TY - JOUR A1 - Böckmann, Christine A1 - Osterloh, Lukas T1 - Runge-Kutta type regularization method for inversion of spheroidal particle distribution from limited optical data JF - Inverse problems in science and engineering N2 - The Runge-Kutta type regularization method was recently proposed as a potent tool for the iterative solution of nonlinear ill-posed problems. In this paper we analyze the applicability of this regularization method for solving inverse problems arising in atmospheric remote sensing, particularly for the retrieval of spheroidal particle distribution. Our numerical simulations reveal that the Runge-Kutta type regularization method is able to retrieve two-dimensional particle distributions using optical backscatter and extinction coefficient profiles, as well as depolarization information. KW - inverse ill-posed problem KW - iterative regularization KW - integral equation KW - laser remote sensing KW - inverse scattering KW - aerosol size distribution KW - 65R32 KW - 47A52 KW - 65R20 KW - 78A46 Y1 - 2014 U6 - https://doi.org/10.1080/17415977.2013.830615 SN - 1741-5977 SN - 1741-5985 VL - 22 IS - 1 SP - 150 EP - 165 PB - Routledge, Taylor & Francis Group CY - Abingdon ER - TY - JOUR A1 - Becker, Christian T1 - Relative differential cohomology JF - Lecture notes in mathematics : a collection of informal reports and seminars JF - Lecture Notes in Mathematics N2 - We study two notions of relative differential cohomology, using the model of differential characters. The two notions arise from the two options to construct relative homology, either by cycles of a quotient complex or of a mapping cone complex. We discuss the relation of the two notions of relative differential cohomology to each other. We discuss long exact sequences for both notions, thereby clarifying their relation to absolute differential cohomology. We construct the external and internal product of relative and absolute characters and show that relative differential cohomology is a right module over the absolute differential cohomology ring. Finally we construct fiber integration and transgression for relative differential characters. Y1 - 2014 SN - 978-3-319-07034-6; 978-3-319-07033-9 U6 - https://doi.org/10.1007/978-3-319-07034-6_2 SN - 0075-8434 VL - 2112 SP - 91 EP - 180 PB - Springer CY - Berlin ER - TY - GEN A1 - Osterloha, Lukas A1 - Böckmann, Christine A1 - Nicolae, Doina A1 - Nemuc, Anca T1 - Regularized inversion of microphysical atmospheric particle parameters: Theory and application (vol 237, pg 79, 2013) T2 - Journal of computational physics Y1 - 2014 U6 - https://doi.org/10.1016/j.jcp.2014.07.041 SN - 0021-9991 SN - 1090-2716 VL - 275 SP - 696 EP - 696 PB - Elsevier CY - San Diego ER - TY - INPR A1 - Conforti, Giovanni A1 - Dai Pra, Paolo A1 - Roelly, Sylvie T1 - Reciprocal class of jump processes N2 - Processes having the same bridges as a given reference Markov process constitute its reciprocal class. In this paper we study the reciprocal class of compound Poisson processes whose jumps belong to a finite set A in R^d. We propose a characterization of the reciprocal class as the unique set of probability measures on which a family of time and space transformations induces the same density, expressed in terms of the reciprocal invariants. The geometry of A plays a crucial role in the design of the transformations, and we use tools from discrete geometry to obtain an optimal characterization. We deduce explicit conditions for two Markov jump processes to belong to the same class. Finally, we provide a natural interpretation of the invariants as short-time asymptotics for the probability that the reference process makes a cycle around its current state. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 6 KW - reciprocal processes KW - stochastic bridges KW - jump processes KW - compound Poisson processes Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-70776 SN - 2193-6943 VL - 3 IS - 6 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - THES A1 - Rudorf, Sophia T1 - Protein Synthesis by Ribosomes Y1 - 2014 ER - TY - JOUR A1 - Roelly, Sylvie A1 - Ruszel, W. M. T1 - Propagation of gibbsianness for infinite-dimensional diffusions with space-time interaction JF - Markov processes and related fields N2 - We consider infinite-dimensional diffusions where the interaction between the coordinates has a finite extent both in space and time. In particular, it is not supposed to be smooth or Markov. The initial state of the system is Gibbs, given by a strong summable interaction. If the strongness of this initial interaction is lower than a suitable level, and if the dynamical interaction is bounded from above in a right way, we prove that the law of the diffusion at any time t is a Gibbs measure with absolutely summable interaction. The main tool is a cluster expansion in space uniformly in time of the Girsanov factor coming from the dynamics and exponential ergodicity of the free dynamics to an equilibrium product measure. KW - infinite-dimensional diffusion KW - cluster expansion KW - non-Markov drift KW - Girsanov formula KW - ultracontractivity KW - planar rotors Y1 - 2014 SN - 1024-2953 VL - 20 IS - 4 SP - 653 EP - 674 PB - Polymat CY - Moscow ER - TY - CHAP A1 - Andersson, H. A1 - Keunecke, A. A1 - Eser, A. A1 - Huisinga, Wilhelm A1 - Reinisch, W. A1 - Kloft, Charlotte T1 - Pharmacokinetic considerations for optimising dosing regimens of a potsdam univ infliximab in patients with Crohn's disease T2 - JOURNAL OF CROHNS & COLITIS Y1 - 2014 U6 - https://doi.org/10.1016/S1873-9946(14)60086-6 SN - 1873-9946 SN - 1876-4479 VL - 8 SP - S44 EP - S44 PB - Oxford Univ. Press CY - Oxford ER - 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 -