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 -