@article{EichmairMetzger2013, author = {Eichmair, Michael and Metzger, Jan}, title = {Unique isoperimetric foliations of asymptotically flat manifolds in all dimensions}, series = {Inventiones mathematicae}, volume = {194}, journal = {Inventiones mathematicae}, number = {3}, publisher = {Springer}, address = {New York}, issn = {0020-9910}, doi = {10.1007/s00222-013-0452-5}, pages = {591 -- 630}, year = {2013}, language = {en} } @inproceedings{HaferKiy2013, author = {Hafer, J{\"o}rg and Kiy, Alexander}, title = {The university-wide introduction of an ePortfolio system as transdisciplinary task}, series = {Proceedings of the PLE Conference 2013: Learning and Diversity in the Cities of the Future}, booktitle = {Proceedings of the PLE Conference 2013: Learning and Diversity in the Cities of the Future}, editor = {Buchem, Ilona and Graham, Attwell and Tur, Gemma}, publisher = {Logos}, address = {Berlin}, pages = {363 -- 373}, year = {2013}, language = {en} } @article{Schmidt2013, author = {Schmidt, Hans-J{\"u}rgen}, title = {The tetralogy of Birkhoff theorems}, series = {General relativity and gravitation}, volume = {45}, journal = {General relativity and gravitation}, number = {2}, publisher = {Springer}, address = {New York}, issn = {0001-7701}, doi = {10.1007/s10714-012-1478-5}, pages = {395 -- 410}, year = {2013}, abstract = {We classify the existent Birkhoff-type theorems into four classes: first, in field theory, the theorem states the absence of helicity 0- and spin 0-parts of the gravitational field. Second, in relativistic astrophysics, it is the statement that the gravitational far-field of a spherically symmetric star carries, apart from its mass, no information about the star; therefore, a radially oscillating star has a static gravitational far-field. Third, in mathematical physics, Birkhoff's theorem reads: up to singular exceptions of measure zero, the spherically symmetric solutions of Einstein's vacuum field equation with can be expressed by the Schwarzschild metric; for , it is the Schwarzschild-de Sitter metric instead. Fourth, in differential geometry, any statement of the type: every member of a family of pseudo-Riemannian space-times has more isometries than expected from the original metric ansatz, carries the name Birkhoff-type theorem. Within the fourth of these classes we present some new results with further values of dimension and signature of the related spaces; including them are some counterexamples: families of space-times where no Birkhoff-type theorem is valid. These counterexamples further confirm the conjecture, that the Birkhoff-type theorems have their origin in the property, that the two eigenvalues of the Ricci tensor of 2-D pseudo-Riemannian spaces always coincide, a property not having an analogy in higher dimensions. Hence, Birkhoff-type theorems exist only for those physical situations which are reducible to 2-D.}, language = {en} } @article{Schmidt2013, author = {Schmidt, Hans-J{\"u}rgen}, title = {The tetralogy of Birkhoff theorems}, issn = {0001-7701}, year = {2013}, abstract = {We classify the existent Birkhoff-type theorems into four classes: First, in field theory, the theorem states the absence of helicity 0- and spin 0-parts of the gravitational field. Second, in relativistic astrophysics, it is the statement that the gravitational far-field of a spherically symmetric star carries, apart from its mass, no information about the star; therefore, a radially oscillating star has a static gravitational far-field. Third, in mathematical physics, Birkhoff's theorem reads: up to singular exceptions of measure zero, the spherically symmetric solutions of Einstein's vacuum field equation with Lambda = 0 can be expressed by the Schwarzschild metric; for Lambda unequal 0, it is the Schwarzschild-de Sitter metric instead. Fourth, in differential geometry, any statement of the type: every member of a family of pseudo-Riemannian space-times has more isometries than expected from the original metric ansatz, carries the name Birkhoff-type theorem. Within the fourth of these classes we present some new results with further values of dimension and signature of the related spaces; including them are some counterexamples: families of space-times where no Birkhoff-type theorem is valid. These counterexamples further confirm the conjecture, that the Birkhoff-type theorems have their origin in the property, that the two eigenvalues of the Ricci tensor of two- dimensional pseudo-Riemannian spaces always coincide, a property not having an analogy in higher dimensions. Hence, Birkhoff-type theorems exist only for those physical situations which are reducible to two dimensions.}, language = {en} } @article{DebusscheHoegeleImkeller2013, author = {Debussche, Arnaud and H{\"o}gele, Michael and Imkeller, Peter}, title = {The stochastic chafee-infante equation}, series = {Lecture notes in mathematics : a collection of informal reports and seminars}, volume = {2085}, journal = {Lecture notes in mathematics : a collection of informal reports and seminars}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-319-00828-8; 978-3-319-00827-1}, issn = {0075-8434}, doi = {10.1007/978-3-319-00828-8_3}, pages = {45 -- 68}, year = {2013}, abstract = {In this preparatory chapter, the tools of stochastic analysis needed for the investigation of the asymptotic behavior of the stochastic Chafee-Infante equation are provided. In the first place, this encompasses a recollection of basic facts about L{\´e}vy processes with values in Hilbert spaces. Playing the role of the additive noise processes perturbing the deterministic Chafee-Infante equation in the systems the stochastic dynamics of which will be our main interest, symmetric ?-stable L{\´e}vy processes are in the focus of our investigation (Sect. 3.1).}, language = {en} } @article{DebusscheHoegeleImkeller2013, author = {Debussche, Arnaud and Hoegele, Michael and Imkeller, Peter}, title = {The source of stochastic models in conceptual climate dynamics}, series = {Lecture notes in mathematics : a collection of informal reports and seminars}, volume = {2085}, journal = {Lecture notes in mathematics : a collection of informal reports and seminars}, number = {3}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-319-00828-8; 978-3-319-00827-1}, issn = {0075-8434}, doi = {10.1007/978-3-319-00828-8}, pages = {151 -- 157}, year = {2013}, language = {en} } @article{DebusscheHoegeleImkeller2013, author = {Debussche, Arnaud and Hoegele, Michael and Imkeller, Peter}, title = {The small deviation of the small noise solution}, series = {Lecture notes in mathematics : a collection of informal reports and seminars}, volume = {2085}, journal = {Lecture notes in mathematics : a collection of informal reports and seminars}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-319-00828-8; 978-3-319-00827-1}, issn = {0075-8434}, doi = {10.1007/978-3-319-00828-8_4}, pages = {69 -- 85}, year = {2013}, language = {en} } @article{ZoellerHolschneiderHainzl2013, author = {Z{\"o}ller, Gert and Holschneider, Matthias and Hainzl, Sebastian}, title = {The Maximum Earthquake Magnitude in a Time Horizon: Theory and Case Studies}, series = {Bulletin of the Seismological Society of America}, volume = {103}, journal = {Bulletin of the Seismological Society of America}, number = {2A}, publisher = {Seismological Society of America}, address = {Albany}, issn = {0037-1106}, doi = {10.1785/0120120013}, pages = {860 -- 875}, year = {2013}, abstract = {We show how the maximum magnitude within a predefined future time horizon may be estimated from an earthquake catalog within the context of Gutenberg-Richter statistics. The aim is to carry out a rigorous uncertainty assessment, and calculate precise confidence intervals based on an imposed level of confidence a. In detail, we present a model for the estimation of the maximum magnitude to occur in a time interval T-f in the future, given a complete earthquake catalog for a time period T in the past and, if available, paleoseismic events. For this goal, we solely assume that earthquakes follow a stationary Poisson process in time with unknown productivity Lambda and obey the Gutenberg-Richter law in magnitude domain with unknown b-value. The random variables. and b are estimated by means of Bayes theorem with noninformative prior distributions. Results based on synthetic catalogs and on retrospective calculations of historic catalogs from the highly active area of Japan and the low-seismicity, but high-risk region lower Rhine embayment (LRE) in Germany indicate that the estimated magnitudes are close to the true values. Finally, we discuss whether the techniques can be extended to meet the safety requirements for critical facilities such as nuclear power plants. For this aim, the maximum magnitude for all times has to be considered. In agreement with earlier work, we find that this parameter is not a useful quantity from the viewpoint of statistical inference.}, language = {en} } @article{ShojaeiFard2013, author = {Shojaei-Fard, Ali}, title = {The global beta-functions from solutions of dyson-schwinger equations}, series = {Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics}, volume = {28}, journal = {Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics}, number = {34}, publisher = {World Scientific}, address = {Singapore}, issn = {0217-7323}, doi = {10.1142/S0217732313501526}, pages = {12}, year = {2013}, abstract = {We apply the geometric interpretation of Dyson-Schwinger equations (DSEs) in terms of equi-singular flat connections to provide a process which relates beta-functions of a DSE under different regularization schemes.}, language = {en} } @article{DebusscheHoegeleImkeller2013, author = {Debussche, Arnaud and H{\"o}gele, Michael and Imkeller, Peter}, title = {The Fine Dynamics of the Chafee-Infante Equation}, series = {Lecture notes in mathematics : a collection of informal reports and seminars}, volume = {2085}, journal = {Lecture notes in mathematics : a collection of informal reports and seminars}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-319-00828-8; 978-3-319-00827-1}, issn = {0075-8434}, doi = {10.1007/978-3-319-00828-8_2}, pages = {11 -- 43}, year = {2013}, abstract = {In this chapter, we introduce the deterministic Chafee-Infante equation. This equation has been the subject of intense research and is very well understood now. We recall some properties of its longtime dynamics and in particular the structure of its attractor. We then define reduced domains of attraction that will be fundamental in our study and give a result describing precisely the time that a solution starting form a reduced domain of attraction needs to reach a stable equilibrium. This result is then proved using the detailed knowledge of the attractor and classical tools such as the stable and unstable manifolds in a neighborhood of an equilibrium.}, language = {en} }