TY - THES A1 - Rudorf, Sophia T1 - Protein Synthesis by Ribosomes Y1 - 2014 ER - TY - JOUR A1 - Rungrottheera, Wannarut A1 - Schulze, Bert-Wolfgang T1 - Weighted spaces on corner manifolds JF - Complex variables and elliptic equations N2 - We study spaces on manifolds with double weights and iterated discrete and continuous asymptotics, and their relationship with corner pseudo-differential operators. KW - manifolds with corners KW - iterated asymptotics KW - operators with corner symbols KW - 35J70 KW - 47G30 KW - 58J40 Y1 - 2014 U6 - https://doi.org/10.1080/17476933.2013.876416 SN - 1747-6933 SN - 1747-6941 VL - 59 IS - 12 SP - 1706 EP - 1738 PB - Routledge, Taylor & Francis Group CY - Abingdon ER - TY - JOUR A1 - Rungrottheera, Wannarut A1 - Schulze, Bert-Wolfgang A1 - Wong, M. W. T1 - Iterative properties of pseudo-differential operators on edge spaces JF - Journal of pseudo-differential operators and applications N2 - Pseudo-differential operators with twisted symbolic estimates play a large role in the calculus on manifolds with edge singularities. We study here aspects of the underlying abstract concept and establish a new result on iteration of quantizations. KW - Pseudo-differential operators KW - Twisted symbolic estimates KW - Quantizations Y1 - 2014 U6 - https://doi.org/10.1007/s11868-014-0100-x SN - 1662-9981 SN - 1662-999X VL - 5 IS - 4 SP - 455 EP - 479 PB - Springer CY - Basel ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Wei, Y. T1 - The Mellin-edge quantisation for corner operators JF - Complex analysis and operator theory N2 - We establish a quantisation of corner-degenerate symbols, here called Mellin-edge quantisation, on a manifold with second order singularities. The typical ingredients come from the "most singular" stratum of which is a second order edge where the infinite transversal cone has a base that is itself a manifold with smooth edge. The resulting operator-valued amplitude functions on the second order edge are formulated purely in terms of Mellin symbols taking values in the edge algebra over . In this respect our result is formally analogous to a quantisation rule of (Osaka J. Math. 37:221-260, 2000) for the simpler case of edge-degenerate symbols that corresponds to the singularity order 1. However, from the singularity order 2 on there appear new substantial difficulties for the first time, partly caused by the edge singularities of the cone over that tend to infinity. Y1 - 2014 U6 - https://doi.org/10.1007/s11785-013-0289-3 SN - 1661-8254 SN - 1661-8262 VL - 8 IS - 4 SP - 803 EP - 841 PB - Springer CY - Basel ER - TY - JOUR A1 - Shebalin, Peter N. A1 - Narteau, Clement A1 - Zechar, Jeremy Douglas A1 - Holschneider, Matthias T1 - Combining earthquake forecasts using differential probability gains JF - Earth, planets and space N2 - We describe an iterative method to combine seismicity forecasts. With this method, we produce the next generation of a starting forecast by incorporating predictive skill from one or more input forecasts. For a single iteration, we use the differential probability gain of an input forecast relative to the starting forecast. At each point in space and time, the rate in the next-generation forecast is the product of the starting rate and the local differential probability gain. The main advantage of this method is that it can produce high forecast rates using all types of numerical forecast models, even those that are not rate-based. Naturally, a limitation of this method is that the input forecast must have some information not already contained in the starting forecast. We illustrate this method using the Every Earthquake a Precursor According to Scale (EEPAS) and Early Aftershocks Statistics (EAST) models, which are currently being evaluated at the US testing center of the Collaboratory for the Study of Earthquake Predictability. During a testing period from July 2009 to December 2011 (with 19 target earthquakes), the combined model we produce has better predictive performance - in terms of Molchan diagrams and likelihood - than the starting model (EEPAS) and the input model (EAST). Many of the target earthquakes occur in regions where the combined model has high forecast rates. Most importantly, the rates in these regions are substantially higher than if we had simply averaged the models. KW - Probabilistic forecasting KW - Earthquake interaction KW - Forecasting and prediction KW - Statistical seismology Y1 - 2014 U6 - https://doi.org/10.1186/1880-5981-66-37 SN - 1880-5981 VL - 66 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Shojaei-Fard, Ali T1 - Counterterms in the context of the universal Hopf algebra of renormalization JF - International journal of modern physics : A, Particles and fields, gravitation, cosmology, nuclear physics N2 - The manuscript discovers a new interpretation of counterterms of renormalizable Quantum Field Theories in terms of formal expansions of decorated rooted trees. KW - Perturbative renormalization KW - renormalization Hopf algebra KW - counterterms KW - rooted trees Y1 - 2014 U6 - https://doi.org/10.1142/S0217751X14500456 SN - 0217-751X SN - 1793-656X VL - 29 IS - 8 PB - World Scientific CY - Singapore ER - TY - INPR A1 - Sultanov, Oskar A1 - Kalyakin, Leonid A1 - Tarkhanov, Nikolai Nikolaevich T1 - Elliptic perturbations of dynamical systems with a proper node N2 - The paper is devoted to asymptotic analysis of the Dirichlet problem for a second order partial differential equation containing a small parameter multiplying the highest order derivatives. It corresponds to a small perturbation of a dynamical system having a stationary solution in the domain. We focus on the case where the trajectories of the system go into the domain and the stationary solution is a proper node. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 4 KW - dynamical system KW - singular perturbation KW - asymptotic methods Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-70460 SN - 2193-6943 VL - 3 IS - 4 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - THES A1 - Supaporn, Worakrit T1 - Categorical equivalence of clones Y1 - 2014 ER - TY - THES A1 - Vu, Dinh Phuong T1 - Using video study to investigate eighth-grade mathematics classrooms in Vietnam T1 - Die Nutzung von Videostudien zur Untersuchung des Mathematikunterrichts in der 8. Klasse in Vietnam N2 - The International Project for the Evaluation of Educational Achievement (IEA) was formed in the 1950s (Postlethwaite, 1967). Since that time, the IEA has conducted many studies in the area of mathematics, such as the First International Mathematics Study (FIMS) in 1964, the Second International Mathematics Study (SIMS) in 1980-1982, and a series of studies beginning with the Third International Mathematics and Science Study (TIMSS) which has been conducted every 4 years since 1995. According to Stigler et al. (1999), in the FIMS and the SIMS, U.S. students achieved low scores in comparison with students in other countries (p. 1). The TIMSS 1995 “Videotape Classroom Study” was therefore a complement to the earlier studies conducted to learn “more about the instructional and cultural processes that are associated with achievement” (Stigler et al., 1999, p. 1). The TIMSS Videotape Classroom Study is known today as the TIMSS Video Study. From the findings of the TIMSS 1995 Video Study, Stigler and Hiebert (1999) likened teaching to “mountain ranges poking above the surface of the water,” whereby they implied that we might see the mountaintops, but we do not see the hidden parts underneath these mountain ranges (pp. 73-78). By watching the videotaped lessons from Germany, Japan, and the United States again and again, they discovered that “the systems of teaching within each country look similar from lesson to lesson. At least, there are certain recurring features [or patterns] that typify many of the lessons within a country and distinguish the lessons among countries” (pp. 77-78). They also discovered that “teaching is a cultural activity,” so the systems of teaching “must be understood in relation to the cultural beliefs and assumptions that surround them” (pp. 85, 88). From this viewpoint, one of the purposes of this dissertation was to study some cultural aspects of mathematics teaching and relate the results to mathematics teaching and learning in Vietnam. Another research purpose was to carry out a video study in Vietnam to find out the characteristics of Vietnamese mathematics teaching and compare these characteristics with those of other countries. In particular, this dissertation carried out the following research tasks: - Studying the characteristics of teaching and learning in different cultures and relating the results to mathematics teaching and learning in Vietnam - Introducing the TIMSS, the TIMSS Video Study and the advantages of using video study in investigating mathematics teaching and learning - Carrying out the video study in Vietnam to identify the image, scripts and patterns, and the lesson signature of eighth-grade mathematics teaching in Vietnam - Comparing some aspects of mathematics teaching in Vietnam and other countries and identifying the similarities and differences across countries - Studying the demands and challenges of innovating mathematics teaching methods in Vietnam – lessons from the video studies Hopefully, this dissertation will be a useful reference material for pre-service teachers at education universities to understand the nature of teaching and develop their teaching career. N2 - Das International Project for the Evaluation of Educational Achievement (IEA) wurde in den 1950er Jahren gegründet. Seitdem führte das IEA viele Studien in Bereich mathematischer Bildung durch, insbesondere die First International Mathematics Study (FIMS) im Jahre 1964, die Second International Mathematics Study (SIMS) in den Jahren 1980–1982 und eine Reihe von Studien, die mit der Third International Mathematics and Science Study (TIMSS) begann und seit 1995 alle vier Jahre durchgeführt wird. Nach Stigler et al. (1999) erreichten US-amerikanische Studenten bei FIMS und SIMS niedrigere Ergebnisse als Schüler anderer Länder (S. 1). Daher wurde TIMSS 1995 erweitert um eine ‘Videotape Classroom Study’ mit dem Ziel, „mehr über die unterrichtlichen und kulturellen Prozesse, die mit Leistung zusammenhängen“, zu erfahren (S. 1; Übersetzung vom engl. Original). Von den Ergebnissen der TIMMS 1995 Video Study ausgehend verglichen Stigler und Hiebert (1999) Unterricht mit „Gebirgszügen, die die Wasseroberfläche durchstoßen“, womit sie ausdrücken sollten, was die Bergspitzen sichtbar, große Teile des Gebirges aber unter dem Wasser verborgen sind (S. 73–78; Übersetzung vom engl. Original). Durch die wiederholte Analyse videographierter Unterrichtsstunden aus Deutschland, Japan und den USA entdeckten sie, dass „die Arten des Unterrichts innerhalb jedes Landes von Stunde zu Stunde ähnlich sind. Zumindest gibt es bestimmte wiederkehrende Aspekte [oder Skripte], welche für viele Stunden eines Landes typisch sind und die Stunden gegenüber anderen Ländern abgrenzen“ (S. 77f.). Sie entdeckten außerdem, dass Unterricht eine „kulturelle Aktivität“ ist, Unterrichtsarten also „verstanden werden müssen in Relation zu den kulturellen Überzeugungen und Annahmen, die sie umgeben“ (S. 85, 88). Hierauf aufbauend war es ein Ziel der Dissertation, kulturelle Aspekte des Mathematikunterricht zu untersuchen und die Ergebnisse mit Mathematikunterricht in Vietnam zu vergleichen. Ein weiteres Ziel war die Erhebung der Charakteristika vietnamesischen Mathematikunterricht durch eine Videostudie in Vietnam und der anschließende Vergleich dieser Charakteristika mit denen anderer Länder. Im Einzelnen befasste sich diese Dissertation mit den folgenden Forschungszielen: - Untersuchung der Charakteristika von Lehren und Lernen in unterschiedlichen Kulturen und vorläufiger Vergleich der Resultate mit dem Lehren und Lernen von Mathematik in Vietnam - Einführung der TIMSS und der TIMSS Video Study und der methodologischen Vorteile von Videostudien für die Untersuchung von Mathematikunterricht in Vietnam - Durchführung der Videostudie in Vietnam, um Unterrichtsskripte des Mathematikunterrichts in 8. Klassen in Vietnam zu identifizieren - Vergleich ausgewählter Aspekte des Mathematikunterrichts in Vietnam mit denen anderer Länder auf der Grundlage der Videostudie in Vietnam und Diskussion von Ähnlichkeiten und Unterschieden zwischen Ländern - Untersuchung der Herausforderungen für eine Innovation der Unterrichtsmethoden im Mathematikunterricht Vietnams Diese Dissertation entstand in der Hoffnung, dass sie eine nützliche Referenz für Lehramtsstudenten zum Verständnis der Natur des Unterrichts und zur Entwicklung der eigenen Lehrerpersönlichkeit darstellen möge. KW - Videostudie KW - Mathematikunterricht KW - Unterrichtsmethode KW - TIMSS KW - Kulturelle Aktivität KW - video study KW - mathematics education KW - teaching methods KW - TIMSS KW - Vietnam Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-72464 ER - TY - JOUR A1 - Wallenta, Daniel T1 - A Lefschetz fixed point formula for elliptic quasicomplexes JF - Integral equations and operator theor N2 - In a recent paper, the Lefschetz number for endomorphisms (modulo trace class operators) of sequences of trace class curvature was introduced. We show that this is a well defined, canonical extension of the classical Lefschetz number and establish the homotopy invariance of this number. Moreover, we apply the results to show that the Lefschetz fixed point formula holds for geometric quasiendomorphisms of elliptic quasicomplexes. KW - Elliptic complexes KW - Fredholm complexes KW - Lefschetz number Y1 - 2014 U6 - https://doi.org/10.1007/s00020-014-2122-4 SN - 0378-620X SN - 1420-8989 VL - 78 IS - 4 SP - 577 EP - 587 PB - Springer CY - Basel ER - TY - THES A1 - Ziese, Ramona T1 - Geometric electroelasticity T1 - Geometrische Elektroelastizität N2 - In this work a diffential geometric formulation of the theory of electroelasticity is developed which also includes thermal and magnetic influences. We study the motion of bodies consisting of an elastic material that are deformed by the influence of mechanical forces, heat and an external electromagnetic field. To this end physical balance laws (conservation of mass, balance of momentum, angular momentum and energy) are established. These provide an equation that describes the motion of the body during the deformation. Here the body and the surrounding space are modeled as Riemannian manifolds, and we allow that the body has a lower dimension than the surrounding space. In this way one is not (as usual) restricted to the description of the deformation of three-dimensional bodies in a three-dimensional space, but one can also describe the deformation of membranes and the deformation in a curved space. Moreover, we formulate so-called constitutive relations that encode the properties of the used material. Balance of energy as a scalar law can easily be formulated on a Riemannian manifold. The remaining balance laws are then obtained by demanding that balance of energy is invariant under the action of arbitrary diffeomorphisms on the surrounding space. This generalizes a result by Marsden and Hughes that pertains to bodies that have the same dimension as the surrounding space and does not allow the presence of electromagnetic fields. Usually, in works on electroelasticity the entropy inequality is used to decide which otherwise allowed deformations are physically admissible and which are not. It is alsoemployed to derive restrictions to the possible forms of constitutive relations describing the material. Unfortunately, the opinions on the physically correct statement of the entropy inequality diverge when electromagnetic fields are present. Moreover, it is unclear how to formulate the entropy inequality in the case of a membrane that is subjected to an electromagnetic field. Thus, we show that one can replace the use of the entropy inequality by the demand that for a given process balance of energy is invariant under the action of arbitrary diffeomorphisms on the surrounding space and under linear rescalings of the temperature. On the one hand, this demand also yields the desired restrictions to the form of the constitutive relations. On the other hand, it needs much weaker assumptions than the arguments in physics literature that are employing the entropy inequality. Again, our result generalizes a theorem of Marsden and Hughes. This time, our result is, like theirs, only valid for bodies that have the same dimension as the surrounding space. N2 - In der vorliegenden Arbeit wird eine diffentialgeometrische Formulierung der Elektroelastizitätstheorie entwickelt, die auch thermische und magnetische Einflüsse berücksichtigt. Hierbei wird die Bewegung von Körpern untersucht, die aus einem elastischen Material bestehen und sich durch mechanische Kräfte, Wärmezufuhr und den Einfluss eines äußeren elektromagnetischen Feldes verformen. Dazu werden physikalische Bilanzgleichungen (Massenerhaltung, Impuls-, Drehimpuls- und Energiebilanz) aufgestellt, um mit deren Hilfe eine Gleichung zu formulieren, die die Bewegung des Körpers während der Deformation beschreibt. Dabei werden sowohl der Körper als auch der umgebende Raum als Riemannsche Mannigfaltigkeiten modelliert, wobei zugelassen ist, dass der Körper eine geringere Dimension hat als der ihn umgebende Raum. Auf diese Weise kann man nicht nur - wie sonst üblich - die Deformation dreidimensionaler Körper im dreidimensionalen euklidischen Raum beschreiben, sondern auch die Deformation von Membranen und die Deformation innerhalb eines gekrümmten Raums. Weiterhin werden sogenannte konstitutive Gleichungen formuliert, die die Eigenschaften des verwendeten Materials kodieren. Die Energiebilanz ist eine skalare Gleichung und kann daher leicht auf Riemannschen Mannigfaltigkeiten formuliert werden. Es wird gezeigt, dass die Forderung der Invarianz der Energiebilanz unter der Wirkung von beliebigen Diffeomorphismen auf den umgebenden Raum bereits die restlichen Bilanzgleichungen impliziert. Das verallgemeinert ein Resultat von Marsden und Hughes, das nur für Körper anwendbar ist, die die selbe Dimension wie der umgebende Raum haben und keine elektromagnetischen Felder berücksichtigt. Üblicherweise wird in Arbeiten über Elektroelastizität die Entropieungleichung verwendet, um zu entscheiden, welche Deformationen physikalisch zulässig sind und welche nicht. Sie wird außerdem verwendet, um Einschränkungen für die möglichen Formen von konstitutiven Gleichungen, die das Material beschreiben, herzuleiten. Leider gehen die Meinungen über die physikalisch korrekte Formulierung der Entropieungleichung auseinander sobald elektromagnetische Felder beteiligt sind. Weiterhin ist unklar, wie die Entropieungleichung für den Fall einer Membran, die einem elektromagnetischen Feld ausgesetzt ist, formuliert werden muss. Daher zeigen wir, dass die Benutzung der Entropieungleichung ersetzt werden kann durch die Forderung, dass für einen gegebenen Prozess die Energiebilanz invariant ist unter der Wirkung eines beliebigen Diffeomorphimus' auf den umgebenden Raum und der linearen Reskalierung der Temperatur. Zum einen liefert diese Forderung die gewünschten Einschränkungen für die Form der konstitutiven Gleichungen, zum anderen benoetigt sie viel schwächere Annahmen als die übliche Argumentation mit der Entropieungleichung, die man in der Physikliteratur findet. Unser Resultat ist dabei wieder eine Verallgemeinerung eines Theorems von Marsden und Hughes, wobei es, so wie deren Resultat, nur für Körper gilt, die als offene Teilmengen des dreidimensionalen euklidischen Raums modelliert werden können. KW - Elastizität KW - Elektrodynamik KW - Mannigfaltigkeit KW - konstitutive Gleichungen KW - Bewegungsgleichung KW - elasticity KW - electrodynamics KW - manifold KW - constitutive relations KW - equation of motion Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-72504 ER - TY - JOUR A1 - Zöller, Gert A1 - Ben-Zion, Yehuda T1 - Large earthquake hazard of the San Jacinto fault zone, CA, from long record of simulated seismicity assimilating the available instrumental and paleoseismic data JF - Pure and applied geophysics N2 - We investigate spatio-temporal properties of earthquake patterns in the San Jacinto fault zone (SJFZ), California, between Cajon Pass and the Superstition Hill Fault, using a long record of simulated seismicity constrained by available seismological and geological data. The model provides an effective realization of a large segmented strike-slip fault zone in a 3D elastic half-space, with heterogeneous distribution of static friction chosen to represent several clear step-overs at the surface. The simulated synthetic catalog reproduces well the basic statistical features of the instrumental seismicity recorded at the SJFZ area since 1981. The model also produces events larger than those included in the short instrumental record, consistent with paleo-earthquakes documented at sites along the SJFZ for the last 1,400 years. The general agreement between the synthetic and observed data allows us to address with the long-simulated seismicity questions related to large earthquakes and expected seismic hazard. The interaction between m a parts per thousand yen 7 events on different sections of the SJFZ is found to be close to random. The hazard associated with m a parts per thousand yen 7 events on the SJFZ increases significantly if the long record of simulated seismicity is taken into account. The model simulations indicate that the recent increased number of observed intermediate SJFZ earthquakes is a robust statistical feature heralding the occurrence of m a parts per thousand yen 7 earthquakes. The hypocenters of the m a parts per thousand yen 5 events in the simulation results move progressively towards the hypocenter of the upcoming m a parts per thousand yen 7 earthquake. KW - Earthquake dynamics KW - Earthquake interaction KW - forecasting KW - prediction KW - Statistical seismology KW - Seismicity and tectonics Y1 - 2014 U6 - https://doi.org/10.1007/s00024-014-0783-1 SN - 0033-4553 SN - 1420-9136 VL - 171 IS - 11 SP - 2955 EP - 2965 PB - Springer CY - Basel ER - TY - JOUR A1 - Zöller, Gert A1 - Holschneider, Matthias T1 - Induced seismicity: What is the size of the largest expected earthquake? JF - The bulletin of the Seismological Society of America N2 - The injection of fluids is a well-known origin for the triggering of earthquake sequences. The growing number of projects related to enhanced geothermal systems, fracking, and others has led to the question, which maximum earthquake magnitude can be expected as a consequence of fluid injection? This question is addressed from the perspective of statistical analysis. Using basic empirical laws of earthquake statistics, we estimate the magnitude M-T of the maximum expected earthquake in a predefined future time window T-f. A case study of the fluid injection site at Paradox Valley, Colorado, demonstrates that the magnitude m 4.3 of the largest observed earthquake on 27 May 2000 lies very well within the expectation from past seismicity without adjusting any parameters. Vice versa, for a given maximum tolerable earthquake at an injection site, we can constrain the corresponding amount of injected fluids that must not be exceeded within predefined confidence bounds. Y1 - 2014 U6 - https://doi.org/10.1785/0120140195 SN - 0037-1106 SN - 1943-3573 VL - 104 IS - 6 SP - 3153 EP - 3158 PB - Seismological Society of America CY - Albany ER -