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Wegeprobleme der Graphentheorie (2008)

Ridder, Johanna

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Publication Date: 2020-08-05

Description: 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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3

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A Perturbation Result for Dynamical Contact Problems (2008)

Klapproth, Corinna ; Deuflhard, Peter ; Schiela, Anton

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Publication Date: 2016-06-09

Description: 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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An Integer Programming Algorithm for Routing Optimization in IP Networks (2008)

Bley, Andreas

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Publication Date: 2020-08-05

Description: 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.

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5

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The Line Connectivity Problem (2008)

Borndörfer, Ralf ; Neumann, Marika ; Pfetsch, Marc

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Publication Date: 2020-12-15

Description: 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.

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6

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Using Model Counting to Find Optimal Distinguishing Tests (2008)

Heinz, Stefan ; Sachenbacher, Martin

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Publication Date: 2020-08-05

Description: 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.

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On the Effects of Minor Changes in Model Formulations (2008)

Achterberg, Tobias ; Koch, Thorsten ; Tuchscherer, Andreas

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Publication Date: 2021-08-05

Description: 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.

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8

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Detecting Orbitopal Symmetries (2008)

Berthold, Timo ; Pfetsch, Marc

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Publication Date: 2022-03-14

Description: 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.

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9

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Optimization and Identification in Regional Hyperthermia (2008)

Weiser, Martin

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Publication Date: 2019-01-29

Description: 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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On Efficiency and Accuracy in Cardioelectric Simulation (2008)

Weiser, Martin ; Erdmann, Bodo ; Deuflhard, Peter

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Publication Date: 2019-05-10

Description: 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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11

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Models for Periodic Timetabling (2008)

Kinder, Mathias

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Publication Date: 2020-08-05

Description: 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.

Description: 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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12

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Experiments with nonlinear extensions to SCIP (2008)

Bley, Andreas ; Koch, Thorsten ; Niu, Lingfeng

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Publication Date: 2020-08-05

Description: 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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Tiefensuche: Bemerkungen zur Algorithmengeschichte (2008)

Grötschel, Martin

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Publication Date: 2020-08-05

Description: 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.

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Language: German

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State constrained optimal control problems with states of low regularity (2008)

Schiela, Anton

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Publication Date: 2016-06-09

Description: 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)

Haack, Fiete

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Publication Date: 2016-06-09

Description: 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.

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Line Planning on Paths and Tree Networks with Applications to the Quito Trolebus System (2008)

Torres, Luis Miguel ; Torres, Ramiro ; Borndörfer, Ralf ; [et al.]

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Publication Date: 2021-02-19

Description: 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.

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On the optimality of Least Recently Used (2008)

Hiller, Benjamin ; Vredeveld, Tjark

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Publication Date: 2020-08-05

Description: 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.

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Angebotsplanung im öffentlichen Nahverkehr (2008)

Borndörfer, Ralf ; Neumann, Marika ; Pfetsch, Marc

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Publication Date: 2020-12-15

Description: 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.

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Constraint Integer Programming: a New Approach to Integrate CP and MIP (2008)

Achterberg, Tobias ; Berthold, Timo ; Koch, Thorsten ; [et al.]

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Publication Date: 2022-03-14

Description: 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.

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An Extended Mathematical Framework for Barrier Methods in Function Space (2008)

Schiela, Anton

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Publication Date: 2016-06-09

Description: 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)

Achterberg, Tobias ; Heinz, Stefan ; Koch, Thorsten

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Publication Date: 2021-08-05

Description: 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.

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On the cardinality constrained matroid polytope (2008)

Stephan, Rüdiger

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Publication Date: 2020-08-05

Description: 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)

Wolf, Thomas

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Publication Date: 2020-08-05

Description: 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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Invertible Mappings of Nonlinear PDEs to Linear PDEs Through Admitted Conservation Laws (2008)

Anco, Stephen ; Bluman, George ; Wolf, Thomas

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Publication Date: 2020-08-05

Description: 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)

Tsarev, Sergey ; Wolf, Thomas

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Publication Date: 2021-02-26

Description: 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)

Wolf, Thomas ; Neun, Winfried

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Publication Date: 2020-12-11

Description: 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)

Erol, Berkan ; Klemenz, Marc ; Schlechte, Thomas ; [et al.]

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Publication Date: 2020-08-05

Description: 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)

Wolf, Thomas

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Publication Date: 2020-08-05

Description: 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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29

Unknown

Probabilistic analysis of Online Bin Coloring algorithms via Stochastic Comparison (2008)

Hiller, Benjamin ; Vredeveld, Tjark

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Publication Date: 2020-08-05

Description: 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.

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30

Unknown

Models for Fare Planning in Public Transport (2008)

Borndörfer, Ralf ; Neumann, Marika ; Pfetsch, Marc

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Publication Date: 2020-12-15

Description: 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.

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31

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Solving Pseudo-Boolean Problems with SCIP (2008)

Berthold, Timo ; Heinz, Stefan ; Pfetsch, Marc

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Publication Date: 2022-03-14

Description: 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.

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32

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Planung von öffentlichem Personenverkehr (2008)

Borndörfer, Ralf ; Grötschel, Martin ; Jaeger, Ulrich

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Publication Date: 2020-08-05

Description: 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.

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Language: German

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33

Unknown

Development and test of a numerical model for pulse thermography in civil engineering (2008)

Weiser, Martin ; Röllig, Mathias ; Arndt, Ralf ; [et al.]

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Publication Date: 2019-05-10

Description: 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.

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34

Unknown

Barrier Methods for Optimal Control Problems with Convex Nonlinear Gradient Constraints (2008)

Schiela, Anton ; Wollner, Winnifried

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Publication Date: 2016-06-09

Description: 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.

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35

Unknown

Interior Point Methods in Function Space for State Constraints - Inexact Newton and Adaptivity (2008)

Schiela, Anton ; Günther, Andreas

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Publication Date: 2016-06-09

Description: 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.

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36

Unknown

Fair Ticket Prices in Public Transport (2008)

Borndörfer, Ralf ; Hoang, Nam-Dung

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Publication Date: 2020-08-05

Description: 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.

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37

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A sharp interface finite volume method for elliptic equations on Cartesian grids (2008)

Oevermann, Michael ; Scharfenberg, Carsten ; Klein, Rupert

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Publication Date: 2014-02-26

Description: 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.

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38

Unknown

Cardinality Constrained Combinatorial Optimization: Complexity and Polyhedra (2008)

Stephan, Rüdiger

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Publication Date: 2020-08-05

Description: 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.

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39

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On the complexity of column generation in survivable network design with path-based survivability mechanisms (2008)

Orlowski, Sebastian ; Pióro, Michal

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Publication Date: 2020-08-05

Description: 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.

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40

Unknown

On the Line Planning Problem in Tree Networks (2008)

Torres, Luis Miguel ; Torres, Ramiro ; Borndörfer, Ralf ; [et al.]

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Publication Date: 2021-02-19

Description: 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.

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41

Unknown

Line Planning on Paths and Tree Networks with Applications to the Quito Trolebus System (Extended Abstract) (2008)

Torres, Luis Miguel ; Torres, Ramiro ; Borndörfer, Ralf ; [et al.]

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Publication Date: 2021-02-19

Description: 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.

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42

Book

Recht verstehen /; Bd. 19 (2008)

Klein, Wolfgang ; Becker, Angelika ; Parádi, Zsuzsa ; [et al.]

Berlin :Akademie Verl.,

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Title: Recht verstehen /; Bd. 19

Contributer: Klein, Wolfgang , Becker, Angelika , Parádi, Zsuzsa , Witzmann, Franziska

Publisher: Berlin :Akademie Verl.,

Year of publication: 2008

Pages: IX, 242 S. : , graph. Darst. ; , 240 mm x 170 mm

Series Statement: Forschungsberichte der Interdisziplinären Arbeitsgruppen der Berlin-Brandenburgischen Akademie der Wissenschaften Bd. 19

ISBN: 978-3-05-004484-2

Type of Medium: Book

Language: German

URL: http://deposit.d-nb.de/cgi-bin/dokserv?id=3119387&prov=M&dok_var=1&dok_ext=htm

Keywords: Private Altersversorgung ; Vertragsbedingung ; Verständlichkeit ; Umfrage ; Private Altersversorgung ; Vertragsbedingung ; Verständlichkeit ; Umfrage

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Zuse Institute Berlin

43

Electronic Resource

Lehrbuch der chemischen Technologie. Von H. Ost u. B. Rassow. 23. Aufl. 1185 S., 437 Abb., 14 Tafeln. Dr. M. Jänecke, Leipzig 1942. Pr. geb. RM. 19,60 (1943)

Helberger

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 80-80

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ISSN: 0044-8249

Keywords: Chemistry ; General Chemistry

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Chemistry and Pharmacology

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1002/ange.19430561110

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44

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Jahresberichte 1941 über Kunstseiden und Zellwollen. Von H. Truttwin. 233 S., 52 Abb. F. Eder, München 1942. Pr. geh. RM. 14, - , geb. RM. 15, - (1943)

Franz, E.

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 80-80

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ISSN: 0044-8249

Keywords: Chemistry ; General Chemistry

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Chemistry and Pharmacology

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1002/ange.19430561111

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45

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Die chemische Analyse in der Stahlindustrie. Von R. Weihrich. (Die chemische Analyse. Herausg. von W. Böttger. Bd. 31.) 3. umgearb. und erw. Aufl. 244 S., 27 Abb., 7 Tab. F. Enke, Stuttgart 1942. Pr. geh. RM. 18, - , geb. RM. 19,80 (1943)

Klinger, P.

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 80-80

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ISSN: 0044-8249

Keywords: Chemistry ; General Chemistry

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Chemistry and Pharmacology

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1002/ange.19430561112

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46

Electronic Resource

KWI. für Medizinische Forschung, Heidelberg (1943)

Kuhn, R.

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 93-93

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ISSN: 0044-8249

Keywords: Chemistry ; General Chemistry

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Chemistry and Pharmacology

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1002/ange.19430561305

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47

Electronic Resource

Colorimetrische Bestimmung der Alpha-Aminosäuren Arginin und Tyrosin im EiweißVorgetragen auf der Kriegsarbeitstagung der Arbeitsgruppe für Analyt. Chemie und der FBBK der Dechema am 24. Oktober 1942 in Frankfurt a. M. (1943)

Rauterberg, E.

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 91-92

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ISSN: 0044-8249

Keywords: Chemistry ; General Chemistry

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Chemistry and Pharmacology

Additional Material: 2 Tab.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1002/ange.19430561304

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48

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Die Mistel als Heilpflanze. Von G. Madaus. (Medizinisch-Biologische Schriftenreihe, Heft 15.) 48 S. P. Rohrmoser, Dresden-Radebeul 1941. Pr. geh. RM. 1, - (1943)

Schmidt, O. C.

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 96-97

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ISSN: 0044-8249

Keywords: Chemistry ; General Chemistry

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Chemistry and Pharmacology

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1002/ange.19430561314

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49

Electronic Resource

Triäthanolamin und andere Äthanolamine. Von E. J. Fischer. 3. Aufl. 213 S. Allgem. Industrieverlag, Berlin 1942. Pr. geb. RM. 14, - (1943)

Hetzer

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 97-97

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ISSN: 0044-8249

Keywords: Chemistry ; General Chemistry

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Chemistry and Pharmacology

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1002/ange.19430561315

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50

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Holzschutzmittel, Prüfung und Forschung. Von B. Schulze, G. Becker, G. Theden. (Wissenschaftliche Abhandlungen der deutschen Materialprüfungsanstalten. II. Folge, Heft 3.) 88 S., 84 Abb. Springer-Verlag, Berlin 1942. Pr. geh. RM. 16,80 (1943)

Liese

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 97-97

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ISSN: 0044-8249

Keywords: Chemistry ; General Chemistry

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Chemistry and Pharmacology

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1002/ange.19430561317

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51

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Die Kartoffel. Von W. Kröner u. W. Völksen. (Beiheft 9 zur Zeitschrift „Die Ernährung“.) 130 S., 4 Abb. J. A. Barth, Leipzig 1942 Pr. kart. RM. 3,80 (1943)

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 97-98

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ISSN: 0044-8249

Keywords: Chemistry ; General Chemistry

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Chemistry and Pharmacology

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1002/ange.19430561320

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52

Electronic Resource

Personal- und Hochschulnachrichten (1943)

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 98-98

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ISSN: 0044-8249

Keywords: Chemistry ; General Chemistry

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Chemistry and Pharmacology

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1002/ange.19430561325

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53

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Umwandlungserscheinungen im festen AggregatzustandNach einem Vortrag am 24. Juli 1942 im Institut für physikalische Chemie in München. (1943)

Schäfer, Klaus

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 99-105

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ISSN: 0044-8249

Keywords: Chemistry ; General Chemistry

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Chemistry and Pharmacology

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1002/ange.19430561502

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54

Electronic Resource

Die Krötengifte Neuere Ergebnisse der chemischen und pharmakologischen Forschung (1943)

Behringer, Hans

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 105-108

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ISSN: 0044-8249

Keywords: Chemistry ; General Chemistry

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Chemistry and Pharmacology

Additional Material: 2 Tab.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1002/ange.19430561503

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55

Electronic Resource

Umsturz im Weltbild der Physik. Von E. Zimmer. 6. Aufl. 296 S., 77 Abb. Knorr & Hirth, München 1942. Pr. geh. RM. 4,50, geb. RM. 5,70 (1943)

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 112-112

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ISSN: 0044-8249

Keywords: Chemistry ; General Chemistry

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Chemistry and Pharmacology

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1002/ange.19430561514

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56

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Institut für angewandte Photochemie der T. H. Berlin (1943)

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 124-124

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ISSN: 0044-8249

Keywords: Chemistry ; General Chemistry

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Chemistry and Pharmacology

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1002/ange.19430561706

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57

Electronic Resource

Verein Deutscher Chemikers (1943)

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 127-127

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ISSN: 0044-8249

Keywords: Chemistry ; General Chemistry

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Chemistry and Pharmacology

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1002/ange.19430561715

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58

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Grundriß der physiologischen Chemie für Studierende. Von A. Hahn. 3. umgearb. Aufl. von „Grundriß der Biochemie“. 255 S., 11 Abb. F. Enke, Stuttgart 1942. Pr. geh. RM. 13, - , geb. RM. 14,60 (1943)

Lohmann, K.

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 127-127

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ISSN: 0044-8249

Keywords: Chemistry ; General Chemistry

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Chemistry and Pharmacology

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1002/ange.19430561713

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Klockmanns Lehrbuch der Mineralogie. Von P. Ramdohr. 12. vollst. umgearbeitete Aufl. 659 S., 606 Abb. F. Enke, Stuttgart 1942. Pr. br. RM. 34, - , geb. RM. 36,80 (1943)

Laves, F.

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 112-112

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Berliner Vortragsveranstaltung des Vereins Deutscher Chemiker im NSBDT (1943)

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 112-112

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Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943)

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Personal-und Hochschulnachrichten (1943)

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 112-112

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Trennung von Kohlenwasserstoffen durch Desorption III (1943)

Harteck, P. ; Suhr, Kl. A.

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 120-123

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Nachweis und Bestimmung des Kaliums mit 4,6-Dinitro-benzfuroxan (1943)

Rathsburg, Hans ; Scheuerer, Anton

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 123-123

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Deutsche Keramische Gesellschaft (1943)

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 124-125

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Rundschau (1943)

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 125-126

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Außeninstitut der T. H. Braunschweig (1943)

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 125-125

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Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943)

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Die Azulene (1943)

Arnold, Herbert

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 7-10

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Entwicklung der Sulfonamid-TherapieNach einem Vortrag auf der Ostdeutschen Vortragsveranstaltung des VDCh am 12. Februar 1942 in Breslau. (1943)

Klarer, J.

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 10-14

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Über einige neuere Ergebnisse der anorganischen ChemieNach einem Vortrag auf der Westdeutschen Vortragsveranstaltung des VDCh am 1./2‥Mai 1942 in Straßburg. (1943)

Klemm, Wilhelm

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 1-7

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Über die Analyse von PhosphorwasserstoffEin ausführlicher Arbeit darüber von K. Beyer erscheint (demnächst) in Z. anorg. allg. Chem. (1943)

Beyer, Karl

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 14-14

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Kaiser Wilhelm-Institut für physikalische Chemie und Elektrochemie, Berlin-Dahlem (1943)

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 15-15

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Physikalischer Verein, Heidelberg (1943)

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Zeitschrift für die chemische Industrie 56 (1943), S. 16-16

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Die Bestimmung von „nitrosen Gasen“Ein ausführlicher Aufsatz von K. Beyer über dieses Thema erscheint (demnächst) in Z. anorg. allg. Chem. (1943)

Beyer, Karl

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 14-15

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KWI. für medizinische Forschung, Heidelberg (1943)

Kuhn, R.

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 16-16

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Rundschau (1943)

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 17-18

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Allgemeine und physikalische Chemie. Teil I und II. Von Werner Schulze. (Sammlung Göschen Bd. 71 und 698.) 146 und 160 S. W. de Gruyter & Co., Berlin 1942. Pr. geb. je Bd. RM. 1,62 (1943)

Kortüm, G.

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 18-18

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Viscosität der Kolloide. Von W. Philippoff. (Handbuch der Kolloidwissenschaft in Einzeldarstellungen. Unter Mitwirkung von Fachgenossen herausgeg. von W. Ostwald. Bd. IX.) 453 S., 254 Abb. Th. Steinkopff, Dresden u. Leipzig 1942. Pr. geh. RM. 45, - , geb. RM. 47, - (1943)

Patat

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 18-18

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Einführung in die organisch-chemische Laboratoriumstechnik. Von K. Bernhauer. 2. Aufl. 170 S., 88 Abb. Springer-Verlag, Wien 1942. Pr. br. RM. 4,80 (1943)

Fischer, F. G.

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 18-19

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Einführung in die organische Chemie. Von O. Diels. 11. veränderte Aufl. 326 S., 33 Abb. J. J. Weber, Leipzig 1942. Pr. geb. RM. 11,50 (1943)

Fischer, F. G.

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 18-18

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Personal-und Hochschulnachrichten (1943)

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 20-20

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Unsere Lebensmittel und ihre Veränderungen. Von W. Ziegelmayer. 3. verb. Aufl. Th. Steinkopff. Dresden u. Leipzig 1942. Pr. geh. RM. 12, - , geb. RM. 13,50 (1943)

Bames

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 19-19

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Walter John † (1943)

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 19-20

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Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943)

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Die Polarographie als Hilfsmittel bei der Konstitutions-Aufklärung (1943)

Proske, Gerhard

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 24-28

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Physikalische Gesellschaft zu Berlin unter Mitwirkung der Deutschen Gesellschaft für technische Physik (1943)

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 29-32

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Diffusion in festen MetallenNach einem Vortrag im Bezirksverband Rheinland-Westfalen des VDCh am 14. November 1941 im Haus der Technik in Essen Ausführliche Zusammenfassung bis 1939: W. Seith: Diffusion in Metallen. Verlag J. Springer, Berlin 1939 (1943)

Seith, W.

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 21-24

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Mitteldeutsche Vortragsveranstaltung des VDCh im NSBDT in Leipzig 9.-10. April 1943 (1943)

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 32-32

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Verein Deutscher Chemiker (1943)

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Zeitschrift für die chemische Industrie 56 (1943), S. 32-32

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Personal- und Hochschulnachrichten (1943)

Weinheim : Wiley-Blackwell

Zeitschrift für die chemische Industrie 56 (1943), S. 32-32

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