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  • 1
    Publication Date: 2020-08-05
    Description: 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.
    Keywords: ddc:510
    Language: German
    Type: reportzib , doc-type:preprint
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  • 2
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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.
    Keywords: ddc:510
    Language: German
    Type: reportzib , doc-type:preprint
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  • 3
    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.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
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  • 4
    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.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
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  • 5
    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.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
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  • 6
    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.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
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  • 7
    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.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
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  • 8
    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.
    Keywords: ddc:510
    Language: English
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  • 9
    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.
    Keywords: ddc:510
    Language: English
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  • 10
    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.
    Keywords: ddc:510
    Language: English
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  • 11
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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.
    Keywords: ddc:510
    Language: English
    Type: masterthesis , doc-type:masterThesis
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  • 12
    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.
    Keywords: ddc:510
    Language: English
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  • 13
    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.
    Keywords: ddc:510
    Language: German
    Type: reportzib , doc-type:preprint
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  • 14
    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.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
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  • 15
    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.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
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  • 16
    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.
    Keywords: ddc:510
    Language: English
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  • 17
    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.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
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  • 18
    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.
    Keywords: ddc:510
    Language: German
    Type: reportzib , doc-type:preprint
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  • 19
    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.
    Keywords: ddc:510
    Language: English
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  • 20
    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.
    Keywords: ddc:510
    Language: English
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  • 21
    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.
    Keywords: ddc:510
    Language: English
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  • 22
    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.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
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  • 23
    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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  • 24
    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.
    Keywords: ddc:510
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  • 25
    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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  • 26
    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.
    Keywords: ddc:510
    Language: English
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  • 27
    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.
    Keywords: ddc:510
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  • 28
    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
    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.
    Keywords: ddc:510
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  • 30
    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.
    Keywords: ddc:510
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    Type: reportzib , doc-type:preprint
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  • 31
    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.
    Keywords: ddc:510
    Language: English
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  • 32
    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.
    Keywords: ddc:510
    Language: German
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  • 33
    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.
    Keywords: ddc:510
    Language: English
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  • 34
    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.
    Keywords: ddc:510
    Language: English
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  • 35
    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.
    Keywords: ddc:510
    Language: English
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  • 36
    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.
    Keywords: ddc:510
    Language: English
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  • 37
    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.
    Keywords: ddc:510
    Language: English
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  • 38
    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.
    Keywords: ddc:510
    Language: English
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  • 39
    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.
    Keywords: ddc:510
    Language: English
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  • 40
    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.
    Keywords: ddc:510
    Language: English
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  • 41
    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.
    Keywords: ddc:510
    Language: English
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  • 42
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 8 (1969) 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 43
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 8 (1969), S. 21-27 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An increase in temperature causes an increase in the amplitudes of intramolecular and intermolecular motions and mainfests itself as an increase in the effective radii of the various atoms, especially hydrogen atoms. If one uses a Lennard-Jones 6-12 potential function to account for nonbonded interactions, this increase in the radius of the hydrogen atom is equivalent to a modification of the coefficient of the repulsive part of the Lennard-Jones potential. Accordingly, this effect of increasing temperature on the helix sense of several polyamino acids is computed by allowing the effective radius of the hydrogen atom to increase. It is found that the preferred sense of several polyamino acid helices changes from right- to left-handed as the temperature is increased. This accounts for recent experimental observations of changes in helix sense with temperature.
    Additional Material: 2 Ill.
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  • 44
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 8 (1969), S. 57-68 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Potentiometric titrations and some complementary optical rotation data are presented for solutions of poly(L- glutamic acid) (PGA) in several H2O-ethanol mixtures. The data allow the determination of the intrinsic pK (pK0), slope of the apparent. pK (pKapp), versus degree of ionization curves and of the enthalpy of ionization as a function of ethanol concentration. The variation of the degree of ionization at which the helix-coil transformation occurs with ethanol and temperature is also determined. Finally free energy, enthalpy, and intropy changes associated with the helix-coil transformation for the uncharged conformers are determined from the titration curves. The effect of the ethanol is to increase the stability of the helical conformation of PGA for both the charged and the uncharged forms of the polymer. The stabilization of the uncharged helix is essentially an entropic effect.
    Additional Material: 8 Ill.
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  • 45
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 8 (1969), S. 91-99 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Infrared spectra of polypeptides were measured in the region of 1800-400 cm-1. For the α-helical form, disordered form, and antiparallel-chain β-form, amide V band- arising from N-H out-of-plane bending models were observed at 610-620, around 650, and 700-705 cm-1, respectively, and amide V′ bands arising from N-D out-of-plane bending modes were observed at 455-465, around 510, and a 515-530 cm-1, respectively. These correlations are useful for conformation diagnoses, particularly for copolyamino-acids or proteins which are not oriented. The nature of low-frequency amide bands are discussed with reference to potential energy distributions calculated for the α-helical form and β form.
    Additional Material: 6 Ill.
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  • 46
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Some experimental data are given on the infrared spectra between 3300 and 3500 cm-1 of dilute solutions in carbon tetrachloride of three types of model compounds: CH3-CONH-CH(R1)-CONH(R2), (I); CH3-CON(CH3)-CH(R1)-CONH(R2), (II) and CH3-CONH-CH(R1)-CON(R2)2, (III). In studying the N-H stretching bands, it was found that there are two types of intramolecular hydrogen bonds in these molecules; these result in two different cyclized conformations, C5 and C7, which contain respectively, five and seven atoms in the ring. By using model substances I, II, and III, in which the nitrogen atoms are unequally substituted, it is possible to identify the N-H stretching bands which are to be ascribed to the N-H oscillators included in the two different chelated conformations. It is found also that the stretching frequency of a free N-H oscillator depends upon the substituent on the nitrogen atom. Thus, it is possible to observe, with some of the model compounds I, four different absorption bands located at 3340, 3420, 3440, and 3460 cm-1. The first two are ascribed to the N-H oscillators included in the H—bonds which lock the C7 and C5 conformations; the last two correspond to free N-H which differ with the substituent on the nitrogen atom.
    Additional Material: 10 Ill.
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  • 47
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 8 (1969), S. 153-155 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 2 Ill.
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  • 48
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 7 (1969), S. 207-213 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Molecular orbital calculations of the extended Hückel type have been used to study the conformations of glycyl and alanyl residues in ground and excited states. The ground-state surfaces show features similar to those obtained with the standard calculational methods in which the total energy is partitioned into components such as torsions, nonbonded and electrostatic interactions. The molecular orbital calculations provide the first independent theoretical check on such calculations. The excited-state surfaces, Uniquely available from the molecular orbital calculations, exhibit a better definition and sharpening of potential minima in the sterically allowed regions.
    Additional Material: 4 Ill.
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  • 49
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We derive equations for calculating the number-, weight-, and z-average lengths between single-strand breaks in DNA molecules. Provision is made for the existence of preformed breaks under genetic control: these are assumed to be fixed in number in each molecule, but may be variable in position. Breaks due to random degradation may be superimposed on the pre-existing breaks. An example is given for illustrative purposes.
    Additional Material: 1 Ill.
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  • 50
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 7 (1969), S. 223-239 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The conformation in solution of fractionated 30 S and 19 S ribosomal RNA from rabbit reticulocytes has been studied by optical rotatory dispersion, analysis of thermal melting profiles and their derivatives, and spectrophotometric acid-base titration. From a consideration of the limitations of these methods, it has been possible to set limiting values on the degree of base-pairing and the lengths of the double helices: between 60 and 80% of the bases in 19 S and 30 S RNA are estimated to be paired. The paired segments are not shorter than 4 base pairs, and evidence from other sources is available which indicates that they are not longer than 8-16 base pairs. The spread of helix lengths is greater in the 30 S than in 19 S RNA; and other differences are noted. Several distinct populations of double helices, differing in their thermal stability, are present. Estimates are presented from spectrophotometric and titration data for the base compositions of the paired and unpaired regions.
    Additional Material: 9 Ill.
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  • 51
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 7 (1969), S. 251-263 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A small perturbation analysis is carried out to determine the stability of a fluid containing two layers of diffusing solutes in a common solvent and acted upon by a uniform gravitational field. It is found that instability can arise even though the unperturbed diffusion does not lead to the formation of a density inversion within the fluid.
    Additional Material: 5 Ill.
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  • 52
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 53
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 7 (1969), S. 475-493 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The kinetics of denaturation of DNA have been studied by relaxation techniques. Examination of the terminal relaxation times for a variety of DNA's under a variety of conditions has shown that DNA denaturation is principally a hydrodynamically limited process. Measurements within the helix-coil transition have demonstrated that the experimentally measured terminal relaxation times are a function of the following: (1) position in the helix-coil transition; (2) ionic strength of the solvent; (3) solvent viscosity; (4) DNA concentration; (5) molecular weight; (6) number and position of single-strand breaks. The dependence of the terminal relaxation time on the above mentioned factors can be attributed to hydrodynamic effects. Thus a hydrodynamic model for DNA unwinding is required. The model which best fits the data involves the assumption of a rotational frictional coefficient independent of molecular weight. This assumption is suggested by the fact that the relaxation time is proportional to the first power of the molecular weight.
    Additional Material: 9 Ill.
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  • 54
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 7 (1969), S. 495-502 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Sodium counterion association with partially neutralized poly(D-glutamic acid) or poly(DL-glutamic acid) was measured by use of Wall's transference method with radioactive sodium. In the region where both polyacids are in completely random coil form, fractions of association were considerably less than that with poly(acrylic acid) in the same region of degree of neutralization. Even in the region where poly (D-glutamic acid) is in the helical form, the fraction of association was less than that with poly(acrylic acid) in the same region. No pronounced characteristics attributable to counterion association corresponding to the helix-coil transition could be found. The association phenomena were discussed on the basis of a rodlike model of polyelectrolyte.
    Additional Material: 2 Ill.
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  • 55
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    Biopolymers 7 (1969), S. 411-415 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The isomerization of poly-L-proline in different solvents has been studied by NMR spectroscopy. Different resonance signals for the CHα protons have been obtained for the two different helical conformations of thus compound, namely form I and form II.
    Additional Material: 4 Ill.
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  • 56
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    Biopolymers 7 (1969), S. 417-422 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Poly-β-N-diphenylmethyl-L-asparagine and poly-γ-N-diphenylmethyl-L-glutamine were prepared from the corresponding N-carboxyanhydrides. Poly-L-aspuragine and poly-L-glutamine were obtained by removal of the diphenylmethyl protecting groups with liquid anhydrous hydrofluoric acid.
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  • 57
    Electronic Resource
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    New York : Wiley-Blackwell
    Biopolymers 7 (1969), S. 379-393 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The Hydrogen-tritium exchange character of poly-D,L-alanine was studied in detail as a model for the hydrogen exchange behavior of the unhindered, polymeric peptide group. The random chain nature of poly-D,L-alanine was evident in the uniformity of exchange rate of all its hydrogens and in the similarity between this rate and that of random chain poly-D,L-lysine and other known, unhindered secondary amide groups. An equilibrium isotope effect favoring the binding of tritium over protium to the extent of 21% was measured. Specific acid and base catalysis of the exchange and the absence of detectable general catalysis were demonstrated. Apparent energy of activation is 17 kcal/mole for deprotonation, largely due to dependence of Kw on temperature, and 15 kcal/mole for protonation, which correlates with the extreme apparent pK. The hydrogen -tritium exchange half-time rate; of poly-D,L-alamine at any pH and temperature (T: °C) is given by the equation: \documentclass{article}\pagestyle{empty}\begin{document}$$ \[t_{\frac{1}{2}} \,(\min )\, = \,200\,\, \times \,10^{0.05{\rm T}} /\,[10^{{\rm pH} - 3} \, + \,10^{3 - {\rm pH}} ]\] $$\end{document}
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  • 58
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    Biopolymers 7 (1969), S. 581-593 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The specific rotation of starch components, corrected for refractive index variation, exhibits a discontinuity in the region of the water-dimethyl sulfoxide (H2O-DMSO) system that corresponds to the composition of the complex 2H2O-DMSO. This discontinuity is a property dependent upon the presence of a number of consecutively linked α-1,4 glucose units and, therefore, must reflect a change in symmetry of a segment, of polymer chain. The optical rotation of amylose between 26.5 and 92.5°C. does not change in DMSO and is only slightly lowered in water at the higher temperature. The behavior of amylose in both DMSO and H2O is like that of a random coil, as indicated by viscosity and sedimentation measurements. These results may be interpreted either as being compatible with models of amylose in solution in which the polymer backbone has helical twist, or as indicating removal of strong interactions between polymer chain segments by a good solvent.
    Additional Material: 6 Ill.
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  • 59
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 3 Ill.
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  • 60
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    Biopolymers 7 (1969), S. 614-618 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 2 Ill.
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  • 61
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    Biopolymers 7 (1969) 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 62
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    Biopolymers 7 (1969), S. 1-3 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 63
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    Biopolymers 7 (1969), S. 5-19 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The osmotic pressure equation for nonideal, associating systems of the type nA +mB ⇄ AnBm, has been derived, by using the assumption yAnBm/yAnyBm = 1. This treatment can also be applied to related associations such as nA + mB ⇄ AB + AB2 + A2B + …. From osmotic pressure experiments on the pure reactants it is possible to obtain the molecular weights (MA and MB) of the reactants and also the virial coefficients (BAA and BBB) of the reactants. The osmotic pressure of a nonreacting mixture of A and B can be calculated from these measurements. It can be used along with osmotic pressure measurements on equilibrium mixtures of A and B to obtain expressions containing the equilibrium constant (or constants) and the cross-virial coefficients (BAB and BBA). Several procedures are described for the evaluation of the equilibrium constant (or constants) and the BAB or BBA terms. It appears that this procedure is a general one which is applicable to associations of the type nA + mB ⇄ AB + A2B + AB2 + …. By correcting for nonideal behavior, one should then be able to apply it to any method available for analyzing ideal associations of the types considered here. In addition it is possible, subject to certain restrictions, to analyze associations of the type 3A + B ⇄ A2 + AB.
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  • 64
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    Biopolymers 7 (1969), S. 39-58 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A method has been developed for characterizing at, submicrogram levels the heterogeneity of histones from purified nuclei. The histones are eluted with a smooth concentration gradient from nuclei trapped in polyacrylamide-gel threads and are collected in a micro fraction collector suitable for volumes in the 10-100 μl range. The gradient and fraction collection systems are governed by cam driven syringes. Samples obtained are subjected to electrophoresis in a starch-gel system and the gels are stained with a highly sensitive stain specific for guanidinium groups. Seven major and a similar number of minor components are demonstrated in the histones. The method of differential elution of trapped macromolecules is suitable for use with systems other than nuclei and histones.
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  • 65
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    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A method is presented for the treatment of distribution functions obtained by ultra-centrifugal sedimentation velocity experiments on the plasma lipoproteins, so that adequate corrections can he made for the effects of diffusion and concentration dependence of the sedimentation coefficient. The method involves the use of modified equations derived from those presented in 1952 by Gosting for the transform from g* (S) to g(S) distributions. The evaluation of the molecular parameters of lipoprotein density and size, from a set of g(Si°) distribution functions obtained in solvents of varying density, is also outlined. Preparations of the β-lipoprotein of human plasma are found to follow a bivariate normal distribution that requires evaluation of five parameters, x̄1, σ1, x̄2, σ2and p. The first two represent the mean and standard deviation of the lipoprotein density, the third and fourth the same quantities for the size, expressed as ft “logarithmic diameter parameter”, and the final value is a measure of the correlation between these two variables.
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  • 66
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    Biopolymers 7 (1969), S. 133-133 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 67
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    Biopolymers 7 (1969) 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 68
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    Biopolymers 7 (1969), S. 155-171 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: High-resolution nuclear magnetic resonance spectra at 100 MHz and 220 MHz have been obtained on two samples of poly-L-alanine of differing molecular weights (2500 and 42 500) in the chloroform-trifluoroacetic acid system under various conditions of solvent composition, temperature, and polypeptide concentration. Separate helix and random coil peaks are observed for the α-CH and peptide NH backbone proton resonances, thereby permitting the determination of helix content. This observation of separate peaks demonstrates that the lifetimes of the helix and random coil portions of poly-L-alanine have lower limits of about 10-1 sec. It is suggested that solvent-peptide versus peptide-peptide hydrogen bond competition, coupled with a destabilizing effect of the trifluoroacetic acid on the helix, is responsible for the helix-random coil transformation.
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  • 69
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    Biopolymers 7 (1969), S. 135-153 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The combination of an agarose gel (Bio-Gel A) and a dioxane-water (1:1) solvent system allowed the fractionation, on a preparative scale, of a very polydisperse, non-derivatized lignin preparation (enzymatically liberated lignin prepared from sweetgum sapwood with Lenzites trabea). Three fractions differing markedly in molecular weight were obtained. A gel of crosslinked alkylated dextran (Sephadex LH-20) with the same solvent system allowed division of the lowest molecular weight fraction into two fractions. These materials were characterized by measurements of intrinsic viscosity and number-average molecular weights in dimethylformamide and dioxane-water. It was established that the two highest molecular weight fractions were associated in an average trimeric form in dioxane-water (1:1) as compared to the form (considered to be molecular) that occurred in dimethylformamide. Molecular size distributions and eluant volumes of the fractions were determined with a Sephadex G-100-formamide system, the latter being one of the most powerful nonaqueous solvents for lignin. Adsorption effects were known to be absent in this case, and the lignin molecules were considered to be unassociated in formamide. The four fractions were distinguishable with the formamide-G-100 system, thus indicating that the original fractionation was based on molecular size. The enzymatically liberated lignin contained molecules that comprised a continuum of molecular weights from approximately monomeric to molecules that were at the limit of the solvating power of dioxane-water (1:1) and dimethylformamide. Limited physicochemical data were consistent with a compact, approximately spherically symmetric shape of the lignin in solution.
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  • 70
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    Biopolymers 7 (1969), S. 189-197 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A comparison has been made of the intrachain potential energy of an infinite straight α-helix of poly-L-alanine with that of the distorted form adopted in a coiled coil conformation. The energy terms included were the van der Waal's, electrostatic, hydrogen-bond, and the rotational potential terms. The results indicate that the potential energies of the structures investigated are almost the same, and so a transformation from one state to another may occur without significant changes in potential energy. Particular care has been taken to ensure that the electrostatic and van der Waal's interaction terms are fully convergent. The values obtained for the α-helix were compared with those already published, and some significant differences were found.
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  • 71
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    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Ultraviolet optical rotatory dispersion curves of mucopolysaccharides exhibit particular Cotton effects in the spectral region of the n-π and π-π amide transitions. Two general patterns emerge: (1) enhancement of negative rotation and of the first negative Cotton effect (troughs 217-220 mμ) and (2) relative dominance of the positive Cotton effect in the π-π transition region (peak ∼198 mμ). Groups (1) and (2) can be correlated with a structural difference in the linkages of the amino sugars: (1) occurs with polymers containing 3-1-linked glycosamino sugars and (2) with glycosamino moieties linked 4-1 by either α- or β-glycosidie bonds. Measurements of the circular dichroic absorption bands support the qualitative conclusions from optical rotation. All mucopolysaccharides exhibit a first, negative band centered at 208-211 mμ, while only those in group (2) show, in addition, a positive band centered at 189-192 mμ. A suggested unifying model considers that difference in kind and/or degree of preferred geometry of the amide groups obtains from two forms of secondary order: (1) having a linear hydrogen bond from the N (acceptor) to the (C2)O - H of the preceding uronic acid and (2) having a linear hydrogen bond from the N (acceptor) to the (C2 or 3) O - H of the following sugar. The hydrogen bonds would have similar strength but opposite directions in two systems towards the nonreducing end (1) or towards the reducing end (2)], closing eight-membered rings
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  • 72
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    Biopolymers 7 (1969), S. 99-106 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The myosin molecule was extracted from the smooth muscle parts of horse esophagus and purified by ammonium sulfate fractionation. The schlieren pattern of the sedimentation velocity run showed a very sharp single peak of.5.9. S (s20,w). Molecular weight of the protein was measured by means of the Archibald and sedimentation equilibrium methods, both in 0.5M KCI buffered by 1/150 M phosphate at pH 7.5 and at 5°C. The values obtained were 6.25 × 105 and 5.81 × 105respectively, for the two methods. The second virial coefficients were 1.1 × 104 and 1.2 × 10-4 ml/g. Denatured smooth muscle myosin was prepared in a solution of 5M guanidine HC1 containing 0.4 M KC1 and 0.2 M β-mercaptoet hanol buffered at pH 8.0. The weight-average molecular weight of the denatured smooth muscle myosin was 2.24 × 105 and the second virial coefficient was 7.6 × 10-4 ml/g. The values described above are in good agreement with those reported for rabbit skeletal myosin with ammonium sulfate fractionation. The molecular dimension of the molecule is estimated as the value for an axial ratio of 100, assuming a rigid rod molecular model for this molecule, both the thermodynamical and hydrodynamical treatment being in a good agreement with this estimation.
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  • 73
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    Biopolymers 7 (1969) 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 74
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    Biopolymers 7 (1969), S. 433-434 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: No. Abstract
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  • 75
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    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The enthalpy change accompanying the double helix-coil transition of polyriboadenylic acid (poly A) in aqueous solution has been measured optically and calorimetrically in the pH range 5.7-4.5. The course of this cooperative transition was followed optically by measuring changes in ultraviolet absorption as a function of temperature at different pH values, and calorimetrically by determining the heat capacity of the solution through the transition region. From the latter measurements, the enthalpy of transition was calculated. It is shown, that ΔH is dependent on pH as it is expected from the influence of protonation of the double helix of poly A.
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  • 76
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    Biopolymers 7 (1969), S. 453-458 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The interaction between ionizable carboxyl groups and the conformation of poly-(glutamic acid) (PGA) in aqueous solution were investigated by the mechanical method. The dynamic rigidity of the PGA solution has a maximum value at the pH corresponding to about 50% neutralization point. This may be due to establishing of a maximum attractive force by proton/charge fluctuation between ionizable carboxyl groups at that pH. The dynamic viscosity has a sharp change in the region of pH 5.5-6.5. It is suggested that this behavior is due to the helix-coil transition.
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  • 77
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    Biopolymers 7 (1969), S. 447-452 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: By use of D2O we found that the shortening of the longitudinal proton relaxation time which occurs in the investigated aqueous yeast DNA solutions (≦ 2.4% with 2% protein) was not based on a hydration effect, but was caused by magnetic impurities only. An estimate shows that the mobility of the hydrated water molecules is reduced by less than two orders of magnitude in comparison with the free water molecules.
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  • 78
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    Biopolymers 7 (1969), S. 435-445 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A general approach to the determination of relative stability of any pair of con-formational states of biological macromolecules or their complexes (in particular, to the determination of relative stability of native and disordered states of the macromolecule) has been suggested. For determining the free energy difference of the two states under the conditions when one of them is considerably more advantageous than the other, it is necessary for the macromolecule to be influenced by the transforming agent which levels free energies of both the conformational states, and to determine the external parameter derivative of the free energy difference in the region of the conformational transition induced by the change in this parameter. If the character of the dependence of this derivative on the external parameter (temperature, solvent composition, etc.) is known, then this allows the determination of the free energy difference of the two states under the conditions considered, even including conditions far from the transition region. The value of the derivative of the free energy difference in the transition region in many cases can be measured directly (in particular, when using calorimetry), while in cases when a direct measurement of the derivative is impossible, it can often he estimated experimentally from the steepness of the conformational transition. The methods of this estimation and also a possible character of the change of the considered derivative during variation of the external parameter are considered for the case when the transforming agent is one of the components of the solvent and, consequently, the derivative of the free energy difference is equal to the difference of number of molecules of this component hound with the macromolecule in two conformational states.
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  • 79
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    Biopolymers 7 (1969), S. 459-474 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Wool-water systems, at water contents above a threshold value of 22.7 g of water per 100 g of wool keratin, yielded curves of specific heat against temperature showing peaks that are ascribed to the fusion of the absorbed water. Integral and incremental heats of fusion were obtained. Integral heats increase as the square of the water content above the threshold, and incremental heats follow a linear relationship. The incremental heat reaches a value of 55 cal/absorbed water, at the saturation water content, at 0°C of 33.9 g of water per 100 g of keratin. The state of the absorbed water is discussed. Clustering of water molecules takes place only above the threshold water content.
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  • 80
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    Biopolymers 8 (1969), S. 173-179 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The laser-excited Raman spectra have been obtained of poly-L-proline in the solid and aqueous solution. In the solid state, the Raman spectra are of the form II which is the left-handed helical form with the peptide bonds in the trans configuration. Dissolution of this form in water produced only minor changes in the Raman spectra. The differences in frequencies produced by dissolving the polymer are associated with vibrational modes of the pyrrolidine ring as indicated by comparison with the Raman spectrum of L-proline. The similarity of the Raman spectra dictates that, the conformations of poly-L-proline chain are similar in the solid and aqueous solution.
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  • 81
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    Biopolymers 8 (1969), S. 181-185 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A comparative study on sonicated calf thymus DNA was made by using electron microscopy and sedimentation methods. The length distribution, established by electron microscopy by using Kleinschmidt's technique, is related to the sedimentation curve obtained with the same solution. The relation permits a determination of the sedimentation constant corresponding to a given length up to 8000 Å and vice versa.
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  • 82
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    Biopolymers 8 (1969), S. 199-216 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The π-electron polarizability of conjugated base molecules such as uracil and adenine are calculated semiempirically by using molecular orbital theories. The Hüekel method and the self-consistent-field (SCF) theory are used in the present calculation. The theoretical values obtained by the Hüekel method are consistently larger than the experimental results. The values obtained by the SCF theory are in good agreement with observed values. It is clearly demonstrated that the SCF method is better than the Hükel method for the calculation of polarizability. The polarizability of the adenine-uracil pair is calculated as the sum of the polarizabilities of adenine and uracil and also calculated by solving the eigenvalue problem for the A-U pair as an entity. The second method gives considerably larger polarizability than the first method. Discussions are presented and it is demonstrated that the second method is the correct way to calculate the polarizability of the A-U pair.
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  • 83
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    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The reversibility of the thermal denaturation of a low-sulfur fraction of solubilized wool keratin (SCMKA) has been studied under a variety of conditions of time, protein concentration, and pH. Two types of irreversibility for the transition have been encountered. One of these is associated with an aggregation of the protein on denaturation to give a product which may contain elements of a β conformation. This type of irreversibility is favored by high protein concentration, and the original conformation may in fact be regained if the aggregated structure is broken down by a solvent such as 8M urea and the urea subsequently removed by dialysis. The other type of irreversibility appears to be due to racemization of the protein. It does not seem to be dependent on protein concentration and is apparent only at temperatures beyond the actual transition range (∼40-65°C) at pH values below 11, At pH 12, however, racemization appears to proceed slowly even at 4°C. The thermal transition at pH 9 and pH 10 has been shown to be multistage in nature. Over the pH range 9-12 there is a progressive decrease in thermal stability with increase of pH. Addition of NaCl at pH 10 leads to an increase in thermal stability of the molecule.
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  • 84
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    Biopolymers 8 (1969), S. 217-235 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We report studies of the optical properties of the proflavine-DNA complex, using absorbance and circular dichroism spectroscopy. From comparison of the absorption spectra of proflavine complexed with calf thymus and T2 DNA, we conclude that stacking of the dyes external to the double helix is comparatively much weaker with T2 DXA, probably because of its glucosylation. Several sources are found for the circular dichroism induced in proflavine when it is complexed with DNA. There is a relatively weak circular dichroism induced when the dye is infinitely dilute on the DNA lattice; this presumably arises from the environmental asymmetry of the binding site. Stronger circular dichroism effects are induced by interaction of intercalated and stacked dyes; studies with T2 DNA, for which stacking seems to be blocked, permit a tentative resolution of effects due to the two modes of binding. One recurring theme of these studies is the observation that the optical properties are quite dependent on environment. The most dramatic example is a strong variation with salt concentration of the amplitude of the circular dichroism induced in the isolated (intercalated) monomer by the surrounding DNA. This suggests that the structure of the intercalated complex is quite sensitive to external conditions.
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  • 85
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    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The binding of n-butanol, benzyl alcohol, and trifluoroethanol to polyproline I (all peptide bonds in cis configuration) and II (all peptide bonds in trans configuration) has been demonstrated. It was found by infrared spectroscopy that hydrogen bonds are formed between the CO groups of the polymer and the OH groups of the alcohols. Their strength increases from n-butanol via benzyl alcohol to trifluoroethanol. The binding of benzyl alcohol could also be followed by optical rotatory dispersion due to the fact that the electronic transitions of the benzyl ring are rendered optically active by the binding to the polymer.
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  • 86
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    Biopolymers 8 (1969), S. 259-274 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The statistical mechanics of the effect of a small number of randomly occurring defects on the melting of a polypeptide chain is developed by using a perturbation of Boltzmann factors technique. The method is illustrated by an example where a second-component impurity contributes more to the energy of the hydrogen-bonded superstructure of the polypeptide chain than does the dominant amino acid residue, resulting in the overall destabilization of the helical conformation.
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  • 87
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    Biopolymers 8 (1969), S. 275-287 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Biological membranes consist mainly of lipids and proteins. At present, the structure of the lipid phase appears to be established, but hypotheses on the molecular organization of the protein are difficult to support. Thus the deformation behavior of whole human erythrocyte ghosts, ghosts after the selective removal of lipids and ghosts stripped of lipids as well as nonlipid components have been examined in the hope of securing indirect information on the organization of the protein. It has been found that large localized deformations result in partial membrane failure and long uniformly wide fibrils, frequently in excess of 3000 Å, are drawn across the rupture. These data are interpreted in terms of currently favored membrane models and the possibility of a fibrous membrane framework consisting predominantly of protein is reviewed. The behavior of the membrane in its various stages of extraction is compared and contrasted to that of synthetic polymer films of known organization.
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  • 88
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    Biopolymers 8 (1969), S. 247-257 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The thermally induced conformational changes of poly-N5-(3-hydroxypropyl)-L-glutamine in water and in methanol-water (3:7 v/v) have been analyzed in terms of the Lifson-Roig theory. The transitions in both solvents can be described by using v = 0.017. The thermodynamic parameters for the random coil-to-helix transition of one amino acid residue at room temperature were found to be: in water, ΔH = - 130 cal/mole and ΔS = - 0.45 e.u.; in methanol-water (3:7 v/v), ΔH = - 170 cal mole and ΔS = - 0.45 e.u. The size distribution of helical segments is broad, and the results of numerical calculations are presented for three degrees of polymerization (DP = 100, 300, and 750).
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  • 89
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    Biopolymers 8 (1969), S. 289-292 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 90
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    Biopolymers 8 (1969), S. 293-295 
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    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 91
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    Biopolymers 8 (1969), S. 297-299 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 92
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    Biopolymers 8 (1969), S. 303-304 
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    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 93
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    Biopolymers 8 (1969), S. 301-301 
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    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 94
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    Biopolymers 8 (1969), S. 304-304 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 95
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 8 (1969) 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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  • 96
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 7 (1969), S. 595-610 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The cyclic dipeptide, L-alanylglycyl anhydride, has been studied by optical rotatory dispersion; both L-alanylglycyl anhydride and the lactam, L-3-aminopyrrolidin-2-one, have been studied by circular dichroism. In hydroxylic solvents the circular dichroism spectra of 3-aminopyrrolidin-2-one can be attributed to an n-π* transition near 220 mμ and a π-π* transition near 190 mμ. In these solvents the optical activity of L-alanylglycyl anhydride can be explained as being due to contributions of n-π* transitions and a split π-π* transition. In acetonitrile, however, the circular dichroism spectrum of 3-aminopyrrolidin-2-one shows an additional apparent minimum near 200 mμ. The CD spectrum of the dipeptide is also quite distinctive in this solvent. The possible nature of the band at 200 mμ and the implications of these findings are discussed.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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  • 97
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 7 (1969), S. 619-623 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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  • 98
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 7 (1969) 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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  • 99
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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  • 100
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 7 (1969), S. 627-648 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The flow birefringence, extinction angles, and intrinsic viscosity have been determined at low velocity gradients for a complex of T2 bacteriophage DNA and methylated serum albumin prepared in dilute solution to a stoichiometry of approximately 90 proteins per DNA molecule. Comparative data upon equivalent solutions of pure uncomplexed T2 DNA are also presented, and these data are completely in accord with the results of previous study. The experimental data are interpreted in terms of current dynamical theory and indicate that the complex has an essentially linear chain structure, consisting of approximately two DNA molecules, which is hydrodynamically indistinguishable from the pure DNA and that extensive internal or intramolecular binding in the complex does not occur. Although interpretation of the results is hampered by an apparent moderate degree of polydispersity in the complex preparations and by relatively large shear extrapolations, the data for both DNA and the complex are substantially in accord with dynamical theory for a nondraining bead subchain model having high kinetic segmental rigidity.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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