@article{BachmannSchmidt1999, author = {Bachmann, Michael and Schmidt, Hans-J{\"u}rgen}, title = {Period-doubling bifurcation in strongly anisotropic Bianchi I quantum cosmology}, series = {General relativity and quantum cosmology : preprints gr-qc}, volume = {9912068}, journal = {General relativity and quantum cosmology : preprints gr-qc}, year = {1999}, language = {en} } @article{BachocBlanchardNeuvial2018, author = {Bachoc, Francois and Blanchard, Gilles and Neuvial, Pierre}, title = {On the post selection inference constant under restricted isometry properties}, series = {Electronic journal of statistics}, volume = {12}, journal = {Electronic journal of statistics}, number = {2}, publisher = {Institute of Mathematical Statistics}, address = {Cleveland}, issn = {1935-7524}, doi = {10.1214/18-EJS1490}, pages = {3736 -- 3757}, year = {2018}, abstract = {Uniformly valid confidence intervals post model selection in regression can be constructed based on Post-Selection Inference (PoSI) constants. PoSI constants are minimal for orthogonal design matrices, and can be upper bounded in function of the sparsity of the set of models under consideration, for generic design matrices. In order to improve on these generic sparse upper bounds, we consider design matrices satisfying a Restricted Isometry Property (RIP) condition. We provide a new upper bound on the PoSI constant in this setting. This upper bound is an explicit function of the RIP constant of the design matrix, thereby giving an interpolation between the orthogonal setting and the generic sparse setting. We show that this upper bound is asymptotically optimal in many settings by constructing a matching lower bound.}, language = {en} } @article{BaerenzungHolschneiderLesur2014, author = {Baerenzung, Julien and Holschneider, Matthias and Lesur, Vincent}, title = {Bayesian inversion for the filtered flow at the Earth's core-mantle boundary}, series = {Journal of geophysical research : Solid earth}, volume = {119}, journal = {Journal of geophysical research : Solid earth}, number = {4}, publisher = {American Geophysical Union}, address = {Washington}, issn = {2169-9313}, doi = {10.1002/2013JB010358}, pages = {2695 -- 2720}, year = {2014}, abstract = {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.}, language = {en} } @article{BaerenzungHolschneiderWichtetal.2020, author = {Baerenzung, Julien and Holschneider, Matthias and Wicht, Johannes and Lesur, Vincent and Sanchez, Sabrina}, title = {The Kalmag model as a candidate for IGRF-13}, series = {Earth, planets and space}, volume = {72}, journal = {Earth, planets and space}, number = {1}, publisher = {Springer}, address = {New York}, issn = {1880-5981}, doi = {10.1186/s40623-020-01295-y}, pages = {13}, year = {2020}, abstract = {We present a new model of the geomagnetic field spanning the last 20 years and called Kalmag. Deriving from the assimilation of CHAMP and Swarm vector field measurements, it separates the different contributions to the observable field through parameterized prior covariance matrices. To make the inverse problem numerically feasible, it has been sequentialized in time through the combination of a Kalman filter and a smoothing algorithm. The model provides reliable estimates of past, present and future mean fields and associated uncertainties. The version presented here is an update of our IGRF candidates; the amount of assimilated data has been doubled and the considered time window has been extended from [2000.5, 2019.74] to [2000.5, 2020.33].}, language = {en} } @article{BagderinaTarkhanov2014, author = {Bagderina, Yulia Yu. and Tarkhanov, Nikolai Nikolaevich}, title = {Differential invariants of a class of Lagrangian systems with two degrees of freedom}, series = {Journal of mathematical analysis and applications}, volume = {410}, journal = {Journal of mathematical analysis and applications}, number = {2}, publisher = {Elsevier}, address = {San Diego}, issn = {0022-247X}, doi = {10.1016/j.jmaa.2013.08.015}, pages = {733 -- 749}, year = {2014}, language = {en} } @article{BagderinaTarkhanov2015, author = {Bagderina, Yulia Yu. and Tarkhanov, Nikolai Nikolaevich}, title = {Solution of the equivalence problem for the third Painleve equation}, series = {Journal of mathematical physics}, volume = {56}, journal = {Journal of mathematical physics}, number = {1}, publisher = {American Institute of Physics}, address = {Melville}, issn = {0022-2488}, doi = {10.1063/1.4905383}, pages = {15}, year = {2015}, abstract = {We find necessary conditions for a second order ordinary differential equation to be equivalent to the Painleve III equation under a general point transformation. Their sufficiency is established by reduction to known results for the equations of the form y ' = f (x, y). We consider separately the generic case and the case of reducibility to an autonomous equation. The results are illustrated by the primary resonance equation.}, language = {en} } @unpublished{BagderinaTarkhanov2013, author = {Bagderina, Yulia Yu. and Tarkhanov, Nikolai Nikolaevich}, title = {Differential invariants of a class of Lagrangian systems with two degrees of freedom}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-63129}, year = {2013}, abstract = {We consider systems of Euler-Lagrange equations with two degrees of freedom and with Lagrangian being quadratic in velocities. For this class of equations the generic case of the equivalence problem is solved with respect to point transformations. Using Lie's infinitesimal method we construct a basis of differential invariants and invariant differentiation operators for such systems. We describe certain types of Lagrangian systems in terms of their invariants. The results are illustrated by several examples.}, language = {en} } @unpublished{BagdonavičiusLevulieneNikulinetal.2004, author = {Bagdonavičius, Vilijandas B. and Levuliene, Ruta and Nikulin, Mikhail S. and Zdorova-Cheminade, Olga}, title = {Tests for homogeneity of survival distributions against non-location alternatives and analysis of the gastric cancer data}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51527}, year = {2004}, abstract = {The two and k-sample tests of equality of the survival distributions against the alternatives including cross-effects of survival functions, proportional and monotone hazard ratios, are given for the right censored data. The asymptotic power against approaching alternatives is investigated. The tests are applied to the well known chemio and radio therapy data of the Gastrointestinal Tumor Study Group. The P-values for both proposed tests are much smaller then in the case of other known tests. Differently from the test of Stablein and Koutrouvelis the new tests can be applied not only for singly but also to randomly censored data.}, language = {en} } @article{BaileyBenZionBeckeretal.2010, author = {Bailey, Iain W. and Ben-Zion, Yehuda and Becker, Thorsten W. and Holschneider, Matthias}, title = {Quantifying focal mechanism heterogeneity for fault zones in central and southern California}, issn = {0956-540X}, doi = {10.1111/j.1365-246X.2010.04745.x}, year = {2010}, abstract = {P>We present a statistical analysis of focal mechanism orientations for nine California fault zones with the goal of quantifying variations of fault zone heterogeneity at seismogenic depths. The focal mechanism data are generated from first motion polarities for earthquakes in the time period 1983-2004, magnitude range 0-5, and depth range 0-15 km. Only mechanisms with good quality solutions are used. We define fault zones using 20 km wide rectangles and use summations of normalized potency tensors to describe the distribution of double-couple orientations for each fault zone. Focal mechanism heterogeneity is quantified using two measures computed from the tensors that relate to the scatter in orientations and rotational asymmetry or skewness of the distribution. We illustrate the use of these quantities by showing relative differences in the focal mechanism heterogeneity characteristics for different fault zones. These differences are shown to relate to properties of the fault zone surface traces such that increased scatter correlates with fault trace complexity and rotational asymmetry correlates with the dominant fault trace azimuth. These correlations indicate a link between the long-term evolution of a fault zone over many earthquake cycles and its seismic behaviour over a 20 yr time period. Analysis of the partitioning of San Jacinto fault zone focal mechanisms into different faulting styles further indicates that heterogeneity is dominantly controlled by structural properties of the fault zone, rather than time or magnitude related properties of the seismicity.}, language = {en} } @article{Bandara2021, author = {Bandara, Lashi}, title = {Functional calculus and harmonic analysis in geometry}, series = {S{\~a}o Paulo journal of mathematical sciences / Instituto de Matem{\´a}tica e Estat{\´i}stica da Universidade de S{\~a}o Paulo}, volume = {15}, journal = {S{\~a}o Paulo journal of mathematical sciences / Instituto de Matem{\´a}tica e Estat{\´i}stica da Universidade de S{\~a}o Paulo}, number = {1}, publisher = {Springer}, address = {Cham}, issn = {1982-6907}, doi = {10.1007/s40863-019-00149-0}, pages = {20 -- 53}, year = {2021}, abstract = {In this short survey article, we showcase a number of non-trivial geometric problems that have recently been resolved by marrying methods from functional calculus and real-variable harmonic analysis. We give a brief description of these methods as well as their interplay. This is a succinct survey that hopes to inspire geometers and analysts alike to study these methods so that they can be further developed to be potentially applied to a broader range of questions.}, language = {en} } @article{BandaraBryan2020, author = {Bandara, Lashi and Bryan, Paul}, title = {Heat kernels and regularity for rough metrics on smooth manifolds}, series = {Mathematische Nachrichten}, volume = {293}, journal = {Mathematische Nachrichten}, number = {12}, publisher = {Wiley-VCH}, address = {Weinheim}, issn = {0025-584X}, doi = {10.1002/mana.201800459}, pages = {2255 -- 2270}, year = {2020}, abstract = {We consider rough metrics on smooth manifolds and corresponding Laplacians induced by such metrics. We demonstrate that globally continuous heat kernels exist and are Holder continuous locally in space and time. This is done via local parabolic Harnack estimates for weak solutions of operators in divergence form with bounded measurable coefficients in weighted Sobolev spaces.}, language = {en} } @article{BandaraMcIntoshRosen2017, author = {Bandara, Lashi and McIntosh, Alan and Rosen, Andreas}, title = {Riesz continuity of the Atiyah}, series = {Mathematische Annalen}, volume = {370}, journal = {Mathematische Annalen}, number = {1-2}, publisher = {Springer}, address = {Heidelberg}, issn = {0025-5831}, doi = {10.1007/s00208-017-1610-7}, pages = {863 -- 915}, year = {2017}, abstract = {We prove that the Atiyah-Singer Dirac operator in L2 depends Riesz continuously on L∞ perturbations of complete metrics g on a smooth manifold. The Lipschitz bound for the map depends on bounds on Ricci curvature and its first derivatives as well as a lower bound on injectivity radius. Our proof uses harmonic analysis techniques related to Calder{\´o}n's first commutator and the Kato square root problem. We also show perturbation results for more general functions of general Dirac-type operators on vector bundles.}, language = {en} } @article{BandaraRosen2019, author = {Bandara, Menaka Lashitha and Rosen, Andreas}, title = {Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of local boundary conditions}, series = {Communications in partial differential equations}, volume = {44}, journal = {Communications in partial differential equations}, number = {12}, publisher = {Taylor \& Francis Group}, address = {Philadelphia}, issn = {0360-5302}, doi = {10.1080/03605302.2019.1611847}, pages = {1253 -- 1284}, year = {2019}, abstract = {On a smooth complete Riemannian spin manifold with smooth compact boundary, we demonstrate that Atiyah-Singer Dirac operator in depends Riesz continuously on perturbations of local boundary conditions The Lipschitz bound for the map depends on Lipschitz smoothness and ellipticity of and bounds on Ricci curvature and its first derivatives as well as a lower bound on injectivity radius away from a compact neighbourhood of the boundary. More generally, we prove perturbation estimates for functional calculi of elliptic operators on manifolds with local boundary conditions.}, language = {en} } @book{BattagliaMayerSchmidt1993, author = {Battaglia Mayer, Alexandra and Schmidt, Hans-J{\"u}rgen}, title = {The de Sitter space-time as attractor solution in eighth order gravity}, series = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik}, volume = {1993, 05}, journal = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {9 S.}, year = {1993}, language = {en} } @article{Baumgaertel2009, author = {Baumgaertel, Hellmut}, title = {Spectral and scattering theory of Friedrichs Models on the positive half line with Hilbert-Schmidt perturbations}, issn = {1424-0637}, doi = {10.1007/s00023-009-0398-8}, year = {2009}, abstract = {The spectral theory of the Friedrichs model on the positive half line with Hilbert-Schmidt perturbations, equipped with distinguished analytic properties, is presented. In general, the (separable) multiplicity Hilbert space is assumed to be infinite-dimensional. The results include a spectral characterization of its resonances and the association of so-called Gamov vectors. Sufficient conditions are presented such that all resonances are simple poles of the scattering matrix. The connection between their residual terms and the associated Gamov vectors is pointed out.}, language = {en} } @article{BaumgaertelGrundling2005, author = {Baumgaertel, Hellmut and Grundling, H.}, title = {Superselection in the presence of constraints}, issn = {0022-2488}, year = {2005}, abstract = {Superselection and constraints occur together in many gauge theories, and here we begin a study of such systems. Our main focus will be to analyze compatibility questions between constraining and superselection, and we will develop an example modelled on QED in which our framework is realized. We proceed from a generalization of Doplicher- Roberts superselection theory to the case of the nontrivial center, and a set of Dirac quantum constraints and find conditions under which the superselection structures will survive constraining in some form. This involves an analysis of the restriction and factorization of superselection structures. (c) 2005 American Institute of Physics}, language = {en} } @article{BaumgaertelKaldassKomy2009, author = {Baumgaertel, Hellmut and Kaldass, Hani and Komy, Soliman}, title = {On spectral properties of the resonances for selected potential scattering systems}, issn = {0022-2488}, doi = {10.1063/1.3072675}, year = {2009}, abstract = {The resonances (poles of the scattering matrix) of quantum mechanical scattering by central-symmetric potentials with compact support and zero angular momentum are spectrally characterized directly in terms of the Hamiltonian by a (generalized) eigenvalue problem distinguished by an additional condition (called boundary condition). The connection between the (generalized) eigenspace of a resonance and corresponding Gamov vectors is pointed out. A condition is presented such that a relation between special transition probabilities and infinite sums of residual terms for all complex-conjugated pairs of resonances can be proved. In the case of the square well potential the condition is satisfied.}, language = {en} } @book{Baumgaertel1994, author = {Baumg{\"a}rtel, Hellmut}, title = {A modified approach to the Doplicher-Roberts theorem on the construction of field algebra and the symmetry group in superselection theory}, series = {Preprint / SFB 288, Differentialgeometrie und Quantenphysik}, volume = {134}, journal = {Preprint / SFB 288, Differentialgeometrie und Quantenphysik}, address = {Berlin}, pages = {33 S.}, year = {1994}, language = {en} } @article{Baumgaertel2006, author = {Baumg{\"a}rtel, Hellmut}, title = {Generalized eigenvectors for resonances in the Friedrichs model and their associated Gamov vectors}, issn = {0129-055X}, doi = {10.1142/S0129055X06002589}, year = {2006}, abstract = {A Gelfand triplet for the Hamiltonian H of the Priedrichs model on R with multiplicity space K, dim K < infinity, is constructed such that exactly the resonances (poles of the inverse of the Livsic-matrix) are (generalized) eigenvalues of H. The corresponding eigen(anti)linear forms are calculated explicitly. Using the wave matrices for the wave (Moller) operators the corresponding eigen(anti)linear forms on the Schwartz space S for the unperturbed Hamiltonian Ho are also calculated. It turns out that they are of pure Dirac type and can be characterized by their corresponding Gamov vector lambda -> k/(zeta(0)-lambda)(-1), zeta(0) resonance, k epsilon K, which is uniquely determined by restriction of S to S boolean AND H-+(2), where H-+(2) denotes the Hardy space of the upper half-plane. Simultaneously this restriction yields a truncation of the generalized evolution to the well-known decay semigroup for t >= 0 of the Toeplitz type on H-+(2). That is: Exactly those pre-Gamov vectors a lambda -> k/(zeta-lambda)(-1), ( from the lower half-plane, k epsilon K., have an extension to a generalized eigenvector of H if zeta is a resonance and if k is from that subspace of K which is uniquely determined by its corresponding Dirac type antilinear form}, language = {en} } @book{Baumgaertel1995, author = {Baumg{\"a}rtel, Hellmut}, title = {Operatoralgebraic methods in quantum field theory : a series of lectures}, publisher = {Akademie Verl.}, address = {Berlin}, pages = {228 S.}, year = {1995}, language = {en} }