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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
    Format: application/pdf
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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
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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.
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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.
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    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.
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    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.
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    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.
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    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.
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    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.
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    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.
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    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.
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    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.
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    Language: English
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  • 42
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    Anatomy and embryology 148 (1975), S. 25-34 
    ISSN: 1432-0568
    Keywords: Cat ; Extraocular muscles ; Muscle architecture ; Myomyous junctions ; Muscle fiber splitting
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary Teasing preparations of cat extraocular muscles (EOM) were used to study the arrangement of muscle fibers and the distribution of the different cholinesterase-positive sites, i.e. (1) large motor endplates, (2) small motor endings of the “en grappe” type, (3) myotendinous junctions and (4) myomyous junctions. The distribution of these cholinesterase-positive structures gives clear evidence of a complex muscle architecture of cat EOM. In the global layer of cat EOM, only multiply innervated muscle fibers run the whole length of the muscle. The focally innervated muscle fibers are generally shorter; they are usually arranged in series of two to three fibers being interconnected by myomyous junctions. Moreover, muscle fiber splitting is frequently present resulting in a netlike arrangement of muscle fibers. Most of the myomyous junctions occur between focally innervated muscle fibers, but also end-to-side connections of focally to multiply innervated muscle fibers are observed; multiply innervated muscle fibers have not been found connected to each other. In this layer, large motor endplates are distributed in several bands between origin and insertion. In the orbital layer all muscle fibers run from tendon to tendon, focally as well as multiply innervated ones. Here, large motor endplates are confined to a band in the middle of the muscle, and myomyous junctions are generally absent. Some functional implications of this complex architecture of cat EOM are discussed.
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  • 43
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    Experimental brain research 23 (1975), S. 259-278 
    ISSN: 1432-1106
    Keywords: Brief light flashes ; Optic tract fibers ; Cat ; After-images ; Ricco's law
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary 1. The action potentials of single optic tract axons were recorded in cats anaesthetized by pentobarbital. The receptive fields were stimulated with brief light flashes (20 or 25 msec) of variable area (0.18≤A≤11.8 degrees) and stimulus intensity (0.36≤I≤360 cd·m−2). 2. Retinal on-center and off-center neurons responded in one of two ways to brief light flashes: oscillatory responses (O-response) to certain stimulus combinations or non-oscillatory responses (N-response) for all stimulus combinations. 3. The O-response of on-center neurons was characterized in its PST-histogram by up to five peaks. Neurons exhibiting an O-response at medium and/or strong stimulus intensities responded at low AxI-values with an N-response. Other neurons, however, exhibited for all stimulus combinations an N-response, in which the instantaneous neuronal impulse rate decreased after an initial peak approximately exponentially with time. 4. The O-response of off-center neurons exhibited with medium AxI-values up to four peaks in the PST-histograms. N-type off-center neurons had at low and medium AxI-values a short primary inhibition period which was followed by a fast rising and slowly decaying activity period. 5. Ricco's law was only valid for small AxI-values not more than one 10log unit above threshold. For higher stimulus values (especially in the O-response) an increment of the stimulus intensity was usually more effective than an equal increment of the stimulus area. 6. On-center and off-center neurons located in about the same region of the retina had a strong tendency to discharge alternately with each other. 7. A superposition model is proposed as an explanation of the experimental data. 8. Possible correlations between the neurophysiological findings and the fast oscillatory after-images seen in corresponding psychophysical experiments are discussed.
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  • 44
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    Experimental brain research 24 (1975), S. 1-14 
    ISSN: 1432-1106
    Keywords: Cerebro-ponto-cerebellar pathway ; Pontine nuclei cells ; Fast and slow relays ; Cat
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary Cerebrally-induced responses of pontine nuclei cells (PN cells) were studied in cats anesthetized with pentobarbitone sodium and with the midbrain transected bilaterally sparing only the cerebral peduncles. After stimulating the subcortical white matter, the internal capsule or the cerebral peduncle, mass potentials were recorded from the cut end of fibres in the brachium pontis (BP) and in the pyramid at the level of the trapezoid body. These potentials were regarded as indicating, respectively, the size of an output volley of PN cells and the size of its causative input volley through the pyramidal tract. BP responses consisted of short- and long-latency potentials which were caused by fast and slow conducting pyramidal tract volleys, respectively. The input-output relations for fast component responses took a characteristic S-shaped form resembling those obtained for the monosynaptic spinal reflex. The input-output relations for slow component responses were almost linear. Both fast and slow BP responses were remarkably potentiated after single or relatively brief repetitive peduncular stimulation, but were depressed after long-lasting high-frequency activation. During repetitive stimulation with varied frequencies, fast and slow BP responses showed different patterns of frequency-dependence of their amplitudes. These results suggest the existence of two separate transmission lines with different properties in the cerebro-ponto-cerebellar pathway.
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  • 45
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    Experimental brain research 24 (1975), S. 57-74 
    ISSN: 1432-1106
    Keywords: Cat ; Cerebral cortex ; Sensori-motor connections ; Columnar organization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary Needle stitch lesions were made in the maximal point of the cerebral projection area of the low threshold muscle afferents near the postcruciate dimple of the cat's posterior sigmoid gyrus. The lesions did not exceed 500 μm in diameter and were restricted to the cortical grey matter. Degenerating nerve fibres and terminals were investigated with Fink-Heimer technique in four cats (survival time: 26, 48 and 96 hours). The cytoarchitectonic areas of the sensori-motor cortex were determined in cresyl violet and van Gieson sections. All lesions were made in area 3a. Degenerating U-fibres originating from the lesion travelled in the white matter to the cortex of area 4 γ, 3b and 2. They reentered the cortex and branched in layer III. Terminal degeneration was found in layer I. The degeneration was distributed to distinct columns with a diameter of about 1 mm. Such columns were observed laterally and medially in area 4 γ, in area 3b near the caudal end of the coronal sulcus, in area 2 near the lateral ansate sulcus and in the forelimb region of SII. The distribution of the cortico-cortical connections from the cerebral projection area of the forelimb group I muscle afferents was discussed in relation to the known cerebral projections of group I muscle afferents, low threshold joint afferents, pacinian afferents and low threshold skin afferents.
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  • 46
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    Experimental brain research 23 (1975), S. 535-554 
    ISSN: 1432-1106
    Keywords: Auditory cortex ; Cat ; Association connexions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary The association connexions of the peri-auditory (SF, Ea and INS) and auditory (AI, AII and Ep) areas of the cat cortex were studied in silver impregnated material of 32 experiments with cortical lesions. The cortex of the lateral bank of the rostral part of the middle suprasylvian sulcus (SF) sends many fibres to AI and to the insular cortex (INS), and has scanty projections upon AII and Ep. In addition, it sends fibres to the visual area 17 as well as to the ventral bank of the medial part of the cruciate sulcus. It receives fibres from the three auditory areas AI, AII and Ep, as well as from Ea and INS. The dorsal part of the anterior ectosylvian gyrus (Ea) projects upon SF, AI, and AII. Ea sends few fibres to Ep, and receives relatively dense projections from AI and AII. The anterior sylvian gyrus (INS) projects heavily upon AII as well as upon the superficial part of SF. It sends few fibres also to Ep. INS receives heavy projections from AII and relatively lighter connections from SF, AI and Ep. The three auditory areas AI, AII and Ep are strongly mutually interconnected. AI and Ep have scanty projections upon the visual area 19, and AI also to the lateral suprasylvian visual area, as well as upon the ventral bank of the medial cruciate sulcus. Correlations of the association connexions with the functions of each area are discussed.
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  • 47
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    Experimental brain research 24 (1975), S. 131-144 
    ISSN: 1432-1106
    Keywords: Lateral reticular nucleus ; Dorsal funiculus ; Trigeminal nerves ; Cerebellum ; Cat
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary 1. The activation of neurones in the mLRN (major portion of lateral reticular nucleus comprising its parvi- and magnocellular parts) by a spinal path ascending in the dorsal funiculus (DF) and by trigeminal afferents has been studied. 2. Stimulation of the DF at C3 activated about one half of the mLRN neurones. The latencies were 2–28 ms. In experiments with the spinal cord interrupted at C3 except for the DF it was shown that cutaneous and high threshold muscle afferents in mainly forelimb nerves were effective. The latencies of the responses to nerve stimulation were 8–27 ms. 3. Stimulation of trigeminal afferents evoked a response in about one third of the mLRN neurones. The latencies were 2–27 ms. 4. Activation from the DF- and trigeminal paths occurred often in the same mLRN neurones and the neurones activated from the two paths had a similar location in the nucleus and a similar termination in the cerebellar cortex. 5. The DF- and trigeminal paths had similar properties. Activation was evoked from both ipsilateral and contralateral nerves. Fast adapting hair receptors were commonly effective. 6. Evidence is presented indicating that the DF- and trigeminal paths share a common final path to the mLRN neurones which is formed by brain stem interneurones intercalated between the DF- and trigeminal nuclei and the mLRN. It is suggested that these interneurones represent a supraspinal motor centre. 7. Activation from the DF- and trigeminal paths occurred with unequal frequency among groups of mLRN neurones activated from different spinal paths ascending in the ipsilateral lateral funiculus (cf. Clendenin et al., 1974a).
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  • 48
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    Experimental brain research 22 (1975), S. 427-430 
    ISSN: 1432-1106
    Keywords: Cat ; Cortex ; Receptive fields ; Vision ; Visual “noise”
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
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  • 49
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    Experimental brain research 23 (1975), S. 425-442 
    ISSN: 1432-1106
    Keywords: Sensory deprivation ; Visual-vestibular interaction ; Cat ; Ontoenesis ; Vestibulo-ocular reflex ; Nystagmus
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary The vestibular system contributes to the stabilisation of visual images on the retina by means of vestibulo-ocular compensatory reactions. The development of vestibular control of eye movements has been studied in twelve week old kittens, reared in total darkness, which have been compared with a control group of kittens reared in normal conditions. Postrotatory nystagmus, nystagmus during sinusoidal oscillations, visual suppression of vestibular nystagmus by fixation and pathological nystagmus following hemilabyrinthectomy, have been used as indicators of the functional state of the vestibulo-ocular control system. The results show that most of the essential features of this control are present in dark-reared kittens. However, differences have been noted which possibly concern precise regulation of compensatory movements and head-eye coordination. The frequency of vestibular nystagmus is much smaller and the initial deviation of post-rotatory nystagmus in the direction of the change of movement is weak or absent in dark-reared kittens. Habituation also seems to operate differently in the two groups of kittens. Visual suppression of vestibular nystagmus is present, however, showing that an important part of the neuronal basis for visual-vestibular interaction has developed.
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  • 50
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    Experimental brain research 22 (1975), S. 113-128 
    ISSN: 1432-1106
    Keywords: Muscle spindle ; Gamma motor control ; Caudate nucleus ; Extensor muscle ; Cat
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary Effects of repetitive stimulation of the contralateral caudate nucleus on the static discharge and dynamic sensitivity of soleus muscle spindle primary and secondary endings were studied in cats anaesthetized with Halothane (Fluothane). By progressive increasing the depth of anaesthesia two different fusimotor effects could be observed. 1. A static facilitatory effect; under light anaesthesia the static discharge of primary and secondary endings were strongly increased. The response of the primary endings to phasic stretch of the muscle was generaly decreased. 2. A depressant effect; under deep anaesthesia the static discharge of primary and secondary endings were decreased. The dynamic sensitivity of the primary endings was lightly increased or remained unaltered. The ventro-lateral part of the caudate nucleus is mainly responsible for these effects. Caudate nucleus fusimotor effects were compared with those induced by gamma dynamic and gamma static fibers stimulations.
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  • 51
    ISSN: 1432-1106
    Keywords: Muscle spindle ; Gamma motor control ; Flexor muscle ; Caudate nucleus ; Cat
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary 1. Effects of repetitive stimulations of caudate nucleus were studied on static and dynamic sensitivities of contralateral flexor (tibialis anterior) muscle spindle primary and secondary endings in cats anaesthetized with Halothane (Fluothane). Fusimotor effects are interpreted in term of gamma dynamic and gamma static activation. 2. Threshold stimulation induce a gamma dynamic effect on the primary endings sensitivity. Secondary endings activity and muscle tension remainded unaltered. 3. A slight increase of the stimulus strength elicit a gamma dynamic-gamma static effect on the primary endings sensitivity. Simultaneously secondary endings activity was increased and muscle contractions induced. 4. Using graded voltage stimulation permit to increase primary and secondary endings activity without muscle contraction. 5. Two stimulations applied at sufficiently short time interval produce different fusimotor effects. The first stimulation induce the general motor effect previously obtained: gamma dynamic-gamma static modulation of primary endings sensitivity, increase of secondary endings activity, muscular contraction. The second stimulation elicit a gamma dynamic effect on primary endings sensitivity and a depressant effect on secondary endings activity during muscular contractions. 6. Tendon organs discharge during caudate nucleus stimulation was studied comparatively with the primary and secondary endings activity.
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  • 52
    ISSN: 1432-1106
    Keywords: Cerebro-ponto-cerebellar pathway ; Pontine nuclei cells ; Fast and slow relays ; Pyramidal collaterals ; Cat
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary Extracellular and intracellular recordings were made from single cells in the pontine nuclei (PN) of the cat. PN cells were identified by antidromic invasion from the cerebellum by stimulating either the brachium pontis (BP) or the white matter near the cerebellar nuclei. The cerebrally-induced impulses excited PN cells postsynaptically with a monosynaptic latency. Both fast and slow conducting cortical fibres contributed to the corticopontine excitation, so that the latency varied over a wide range. Measurements of the latencies for antidromic and corticopontine excitation and of the distances between stimulated sites permitted the calculation of conduction velocities of PN cell axons and of their cortical input fibres. PN cells with fast conducting axons received convergence from both fast and slow cortical fibres, whereas PN cells with slow axons were innervated only by slow cortical fibres. The majority of PN cells were also excited by stimulating the medullary pyramid through collaterals of the pyramidal tract. Evidence of abundant pyramidal collaterals was provided by the collision technique. The functional role of the PN is discussed in connection with the cerebro-cerebellar loop circuits.
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  • 53
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    Pflügers Archiv 357 (1975), S. 313-321 
    ISSN: 1432-2013
    Keywords: Spino-Bulbo-Spinal Reflex ; Nucleus Reticularis Gigantocellularis ; Descending Inhibition ; Spinal Cord ; Cat
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary 1. In precollicular decerebrate cats, the nucleus reticularis gigantocellularis in the medulla was identified to be critically involved in the spino-bulbospinal (SBS) reflex system. 2. Electrolytic lesion placed in this nucleus eliminated the SBS reflex and its associated effects in the spinal cord. 3. Ascending volleys from the spinal cord were found to excite neurons within this nucleus, whereupon further direct stimulation was able to enhance the inhibitory effects of the SBS reflex on spinal motoneurons. These interactions were also facilitated by physostigmine and suppressed by atropin,, indicating the cholinoceptive nature of these neurons, another criterion which qualified them as being associated with the SBS reflex. 4. The functional roles of SBS reflex and nucleus reticularis gigantocellularis in somatic and visceral activities were discussed.
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  • 54
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    Pflügers Archiv 353 (1975), S. 43-57 
    ISSN: 1432-2013
    Keywords: Motoneurone ; Inhibition ; Post-Tetanic Potentiation ; Spinal Cord ; Cat
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary The after effects of orthodromic tetanization on the discharge pattern of gastrocnemius motoneurones were investigated in decerebrate and spinalized cats. During stimulation of intact gastrocnemius nerves at 20 Hz, small motoneurones showed tonic activity, while large motoneurones exhibited phasic activity. Following tetanization for 8 sec, large motoneurones followed the 20 Hz stimulation in 1∶1 order, whereas small motoneurones became silent for about 37 sec. Thereafter, the impulse rate of large motoneurone decreased while that of small motoneurone increased, progressively reaching the pre-tetanic values in about 72 sec. When gastrocnemius nerves were tetanized for 20 sec, potentiation of large motoneurones and depression of small motoneurones lasted for about 120 sec. Post-tetanic potentiation of large motoneurone was still observed during stimulation with 40 Hz but not with 80 Hz. Inhibition of a small tonic motoneurone during repetitive activity of a large motoneurone was observed during stimulation of Group I+II afferents following injection of 0.025 mg/kg strychnine. Another strychnine injection of the same dose reduced this inhibition. It was concluded that large-phasic motoneurones may be highly susceptible to post-tetanic potentiation; and that small-tonic motoneurones may be inhibited by large motoneurones through a recurrent circuit.
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  • 55
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    Experimental brain research 23 (1975), S. 85-90 
    ISSN: 1432-1106
    Keywords: Cat ; Retina ; Ganglion cell ; Latency
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary The axonal conduction latency of brisk-sustained and brisk-transient cat retinal ganglion cells increases with proximity to the area centralis. The trend is gradual with considerable local scatter of latencies, and is similar for cells with crossed and uncrossed axons.
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  • 56
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    Springer
    Experimental brain research 23 (1975), S. 279-291 
    ISSN: 1432-1106
    Keywords: Tendon organs ; Static force sensitivity ; Motor units ; Contraction strength ; Cat
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary The static force sensitivity of soleus tendon organ (Ib) afferents has been studied by noting their responses to graded force development produced by isometric contractions of either the whole muscle or single motor units. Data included responses of 23 Ib afferents to contraction of 8 whole muscles (8 experiments) and 16 Ib afferents to contraction of 30 motor units (5 experiments). Tendon organ responses of varying magnitude to contraction of the whole muscle or several of its individual motor units could be explained by differences in the number of muscle fibers that insert into each receptor's capsule and by differences in the contraction strength of these fibers. This finding suggests that soleus tendon organs have similar absolute sensitivities to static force development. An estimate was made of this absolute sensitivity and the value obtained (314 pps/g of force actually coupled to the receptor) is 2 orders of magnitude greater than those previously reported indices that simply relate Ib firing rate to force as measured at the tendon. The relationship between force exerted on a tendon organ's capsule and Ib firing rate is shown to be curvilinear and in keeping with a possible saturation effect that reduces the receptor's responsiveness to active contractions at relatively long muscle lengths.
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  • 57
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    Cell & tissue research 161 (1975), S. 293-301 
    ISSN: 1432-0878
    Keywords: Pineal gland ; Monkey (Cercopithecus aethiops) ; Cat ; Central innervation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine
    Notes: Summary Silver-impregnated series of cat and monkey (Cercopithecus aethiops) brains were studied in an attempt to demonstrate the existence of nervous connections between the brain and the pineal gland via the pineal stalk (central pineal connections). The presence of such connections between both the pineal gland and the habenular area, and between the pineal gland and the posterior commissure was verified in this study. A well defined median nerve tract between the pineal gland and the posterior commissure is described.
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  • 58
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    International Journal of Chemical Kinetics 7 (1975), S. 1-13 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The temperature dependence of the vibration-vibration energy transfer between the v3 mode of N2O and the first vibrational level of CO was determined over a range of 780 to 1400°K using a shock tube. Several mixtures of CO-N2O were tested, diluted in 95% Ar. The Landau-Teller plot of the vibration-vibration relaxation times has a least squares line of \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm log}_{{\rm 10}} p\tau _{{\rm VV}} = 2.69T^{ - 1/3} - 1.70 $$\end{document} where pτvv is in atm ·μsec and T in °K. The measured kinetic reaction was determined to be \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm N}_{\rm 2} {\rm O(001) + CO(O)} \to {\rm N}_{\rm 2} {\rm O}(000) + {\rm CO(1) + 81cm}^{{\rm - 1}} $$\end{document} The transfer probabilities for this process were found to vary directly with temperature.
    Additional Material: 9 Ill.
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  • 59
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The activation energy parameters for the reaction of PdX42- (X=Cl-, Br-) in aqueous halide acid solution with thiourea (tu) and selenourea (seu) have been determined. High rates of reaction parallel low enthalpies and appreciable negative entropy of activation. The rate law in each case simplifies to kobs=k[L] where L=tu or seu, and only ligand-dependent rate constants are observed at 25°C. The ligand-dependent rate constants for the first identifiable step in the PdCl42- + X system is (9.1±0.1) × 103 M-1 sec-1 and (4.5±0.1) × 104 M-1 sec-1 for X=tu and seu, respectively, while for the PdBr42- + X system it is (2.0±0.1) × 104 M-1 sec-1 and (9.0±0.1) × 104 M-1 sec-1 for X=tu and seu, respectively.
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  • 60
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    International Journal of Chemical Kinetics 7 (1975), S. 125-142 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A detailed shock-tube investigation of the ignition in H2 + Cl2 + Ar mixtures in a shock tube is presented, and the mechanism of the reaction is discussed. Ignition delay times were determined from pressure and heat flux measurements behind reflected shock waves. The induction times measured ranged between 35 and 2100 μsec over the temperature range of 830-1260°K. The experimental results of close to seventy tests can be correlated by the relationship \documentclass{article}\pagestyle{empty}\begin{document}$$ t_{{\rm ig}} = 10^{ - 12.73} \exp (18.75 \times 10^3 /RT) \cdot [{\rm Cl}_{\rm 2}]^{ - 0.66} [{\rm H}_{\rm 2}]^{ - 0.60} [{\rm Ar]}^{{\rm 0}{\rm .40 }} \,\sec. $$\end{document} where the concentrations are expressed in mole/cm3. The above relationship served as a basis for a computer modeling of the ignition delay times. Ten calculations, simulating typical laboratory experiments, were run by the computer for each reaction scheme and the obtained temperature and composition dependence of the induction times were compared with the ones observed experimentally. A reaction scheme based on a simple exothermal chain propagation could not reproduce the experimental relationship. When the energy branching reaction HCl*(ν) + Cl2 → (HCl3) → HCl + Cl + Cl was added to the reaction scheme, a much better agreement with the experiment was obtained. It is believed that the above reaction does take place and that it is the main supplier of atoms to the system.
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  • 61
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    International Journal of Chemical Kinetics 7 (1975), S. 205-214 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Spectrophotometric methods have been used to obtain rate laws and rate parameters for the following reactions: with ka, kb, Ea, Eb having the values 85±5 l./mole · s, 5.7±0.2 s-1 (both at 298.2°K), and 56±4 and 66±2 kJ/mole, respectively. with kc=0.106±0.004 l./mole ·s at 298.2°K and Ec=67±2 kJ/mole. with kd=(3.06 ±; 0.15) × 10-3 l./mole ·s at 298.2°K and Ed=66±2 kJ/mole.Mechanisms for these reactions are discussed and compared with previous work.
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  • 62
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    International Journal of Chemical Kinetics 7 (1975), S. 249-272 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The kinetics of decarbonylation of [Ir(CO)(dp)2]Cl and [IrCl(CO)2(Ph3P)2] has been studied in different solvents, at temperatures between -25° and +70°C, by means of reactors of defined fluid dynamics which allow a separation to be made between “physical” and “chemical” rate constants. Chemical rate constants have been found to depend markedly on the diffusion coefficients of carbon monoxide in the various solvents. The process of decarbonylation has been described, for both reactions, by the sequence: structural isomerization, characterized by a very low preexponential factor, decomposition of the less stable isomer against the solvent's barrier, and diffusion of carbon monoxide to the gas-liquid interface. The kinetic problems involved in the determination of rate constants and their implications have been emphasized.
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  • 63
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    International Journal of Chemical Kinetics 7 (1975), S. 287-300 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The overall photobromination reactions \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm Br}_{\rm 2} + {\rm R}_{\rm F} {\rm I} \to {\rm IBr} + {\rm R}_{\rm F} {\rm Br} $$\end{document} have been studied using a competitive technique. Relative Arrhenius parameters were obtained for the rate-determining step These were placed on an absolute basis using previous-absolute values of A and E for RFI=CF3I. The activation energies were used to calculate bond dissociation energies D(R—I) with the following results: TextRF-E16D(RF-I)(kcal/mole)CF3I10.852.6C2F5I8.850.6n-C3F7I7.449.2i-C3F7I7.549.2n-C4F9I6.748.4E16 from [1]The D(RF-I) are compared with related D(R—I) and it is concluded that for a given alkyl group RH and the corresponding perfuloroalkyl group RF, D(RH-I) 〉 D(RF-I) whereas it has previously been found that D(RH-X;) 〈 D(RF-X) where X is not iodine.
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  • 64
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    International Journal of Chemical Kinetics 7 (1975), S. 341-349 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The rates of reaction of t-BuOOK, t-BuOK, n-BuOOK, and p-MeC6H4OKwith p-nitrophenyl diphenylphosphinate 1 and with p-nitrophenyl benzoate 2 have been measured in toluene both in the absence and in the presence of crown polyether dicyclohexyl-18-crown-6 3a. The rates of nucleophilic displacementon 1 by HOO-, t-BuOO-, and some “nonalpha” oxyanions in water have also been determined. Solvent transfer from water to toluene results in increasing the nucleophilic reactivity of the t-butyl hydroperoxide anion. Rate ratios QQa are given which allow one to estimate the enhanced reactivity of t-BuOO- (an α-nucleophile) compared to oxygen nucleophiles of comparable base strength toward 1 and 2. These are for substrate 1, Qα (water) ≃ 6.5 and Qα (toluene) ≃ 2.7; for substrate 2, Qα (water) ≃ 5.5 and Qα (toluene) ≃ 5. The hypothesis is advanced that solvation is not a major factor in determining the α-effect of the t-butylhydroperoxide anion.
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  • 65
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    International Journal of Chemical Kinetics 7 (1975), S. 633-636 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 1 Ill.
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  • 66
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    International Journal of Chemical Kinetics 7 (1975) 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 67
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    International Journal of Chemical Kinetics 7 (1975), S. 463-471 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A consecutive single-route reaction is considered. When two (groups of) steps compete in controlling the overall reaction rate, there exists a general rule that the earlier step in the flow of the overall reaction tends to be rate-determining with the increase of the reaction affinity. The latter may, however, be distributed more or less evenly to both steps.
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  • 68
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    International Journal of Chemical Kinetics 7 (1975), S. 479-507 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The mechanisms of the pyrolyses of the n-alkanes C3H8, n-C4H10, and n-C5H12 at temperatures between 390 and 560°C have been studied by the construction and evaluation of sets of several hundred reactions. Rate parameter values were assigned using literature data and calculated estimates. Time-dependent numerical solutions were computed for the experimental conditions of several rate and product studies reported in the literature. The comparisons of these a priori computations with experiment show excellent agreement for propane and agreement for butane and pentane within the estimated error limits of the assigned rate parameters. These results demonstrate that the general “state of knowledge” of the mechanism of alkane pyrolysis, namely, the reactions and their rate parameters, is such that reasonable a priori predictions of experimental results can be made. Discussions of the major stepwise processes in the pyrolyses are presented, and the importance of allyl radicals in termination is demonstrated.
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  • 69
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    International Journal of Chemical Kinetics 7 (1975), S. 547-555 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The decomposition rate of chemically activated ethyltrimethylgermane from the reaction 1CH2 + (CH3)4Ge, where 1CH2 was produced from diazomethane photolysis at 3660 Å, is 8.6 × 105 sec-1. This result combined with RRKM theory and critical energy estimates yields an Arrhenius A factor of log[A (sec-1)/methyl] = 14.7 ± 0.8 for methyl rupture from germanium.Log A values for methyl rupture from carbon, silicon, and germanium linearly correlate with the vibrational-rotational entropies of the corresponding tetramethyls. Extrapolation predicts log[A (sec-1)/methyl] = 14.4 and 14.3 for methyl rupture from tin and lead, respectively.
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  • 70
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    International Journal of Chemical Kinetics 7 (1975), S. 625-631 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The addition of methoxy radicals to several olefins has been studied by a competitive method at 127°C in gas phase. The thermal decomposition of dimethyl peroxide was used as methoxy radical source. The rate of addition to the double bond was measured relative to the oxidation of carbon monoxide. For the addition to ethylene it was obtained that \documentclass{article}\pagestyle{empty}\begin{document}$$ k_{{\rm add}} = \left({3.7 \pm 0.8} \right) \times 10^4 M^{ - 1} \cdot {\rm s}^{{\rm - 1}} $$\end{document} This rate constant is similar to the one shown by methyl radicals under similar conditions. From the relative rate of addition to several chlorinated and fluorinated olefins it can be concluded that methoxy radicals show very little “electrophilic” character.
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  • 71
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    International Journal of Chemical Kinetics 7 (1975) 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 72
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    International Journal of Chemical Kinetics 7 (1975), S. 33-37 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The present study reports the measurement of the V-V energy transfer rates for the CO*—COS system in the temperature range of 195 to 370°K. The measured rates exhibit a slight inverse temperature dependence. The experimental results are compared to prediction based on a model of long-range dipole-dipole interactions between colliding molecules. The effect of single quantum rotational transitions is compared to that of multiquantum rotational transitions.
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  • 73
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    International Journal of Chemical Kinetics 7 (1975), S. 77-86 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Electronically excited tin atoms Sn(51D2), 1.068 eV above the 53P0 ground state, have been generated by the pulsed irradiation of tin tetramethyl and monitored photoelectrically in absorption by time-resolved attenuation of atomic resonance radiation at λ=285.06 nm [Sn((5d3F20) ← (5p2 1D2))]. Deactivation rate constants are reported for the quenching of Sn(51D2) with a range of collision partners and the resulting data are compared with those for analogous states within group IV, namely, C(21D2) and Pb(61D2). The data are discussed in terms of correlations based on both the weak and strong spin orbit coupling approximations.
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  • 74
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    International Journal of Chemical Kinetics 7 (1975), S. 661-677 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The oxidation of acetylene by water vapor was studied behind the reflected shock in a single-pulse shock tube. Computer simulation experiments reproduced the experimental results in the temperature range of 1500 to 2000°K. The kinetic scheme suggested here involves three major processes, (1) production of hydrogen atoms by the sequence of reactions which lead from acetylene to carbon; (2) production of OH radicals, mainly by the reaction H + H2O → H2 + OH, and (3) fast oxidation of the acetylene and other C/H species by the available oxidants in the system. The experimental results of methane oxidation suggest that methane is converted to acetylene prior to its oxidation. The implication of the experimental results to processes occurring in planetary atmospheres as a result of thunder shock waves is briefly discussed.
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  • 75
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    International Journal of Chemical Kinetics 7 (1975), S. 443-451 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The equilibrium quotients for the formation of Co(NH3)5Cl2+ from Co(NH3)5OH23+ and Cl- were 3.74±0.25 M-1 and 6.07±0.54 M-1 at 45.0°C in 10:1 mole ratio water: dimethyl sulfoxide and in 25 w/w % aqueous ethanol, respectively, and those forthe formation of the ion pair Co(NH3)5OH23+ . Cl- were 1.21±0.20 M-1 and 1.58±0.17 M-1, respectively, in the same solvents. The aquation and anation rateconstants were determined at 45.0°C for these two solvents over the range of chloride-ion concentrations 0.0 ≤ [Cl-] ≤ 0.9 M. The aquation rate constant was essentially independent of chloride-ion concentration in each solvent over this range. The inverse of the pseudo-first-order anation rate constant was linearly dependent on the inverse of the chloride-ion concentration in each solvent. The least squares relationships between (1/kan) and (1/[Cl-]) gave intercepts and ratios of intercept to slope which were analyzed interms of Id and D mechanisms. It was concluded that the data were not satisfied by a D mechanism, but that they were consistent with an Id mechanism.
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  • 76
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    International Journal of Chemical Kinetics 7 (1975), S. 535-546 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The reaction between a hydroquinone aqueous solution and manganese dioxide has been investigated by electron paramagnetic resonance spectroscopy. A very stable p-benzosemiquinone anion is formed when an aqueous solution of hydroquinone is passed through a column of manganese dioxide. The kinetics for the reaction between hydroquinone and manganese dioxide follow the equation \documentclass{article}\pagestyle{empty}\begin{document}$$ \frac{{dC}}{{d\left({W/F} \right)}} = k_1 ^0 \left({A_0 - C} \right) - k_2 ^0 C $$\end{document} where A0 is the initial concentration of hydroquinone, C is the concentration of p-benzosemiquinone anions, W is the amount of manganese dioxide, F is the feed rate of a hydroquinone aqueous solution, and k10 and k20 are constants; k10 = 3.1 × 10-2 (cm3/g MnO2· min), k20 = 3.2 (cm3/g MnO2·min).A mechanism for the reaction is proposed such that Mn(IV) in manganese dioxide is reduced to Mn(II) with hydroquinone from which the semiquinone anion is formed via a neutral semiquinone. The formation of semiquinone anions from several substituted hydroquinones is also discussed.
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  • 77
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    International Journal of Chemical Kinetics 7 (1975), S. 575-587 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Solvent-solute interactions in the peroxyacid oxidations are believed to be specific rather than electrostatic in nature. The kinetic solvent effects reported for the oxidations of organic sulfides, olefins, acetylenes, nitrosobenzenes, thioketones, and aryl sulfines reveal that in each case the rates are fast in nonbasic solvents (e.g., benzene, nitrobenzene, and halogenated hydrocarbons) relative to those in basic solvents such as DMF, dioxane, and alcohols. The rates in CF3CH2OH and aqueous or partially aqueous media are again higher than those in the basic solvents. This remakably similar pattern of sensitivity of rates to changes in the solvent nature appears to be characteristic of these oxidations as demonstrated by the existence of linear free-energy relationship. The behavior is best understood in terms of cyclic transition states for these oxidations in which charge separation is avoided by intra- or intermolecular hydrogen bonding depending on the nature of the solvent. Solvent effects on sulfoxide oxidation and on oxidations by hydrogen peroxide and t-butylhydroperoxide are also briefly discussed.
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    International Journal of Chemical Kinetics 7 (1975), S. 637-638 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 79
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    International Journal of Chemical Kinetics 7 (1975), S. 679-688 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The pyrolysis of tetrafluorohydrazine has been studied from 578 to 791°K. The stoichiometry has been established as \documentclass{article}\pagestyle{empty}\begin{document}$$ 6{\rm NF}_{\rm 2} \to 4{\rm NF}_{\rm 3} + {\rm N}_{\rm 2} $$\end{document} Reaction rates have been measured and the effects of surface area, inert gas pressure, and nitric oxide have been examined. The rate-determining step proposed is \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm 2NF}_{\rm 2} \to {\rm NF}_{\rm 3} + {\rm NF} $$\end{document} and the general rate expression obtained for this is \documentclass{article}\pagestyle{empty}\begin{document}$$ k_1 = 10^{9.0 \pm 0.4} \exp {{ - 36,950 \pm 500} \mathord{\left/ {\vphantom {{ - 36,950 \pm 500} {RTM^{ - 1} \cdot \sec ^{ - 1} }}} \right. \kern-\nulldelimiterspace} {RTM^{ - 1} \cdot \sec ^{ - 1} }} $$\end{document}
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  • 80
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    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The high-pressure absolute rate constants for the decomposition of nitrosobenzene and pentafluoronitrosobenzene were determined using the very-low-pressure pyrolysis (VLPP) technique.Bond dissociation energies of DH0(C6H5—NO) = 51.5 ± 1 kcal/mole and DH0 (C6F5—NO) = 50.5 ± 1 kcal/mole could be deduced if the radical combination rate constant is set at log kr(M-1·sec-1) = 10.0 ± 0.5 for both systems and the activation energy for combination is taken as 0 kcal/mole at 298°K. δHf0(C6H5NO), δHf0(C6F5NO), and δHf0(C6F5) could be estimated from our kinetic data and group additivity. The values are 48.1 ± 1, -160 ± 2, and - 130.9 ± 2 kcal/mole, respectively. C-X bond dissociation energies of several perfluorinated phenyl compounds, DH0(C6F5-X), were obtained from the reported values of δHf0(C6F5X) and our estimated δHf0(C6F5) [X = H, CH3, NO, Cl, F, CF3, I, and OH].
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    International Journal of Chemical Kinetics 7 (1975), S. 785-795 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The kinetics of chlorine atom abstraction from trichloromethyl groups of the haloethanes (XCCl3), CF3CCl3, CH3CCl3, C2Cl6, C2Cl5H, and CH2ClCCl3, by radiolytically generated cyclohexyl radicals was studied in the liquid phase by a competitive method. The chlorine atom abstraction data were put on an absolute basis by comparing the rates of the metathetical reactions with the known rate of addition of cyclohexyl radicals to C2Cl4.The following Arrhenius parameters were obtained: The error limits are the standard deviations from least mean square Arrhenius plots. It is shown that the neighboring group effect on the rate of chlorine atom abstraction from the trichloromethyl groups can be correlated with Taft polar substituent constants.
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    International Journal of Chemical Kinetics 7 (1975) 
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    Keywords: Chemistry ; Physical Chemistry
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    Topics: Chemistry and Pharmacology
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  • 83
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The homogeneous exchange reaction between tetradeutero methane and ammonia was studied behind reflected shocks in a single-pulse shock tube over the temperature range of 1300-1800°K. The rate of production of CD3H at the early stages of the reaction in mixtures ranging between 1-4.5% NH3 and 1-4.3% CD4 in argon is given by d[CD3H]/dt=kb [CD4]0[NH3]0, where kb=8 × 1016 exp (-65.3 × 103/RT) cm3/mole·sec. This activation energy is considerably lower than the one that may be expected on the basis of a pure free radical mechanism. It is rationalized by C2D6 impurities in the methane. No clear answer can be obtained regarding the role of a four-center intermediate in this reaction.
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  • 84
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    International Journal of Chemical Kinetics 7 (1975), S. 879-894 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The specific decomposition rates of chemically activated methylcyclobutane produced from CH2(1A1) reaction with cyclobutane have been determined. CH2(1A1)was produced from ketene photolyses at 3340 and 3130 Å and from diazomethane photolyses at 4358 and 3660 Å. Comparisons of the excitation energies of the methylcyclobutane, determined by RRKM theory calculations, and the experimental results for the ketene systems, with thermochemically predicted maximum excitation energies, favor an Arrhenius A factor in the range of 5 × 1015 to 1 × 1016 sec-1 for methylcyclobutane. This result is consistent with (1) the comparison of RRKM theory calculations and the experimental unimolecular falloff for methylcyclobutane, (2) the comparison of experimental A factors for cyclobutane and other alkylcyclobutane decompositions, and (3) two out of three reported experimental A factors for methylcyclobutane. An analysis of these and previous results leads to a value of the CH2(1A1) ↔ CH2(3B1) energy splitting of 9±3 kcal/mole.
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  • 85
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    International Journal of Chemical Kinetics 7 (1975), S. 973-979 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The thermal decompositions of ethyl chloride, iso propyl chloride, and tertiary butyl chloride were studied in a static system in the pressure range of 0.1-300 torr. The following Arrhenius equations for the high-pressure limit were obtained: The pressure dependence of the first-order rate constant (falloff) for these three unimolecular dehydrochlorination reactions, starting with approximately equal kω values, by proper choice of temperature, is shifted to lower pressures with increasing molecular size:
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  • 86
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    International Journal of Chemical Kinetics 7 (1975), S. 23-31 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The high-temperature oxidation of formaldehyde in the presence of carbon monoxide was investigated to determine the rate constant of the reaction HO2 + CO = CO2 + OH (10). In the temperature range of 878-952°K from the initial parts of the kinetic curves of the HO2 radicals and CO2 accumulation at small extents of the reaction, when the quantity of the reacted formaldehyde does not exceed 10%, it was determined that the rate constant k10 is \documentclass{article}\pagestyle{empty}\begin{document}$$ k_{10} = (1.7 \pm 0.5) \times 10^{ - 10} \exp [ - (23,000 \pm 3000/RT)]\,{\rm cm}^{\rm 3} /{\rm molec}{\rm.sec} $$\end{document} A computer program was used to solve the system of differential equations which correspond to the high-temperature oxidation of formaldehyde in the presence of carbon monoxide. The computation confirmed the experimental results. Also discussed are existing experimental data related to the reaction of HO2 with CO.
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  • 87
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Modified nuclear recoil techniques have been used to obtain accurate relative bimolecular rate coefficients for thermally induced hydrogen abstraction reactions by atomic fluorine. New results are reported for 12 hydrocarbons and partially fluorinated hydrocarbons studied at 303°K.
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  • 88
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    International Journal of Chemical Kinetics 7 (1975), S. 45-62 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The mechanism of the electronically excited sulfur-dioxide sensitized isomerization of cis-2-butene has been studied through the measurement of the initial quantum yields of trans-2-butene formation in 3130-A irradiated gaseous binary mixtures of SO2 and cis-2-butene and ternary mixtures of SO2, cis-2-butene, and CO2. The kinetic treatment of the present data from the SO2—C4H8 mixtures and those of recent similar studies of Penzhorn and Güsten [3] and Cox [4] are all consistent with the involvement of only the long-lived fluorescent 1B1 and phosphorescent 3B1 states of SO2 in the isomerization mechanism. The data give (k2a + k2b)=0.21±0.04; SO2(1B1) + SO2 → SO2(3B1) + SO2(2a); SO2(1B1) + SO2 → (2SO2) (2b). The analogous intersystem crossing ratio for the SO2(1B1)-cis-2-butene quenching collisions is the largest observed among the many quencher molecules studied; the value lies in the range of 0.85 to 0.37, with the extremes representing different choices of alternative data and possible mechanisms. From the present data the ratio of the SO2(3B1) quenching rate constant with SO2 to that with cis-2-butene as quencher is estimated to be (2.7±1.2) × 10-3, in good agreement with our directly measured ratio from lifetime studies (2.91±0.23) × 10-3 [30-32], and the value found in isomerization studies by Cox (2.40±0.09) × 10-3 [4]. The simple two-excited state mechanism, which is seemingly applicable to the relatively low-pressure binary SO2-butene mixture results, is not adequate to explain the data obtained in experiments with large quantities of added CO2 gas. Here an “excess” quantum yield of isomerization is observed. Several alternative mechanisms can be used to rationalize these results, but all alternatives must incorporate some other excited SO2 species (X) as well as SO2(3B1) and SO2(1B1). The kinetics suggest that the ill-defined state is unreactive toward the olefin and decays nonradiatively to SO2 largely in experiments at the lower pressures, X → SO2 (11); it may generate SO2(3B1) in a collisionally induced process at high added inert gas (CO2) pressures, X + CO2 → SO2(3B1) + CO2 (10a) and X + CO2 → SO2 + CO2 (10b). The data give k11/(k10a + k10b)=0.026 mole/l.
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  • 89
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    International Journal of Chemical Kinetics 7 (1975), S. 143-157 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The kinetics of the reactions of O(3P) and D atoms with cyclohexane have been investigated using fast-flow techniques. The rates of reaction were computed by monitoring changes in both atom and cyclohexane concentrations using electron spin resonance and mass spectrometric methods, respectively. The O(3P) + C6H12 reaction was studied over a temperature range of 344 to 513°K and we obtain a specific rate constant of (3.2±0.6) × 1014 exp (-4400±400/RT) cm3/mole·sec for this reaction. The only reaction product detectable mass spectrometrically under flow conditions of excess oxygen atoms is formaldehyde.The D + C6H12 reaction was studied over a temperature range of 297 to 596°K. A specific rate constant of (4.1±1.0) × 1013 exp (-4000±300/RT) cm3/mole·sec was obtained for this reaction. On the basis of the results obtained in these studies, the important primary process in both the O(3P) and D atom reactions is concluded to be abstraction of a hydrogen atom from the cyclohexane molecule.
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  • 90
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    International Journal of Chemical Kinetics 7 (1975), S. 161-182 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The quantum yields of SO3 formation have been determined in pure SO2 and in SO2 mixtures with NO, CO2, and O2 using both flow and static systems. In separate series of experiments excitation of SO2 was effected within the forbidden band, SO2(3B1) ← \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm SO}_2 (\tilde X,^1 A_1 ) $$\end{document}, and within the first allowed singlet band at 3130 Å. The values of ΦSO3 were found to be sensitive to the flow rate of the reactants. These results and the apparently divergent quantum yield results of Cox [10], Allen and coworkers [24, 26, 29], and Okuda and coworkers [11] were rationalized quantitatively in terms of the significant occurrence of the reactions SO + SO3 → 2SO2 (2), and 2SO → SO2 + S [or (SO)2] (3), in experiments of long residence time. From the present rate data, values of the rate constants were estimated, k2=(1.2±0.7) × 106; k3=(5±4) × 105 l·/mole · sec. ΦSO3 values from triplet excitation experiments at high flow rates of NO—SO2 and CO2—SO2 mixtures showed the sole reactant with SO2 leading to SO3 formation in this system to be SO2(3B1); SO2(3B1) + SO2 → SO3 + SO(3Σ-) (la); k1a=(4.2±0.4) × 107 l./mole · sec. With excitation of SO2 at 3130 Å both singlet and triplet excited states play a role in SO3 formation. If the reactive singlet state is 1B1, the long-lived fluorescent state, SO2(1B1) + SO2 → SO3 + SO (1 Δ or 3Σ-) (lb), then k1b=(2.2±0.5) × 109 l./mole · sec. From the observed inhibition of SO3- formation by added nitric oxide, it was found that the SO3-forming triplet state, generated in this singlet excited SO2 system, had a relative reactivity toward SO2 and NO which was equal within the experimental error to that observed here for the SO2(3B1) species. Either SO2(3B1) molecules were created with an unexpectedly high efficiency in 3130 Å excited SO2(1B1) quenching collisions, or another reactive triplet (presumably 3A2 or 3B2) of almost identical reactivity to SO2(3B1) was important here.
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  • 91
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    International Journal of Chemical Kinetics 7 (1975), S. 273-285 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The kinetics of the thermal bromination reaction \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm Br + CF}_{\rm 3} {\rm I} \to {\rm IBr + CF}_{\rm 3} {\rm Br} $$\end{document} have been studied in the range of 173-321°C. For the step we obtain \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm log}\,k_{11} \,({\rm cm}^{\rm 3} /{\rm mole} \cdot {\rm sec) = (13}{\rm .19) - (10840} \pm {\rm 460)/}\theta $$\end{document} where θ=2.303RT cal/mole. From the activation energy for reaction (11), we calculate that \documentclass{article}\pagestyle{empty}\begin{document}$$ D({\rm CF}_{{\rm 3}^{\rm - } } {\rm I) = 52}{\rm .6} \pm {\rm 1}{\rm .1}\,{\rm kcal/mole}\,{\rm at 25}{}^{\rm 0}{\rm C} $$\end{document} This is compared with previously published values of D(CF3-I). The relevance of the result to published work on kc for a combination of CF3 radicals is discussed.
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  • 92
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    International Journal of Chemical Kinetics 7 (1975), S. 331-339 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The rate of the inhibited pyrolysis of pentachloroethane was studiedover the temperature range of 820 to 865°K using the toluene-carrier technique in a stirred-flow reactor. The pyrolysis rate was found to be first order in reactant, and the rate constant is described by k=1011.6±0.7 exp [(-48,200±2600)/RT] sec-1. An increase by a factor of 6.6 in the surface/volume of the reactor had a negligible effect on the rate. This observation, in addition to a reevaluation of earlier kinetic data for the pyrolysis of pentachloroethane, lead to the following conclusions concerning the pyrolysis mechanism. The initiation and termination as well as the propagation reactions were homogeneous, the termination involved both Cl and C2Cl5 radicals (crosstermination), and autocatalysis was caused by interaction between chlorine and pentachloroethane rather than by dissociation of molecular chlorine.
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  • 93
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    International Journal of Chemical Kinetics 7 (1975), S. 399-415 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The oxidation of CFClCFCl and CF2CCl2 were studied at room temperature by chlorine- and oxygen-atom initiation. The chlorine-atom initiated oxidation of CFClCFCl yields CCl2FCF(O) as the exclusive product. Its quantum yield is ∼420, which gives k3a/k3b=210 where reactions (3a) and (3b) are The O(3P)—CFClCFCl reaction gives CClFO with a quantum yield of 0.80, polymer, and small amounts of an unidentified product which is probably cyclo-(CFCl)3. Thereaction paths are with k9a/k9=0.80. The overall reaction of O(3P) with CFClCFCl proceed one fifth as fast as the O(3P)-C2F4 reaction. When O2 is also present, the same free-radical chain oxidation occurs by O(3P)initiation as by chlorine-atom initiation.The chlorine-atom initiated oxidation of CF2CCl2 gives CF2ClCCl(O) as the major product, with quantum yields ranging from 42 to 85. Smaller amounts of CF2O and CCl2O are produced in equal amounts with quantum yields of ∼3.5. The reactions responsible for the products are The O(3P)-CF2CCl2interaction yields CF2O and with quantum yields of 1.0 and ∼0.85, respectively. In thepresence of O2 the radical chain products are observed, but the mechanism is different than that for other chloroolefins.
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  • 94
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    International Journal of Chemical Kinetics 7 (1975), S. 639-648 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Rate constants for the combination of methyl radicals with NO and O2 have been measured by flash photolysis of azomethane coupled with product analysis by gas chromatography. Values of the rate constants have been obtained over the pressure region from 50 to 700 torr with He, N2, and Ar as quenching molecules.The high-pressure limits were obtained through an RRKM model calculation and were found to be \documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c} {{\rm CH}_{\rm 3} + {\rm NO} + {\rm M} \to {\rm CH}_{\rm 3} {\rm NO} + {\rm M}} \hfill & {k_\infty = 3.2 \times 10^{ - 11} {{{\rm cm}^{\rm 3} } \mathord{\left/ {\vphantom {{{\rm cm}^{\rm 3} } {{\rm molec} \cdot {\rm sec}}}} \right. \kern-\nulldelimiterspace} {{\rm molec} \cdot {\rm sec}}}} \hfill \\ {{\rm CH}_{\rm 3} + {\rm O}_{\rm 2} + {\rm M} \to {\rm CH}_{\rm 3} {\rm O}_{\rm 2} + {\rm M}} \hfill & {k_\infty = 1.7 \times 10^{ - 12} {{{\rm cm}^{\rm 3} } \mathord{\left/ {\vphantom {{{\rm cm}^{\rm 3} } {{\rm molec} \cdot {\rm sec}}}} \right. \kern-\nulldelimiterspace} {{\rm molec} \cdot {\rm sec}}}} \hfill \\ \end{array} $$\end{document} The rate constants were measured relative to the methyl combination reaction k1 with k1 = 9.5 × 10-11 cm3/molec · sec. The RRKM model suggests D0(CH3—O2) = 32 ± 3 kcal/mole.
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  • 95
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    International Journal of Chemical Kinetics 7 (1975), S. 907-917 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The mechanism and kinetics of the reaction of O(3P) atoms with propane were investigated using molecular modulation spectroscopy, with the O(3P) atoms being generated by the Hg photosensitized decomposition of N2O. The absorption spectrum of the X2II3/2 state of OH was observed in the ultraviolet between 307 and 309 nm, and it was confirmed that OH was the product of the O(3P) reaction with propane. The rate constants for the reactions of O(3P) and OH with propane were determined to be 3.9±0.7±1010 and 1.19±0.05±1012 cm3/mole·sec, respectively, at T=56±5°C.
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  • 96
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    International Journal of Chemical Kinetics 7 (1975), S. 919-926 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Kinetics of protonation of Li+, Na+, K+, and Cs+ salts of anthracene radical anions (A-·,Cat+) and dianions (A2-, 2Cat+) by MeOH and MeOD in tetrahydrofuran (THF) and dimethoxyethane (DME) led to the determination of the isotope effect (kH/kD) in the following reactions: \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm MeOH(MeOD) + A}\bar \cdot {\rm,Cat}^{\rm + } \to MeO^ - {\rm,Cat}^{\rm + } {\rm + AH} \cdot {\rm (D)} $$\end{document} \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm (MeOH)}_{\rm 2} {\rm or (MeOD)}_{\rm 2} {\rm + A}\bar \cdot {\rm,Cat}^{\rm + } \to {\rm MeOH,MeO}^ - {\rm,Cat}^{\rm + } {\rm + AH} \cdot {\rm (D)} $$\end{document} \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm MeOH (MeOD) + A}^{{\rm 2 - }} {\rm,2Cat}^{\rm + } \to {\rm MeO}^ - {\rm,Cat}^{\rm + } {\rm + AH(D)}^{{\rm - 1}},{\rm Cat}^{\rm +} $$\end{document} \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm MeOH (MeOD) + (A,Cat}^{\rm + } {\rm,A}^{{\rm 2 - }} {\rm,Cat}^{\rm + }) \to {\rm MeO}^ - {\rm,Cat}^{\rm + } {\rm + A + AH(D)}^{\rm - },{\rm Cat}^{\rm +} $$\end{document}Studies of cation and solvent influence on the rate constants of these reactions and on the magnitude of the isotope effect permitted us to draw some conclusions about the structure of the pertinent transition states. It seems that only the tight A-·,Na+ pairs participate in the protonation, and on this basis the fraction of tight ion paris of A-·,Na+ in DME was estimated. Our results have been compared with data reported in the literature.
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  • 97
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    International Journal of Chemical Kinetics 7 (1975), S. 109-123 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A very low-pressure pyrolysis (VLPP) apparatus has been constructed and shown to yield kinetic data consistent with other VLPP systems. The technique has been applied to the pyrolysis of cyclobutyl cyanide over the temperature range of 833-1203°K. The reaction was found to proceed via a single pathway to yield ethylene and vinyl cyanide. If A∞ is based on previous high-pressure data for this reaction and for cyclobutane pyrolysis, then RRKM theory calculations show that the experimental unimolecular rate constants are consistent with the high-pressure Arrhenius parameters given by \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm log}\,k_\infty ({\rm sec}^{{\rm - 1}}) = 15.0 - (57.0 \pm 1.0)/\theta $$\end{document} where θ=2.303 RT in kcal/mole. If A∞ is adjusted relative to the more recent parameters for cyclobutane pyrolysis suggested by VLPP studies, then the Arrhenius expression becomes \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm log }\,k_\infty ({\rm sec}^{{\rm - 1}}) = 15.9 - (59.1 \pm 1.0)/\theta $$\end{document} The cyano group reduces the activation energy for cyclobutane pyrolysis by 6±1 kcal/mole, and on the basis of a biradical mechanism this value may be attributed to the cyano stabilization energy.
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  • 98
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    International Journal of Chemical Kinetics 7 (1975), S. 183-194 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The kinetics of chlorine atom abstraction from the chloromethanes (CM)CCl4, CHCl3, and CH2Cl2 by radiolytically generated cyclohexyl radicals has been studied in the liquid phase by a competitive method. The halogen abstraction data have been put on an absolute basis by comparing the rates of the metathetical reactions with the known rate of addition of cyclohexyl radicals to C2Cl4.The following Arrhenius parameters were obtained: TextCMlog A(CM)/A(C2Cl4)E(CM)—E(C2Cl4)(kcal/mole)log A(CM)(1./mole·sec)E(CM) (kcal/mole)Temperaure Range(°K)CCl40.72±0.02-1.42±0.059.40±0.085.88±0.15333-453CHCl30.77±0.062.86±0.019.45±0.1210.16±0.11392-492CH2Cl20.56±0.126.37±0.279.42±0.1813.67 ± 0.37463-543The error limits are the standard deviations from least mean square Arrhenius plots.The possible application of the Evans-Polanyi relationship to chlorine atom abstraction reaction from CM is considered.
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  • 99
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    International Journal of Chemical Kinetics 7 (1975), S. 223-247 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: High-temperature (〉1000°K) pyrolysis of acetaldehyde (∼1% in an atmosphere of pure nitrogen) was examined in a turbulent flow reactor which permits accurate determination of the spatial distribution of the stable species. Results show that the products in order of decreasing importance are CO, CH4, H2, C2H6, and C2H4. Rates of formation were consistent with the Rice-Herzfeld mechanism by including reactions to explain C2H4 formation and the possible presence of ketene. A steady-state treatment of the complete mechanism indicates that the overall reaction order decreases from \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{3}{2} $\end{document} to 1, which is supported by the new experimental data. Using earlier low-temperature results, the rate constant for the reaction CH3CHO → CH3 + CHO (1) was found as k1=1015.85±0.21 exp (-81,775±1000/RT) sec-1. Also, data for the ratio of rate constants for reactions CH3CHO + CH3 → CH4 + CH3CO (4) and 2CH3 → C2H6(6) were fitted to the empirical expression k4/k61/2=10-13.89±0.03T6.1 exp(-1720±70/RT) (cm3/mole·sec)1/2 and causes for the curvature are discussed. The noncatalytic effect of oxygen on acetaldehyde pyrolysis at high temperature is explained.
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  • 100
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    International Journal of Chemical Kinetics 7 (1975), S. 15-22 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The gas-phase photolysis of perfluoroacetone in the presence of ethane has been shown to result in the production of significant amounts of 1, 1-bis(trifluoromethyl)propanol-1, (CF3)2(C2H5)COH, and 1, 1, 4, 4-tetrakis(trifluoromethyl)butane-1, 4-diol, (CF3)2C(OH)-CH2CH2C(OH)(CF3)2. A mechanism is presented which accounts for the relative rates of formation of these products at room temperature.
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