some fractionations by the thermal gradient method. It is suggested that adsorption on the surface of the beads is responsiblp for the adverse effect of chemical heterogeneity on the fractionation and that possibly an adsorption which increases with molecular weight contributes to fractionation by the elution and thermal gradient methods.
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/app.1961.070051516
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  • 90
    Digitale Medien
    Digitale Medien
    Effects of by-products, trace components, and similar compounds in viscose on ripening (1961)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 5 (1961), S. 375-383 
    Details
    ISSN: 0021-8995
    Schlagwort(e): Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Maschinenbau , Physik
    Notizen: The effects on viscose ripening of a variety of materials are reported. (1) Normal constituents (Na2CO3, Na2CS3, NaCl) appeared not to affect ripening; however, Na2S retarded ripening. By-product removal appeared to retard ripening. (2) Oxidizing agents (H2O2, Na2Sx) accelerated ripening; reducing agent (Na2SO3) retarded ripening; this is suggestive of possible addition product formation. (3) Na2SO4, (CH3)2SO, KClO3, Na2BH4 showed no effect on ripening. (4) Salts which precipitated as hydroxides or carbonates did not appear to affect ripening. (5) Salts which formed insoluble sulfides resulted in an initial increase in ripening rates. In later stages, ripening proceeded normally, probably after the salts were removed from solution as insoluble sulfides. (6) FeCl3, BiCl3 and Na3AsO3 appeared to retard ripening. (7) A comparison of the effect on ripening of the trivalent state of elements in group V of the periodic table showed that the rate of ripening decreased with the oxidation potential of the element. (8) The addition of sodium zincate retarded ripening and suggested possible cross-linking of xanthate and by-product sulfur, or of two xanthate groups. (9) Addition of tin and chromium salts at the 0.5% level resulted in gelation of the viscose within 30 min. after the addition.
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/app.1961.070051601
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  • 91
    Digitale Medien
    Digitale Medien
    Radiation crosslinking of vinyl chloride-vinyl stearate copolymer (1961)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 5 (1961), S. 388-396 
    Details
    ISSN: 0021-8995
    Schlagwort(e): Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Maschinenbau , Physik
    Notizen: The crosslinking of internally plasticized polyvinyl chloride-stearate copolymer by irradiation with high-energy electrons was studied. Based on gel yields and swelling as a measure of relative crosslinking, the effect of added tetra-functional monomers, and of carbon black and silica fillers are discussed. Crosslinking by dicumyl peroxide a t 170°C. even in the presence of a stabilizer, causes concurrent decomposition (dehydrochlorination) which is avoided in the radiation-crosslinking process. The heat stability of the copolymer is not impaired by radiation crosslinking under the proper conditions. Results of tensile measurements a t 25 and 150°C. are given for the radiation-crosslinked copolymer with and without filler reinforcement.
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/app.1961.070051603
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  • 92
    Digitale Medien
    Digitale Medien
    Studies on the γ-irradiation of natural rubber latex. The effects of organic halogen compounds on crosslinking by γ-irradiation (1961)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 5 (1961), S. 401-407 
    Details
    ISSN: 0021-8995
    Schlagwort(e): Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Maschinenbau , Physik
    Notizen: As the accelerating effect of water in the crosslinking reaction of rubber in natural latex by γ-irradiation was assumed to stem from the decomposition of water into radicals by γ-irradiation, more effective reagents were sought among the organic halides which have greater G values for radical formation by γ-irradiation and, simultaneously, an affinity for rubber greater than that of water. 1,2-Dichloroethane, chloroform, carbon tetrachloride, and benzene (for comparison) were tested, and these compounds, except for benzene, were found to accelerate the reaction in proportion to their G values for radical formation. Benzene was found to have no effect, in concentrations between 1 and 5 phr. The optimum dosage was decreased to 2.1 × 106, 1.0 × 106, and 7.6 × 105 r by the addition of 1, 3, and 5 phr of carbon tetrachloride, respectively, and was assumed to have decreased to 1.17 × 107, 9.0 × 106, and 7.6 × 106 r with 1, 3, and 5 phr of 1,2-dichloroethane, and to 8.6 × 106, 6.2 × 106, and 5.2 × 106 r with 1, 3, and 5 phr of chloroform, respectively. The physical properties of the films obtained at the optimum dosages under these accelerating conditions were equal to those of the latex irradiated up to the optimum dosage with no addition of halide. No side reactions occurred during the halide-accelerated crosslinking that were sufficiently extensive to influence the infrared spectra.
    Zusätzliches Material: 15 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/app.1961.070051605
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  • 93
    Digitale Medien
    Digitale Medien
    The estimation of catalytic parameters of metal acetylacetonates in isocyanate polymerization reactionsContribution No. 202. (1961)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 5 (1961), S. 424-427 
    Details
    ISSN: 0021-8995
    Schlagwort(e): Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Maschinenbau , Physik
    Notizen: The polyaddition process involving a hydroxy-terminated linear polyester and an organic diisocyanate in the presence of a series of metal acetylacetonates has been investigated. The method involved kinetic analysis of plasticity build-up in a Brabender Plastograph. Catalytic orders and relative catalytic constants (kc/k0) were determined for Mn(Aa)3, VO(Aa)2, V(Aa)3, Fe(Aa)3, Cu(Aa)2, Co(Aa)3, and Cr(Aa)3; the constants decrease in that order. Catalytic orders are unity for all complexes save manganese, which is 1.75. No correlation between dissociation potential and catalytic coefficient has been found, and it is believed that catalysis may be associated with the paramagnetic properties of the metal.
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/app.1961.070051607
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  • 94
    Digitale Medien
    Digitale Medien
    The strain dependence of rubber viscoelasticity. Part III. Natural and butyl rubber at high extensions (1961)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 5 (1961), S. 428-435 
    Details
    ISSN: 0021-8995
    Schlagwort(e): Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Maschinenbau , Physik
    Notizen: Dynamic Young's moduli are derived from observations of wave propagation in stretched filaments of natural and butyl rubbers. Extensions up to about 700% are studied within a temperature range of -45 to +50°C. and a frequency range of 0.2 to 20 kycles/sec. At constant temperature and frequency both the real (E') and imaginary (E″) components increase with increasing extension. The loss factor (E″/E') decreases with increasing extension, but the decrease is more pronounced for the butyl rubber so that the large difference in damping between the two polymers in the unstrained state is greatly reduced at high extensions. Approximate relaxation spectra are derived for the strained materials on the basis of several assumptions regarding the applicability of the WLF equation. It is found that the spectra are displaced in the direction of longer times by increasing extension; this is equivalent to an increase in the monomeric friction coefficient with extension. The effect is more pronounced for the natural rubber than for the butyl, and consequently the ratio of the friction coefficients (butyl:natural) falls from several hundred unstrained state to approximately 3 at 550% extension.
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/app.1961.070051608
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  • 95
    Digitale Medien
    Digitale Medien
    Viscoelastic factors in the strength of elastomers under complex stress by a puncture methodPresented at the Tenth Canadian High Polymer Forum, Ste. Marguerite, Quebec, September 7-9, 1960.Contribution No. 262 from the research laboratory of the Goodyear Tire & Rubber Company. (1961)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 5 (1961), S. 442-451 
    Details
    ISSN: 0021-8995
    Schlagwort(e): Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Maschinenbau , Physik
    Notizen: Investigations of the viscoelastic aspects of the mechanical behavior of polymers have been limited almost exclusively to relatively simple conditions of homogeneous stress, that is, to tension or shear loadings. In the present work a study has been made from the viscoelastic standpoint of the response of several elastomers to a much more complex type of stress distribution arising from penetration up to failure by a cylindrical indentor for a range of temperatures and rates of penetration. The failure or “puncture point” was determined by a dip in the recorded curve of load versus depth of penetration. The puncture strength values were reduced to 25°C. by applying the ratio of absolute temperatures and plotted against the logarithm of the reciprocal of the rate of penetration. These curves were then shifted on the time scale to give a master curve after the manner of Tobolsky and of Ferry. The logarithms of the shift factors thus obtained were related to the reciprocal of the absolute temperature over the range studied. The results indicate a broader generality for the viscoelastic principle of time-temperature equivalence than has usually been supposed.
    Zusätzliches Material: 13 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/app.1961.070051610
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  • 96
    Digitale Medien
    Digitale Medien
    Status of investigations for improving weatherability of linear polyethylene and copolymers (1961)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 5 (1961), S. 612-619 
    Details
    ISSN: 0021-8995
    Schlagwort(e): Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Maschinenbau , Physik
    Notizen: In an attempt to extend the outdoor serviceability of items molded from linear polyethylene and copolymers, three ultraviolet absorbers, namely, Cyasorb UV-9 (2-hydroxy-4-methoxybenzophenone), Cyasorb UV-314 (2,2′-dihydroxy-4-n-octoxybenzophenone), and TBS (4-tert-butyl phenyl salicylate), sixteen different pigments, and combinations of both ultraviolet absorber and pigment were investigated. Injection-molded test specimens were employed in this study. The laboratory source of radiation to which these samples were exposed was an Atlas XW Weatherometer. Similar samples also were exposed at various outdoor locations including Phoenix, Arizona, Summit, New Jersey, and Newark, New Jersey, to utilize practical conditions of outdoor weathering. During these weathering studies surface cracking was observed as occurring at approximately the same time as a significant decrease in tensile strength, elongation, and melt index. Such observations became a method of rapidly screening a large number of formulations for resistance to ultraviolet radiation. For optimal outdoor serviceability with respect to retention of elongation, tensile strength, and melt index properties of molded items, the following steps are necessary. A high-density resin having as low a melt index as possible is selected. The molded item is designed to minimize the formation of molded-in stresses and strains. Proper selection of UV absorbers, pigments, and combinations of both are made. Pigments such as green, orange, peacock blue, monastral purple, red, and black, in high concentrations, will prolong the outdoor weatherability of a given product.
    Zusätzliches Material: 6 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/app.1961.070051717
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  • 97
    Digitale Medien
    Digitale Medien
    Viscoelastic properties of regenerated cellulose sheet (1961)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 5 (1961), S. 647-654 
    Details
    ISSN: 0021-8995
    Schlagwort(e): Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Maschinenbau , Physik
    Notizen: The viscoelastic properties of regenerated cellulose containing several different softeners or water only were investigated. Measurements of creep and Young's modulus were made on the Instron tensile tester, and the creep curves were fitted to a mechanical model consisting of Voigt and Maxwell elements of springs and dashpots in series. The elastic and viscous parameters were determined for the various softened films and compared with each other and with measurements of Young's modulus. It was found that the elastic modulus is a function of the effective molar concentration of the softener in the film which is related to its ability to break hydrogen bonds. The inelastic deformation was found to be a linear function of the heat of vaporization of softener (including water) in the film which is related to hydrogen-bonding energy. Thus, inelastic deformation requires breaking of interchain hydrogen bonds in contrast to pure elastic deformation which involves stretching of hydrogen bonds. A relationship of the Voigt unit and of the Maxwell unit on the composition of the cellulose-softener system and on cellulose-softener interaction has been demonstrated.
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/app.1961.070051806
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  • 98
    Digitale Medien
    Digitale Medien
    Polysaccharide B-1459: A new hydrocolloid polyelectrolyte produced from glucose by bacterial fermentationPresented before the Division of Carbohydrate Chemistry at the 136th National Meeting of the American Chemical Society, Atlantic City, September 1959. (1961)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 5 (1961), S. 519-526 
    Details
    ISSN: 0021-8995
    Schlagwort(e): Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Maschinenbau , Physik
    Notizen: The exocellular polysaccharide fermented from glucose in good yield by Xanthomonas campestrìs NRRL B-1459, has been characterized. The general aspects of chemical constitution have been established, as well as the physical properties related to practical applicability. This macromolecular polysaccharide is composed of D-mannose, D-glucose, D-glucuronic acid (as the potassium salt), and a small proportion of acetyl groups. It can be produced on an industrial scale and is stable is storage. Analytical fractionation indicates fairly sharp molecular distribution for the native polysaccharide. The polysaccharide forms homogeneous dispersions in water which show plastic rheological properties and viscosity comparable with that of high-grade plant gums. Outstanding characteristics of practical significance are the atypical insensitivity of solution viscosity to salt effects and to heat, especially when salt is present. Solutions of low concentration show a restricted viscosity decrease upon salt addition; those of higher concentrations show substantial increases. Viscosity is enhanced still further by monovalent cations at basic pH and by divalent cations at neutral or slightly basic pH. Salt moderates or eliminates any viscosity decrease due to heat and, in somewhat higher concentrations, it increases the viscosity of heated solutions. Heating or deacetylating Polysaccharide B-1459 causes no impairment of its properties, but actual improvement. The constitutional basis for these unusual properties is discussed.
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/app.1961.070051704
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  • 99
    Digitale Medien
    Digitale Medien
    Digital recording and automatic computation of film tensile stress-strain dataPresented at ASTM Committee D-20 Meeting, Detroit, Michigan, October 3, 1960. (1961)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 5 (1961), S. 527-533 
    Details
    ISSN: 0021-8995
    Schlagwort(e): Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Maschinenbau , Physik
    Notizen: A system is described for automatic collection of stress-strain data for polymeric films on magnetic tape for subsequent automatic data reduction and computation of a variety of stress-strain parameters. Two shaft analog-to-digital encoders attached to a conventional tensile tester feed digital information to an incremental pulse recorder which stores all stress and strain data in two channels on 0.625-in. magnetic tape. Specimen information and test constants are inserted by the operator through a keyboard located at the tensile tester. The tape is subsequently fed into a standard digital computer through a special incremental pulse magnetic tape reader. The data pulses are internally stored and converted by means of a special program into eight significant stress-strain parameters for polymeric film samples, plus averages and standard deviations for groups of replicate determinations. These parameters include: corrected length of specimen, initial maximum tensile modulus, offset yield stress, strain at break, strain at maximum stress, maximum tensile stress, tensile stress at break, and work to break. While the program described applies to polymer film testing, both it and the digital recording equipment accessories are applicable with suitable modification, to any analog experimental data. Significant savings in man-hours and increased information output result from use of this system.
    Zusätzliches Material: 5 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/app.1961.070051705
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  • 100
    Digitale Medien
    Digitale Medien
    Effects of heterogeneous acetylation and methylation on mechanical properties of isotropic cellulose film (1961)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 5 (1961), S. 545-552 
    Details
    ISSN: 0021-8995
    Schlagwort(e): Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Maschinenbau , Physik
    Notizen: The effects on mechanical properties of heterogeneous acetylation and methylation of isotropic cellulose films have been studied. The effects on breaking load, extensibility, yield point, elastic recovery, and initial Young's modulus in the air-dry state were very small. It is concluded that these properties are not markedly influenced in cellulose derivatives by variation of the nature of the intermolecular cohesive forces in the way that might have been anticipated from the analogy of a simple molecular network. It is suggested that the lack of effect of such treatments, and also the cause of the low elastic recovery in cellulose and its derivatives, may be connected with molecular stiffness, dipole distribution, and supracrystalline structure. Cellulose and its derivatives are contrasted with nylon in this respect. The effects of methylation or acetylation on mechanical properties in water are much more extensive and are attributed to a solubilizing effect which, in the case of progressive acetylation, is ultimately opposed by the formation of acetate-acetate intermolecular bonds that are relatively stable to water.
    Zusätzliches Material: 12 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/app.1961.070051708
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