Loop-fusion cohomology and transgression

`Loop-fusion cohomology' is defined on the continuous loop space of a manifold in terms of \vCech cochains satisfying two multiplicative conditions with respect to the fusion and figure-of-eight products on loops. The main result is that these cohomology groups, with coefficients in an abelian group, are isomorphic to those of the manifold and the transgression homomorphism factors through the isomorphism.Comment: 10 pages. v2 contains minor correction

Bigerbes

The bigerbes introduced here give a refinement of the notion of 2-gerbes, representing degree four integral cohomology classes of a space. Defined in terms of bisimplicial line bundles, bigerbes have a symmetry with respect to which they form 'bundle 2-gerbes' in two ways; this structure replaces higher associativity conditions. We provide natural examples, including a Brylinski-McLaughlin bigerbe associated to a principal G-bundle for a simply connected simple Lie group. This represents the first Pontryagin class of the bundle, and is the obstruction to the lifting problem on the associated principal bundle over the loop space to the structure group consisting of a central extension of the loop group; in particular, trivializations of this bigerbe for a spin manifold are in bijection with string structures on the original manifold. Other natural examples represent 'decomposable' 4-classes arising as cup products, a universal bigerbe on K(Z,4) involving its based double loop space, and the representation of any 4-class on a space by a bigerbe involving its free double loop space. The generalization to 'multigerbes' of arbitrary degree is also described.Comment: 56 pages. Version 2 includes the free loop version of the Brylinski-McLaughlin bigerbe and its relation to string structures, as well as a discussion of multigerbes of arbitrary orde

Comparison of Time Series and Random-Vibration Theory Site-Response Methods

The random-vibration theory (RVT) approach to equivalent-linear site-response analysis is often used to simulate site amplification, particularly when large numbers of simulations are required for incorporation into probabilistic seismic-hazard analysis. The fact that RVT site-response analysis does not require the specification of input-time series makes it an attractive alternative to other site-response methods. However, some studies have indicated that the site amplification predicted by RVT site-response analysis systematically differs from that predicted by time-series approaches. This study confirms that RVT site-response analysis predicts site amplification at the natural site frequencies as much as 20%-50% larger than time-series analysis, with the largest overprediction occurring for sites with smaller natural frequencies and sites underlain by hard rock. The overprediction is caused by an increase in duration generated by the site response, which is not taken into account in the RVT calculation. Correcting for this change in duration brings the RVT results within 20% of the time-series results. A similar duration effect is observed for the RVT shear-strain calculation used to estimate the equivalent-linear strain-compatible soil properties. An alternative to applying a duration correction to improve the agreement between RVT and time-series analysis is the modeling of shear-wave velocity variability. It is shown that introducing shear-wave velocity variability through Monte Carlo simulation brings the RVT results consistently within +/- 20% of the time-series results.Nuclear Regulatory Commission NRC-04-07-122Civil, Architectural, and Environmental Engineerin

An index theorem of Callias type for pseudodifferential operators

We prove an index theorem for families of pseudodifferential operators generalizing those studied by C. Callias, N. Anghel and others. Specifically, we consider operators on a manifold with boundary equipped with an asymptotically conic (scattering) metric, which have the form D + i \Phi, where D is elliptic pseudodifferential with Hermitian symbols, and \Phi is a Hermitian bundle endomorphism which is invertible at the boundary and commutes with the symbol of D there. The index of such operators is completely determined by the symbolic data over the boundary. We use the scattering calculus of R. Melrose in order to prove our results using methods of topological K-theory, and we devote special attention to the case in which D is a family of Dirac operators, in which case our theorem specializes to give families versions of the previously known index formulas.Comment: 18 pages, 1 figure. Revisions incorporated as suggested by referee report. To appear in the Journal of K-theor

Vorteilhaftigkeitsanalyse zweier softwarebasierter Entscheidungsspiele zur Unterstützung in der universitären Lehre

Softwarebasierte Entscheidungspiele und Geschäftssimulationen werden für Unternehmen immer wichtiger. Sie werden unterstützend bei innerbetrieblichen Weiterbildungsmaßnahmen eingesetzt und bilden eine Entscheidungsgrundlage in der Personalrekrutierung. Der drastische Preisverfall der Hardware in der vergangenen Dekade sowie die Durchsetzung des Internets - einhergehend mit einer steigenden Bereitschaft, Computer als Instrumente in der Lehre einzusetzen - führten dazu, dass in den Universitäten und bei rund 37% aller deutschen Firmen Planspiele genutzt werden. Auch die Versicherungswirtschaft und die Versicherungswissenschaft machen sich diese Entwicklung zu Nutze, um Mitarbeitern oder Studenten das Wirtschaften in Versicherungsunternehmen und damit zusammenhängende theoretische Grundlagen modellhaft zu veranschaulichen. Insbesondere die Planspiele TOPSIM von der TERTIA-Edusoft GmbH und INSGAME finden hier Anwendung. In der vorliegenden Arbeit werden beide Spiele mittels einer Nutzwertanalyse verglichen, um die Eignung beider Werkzeuge für den Einsatz in der universitären Ausbildung zu überprüfen. Sich richtet sich an Institutionen, die erwägen, softwarebasierte Entscheidungsspiele zu Ausbildungs- oder Weiterbildungszwecken einzusetzen, und sie soll mit der Gegenüberstellung der beiden Spiele eine Entscheidungsgrundlage für deren Nutzung geben. Einem interdisziplinären Ansatz folgend werden die Planspiele der Versicherungswirtschaft mit einem Controllinginstrument unter Rückgriff auf Elemente der Informatik und der Linguistik bewertet, um ein pädagogisches Ziel zu erreichen