TY - INPR A1 - Dereudre, David A1 - Roelly, Sylvie T1 - Path-dependent infinite-dimensional SDE with non-regular drift : an existence result N2 - We establish in this paper the existence of weak solutions of infinite-dimensional shift invariant stochastic differential equations driven by a Brownian term. The drift function is very general, in the sense that it is supposed to be neither small or continuous, nor Markov. On the initial law we only assume that it admits a finite specific entropy. Our result strongly improves the previous ones obtained for free dynamics with a small perturbative drift. The originality of our method leads in the use of the specific entropy as a tightness tool and on a description of such stochastic differential equation as solution of a variational problem on the path space. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3(2014)11 KW - Infinite-dimensional SDE KW - non-Markov drift KW - non-regular drift KW - variational principle KW - specific entropy Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-72084 SN - 2193-6943 VL - 3 IS - 11 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Grewe, Volker A1 - Brinkop, Sabine A1 - Joeckel, Patrick A1 - Shin, Seoleun A1 - Reich, Sebastian A1 - Yserentant, Harry T1 - On the theory of mass conserving transformations for Lagrangian methods in 3D atmosphere-chemistry models JF - Meteorologische Zeitschrift KW - Lagrangian modelling KW - chemistry KW - transformations Y1 - 2014 U6 - https://doi.org/10.1127/0941-2948/2014/0552 SN - 0941-2948 SN - 1610-1227 VL - 23 IS - 4 SP - 441 EP - 447 PB - Schweizerbart CY - Stuttgart ER - TY - INPR A1 - Gairing, Jan A1 - Högele, Michael A1 - Kosenkova, Tetiana A1 - Kulik, Alexei Michajlovič T1 - On the calibration of Lévy driven time series with coupling distances : an application in paleoclimate N2 - This article aims at the statistical assessment of time series with large fluctuations in short time, which are assumed to stem from a continuous process perturbed by a Lévy process exhibiting a heavy tail behavior. We propose an easily implementable procedure to estimate efficiently the statistical difference between the noisy behavior of the data and a given reference jump measure in terms of so-called coupling distances. After a short introduction to Lévy processes and coupling distances we recall basic statistical approximation results and derive rates of convergence. In the sequel the procedure is elaborated in detail in an abstract setting and eventually applied in a case study to simulated and paleoclimate data. It indicates the dominant presence of a non-stable heavy-tailed jump Lévy component for some tail index greater than 2. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 2 KW - time series with heavy tails KW - index of stability KW - goodness-of-fit KW - empirical Wasserstein distance Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-69781 SN - 2193-6943 VL - 3 IS - 2 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Blanchard, Gilles A1 - Dickhaus, Thorsten A1 - Roquain, Etienne A1 - Villers, Fanny T1 - On least favorable configurations for step-up-down tests JF - Statistica Sinica KW - False discovery rate KW - least favorable configuration KW - multiple testing; Y1 - 2014 U6 - https://doi.org/10.5705/ss.2011.205 SN - 1017-0405 SN - 1996-8507 VL - 24 IS - 1 SP - 1 EP - U31 PB - Statistica Sinica, Institute of Statistical Science, Academia Sinica CY - Taipei ER - TY - JOUR A1 - Alsaedy, Ammar A1 - Tarkhanov, Nikolai Nikolaevich T1 - Normally solvable nonlinear boundary value problems JF - Nonlinear analysis : theory, methods & applications ; an international multidisciplinary journal N2 - We investigate nonlinear problems which appear as Euler-Lagrange equations for a variational problem. They include in particular variational boundary value problems for nonlinear elliptic equations studied by F. Browder in the 1960s. We establish a solvability criterion of such problems and elaborate an efficient orthogonal projection method for constructing approximate solutions. KW - Nonlinear Laplace operator KW - Boundary value problem KW - Dirichlet to Neumann operator Y1 - 2014 U6 - https://doi.org/10.1016/j.na.2013.09.024 SN - 0362-546X SN - 1873-5215 VL - 95 SP - 468 EP - 482 PB - Elsevier CY - Oxford ER - TY - JOUR A1 - Hafer, Jörg A1 - Kiy, Alexander A1 - Lucke, Ulrike T1 - Moodle & Co. auf dem Weg zur Personal Learning Environment JF - eleed N2 - Ausgehend von der typischen IT‐Infrastruktur für E‐Learning an Hochschulen auf der einen Seite sowie vom bisherigen Stand der Forschung zu Personal Learning Environments (PLEs) auf der anderen Seite zeigt dieser Beitrag auf, wie bestehende Werkzeuge bzw. Dienste zusammengeführt und für die Anforderungen der modernen, rechnergestützten Präsenzlehre aufbereitet werden können. Für diesen interdisziplinären Entwicklungsprozess bieten sowohl klassische Softwareentwicklungsverfahren als auch bestehende PLE‐Modelle wenig Hilfestellung an. Der Beitrag beschreibt die in einem campusweiten Projekt an der Universität Potsdam verfolgten Ansätze und die damit erzielten Ergebnisse. Dafür werden zunächst typische Lehr‐/Lern‐bzw. Kommunikations‐Szenarien identifiziert, aus denen Anforderungen an eine unterstützende Plattform abgeleitet werden. Dies führt zu einer umfassenden Sammlung zu berücksichtigender Dienste und deren Funktionen, die gemäß den Spezifika ihrer Nutzung in ein Gesamtsystem zu integrieren sind. Auf dieser Basis werden grundsätzliche Integrationsansätze und technische Details dieses Mash‐Ups in einer Gesamtschau aller relevanten Dienste betrachtet und in eine integrierende Systemarchitektur überführt. Deren konkrete Realisierung mit Hilfe der Portal‐Technologie Liferay wird dargestellt, wobei die eingangs definierten Szenarien aufgegriffen und exemplarisch vorgestellt werden. Ergänzende Anpassungen im Sinne einer personalisierbaren bzw. adaptiven Lern‐(und Arbeits‐)Umgebung werden ebenfalls unterstützt und kurz aufgezeigt. Y1 - 2014 UR - https://eleed.campussource.de/archive/10/4085 SN - 1860-7470 VL - 2014 IS - 10 ER - TY - INPR A1 - Pornsawad, Pornsarp A1 - Böckmann, Christine T1 - Modified iterative Runge-Kutta-type methods for nonlinear ill-posed problems N2 - This work is devoted to the convergence analysis of a modified Runge-Kutta-type iterative regularization method for solving nonlinear ill-posed problems under a priori and a posteriori stopping rules. The convergence rate results of the proposed method can be obtained under Hölder-type source-wise condition if the Fréchet derivative is properly scaled and locally Lipschitz continuous. Numerical results are achieved by using the Levenberg-Marquardt and Radau methods. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 7 KW - ill-posed problems KW - Runge-Kutta methods KW - regularization methods KW - Hölder-type source condition KW - stopping rules Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-70834 SN - 2193-6943 VL - 3 IS - 7 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Högele, Michael A1 - Pavlyukevich, Ilya T1 - Metastability of Morse-Smale dynamical systems perturbed by heavy-tailed Lévy type noise N2 - We consider a general class of finite dimensional deterministic dynamical systems with finitely many local attractors each of which supports a unique ergodic probability measure, which includes in particular the class of Morse–Smale systems in any finite dimension. The dynamical system is perturbed by a multiplicative non-Gaussian heavytailed Lévy type noise of small intensity ε > 0. Specifically we consider perturbations leading to a Itô, Stratonovich and canonical (Marcus) stochastic differential equation. The respective asymptotic first exit time and location problem from each of the domains of attractions in case of inward pointing vector fields in the limit of ε-> 0 has been investigated by the authors. We extend these results to domains with characteristic boundaries and show that the perturbed system exhibits a metastable behavior in the sense that there exits a unique ε-dependent time scale on which the random system converges to a continuous time Markov chain switching between the invariant measures. As examples we consider α-stable perturbations of the Duffing equation and a chemical system exhibiting a birhythmic behavior. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 5 KW - hyperbolic dynamical system KW - Morse-Smale property KW - stable limit cycle KW - small noise asymptotic KW - multiplicative noise Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-70639 SN - 2193-6943 VL - 3 IS - 5 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Koppitz, Jörg A1 - Musunthia, Tiwadee T1 - Maximal subsemigroups containing a particular semigroup JF - Mathematica Slovaca N2 - We characterize maximal subsemigroups of the monoid T(X) of all transformations on the set X = a"center dot of natural numbers containing a given subsemigroup W of T(X) such that T(X) is finitely generated over W. This paper gives a contribution to the characterization of maximal subsemigroups on the monoid of all transformations on an infinite set. KW - maximal subsemigroup KW - transformations on infinite set Y1 - 2014 U6 - https://doi.org/10.2478/s12175-014-0280-0 SN - 0139-9918 SN - 1337-2211 VL - 64 IS - 6 SP - 1369 EP - 1380 PB - De Gruyter CY - Warsaw 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 - 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 - 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 - 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 - Amezcua, Javier A1 - Ide, Kayo A1 - Kalnay, Eugenia A1 - Reich, Sebastian T1 - Ensemble transform Kalman-Bucy filters JF - Quarterly journal of the Royal Meteorological Society N2 - Two recent works have adapted the Kalman-Bucy filter into an ensemble setting. In the first formulation, the ensemble of perturbations is updated by the solution of an ordinary differential equation (ODE) in pseudo-time, while the mean is updated as in the standard Kalman filter. In the second formulation, the full ensemble is updated in the analysis step as the solution of single set of ODEs in pseudo-time. Neither requires matrix inversions except for the frequently diagonal observation error covariance. We analyse the behaviour of the ODEs involved in these formulations. We demonstrate that they stiffen for large magnitudes of the ratio of background error to observational error variance, and that using the integration scheme proposed in both formulations can lead to failure. A numerical integration scheme that is both stable and is not computationally expensive is proposed. We develop transform-based alternatives for these Bucy-type approaches so that the integrations are computed in ensemble space where the variables are weights (of dimension equal to the ensemble size) rather than model variables. Finally, the performance of our ensemble transform Kalman-Bucy implementations is evaluated using three models: the 3-variable Lorenz 1963 model, the 40-variable Lorenz 1996 model, and a medium complexity atmospheric general circulation model known as SPEEDY. The results from all three models are encouraging and warrant further exploration of these assimilation techniques. KW - Kalman-Bucy Filter KW - Ensemble Kalman Filter KW - stiff ODE KW - weight-based formulations Y1 - 2014 U6 - https://doi.org/10.1002/qj.2186 SN - 0035-9009 SN - 1477-870X VL - 140 IS - 680 SP - 995 EP - 1004 PB - Wiley-Blackwell CY - Hoboken ER - TY - THES A1 - Dyachenko, Evgeniya T1 - Elliptic problems with small parameter T1 - Elliptische Problemen mit kleinem Parameter N2 - In this thesis we consider diverse aspects of existence and correctness of asymptotic solutions to elliptic differential and pseudodifferential equations. We begin our studies with the case of a general elliptic boundary value problem in partial derivatives. A small parameter enters the coefficients of the main equation as well as into the boundary conditions. Such equations have already been investigated satisfactory, but there still exist certain theoretical deficiencies. Our aim is to present the general theory of elliptic problems with a small parameter. For this purpose we examine in detail the case of a bounded domain with a smooth boundary. First of all, we construct formal solutions as power series in the small parameter. Then we examine their asymptotic properties. It suffices to carry out sharp two-sided \emph{a priori} estimates for the operators of boundary value problems which are uniform in the small parameter. Such estimates failed to hold in functional spaces used in classical elliptic theory. To circumvent this limitation we exploit norms depending on the small parameter for the functions defined on a bounded domain. Similar norms are widely used in literature, but their properties have not been investigated extensively. Our theoretical investigation shows that the usual elliptic technique can be correctly carried out in these norms. The obtained results also allow one to extend the norms to compact manifolds with boundaries. We complete our investigation by formulating algebraic conditions on the operators and showing their equivalence to the existence of a priori estimates. In the second step, we extend the concept of ellipticity with a small parameter to more general classes of operators. Firstly, we want to compare the difference in asymptotic patterns between the obtained series and expansions for similar differential problems. Therefore we investigate the heat equation in a bounded domain with a small parameter near the time derivative. In this case the characteristics touch the boundary at a finite number of points. It is known that the solutions are not regular in a neighbourhood of such points in advance. We suppose moreover that the boundary at such points can be non-smooth but have cuspidal singularities. We find a formal asymptotic expansion and show that when a set of parameters comes through a threshold value, the expansions fail to be asymptotic. The last part of the work is devoted to general concept of ellipticity with a small parameter. Several theoretical extensions to pseudodifferential operators have already been suggested in previous studies. As a new contribution we involve the analysis on manifolds with edge singularities which allows us to consider wider classes of perturbed elliptic operators. We examine that introduced classes possess a priori estimates of elliptic type. As a further application we demonstrate how developed tools can be used to reduce singularly perturbed problems to regular ones. N2 - In dieser Dissertation betrachten wir verschiedene Aspekte der Existenz und Korrektheit asymptotischer Lösungen für elliptische Differentialgleichungen und Pseudodifferentialgleichungen. Am Anfang betrachtet die Arbeit den Fall eines allgemeinen elliptischen Grenzwertproblems in partiellen Ableitungen. Hierbei hängen die Koeffizienten von einem kleinen Parameter ab. Solche Gleichungen wurden schon reichlich untersucht, aber es gibt immer noch theoretische Lücken. Unser Ziel ist eine allgemeine Theorie elliptischer Operatorklassen mit kleinen Parametern. Zu diesem Zweck untersuchen wir im Detail den Fall eines beschränkten Gebietes mit glattem Rand. Zuerst konstruieren wir formale Lösungen als Potenzreihe einer kleinen Variablen. Weiter untersuchen wir ihre asymptotischen Eigenschaften. Dazu reicht es aus, beidseitige A-Priori Abschätzungen für diejenigen Randwertproblemoperatoren zu bestimmen, die gleichmäßig stetig von den kleinen Parametern abhängen. Solche Abschätzungen gelten nicht in Funktionenräumen, die in der klassischen elliptischen Theorie benutzt werden. Um diese Beschränkungen zu überwinden, nutzen wir Normen abhängig vom kleinen Parameter. Änliche Normen finden sich oft in der Literatur, aber ihre Eigenschaften wurden unzureichend untersucht. Unsere theoretische Forschung zeigt, dass die gewöhnliche elliptische Methode korrekt durchgeführt werden kann. Die erhaltenen Abschätzungen erlauben das Fortsetzen der Normen auf kompakte Mannigfältigkeiten mit Rand. Unsere Forschung wird mit algebraischen Bedingungen für die Operatoren abgeschlossen. Wir zeigen, dass diese Bedingungen äquivalent zu der Existenz der A-Priori-Abschätzungen sind. Im zweiten Schritt erweitern wir das Konzept der Elliptizität mit kleinen Parametern zu allgemeineren Operatorklassen. Zuerst wollen wir den Unterschied in asymptotischen Mustern zwischen der erhaltenen Reihe und Lösungen ähnlicher Probleme untersuchen. Deshalb untersuchen wir die Wärmeleitungsgleichung in einem beschränkten Gebiet mit einem kleinen Parameter in der Zeitableitung. In diesem Fall tangiert der Rand die Charakteristik endlich oft. Es ist bekannt, dass die Lösungen unregulär im Allgemeinen in Umgebungen solcher Stellen sind. Wir nehmen an, dass der Rand an solchen Stellen nicht glätt sein kann und kaspydalische Singularitäten hat. Wir haben eine formale asymptotische Zerlegung gefunden und einen Schwellenwert gezeigt, sodass die asymptotische Eigenschaft der Reihe nicht mehr gilt, wenn der Randparameter diesen Schwellenwert übersteigt. Der letze Teil der Arbeit führt ein allgemeines Konzept der Elliptizit\"at mit einem kleinen Parameter ein. Mehrere theoretische Erweiterungen auf Pseudodifferentialoperatoren wurden schon in früheren Studien vorgeschlagen. Als neuen Beitrag wenden wir die Analysis auf Manigfältigkeiten mit Kantensingularitäten an. Dies lässt es zu, allgemeinere gestörte Operatorklassen zu betrachten. Wir beobachten, dass die eingef\"uhrten Klassen A-Priori-Abschätzungen elliptischer Gestalt haben. Als weitere Anwendung demonstrieren wir, wie die entwickelten Mittel zum Reduzieren singular gestörter Probleme zu regulären Fällen benutzt werden können. KW - elliptische Gleichungen KW - kleine Parameter KW - elliptic problems KW - small parameter KW - boundary layer Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-72056 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 - JOUR A1 - Bagderina, Yulia Yu. A1 - Tarkhanov, Nikolai Nikolaevich T1 - Differential invariants of a class of Lagrangian systems with two degrees of freedom JF - Journal of mathematical analysis and applications KW - Equivalence KW - Differential invariant KW - Euler-Lagrange equations Y1 - 2014 U6 - https://doi.org/10.1016/j.jmaa.2013.08.015 SN - 0022-247X SN - 1096-0813 VL - 410 IS - 2 SP - 733 EP - 749 PB - Elsevier CY - San Diego ER - TY - JOUR A1 - Bär, Christian A1 - Becker, Christian T1 - Differential characters and geometric chains JF - Lecture notes in mathematics : a collection of informal reports and seminars JF - Lecture Notes in Mathematics N2 - We study Cheeger-Simons differential characters and provide geometric descriptions of the ring structure and of the fiber integration map. The uniqueness of differential cohomology (up to unique natural transformation) is proved by deriving an explicit formula for any natural transformation between a differential cohomology theory and the model given by differential characters. Fiber integration for fibers with boundary is treated in the context of relative differential characters. As applications we treat higher-dimensional holonomy, parallel transport, and transgression. Y1 - 2014 SN - 978-3-319-07034-6; 978-3-319-07033-9 U6 - https://doi.org/10.1007/978-3-319-07034-6_1 SN - 0075-8434 VL - 2112 SP - 1 EP - 90 PB - Springer CY - Berlin ER - TY - JOUR A1 - Bubenzer, Johannes T1 - Cycle-aware minimization of acyclic deterministic finite-state automata JF - Discrete applied mathematics N2 - In this paper a linear-time algorithm for the minimization of acyclic deterministic finite-state automata is presented. The algorithm runs significantly faster than previous algorithms for the same task. This is shown by a comparison of the running times of both algorithms. Additionally, a variation of the new algorithm is presented which handles cyclic automata as input. The new cycle-aware algorithm minimizes acyclic automata in the desired way. In case of cyclic input, the algorithm minimizes all acyclic suffixes of the input automaton. KW - Minimization KW - Deterministic finite state automata KW - Algorithmic Y1 - 2014 U6 - https://doi.org/10.1016/j.dam.2013.08.003 SN - 0166-218X SN - 1872-6771 VL - 163 SP - 238 EP - + PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Kind, Josephine T1 - Creation of topographic maps JF - Process design for natural scientists: an agile model-driven approach N2 - Location analyses are among the most common tasks while working with spatial data and geographic information systems. Automating the most frequently used procedures is therefore an important aspect of improving their usability. In this context, this project aims to design and implement a workflow, providing some basic tools for a location analysis. For the implementation with jABC, the workflow was applied to the problem of finding a suitable location for placing an artificial reef. For this analysis three parameters (bathymetry, slope and grain size of the ground material) were taken into account, processed, and visualized with the The Generic Mapping Tools (GMT), which were integrated into the workflow as jETI-SIBs. The implemented workflow thereby showed that the approach to combine jABC with GMT resulted in an user-centric yet user-friendly tool with high-quality cartographic outputs. Y1 - 2014 SN - 978-3-662-45005-5 IS - 500 SP - 229 EP - 238 PB - Springer CY - Berlin 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 - JOUR A1 - Guo, Li A1 - Paycha, Sylvie A1 - Zhang, Bin T1 - Conical zeta values and their double subdivision relations JF - Advances in mathematics N2 - We introduce the concept of a conical zeta value as a geometric generalization of a multiple zeta value in the context of convex cones. The quasi-shuffle and shuffle relations of multiple zeta values are generalized to open cone subdivision and closed cone subdivision relations respectively for conical zeta values. In order to achieve the closed cone subdivision relation, we also interpret linear relations among fractions as subdivisions of decorated closed cones. As a generalization of the double shuffle relation of multiple zeta values, we give the double subdivision relation of conical zeta values and formulate the extended double subdivision relation conjecture for conical zeta values. KW - Convex cones KW - Conical zeta values KW - Smooth cones KW - Decorated cones KW - Subdivisions KW - Multiple zeta values KW - Shuffles KW - Quasi-shuffles KW - Fractions with linear poles KW - Shintani zeta values Y1 - 2014 U6 - https://doi.org/10.1016/j.aim.2013.10.022 SN - 0001-8708 SN - 1090-2082 VL - 252 SP - 343 EP - 381 PB - Elsevier CY - San Diego 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 - THES A1 - Supaporn, Worakrit T1 - Categorical equivalence of clones Y1 - 2014 ER - TY - JOUR A1 - Holschneider, Matthias A1 - Zöller, Gert A1 - Clements, R. A1 - Schorlemmer, Danijel T1 - Can we test for the maximum possible earthquake magnitude? JF - Journal of geophysical research : Solid earth Y1 - 2014 U6 - https://doi.org/10.1002/2013JB010319 SN - 2169-9313 SN - 2169-9356 VL - 119 IS - 3 SP - 2019 EP - 2028 PB - American Geophysical Union CY - Washington ER - TY - INPR A1 - Conforti, Giovanni A1 - Léonard, Christian A1 - Murr, Rüdiger A1 - Roelly, Sylvie T1 - Bridges of Markov counting processes : reciprocal classes and duality formulas N2 - Processes having the same bridges are said to belong to the same reciprocal class. In this article we analyze reciprocal classes of Markov counting processes by identifying their reciprocal invariants and we characterize them as the set of counting processes satisfying some duality formula. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 9 KW - counting process KW - bridge KW - reciprocal class KW - duality formula Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-71855 SN - 2193-6943 VL - 3 IS - 9 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Baerenzung, Julien A1 - Holschneider, Matthias A1 - Lesur, Vincent T1 - Bayesian inversion for the filtered flow at the Earth's core-mantle boundary JF - Journal of geophysical research : Solid earth N2 - The inverse problem of determining the flow at the Earth's core-mantle boundary according to an outer core magnetic field and secular variation model has been investigated through a Bayesian formalism. To circumvent the issue arising from the truncated nature of the available fields, we combined two modeling methods. In the first step, we applied a filter on the magnetic field to isolate its large scales by reducing the energy contained in its small scales, we then derived the dynamical equation, referred as filtered frozen flux equation, describing the spatiotemporal evolution of the filtered part of the field. In the second step, we proposed a statistical parametrization of the filtered magnetic field in order to account for both its remaining unresolved scales and its large-scale uncertainties. These two modeling techniques were then included in the Bayesian formulation of the inverse problem. To explore the complex posterior distribution of the velocity field resulting from this development, we numerically implemented an algorithm based on Markov chain Monte Carlo methods. After evaluating our approach on synthetic data and comparing it to previously introduced methods, we applied it to a magnetic field model derived from satellite data for the single epoch 2005.0. We could confirm the existence of specific features already observed in previous studies. In particular, we retrieved the planetary scale eccentric gyre characteristic of flow evaluated under the compressible quasi-geostrophy assumption although this hypothesis was not considered in our study. In addition, through the sampling of the velocity field posterior distribution, we could evaluate the reliability, at any spatial location and at any scale, of the flow we calculated. The flow uncertainties we determined are nevertheless conditioned by the choice of the prior constraints we applied to the velocity field. Y1 - 2014 U6 - https://doi.org/10.1002/2013JB010358 SN - 2169-9313 SN - 2169-9356 VL - 119 IS - 4 SP - 2695 EP - 2720 PB - American Geophysical Union CY - Washington ER - TY - BOOK A1 - Pilipenko, Andrey T1 - An introduction to stochastic differential equations with reflection T3 - Lectures in pure and applied mathematics N2 - These lecture notes are intended as a short introduction to diffusion processes on a domain with a reflecting boundary for graduate students, researchers in stochastic analysis and interested readers. Specific results on stochastic differential equations with reflecting boundaries such as existence and uniqueness, continuity and Markov properties, relation to partial differential equations and submartingale problems are given. An extensive list of references to current literature is included. This book has its origins in a mini-course the author gave at the University of Potsdam and at the Technical University of Berlin in Winter 2013. T3 - Lectures in pure and applied mathematics - 1 KW - Diffusionsprozess KW - Reflektierende Randbedingungen KW - stochastische Differentialgleichungen KW - diffusion process KW - reflecting boundary KW - stochastic differential equations Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-70782 SN - 978-3-86956-297-1 SN - 2199-4951 SN - 2199-496X IS - 1 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Aizenberg, Lev A. A1 - Tarkhanov, Nikolai Nikolaevich T1 - An integral formula for the number of lattice points in a domain N2 - Using the multidimensional logarithmic residue we show a simple formula for the difference between the number of integer points in a bounded domain of R^n and the volume of this domain. The difference proves to be the integral of an explicit differential form over the boundary of the domain. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 3 KW - logarithmic residue KW - lattice point Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-70453 SN - 2193-6943 VL - 3 IS - 3 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Fedchenko, Dmitry A1 - Tarkhanov, Nikolai Nikolaevich T1 - An index formula for Toeplitz operators N2 - We prove a Fedosov index formula for the index of Toeplitz operators connected with the Hardy space of solutions to an elliptic system of first order partial differential equations in a bounded domain of Euclidean space with infinitely differentiable boundary. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3(2014)12 KW - Toeplitz operators KW - Fredholm property KW - index Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-72499 SN - 2193-6943 VL - 3 IS - 12 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Klein, Markus A1 - Leonard, Christian A1 - Rosenberger, Elke T1 - Agmon-type estimates for a class of jump processes JF - Mathematische Nachrichten N2 - In the limit 0 we analyse the generators H of families of reversible jump processes in Rd associated with a class of symmetric non-local Dirichlet-forms and show exponential decay of the eigenfunctions. The exponential rate function is a Finsler distance, given as solution of a certain eikonal equation. Fine results are sensitive to the rate function being C2 or just Lipschitz. Our estimates are analogous to the semiclassical Agmon estimates for differential operators of second order. They generalize and strengthen previous results on the lattice Zd. Although our final interest is in the (sub)stochastic jump process, technically this is a pure analysis paper, inspired by PDE techniques. KW - Decay of eigenfunctions KW - semiclassical Agmon estimate KW - Finsler distance KW - jump process KW - Dirichlet-form Y1 - 2014 U6 - https://doi.org/10.1002/mana.201200324 SN - 0025-584X SN - 1522-2616 VL - 287 IS - 17-18 SP - 2021 EP - 2039 PB - Wiley-VCH CY - Weinheim ER - TY - INPR A1 - Flandoli, Franco A1 - Högele, Michael T1 - A solution selection problem with small stable perturbations N2 - The zero-noise limit of differential equations with singular coefficients is investigated for the first time in the case when the noise is a general alpha-stable process. It is proved that extremal solutions are selected and the probability of selection is computed. Detailed analysis of the characteristic function of an exit time form on the half-line is performed, with a suitable decomposition in small and large jumps adapted to the singular drift. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 8 KW - stochastic differential equations KW - singular drifts KW - zero-noise limit KW - Peano phenomena KW - non-uniqueness Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-71205 SN - 2193-6943 VL - 3 IS - 8 PB - Universitätsverlag Potsdam CY - Potsdam 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 -