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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
    Type: reportzib , doc-type:preprint
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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
    Type: reportzib , doc-type:preprint
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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
    Type: reportzib , doc-type:preprint
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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
    Type: reportzib , doc-type:preprint
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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
    Type: reportzib , doc-type:preprint
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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.
    Keywords: ddc:510
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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
    Type: reportzib , doc-type:preprint
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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
    Language: English
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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.
    Keywords: ddc:510
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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
    Language: English
    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
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The two-state theory of protein denaturation, in which it is assumed that a protein exists as two species, native and denatured, is examined by three approaches in this paper. First, the point is made that denaturation of an isolated molecule involves a continuous shift in the probabilities of occurrence of many states generated by the partition function for the protein. It is argued that the maximum term approximation does not lead to a two-state mechanism of denaturation, and that the extent of cooperation implied by the two-state theory should give very much sharper transitions than are actually found in proteins. Second, the two-state theory is applied to the various model systems treated in this series of papers, and is found to be inadequate. Since the detailed behaviour of the models is known, it is possible to deduce the effect of the incorrect application of the two-state theory to a system that “denatures” by gradual unwinding. This exercise is useful when, thirdly, we examine experimental data that seem to depart radically from a two-state interpretation. We conclude that a mechanism of gradual unwinding is the most generally valid assumption, and that the two-state theory has no theoretical or experimental support.
    Additional Material: 5 Ill.
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  • 43
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 3 (1965), S. 481-489 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Three types of band-forming centerpieces useful in band centrifugation in the analytical ultracentrifuge are described. The mode of filling and the advantages and disadvantages of each type are discussed.
    Additional Material: 6 Ill.
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  • 44
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 3 (1965), S. 497-508 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The ability of periodate-oxidized amylose to form aggregates in aqueous solution was studied by sedimentation, light scattering, and viscosity analyses. Ultracentrifuge schlieren patterns show that aggregation can be appreciable at pH 3.0 and 1.0. The hydroxyl ion-catalyzed degradation of the oxidized amylose is faster at pH 3.0 than at pH 1.0. Viscosity and sedimentation analyses conducted at pH 3.0 show that a minimum in the degree of aggregation of the oxidized molecules is obtained at 15-25% oxidation. Solubulity studies and x-ray diffraction patterns on retrograded amylose show that maximum solubility of the retrograded amylose is obtained by oxidizing to the extent of 25-35%. It was therefore concluded that in the general range of 20-30% periodate oxidation, the oxidized amylose has a minimum ability to form intermolecular hydrogen bonds. Outside of this range, oxidized amylose readily forms aggregates in aqueous solutions.
    Additional Material: 6 Ill.
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  • 45
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 3 (1965), S. 491-496 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Calorimetric measurements of the heat of the addition of the second strand of poly U to poly (A + 2U) to form the three-stranded poly (A + 2U) complex in 0.1M and 0.5M NaCl at 24 and 37°C. are reported. A value of ΔH = -3800 cal./mole of poly (A + 2U) formed was found to be fairly insensitive to the experimental conditions employed. The heat of the addition of the third strand to the preformed poly (A + U) helix is considerably less exothermic than the heat of reaction between poly A and poly U to form poly (A + U). The insensitivity of the heat of addition of the third strand (poly U) to changes in salt concentration and temperature lends qualitative support to the earlier hypothesis that the major portion of the variation of the ΔH of the poly A and poly U reaction with experimental conditions arises from differences in the conformation of poly A. Combining the information obtained in this study for the ΔH of the reaction forming poly (A + 2U) with data for the ΔH of the formation of poly (A + U) indicates that the conversion of poly (A + U) to poly (A + 2U) is opposed by an enthalpy change which increases with temperature. Extrapolation of these values to 52°C. where poly (A + U) is transformed to poly (A + 2U) in 0.5M NaCl leads to a value of ΔH = +3800 cal./mole (A + 2U) formed and ΔS = 11.5 cal./mole of (A + 2U) formed. It is concluded from the calorimetric data that the driving force for the poly (A + U) to poly (A + 2U) conversion reaction is the favorable entropy change.
    Additional Material: 1 Tab.
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  • 46
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 3 (1965) 
    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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  • 47
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 3 (1965), S. 461-480 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The effect of salt type and concentration on the transformation of an oriented crystalline collagen tendon into a crosslinked network under conditions of equilibrium swelling was investigated. Our main observations are the following. The degree of swelling of crystalline tendons increases at low salt concentration Cs, and decreases at higher Cs for a wide variety of salts. The observation is not reconcilable with swelling taking place in interfibrillar spaces or structural voids. Within the tropocollagen units and at their ends, regions of reduced organization are postulated (as suggested by Bear and by Schmitt) which are able to interact with the diluent in the amorphous-like manner. At least four different factors should be considered in assessing the role of salt and salt concentration on the shrinkage temperature Ts under isoelectric conditions. They are: (1) specific effects, (2) diluent effects, (3) crosslinking effects, and (4) nonequilibrium effects. The diluent effects are correlated with the salting-in-salting-out power of the ions which was characterized in Part I of this series. Smaller amounts of diluents are generally available to the tendon when the salt has a higher salting-out power, and this corresponds to higher shrinkage temperatures, other conditions being the same. The crosslinking effect raises Ts due to a reduction of the diluent content and, probably for p-benzoquinone and formaldehyde, also to a reduction of the conformational entropy in the molten state. Nonequilibrium effects arise from the fact that shrinkage and recrystallization are kinetically hindered when the tendon is highly deswollen in strong salting-out solutions, or when the salt has a crosslinking power. The specific effect is the only effect which is not related to the amount of diluent present in the tendon. Its origin is less clear. For anions such as Cl- and SCN-, it is possibly related to an ability of the ion to prevent intersegmental hydrogen bonding and water carbonyl bridges. The competition of several of the above effects for a given salt solution makes possible various types of dependence of Ts upon Cs: Ts may either continuously decrease or continuously increase with increasing Cs, or it may go through a minimum. In absence of salt, the cooperative character of the transition at the pH at which maximum swelling occurs appears extremely reduced. The large swelling maintains the tendon in the elongated state and this simulates a continuous decrease of Ts on lowering pH. In presence of small quantities of salt, which reduce swelling, the transition is sharp and Ts is decreased with pH up to pH 2, when maximum swelling occurs, and then reincreases on further lowering of the pH. The dependence of Ts upon Cs is more complex than under isoelectric conditions. There is generally an increase of Ts with Cs which is equivalent to an increase of the denaturation temperature with Cs for helical polyelectrolytes in solution. At higher salt concentrations, however, Ts may decrease again, and possibly increase again at still higher salt concentrations, depending upon the effect of the salt solution in the isoelectric zone.
    Additional Material: 11 Ill.
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  • 48
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: By using the Nemethy-Scheraga theory of water structure, a calculation was made of the energy changes for the rupture of a DH…A solute-solute hydrogen bond in water. A partition function was also obtained for the binding of water and other solutes to the DH and A groups in the special case where these are the NH and CO groups of a random coil polypeptide chain. In subsequent papers of this series, these calculated quantities will be used in a statistical mechanical treatment of the helix-coil transition for polypeptides in water.
    Additional Material: 4 Tab.
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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: A partition function is derived for a simple model of interacting helices in a short (20 residues) chain of poly-L-alanine. It is found that interhelical hydrophobic bonds effect a marked stabilization of helical forms, and give rise to a sharp transition of the type found in many proteins.
    Additional Material: 4 Ill.
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  • 50
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Crosslinked synthetic polypeptides of poly Glu51Lys33Tyr16 (mol. wt. 31,000) and of poly Glu52Lys33Tyr15 (No. 3) (mol. wt. 52,000) containing from one to six crosslinks per molecule have been prepared by use of FFDNB, WRK and ICD reagents.The monomeric fractions of these derivatives were isolated by Sephadex G-100 chromatography. The number of crosslinks per molecule of DNPene derivatives was determined by total hydrolysis of the derivatives, isolation of O, N∊-DNPene-Tyr-Lys bridges by paper chromatography and then spectrophotometric quantitation. The number of the amide-type crosslinks in Am derivatives was established by their deamination followed by total hydrolysis and quantitation of the remaining lysine residues. Crosslinked derivatives appear to have a more compact structure, as judged by their behavior on the Sephadex columns and by their intrinsic viscosities. They were further characterized in regard to their amino acid composition, average number of the crosslinks per molecule, nitrogen content, solubility, root-mean-square end-to-end distance, and their spectral properties. Their properties recommend them as useful models for the study of the tertiary structure of proteins in solution.
    Additional Material: 1 Ill.
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  • 51
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The introduction of intramolecular amide bonds into synthetic polypeptides produces molecules with organized spatial structure which are good models for the tertiary structure of proteins. Polarization of fluorescence measurements were used to study the internal structure and the overall rigidity of the intramolecularly crosslinked polypeptides. The graph of [(1/p) + (1/3)] against T/η changes from a straight line to a continuous curve: the temperature at which this change occurs and the slope of the straight line segment measure the stability of the internal structure of the molecule. The introduction of one to six crosslinks produces an organized internal structure that becomes more stable as the number of crosslinks increases. In contrast to the fluorescence measurements, the intrinsic viscosities, reflecting the overall hydrodynamic domain of the molecules, change (decrease) to the same extent whether one, four, or six intramolecular crosslinks are present. The overall rigidity of the polymers can be assessed by the rotational relaxation time ρh and the polarization at 10°C. p10. Both of these criteria show that the presence of six crosslinks significantly increases the rigidity, but one or four does not. The various hydrodynamic measurements may be fitted into a hierarchy of discrimination: intrinsic viscosity, sedimentation, and diffusion for size and shape; rotational relaxation time and polarization of fluorescence at a given temperature for overall molecular rigidity; and transition temperature and rate at which it is attained for internal molecular detail.
    Additional Material: 4 Ill.
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  • 52
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    New York : Wiley-Blackwell
    Biopolymers 3 (1965), S. 57-68 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A theory for the dependence of the net thermodynamic solvation of a macroion in an electrolyte solution is presented. The solvation in moles salt/mole macroion is shown to approach - |Zp|/v in the limit of infinite dilution of salt and macroion. The solvation in moles water/mole macroion is shown to approach zero at zero water activity. Isopiestic determinations of the hydration of sodium deoxyribonucleate in NaCl, Na2SO4, and NaClO4 solutions indicate that short-range interactions of the NaDNA with solvent account for more than half of the observed solvation. The net hydration appears to be predominantly influenced only by water activity.
    Additional Material: 3 Ill.
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  • 53
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    New York : Wiley-Blackwell
    Biopolymers 3 (1965), S. 69-78 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The cohesive energy densities (CED) of three amylose derivatives have been estimated from viscosity measurements in a range of solvents, by using methods proposed by Mangaraj and Bristow and Watson. The values assigned to the triacetate, (2.5) nitrate, and tricarbanilate are 92 ± 2, 90 ± 2, and 87 ± 2 cal./cc., respectively. The CED of unsubstituted amylose has been measured and found to be 154 ± 4 cal./cc. The results are discussed in relation to solvent power, structure, and possible correlation with the internal pressure of the polymer.
    Additional Material: 3 Ill.
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  • 54
    Electronic Resource
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    New York : Wiley-Blackwell
    Biopolymers 3 (1965), S. 115-119 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Viscosity measurements and calculated rotary diffusion constants show that collagen undergoes photopolymerization when irradiated with ultraviolet light of 2537 A. Fibril formation at the same time is inhibited. The results are correlated with the aromatic amino acid content of the dangling peptides protruding from the rigid portion of the macromolecule.
    Additional Material: 3 Ill.
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  • 55
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: It is shown how the technique of fluorescence may be used to assess conclusions about conformation which are based on a statistical mechanical treatment of simple protein models. Specifically, the state of bonding and distance between two chromophores in a molecule depend on the overall conformation, which can be computed for model systems. On the assumption that the intensity and polarization of fluorescence are affected by exciton transfer between the chromophores, it is possible to compute the effect of conformation on fluorescence. It is demonstrated that the conformational changes computed in the preceding paper will give rise to marked changes in the intensity and polarization of fluorescence.
    Additional Material: 3 Ill.
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  • 56
    Electronic Resource
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    Biopolymers 3 (1965), S. 421-437 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Intrinsic viscosity-temperature studies for isoelectric gelatin in KCl and KSCN aqueous solutions and equilibrium degree of swelling, ν-1, measurements for amorphous crosslinked rat tail tendons in the same solutions were carried out. On increasing salt concentration Cs, both [η] and ν-1 increase, go through a maximum, and then decrease at high Cs, KCl being more effective than KSCN in bringing about this decrease. The trend observed is similar to the variation of solubility of polypeptides and soluble proteins with Cs. By regarding a water-salt solution of a given Cs as a single diluent interacting with the protein modified by solvation and binding of ions, usual polymer solution theories were applied to the experimental results. Thus, quantities related to the entropy and enthalpy components of the excess chemical potential of the diluents were obtained. The data indicate that the initial increase of [η] and ν-1 with Cs results from the balance of an enthalpy component which, on increasing Cs, becomes less favorable to dilution and an entropy component which, conversely, becomes more favorable. The subsequent decrease of [η] and ν-1 with Cs is due to the prevailing of the enthalpy component. The maximum is reached at higher Cs for KSCN than for KCl, primarily because of the large increase in the entropy component operated by the former salt. The increase of the entropy parameter with Cs is associated to a breaking down of the coordinated water structure and to an alteration of the conformation of the macro molecules due to ion-dipole interaction and to ion absorption. The decrease in exothermicity of dilution with Cs indicates a reduced thermodynamic affinity of the diluent toward the polymer which probably results from alteration of the nature of both polymer and diluent.
    Additional Material: 6 Ill.
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  • 57
    Electronic Resource
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    New York : Wiley-Blackwell
    Biopolymers 3 (1965), S. 535-543 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The molecular weight distribution of poly-γ-benzyl-L-glutamate prepared by N-carboxy anhydride (NCA) polymerization with the use of di-n-butylamine, diisopropylamine, and sodium methoxide as initiators was investigated. In every case, narrow distributions were found. Moreover the results allow us to conclude that the same polymerization mechanism is operative with each of the above initiators. The experimental distribution curves show fairly good agreement with the theoretical distributions expected for a polymerization process without termination.
    Additional Material: 3 Ill.
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  • 58
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    Biopolymers 3 (1965), S. 545-554 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The influence of counterion radius on the polyelectrolyte behavior of poly-L-cysteate in aqueous solution under different conditions was investigated. A linear relationship was found between a critical concentration in solution of the synthetic charged poly-peptide and the crystallographic radius of different counterions, indicating that the stability of this macromolecule is inversely proportional to the size of the cations.
    Additional Material: 11 Ill.
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  • 59
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    Biopolymers 3 (1965), S. 573-583 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: X-ray diffraction patterns from dilute solutions of poly-3,5-dibromo-L-tyrosine in dimethylformamide and equivalent concentrations of 2,6-dibromophenol in the same solvent are compared. The intensity difference as a function of scattering angle is indicative of the arrangement of residues in the polymer. A novel averaging procedure is used to compute the intensity patterns arising from regular arrays of bromine atoms. Interbromine spacings measured on a Drieding model of a right-handed α-helix with side groups restricted to rigid positions of maximum stagger give moderate agreement with experiment. Very good agreement with observations is obtained by allowing for a small oscillation of phenyl rings which effectively cancels out the contribution of large distances to the intensity curve.
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  • 60
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Aqueous solutions of ribonuclease and human serum albumin were subjected to periods of controlled heating and the nuclear magnetic spin-lattice relaxation times, T1, of the water protons measured. The heat treatment causes an initial increase in the relaxation times of the water protons. These T1 variations indicate that a configurational change, compatible with a disordering of the protein structure occurs, which involves an increase in various modes of internal mobility. The T1 measurements also indicate a close, ordered association of the water molecules and the protein.
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  • 61
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    Biopolymers 3 (1965), S. 594-594 
    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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    New York : Wiley-Blackwell
    Biopolymers 3 (1965), S. 609-616 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The melting characteristics of unfractionated yeast s-RNA in neutral aqueous solution have been examined by high-resolution proton magnetic resonance spectroscopy. These studies indicate that the bases of s-RNA become rotationally activated at lower temperatures than their associated ribose units. These observations, as well as the recently determined base sequence of an alanine-specific s-RNA, suggest that base complementarity may not be the primary determinant in the stabilization of the secondary structure of s-RNA. In addition, evidence for exchange of C8-protons of purine bases of s-RNA with D2O was obtained at temperatures above 70°C.
    Additional Material: 4 Ill.
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  • 63
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    Biopolymers 3 (1965), S. 617-624 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Anomalous optical rotatory dispersion (ORD) is induced in symmetric dyes when bound in metachromatic complexes with chondroitin sulfates (ChS) and kerato sulfate (KS) from mammalian and shark origin as well as with heparin (H) providing inference that secondary structures exist in these biopolymers. The induced rotation occurs in the absorption band of the bound dye and differs in shape and/or spectral position from the classical Cotton effect seen with single optically active chromophores. The AO:ChS complex has an induced ORD curve similar to that of the exciton band of a helical polymer. Strength of the induced rotations with methylene blue increases with the degree of metachromasy of the 1:1 complex. The sense of the MB Cotton effects may depend upon the conformations of the repeating dimeric units, since MB complexes with ChS (alternating 1-3,1-4 β-glycosides) give (+) effects while MB:H (1-4 α-glycosides) have (-) effects in the γ band region. Preliminary evidence for the occurrence of Cotton effects with the mucopolysaccharides themselves in the ultraviolet region was obtained. The sign of the Cotton effect for ChS-C is (-), trough about 45.9 kK., crossover about 48.8 kK. whereas that for H is (+), peak about 50.4 kK.
    Additional Material: 2 Ill.
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  • 64
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Poly-N5-(3-hydroxypropyl)-L-glutamine (PHPG) samples of molecular weights from 20,000 to 140,000 were synthesized by the action of 3-amino-1-propanol on poly-γ-benzyl-L-glutamate. PHPG is freely soluble in water and in a variety of organic solvents and was shown to be devoid of functional groups ionizing in the pH range 2-12. From hydrodynamic data (viscosity, sedimentation, diffusion) and optical rotatory measurements (ORD in the range 289-650 mμ, circular dichroism and Cotton effects in the range 210-280 mμ) on samples of different molecular weight it was concluded that PHPG is largely helical in methanol, ethylene glycol, formamide, dimethylform-amide, n-butylamine, and acetic acid, and randomly coiled in dichloroacetic acid and formic acid. In water the polymer is partly helical, the degree of helicity increasing with decreasing temperature and increasing molecular weight. The following solutes were found to decrease the helicity in the order indicated: NaOH 〉 guanidinium chloride 〉 urea 〉 HCl 〉 LiBr 〉 NaBr 〉 NaCl 〉 H2O. Detergents do not destroy the helical conformation. Helix-coil transition curves were obtained for the solvent pairs: methanol-water, acetic acid-water, and chloroform-dichloroacetic acid. Thermal transitions were observed in water, water-methanol (70:30 v/v), and dichloroacetic acid-ethylene dichloride (22:78 v/v), the latter being of the “inverted” type. Heats of helix formation were calculated and their significance is discussed.
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  • 65
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    Biopolymers 3 (1965), S. 681-686 
    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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  • 66
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Polyadenylic acid is degraded into mononucleotides and low molecular weight oligonucleotides in a 20 hr. period at 64°C. by the action of Mn (II), Co (II), Ni (II), and Cu (II) ions, and in a 2 hr. period by Zn (II) ions. The latter also degrade poly C, poly U, and RNA at approximately the same rate, but poly I is degraded very much more slowly. No such difference in reaction rates can be observed in the alkaline degradation of polynucleotides. The sluggishness of the reaction with poly I is not due to any highly ordered structure of the zinc-poly I complex, but probably to the weakening of the zinc-phosphate bond through simultaneous binding of the zinc to the inosine base. Evidence for such a hypothesis is derived from the inhibition of the zinc degradation of poly A by inosinic acid or poly I. No drastic difference in the nucleotide composition of the undegraded residue can be observed in the degradation of RNA by zinc and by alkali.
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  • 67
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Evidence is presented that polyriboadenylic acid (Poly A) is a single-strand flexible helix of stacked bases at neutral pH and room temperature. As the temperature is raised the stacking decreases, but there is still perceptible order at 80°C. The thermal transition from the double-strand helix (which exists at low pH) to the single-strand helix has been followed by optical rotatory dispersion, optical absorption, and viscosity measurements.
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  • 68
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The binding curves of various aminoacridines on calf thymus DNA have been determined by a spectrophotometric method. The dominant role of electrostatic forces in the interaction has been confirmed by the effect of ionic strength. Side chain and ring substituents in the aminoacridines do not inhibit binding, since this decreases in the order: acranil 〉 neomonacrin 〉 atebrin 〉 9-aminoacridine ∼ proflavine 〉 9-amino-1,2,3,4-tetrahydroacridine (THA). The last named shows the effect of diminishing the flat area of the rings in the aminoacridines. The shape of the binding curves of proflavine, 9-aminoacridine, and THA on thermally denatured DNA show that about 30-50% more binding sites are available to these cations on denatured DNA than on native DNA, but that the binding constants are the same. These observations are discussed in relation to the intercalation and other models for the interaction. It is concluded that exact and complete intercalation is not a necessary condition of strong binding and that other, less regular, models, in which the positive ring nitrogens of the acridines are close to the DNA phosphates and the acridine rings partially interact with the DNA base rings, are probably more consistent with the effect of denaturation of DNA on the binding curves which are characteristic of the interaction in solution.
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  • 69
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In an attempt to clarify certain questions of the configuration of amylose in aqueous solution, carboxymethyl groups were introduced into corn amylose (degree of substitution ca. 0.8) and certain properties of the derivative (CMA) studied. The intrinsic viscosity exhibits a strong increase between pH 2 and 6 but remains constant at higher pH. A pH 6 and above, CMA exhibits typical polyelectrolyte behavior. CMA does not form a complex with iodine at pH 6 or above but does form a violet-colored complex at low pH. The absorption maximum of the CMA complex lies at a somewhat lower wavelength (550 mμ) than that of the complex formed by the parent amylose. The reduced viscosity and specific optical rotation of the CMA-iodine complex remains constant up to a concentration of 1.2 mg. iodine/100 mg. CMA, then both properties decrease with further increases of iodine content. All of the above results and hydrogen ion titration behavior are in agreement with the hypothesis that CMA exists as a coil of short helical segments in acid solution and that these helical segments break down on ionization of the carboxyl groups. The specific optical rotation of CMA increases between pH 2 and 6, remains constant between pH 6 and 12, and decreases above pH 12. This later result shows that the similar decrease in rotation seen in amylose cannot be attributed, at least entirely, to a helix-coil transition. There must be another effect on optical rotation, direct or indirect, of the ionization of hydroxyl groups.
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  • 70
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    Biopolymers 3 (1965), S. 209-212 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 2 Tab.
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  • 71
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A mathematical method has been developed, together with a digital computer program for its evaluation, for the determination of possible conformations of a polypeptide chain for any given amino acid sequence. Allowed conformations were required to satisfy predetermined criteria regarding the locations of potential energy minima for rotation around single bonds, steric restrictions arising from van der Waals contacts between atoms, and the formation of a closed polypeptide loop by means of a peptide linkage or a disulfide bridge. Requirements for specific noncovalent interactions can also be considered. Various assumptions regarding the selection of the minima for rotational potentials and of the van der Waals contact distances are discussed. According to the assumptions adopted in the paper, 21 conformations are allowed for a glycine residue which is part of a dipeptide. These conformations are assumed to lie at minima of the rotational potential function, and satisfy simultaneously the steric requirements. Dipeptides containing alanine or other residues are restricted to 7 such conformations. As an example of the applicability of the method, the computation was performed for the smallest loop containing a disulfide bridge in the ribonuclease molecule, i.e., the cyclic octapeptide formed by residues 65 to 72. Only 15 allowed conformations were found for the loop as a whole. Parameters characterizing these allowed conformations are tabulated. Approximate calculations indicate the importance of steric restrictions and of the presence of side chains in reducing the conformational freedom of this peptide. Further potentialities of the method are discussed.
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  • 72
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A combinatorial formulation of the partition function is developed for short polypeptide chains, where summations can be evaluated. From the complete combinatorial expression it is possible to assess the validity of any approximations which are made in evaluating the partition function. It is shown that it is an excellent approximation to consider the hydrogen-bonded portion of a short (20 residues) chain as consisting of a single helical sequence of any size, with all sizes of helical sequences being about equally probable at the transition temperature. Another approximation, involving a linear dependence of the energy and entropy on the number of hydrogen bonds, helps to clarify the nature of the intermediate states in the denaturation process. Expressions are developed which incorporate the effect of hydrophobic bonds on the stability of the α-helix, and the binding of water to the random coil. It is concluded that hydrophobic bonds in helical sequences can greatly stabilize the helix, but that similar bonds in the random coil can largely offset this stabilization.
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  • 73
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The Lifson-Roig matrix theory of the helix-coil transition in polyglycine is extended to situations where side-chain interactions (hydrophobic bonds) are present both in the helix and in the random coil, as discussed for short chains in paper II of this series. It is shown that the conditional probabilities of occurrence of any number and size of hydrophobic pockets in the random coil can be adequately described by a 2 × 2 matrix. This is combined with the Lifson-Roig 3 × 3 matrix to produce a 4 × 4 matrix which represents all possible combinations of any amount and size sequence of α-helix with random coil containing all possible types of hydrophobic pockets in molecules of any given chain length.
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  • 74
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    New York : Wiley-Blackwell
    Biopolymers 3 (1965) 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 75
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The method of sequence-generating functions is applied to long polypeptide chains to describe various types of hydrophobic bonding in the random coil. These results are then combined with a similar treatment of the α-helix in order to discuss the helix-coil transition in single helices and in molecules whose helical segments interact by side-chain hydrophobic bonding. Numerical calculations, based on the equations derived in this and preceding papers, are presented to show the relative probabilities of occurrence in the random coil of neighbor-neighbor hydrophobic bonds and pockets of hydrophobic bonding, and the relative probabilities of occurrence of the various states in a system of interacting helices. A discussion is also presented of the dependence of the helix-coil nucleation and growth parameters on solvent and side chain.
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  • 76
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The partition function of paper II for short polypetide chains is incorporated here into one for a simple model for side-chain hydrogen bonds between helices. It is thus possible to calculate the fraction of amide hydrogen bonds, the fraction of side-chain hydrogen bonds, and the number of bound protons as a function of temperature and pH. Illustrative data are presented for the probabilities of occurrence of intermediate structures and for the influence of the overall conformation on the observed pK's of ionizable groups.
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  • 77
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    Journal of Applied Polymer Science 9 (1965), S. 31-38 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The swelling and dissolution of heat-set nylon 6 fiber in aqueous sulfuric acid were examined. Steam-set fiber having good dyeability swells with much more difficulty than the dry-heat-set and unset fibers. Similar phenomena are seen in the examination of density of nylon 6 fiber subjected to heat setting, and it is found that the resistance to swelling depends on the crystalline region rather than on the amorphous region.
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  • 78
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The infrared spectrum of deuterated ε-caprolactam was examined. It was confirmed spectroscopically that the hydrogen of the N—H group in ε-caprolactam is exchanged for deuterium after repeated exchange reactions. The deuterated ε-caprolactam was polymerized, and the infrared spectrum of the polymer (called as N—D polymer) is compared with that of the normal nylon 6 polymer (called N—H polymer) which was steam-set in D2O vapor at 135°C. Characteristic absorption bands of N—D polymer are observed at 967, 896, 888, 876, and 719 cm.-1. The water accessibility of both N—H and N—D polymer was estimated from the spectra of both samples subjected to the repeated steam setting in D2O and H2O alternately at 130°C. The results show that at the initial stage of the repeated steam setting, H2O and D2O molecules may penetrate into the ordered regions in the polymers and partially break down intermolecular hydrogen bonds; such phenomenon may be followed by an exchange reaction and recrystallization. Subsequent stages of steam setting, however, no longer bring about such an effect.
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  • 79
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    Journal of Applied Polymer Science 9 (1965), S. 91-115 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The degree of penetration, the diffusion constant, and the uptake of dyestuffs of different molecular sizes were measured in undrawn and drawn nylon 6 filament, heat-set under various conditions in order to determine the pore structure in the amorphous regions. Unset and dry-heat-set nylon 6 can be penetrated only with difficulty by the dyestuffs having molecular lengths above about 30 and 25 A., respectively. The apparent diffusion coefficients and molecular weight of dyestuffs are approximately hyperbolic. The relations are considerably different, depending on the degree of drawing and conditions of the heat setting. Further, the relations among molecular size, amount of absorbed dyestuffs, and fraction of amorphous region capable of being penetrated by dyestuff are discussed with reference to the lateral-order distribution of nylon 6, as evaluated from the accessibility to D2O vapor.
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  • 80
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    Journal of Applied Polymer Science 9 (1965), S. 3795-3818 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The effect of low plasticizer concentrations on the glass transition temperature of poly(methyl methacrylate) (PMMA) has been studied experimentally for diethyl phthalate (DEP) and methyl methacrylate (MMA) as plasticizers. Volume dilatometry, differential thermal analysis, and a torsional pendulum were used to determine glass transition temperatures. The monomer-plasticized PMMA samples were prepared by polymerizing MMA to a limiting conversion which was found to depend primarily on temperature. At temperatures slightly above the glass transition temperature of a MMA-PMMA system, a polymerization reaction occurred at a rate rapid enough to complicate the interpretation of the dilatometric and differential thermal analysis methods for determining the glass transition temperature. However, the torsional pendulum method could be used since it did not require measurements to be made at temperatures where polymerization could occur. The differential thermal analysis results showed that the temperature at which the polymerization reaction was first detectable was related to the glass transition temperature of the MMA-PMMA solution. The measured glass transition temperatures were compared with the predictions of the theories of Fox, Kelley, and Bueche, and Dimarioz and Gibbs on the effect of plasticizer concentration on the depression of the glass transition temperature.
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  • 81
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Three methods of measuring thermal oxidative stability of polypropylene have been compared. The oxygen absorption and the sealed tube tests give comparable results. The polymer lifetimes in circulating oven-aging tests differ significantly from those obtained by the first two methods. The oven-aging lifetime is aparently influenced to a large extent by the volatilization of the added stabilizer and of the oxidation products, the former decreases whereas the latter increases the polymer lifetime. The optimum composition of a synergistic stabilizer system was found to vary with the test method.
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  • 82
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    Journal of Applied Polymer Science 9 (1965), S. 3845-3850 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: During a program to evaluate the gel permeation chromatography (GPC) technique for measuring the molecular size distribution of polymers, three experimental epichlorohydrin-bisphenol A polymers were sent to Waters Associates for analysis with the commercially available instrument. The resulting distribution curves were used to calculate weight-average and number-average chain lengths of the samples. These values were found to give good straight-line correlations with weight-average and number-average molecular weights measured by absolute methods. Thus the GPC method gives meaningful information about the molecular size distribution of polymers which can be used to obtain rapid estimates of molecular weight.
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  • 83
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Stress-strain curves at various temperatures and secant modulus vs. temperature curves were used to investigate the differences that exist between peroxide crosslinked polyethylene, and vulcanized rubber. A series of hypotheses in terms of crosslinking density and crystallinity is advanced to help visualize the differences between crosslinked polyethylene and cured rubber. The same techniques were used to investigate the nature of crosslinked ethylene-ethyl acrylate copolymers. These copolymers, being more flexible than polyethylene, appear similar to “mechanical rubber,” particularly after crosslinking. Recent experiments, however, indicate that profound differences exist. The performance of crosslinked polyethylene and of ethylene copolymers at elevated temperatures depends on crosslinking density, while at lower temperatures it is dominated by polyethylene crystalline morphology. This latter factor makes crosslinked polyethylene at ambient temperature a completely different product from vulcanized rubber. It also means that a crosslinked polyethylene will have lower crosslinking density than most rubber compositions of equivalent room temperature stiffness. A good indication of crosslinking density of crystalline polyolefins may be obtained by measuring mechanical properties such as modulus at elevated temperatures. Use of reactive co-agents is effective in raising crosslinking density to the point where fairly good elevated temperature properties are obtained without increasing the room temperature rigidity.
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  • 84
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    Journal of Applied Polymer Science 9 (1965), S. 3903-3908 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: An apparatus was designed to measure the osmotic pressure of solvent-polymer systems. The method is unique in that semirigid polymers may be incorporated as the solute component without specimen fissures occurring from excessive solvent dilative action. The advantages of this technique are: high polymeric materials both elastomeric and plastic can be structurally characterized by the same technique; the calculated effective molecular weight of the polymer network will reflect a value consistent with the polymer's performance characteristics; and the method is only restricted to lyophilic polymer-solvent systems.
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  • 85
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    Journal of Applied Polymer Science 9 (1965), S. 1291-1297 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The quantitative theory of free radical mechanisms in emulsion polymerizations is reexamined. It is suggested that existing descriptions are not entirely consistent with physically realizable situations. The proposed modifications result in a closer resemblance to homogeneous systems. Explicit expressions for the distribution of radicals are also given. The importance of interphase transfer is emphasized.
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  • 86
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    Journal of Applied Polymer Science 9 (1965), S. 1273-1283 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: A model equation derived for the viscosity-average degree of polymerization (P̄v) for the incremental addition of modifiers, P̄v = K{(exp{arx1} - 1) + [2/(2 + exp {x1r})]a(exp{arx2} - exp{arx1})}1/a indicates a minimum should occur in a curve of P̄v versus conversion at which the increments are added, x1. Incremental addition of commercial tert-dodecyl mercaptan in the laboratory to SBR recipes at 5°C. showed effects contrary to those predicted by the model equation, but incremental addition experiments with tert-nonyl mercaptans resulted in a minimum in viscosity versus x1 curves, changed the molecular weight distribution, and required 34 wt.-% less mercaptan than did the tert-dodecyl mercaptan control (all the tert-dodecyl mercaptan added initially). Incremental addition of tert-nonylmercaptan in pilot plant 20-gal. autoclave reactors gave essentially the same results found in the laboratory bottle experiments. The stress-strain and mixing properties of the incrementally modified polymer and the tert-dodecyl mercaptanmodified control were essentially the same within experimental error. Conditions required for successful application of the incremental modifier technique are given.
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  • 87
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 9 (1965), S. 1323-1340 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Terpolymers from 1,3-butadiene, styrene, and vinylpyridine are important as rubbers, and, in latex form, as components of rubber-to-fabric adhesives. Three monomer mixtures having the approximate weight composition butadiene/styrene/2-methyl-5-vinylpyridine 70/15/15, 25/48/27, and 38.5/49/12.5 have been emulsion-polymerized at 30°C., and the terpolymer composition as a function of the conversion has been studied. The six monomer reactivity ratios have been determined by binary copolymerizations at 30°C. and checked by low conversion bulk terpolymerizations. Average and instantaneous composition-conversion curves have been calculated, on the assumption of a constant reaction volume, by numerical integration of the terpolymerization equations on electronic computer. Details, of general applicability, for calculations are given. The experimental results of the emulsion terpolymerizations fit satisfactorily the calculated curves over a wide range of conversions.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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  • 88
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 9 (1965), S. 1363-1366 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The radiation-induced vulcanization of cis-polybutadiene (Europrene Cis, 92% cis-configuration) was investigated. The crosslinking density of irradiated rubber was determined by two methods: equilibrium swelling and equilibrium compression modulus. The inhibition and acceleration of radiation-induced crosslinking by addition to Europrene Cis of sulfur, Thiurame, Elastopar, Arubrene, paraffin oil, or barium sulfate was studied. The chemical resistance of radiation vulcanizates to 10% nitric acid was determined.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
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  • 89
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 9 (1965), S. 999-1003 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Yellow coloration develops in polystyrene under 2537 A. radiation a t comparable rates whether or not oxygen is present. Thus the commonly accepted view that coloration is a manifestation of oxidation is wrong. The coloration increases in intensity with time but does not move toward the red end of the spectrum, behavior which is typical of poly(vinyl chloride), polyacrylonitrile, etc., and which is due to the development of long conjugation sequences. It is suggested that the color in polystyrene is due to conjugated carbon-carbon unsaturation in the polystyrene backbone but that the lack of mobility of the molecules within the rigid polymer films prevents long sequences of double bonds becoming coplanar and color consequently moving through the spectrum. The rapid darkening of irradiated polymer which occurs on melting is probably due to relaxation of this rigidity allowing coplanarity of longer sequences.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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  • 90
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 9 (1965), S. 1019-1040 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: A number of catalytic solvents have been discovered for the polyurethane foaming process. These solvents include N,N-dimethylformamide (DMF), dimethyl sulfoxide (DMSO), formamide, and a number of others. The catalytic effectiveness of a given solvent appears to be dependent on its dipole moment, water solubility, and the size or bulkiness of the groups which are attached to the carbonyl carbon or sulfur atom of the amides and sulfoxides, respectively. Steric effects play a very important role in controlling the catalytic efficiency of these solvents. A mechanism is proposed for the catalytic action of these solvents in the polyurethane reaction.
    Additional Material: 5 Ill.
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  • 91
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 9 (1965), S. 1067-1072 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Kinetic equations for the decomposition of S-hydroxymethyl cellulose xanthate in the presence of acid and formaldehyde are derived. The assumed mechanism involves an equilibrium between the S-hydroxymethyl cellulose xanthate and cellulose xanthic acid and xanthate ion. Decomposition appears to proceed via interaction between the cellulose xanthate ion and hydrogen ion which form an activated complex that subsequently decomposes to cellulose and carbon disulfide. The equations derived show the proper dependence on acid and formaldehyde concentrations. An estimate of the equilibrium constant between cellulose xanthate and S-hydroxymethyl cellulose xanthate is calculated from the rate constants.
    Type of Medium: Electronic Resource
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  • 92
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 9 (1965), S. 1579-1584 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: In a previous paper it was shown that the vulcanization obtained with ethylene-propylene-diene terpolymer is equivalent or superior to that obtained with ethylene-propylene copolymer when a peroxide-dimethacrylate coagent cure system was used. In order to determine the effect of the unsaturation on the physical properties in the terpolymer, the terpolymer had been hydrogenated to remove the double bonds. Infrared spectra and bromination were used to check the extent of hydrogenation. Tensile strength, Shore A hardness, per cent elongation, and modulus indicated no decrease in vulcanization efficiency after hydrogenation. The data show that the unsaturation in the terpolymer does not contribute to the vulcanization cure with the peroxide-dimethacrylate coagent curing system.
    Additional Material: 1 Ill.
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  • 93
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 9 (1965), S. 1585-1591 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: It is known that aromatic hydrocarbons are more stable to ionizing radiation than are saturated hydrocarbons. It is shown here that polyethylene can be more stable to radiation either by mixing aromatic compounds with the polyethylene or by grafting styrene onto the polyethylene. In either case, the polymer has greater radiation resistance than predicted from the law of averages. Aromatic compounds which have the greatest resonance energy protect the polymer to the greatest extent. In mixtures, polystyrene gives the least protection, and naphthalene, anthracene, and phenanthrene give the greatest protection. Polyethylene grafted with styrene has better radiation resistance than does a polyethylene-polystyrene mixture. The G(H2) was calculated for each sample, and curves are presented illustrating the effect.
    Additional Material: 3 Ill.
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  • 94
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Analytical and experimental studies of surface tension and viscosity properties of Dow resins PS-2 and 276V-2 are described. This investigation was undertaken to provide information on materials of interest for thermoplastic recording. It was found that external plasticization lowered the surface tension of the polystyrene while greatly decreasing the viscosity. Typical values for a 25% mixture of PS-2 in 276V-2 are γ = 35 dynes/cm. and η = 20 poise at 80°C.
    Additional Material: 3 Ill.
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  • 95
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 9 (1965), S. 1599-1599 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Type of Medium: Electronic Resource
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  • 96
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 9 (1965), S. 1631-1639 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: According to mechanisms described in the literature, photodecomposition of nylon 66 proceeds through the abstraction of the hydrogen on the carbon α to the amide NH group by a free radical which has been activated by photo absorption. In the propagation phase, the α-carbon radical could readily react with atmospheric oxygen to form a hydroperoxide. The formation of a hydroperoxide in the photodecomposition scheme for nylon 66 has been detected but has not been measured quantitatively. With the colorimetric method described in this paper, it is now possible to determine the peroxide content in a polyamide to a level of 1 μmole/g. with a relative precision of less than 5%. The polyamide is dissolved in tetrafluoropropanol, to which aliquots of potassium iodide and glacial acetic solutions are added. The absorbance of the liberated iodine is measured in a 1-cm. cell at 400 mμ and the hydroperoxide concentration determined from a calibration curve constructed from hydrogen peroxide solution standards. The rate of peroxide formation, which is dependent on the wavelength of ultraviolet radiation, can be correlated to the strength loss exhibited by a nylon 66 yarn free from antioxidant and delustrant. In addition, an increase in the level of thermal degradation will accelerate yarn strength loss and peroxide formation under ultraviolet exposure. The hydroperoxide begins to decompose at about 100°C. Yarn finish will contribute to the peroxide formation during exposure.
    Additional Material: 8 Ill.
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  • 97
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 9 (1965), S. 1653-1668 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The infrared spectra of methane, n-butane-, and n-dodecane-sulfonic acids, their esters, alkali metal, silver and amine salts, amides, and chlorides are compared with analogous structures derived from chlorinated and chlorosulfonated polyethylenes. The Bellamy and William's linear relationship between vSO2 (asym.) and vSO2 (sym.) is valid for both the simple alkane sulfonic acid derivatives and those of chlorinated and chlorosulfonated polyethylenes.
    Additional Material: 1 Ill.
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  • 98
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 9 (1965), S. 1669-1680 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Copolymerization of vinyl chloride with trans-1,2-dichloroethylene was carried out at various temperatures, and the properties of the copolymers obtained by the emulsion copolymerization at low temperature were examined. In the case of bulk copolymerization at temperatures higher than room temperature, the rate of polymerization, the equilibrium conversion, and [η] were lowered with increasing content of trans-1,2-dichloroethylene in the initial monomer mixture, but the Tg and softening point of the copolymers containing about 15% of 1,2-dichloroethylene unit were about 10°C. higher than these of conventional PVC resin, in spite of their inability to form films. The monomer reactivity ratios at 50°C. were 5.39 (VC) and 0.072 (trans-DCE). Emulsion copolymerization was carried out at -30°C. with the use of a redox initiator system (hydrogen peroxide-ferrous sulfate-ascorbic acid), in order to increase both the [η] and the rate of polymerization. The copolymers prepared at low temperature had higher Tg and better solubility than the VC homopolymer polymerized at the same condition or conventional PVC resin. The results of the infrared absorption spectra, the solubilities, and the calculation of sequence length of VC monomer unit in the polymer chain indicated that the stereoregularity and the crystallinity of the low temperature copolymers were lower than those of the low temperature VC homopolymers. It was concluded that higher Tg and good solubility of the low temperature copolymer were brought about by the prevention of the free rotation of the polymer chain by the random distribution of 1,2-dichloroethylene units in the polymer chain.
    Additional Material: 4 Ill.
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  • 99
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 9 (1965), S. 1681-1700 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Endgroups of unsaturated polyesters formulated with mole ratios of 2/1/3 and 1/1/2 isophthalic acid/maleic anhydride/propylene glycol were modified. Carboxylic acid content was effectively reduced by esterification with alcohols or epoxides, amidation with phenyl isocyanate, or neutralization with amines. Hydroxyl content was reduced by esterification with acids or anhydrides and urethane formation with phenyl isocyanate. Chemical resistance was determined by measuring the decrease in flexural strength and modulus with exposure to 10% solutions of sodium hydroxide and sulfuric acid at 82°C. A 2-week test using the medium chemical-resistant 2/1/3 polyester indicated that any modification which decreased the carboxylic acid content improved chemical resistance. Modifications which increased or decreased the hydroxyl content had no significant effect in the 2-week tests; however, decrease of hydroxyl content appeared important in 6-month exposure tests. The 1/1/2 resins which have high initial chemical resistance had poorer chemical resistance after endgroup modification than the unmodified 1/1/2 resin, with the exception of the phenyl isocyanate-modified product which was equal to the unmodified resin. Water (0.8%) and xylene (0.1%) had no effect on chemical resistance. However, larger amounts of residual solvent were disadvantageous.
    Additional Material: 7 Ill.
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  • 100
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The initial rates have been determined for the second-order equilibrium reaction of phenyl isocyanate with a series of phenyl-substituted 1,1-pentamethylene-3-phenyl ureas in the presence of butyltin trichloride catalyst in chlorobenzene at 60°C. These results were compared with the rates of reaction of phenyl isocyanate with 1,1-di-n-butyl-3-phenylurea, 1,3-diphenyl-1-methylurea, N-phenylbenzamide, methyl-N-phenyl carbamate, and 1-butanol. The activation energy for the butyltin trichloride-catalyzed reaction of phenyl isocyanate and 1,1-pentamethylene-3-phenylurea was 12 kcal./mole. At 60°C. this reaction was approximately 11 times as fast as the reverse reaction. The rate of the reaction of phenyl isocyanate and 1,1-pentamethylene-3-phenylurea was directly proportional to the concentration of butyltin trichloride. The activity of this catalyst was 28 times as great as that of triethyltin chloride. Dibutyltin dilaurate, dibutyltin diacetate, dibutylin dichloride, tributyltin chloride, tetramethyltin, trimethyltin bromide, triethyltin fluoride, and 1,2,4-trimethylpiperazine were not catalysts for these reactions. The ureas formed solid complexes with stannic chloride and with butyltin trichloride in which the tin compounds were coordinated through the carbonyl oxygen. A tentative reaction mechanism has been proposed, which involves nucleophilic attack of the urea on the isocyanate through an intermediate ternary complex. The stannic chloride-catalyzed reaction of ureas with isocyanates at room temperature has been shown to have wide application.
    Additional Material: 5 Ill.
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