TY  - JOUR
A1  - Fedchenko, Dmitry
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A Rado theorem for the porous medium equation
JF  - Boletin de la Sociedad Matemática Mexicana
N2  - We prove that if u is a locally Lipschitz continuous function on an open set chi subset of Rn + 1 satisfying the nonlinear heat equation partial derivative(t)u = Delta(vertical bar u vertical bar(p-1) u), p > 1, weakly away from the zero set u(-1) (0) in chi, then u is a weak solution to this equation in all of chi.
KW  - Quasilinear equations
KW  - Removable sets
KW  - Porous medium equation
Y1  - 2017
U6  - https://doi.org/10.1007/s40590-017-0169-3
SN  - 1405-213X
SN  - 2296-4495
VL  - 24
IS  - 2
SP  - 427
EP  - 437
PB  - Springer
CY  - Cham
ER  - 
TY  - JOUR
A1  - Dimitrova, Ilinka
A1  - Koppitz, Jörg
T1  - On the semigroup of all partial fence-preserving injections on a finite set
JF  - Journal of Algebra and Its Applications
N2  - For n∈N , let Xn={a1,a2,…,an} be an n-element set and let F=(Xn;<f) be a fence, also called a zigzag poset. As usual, we denote by In the symmetric inverse semigroup on Xn. We say that a transformation α∈In is fence-preserving if x<fy implies that xα<fyα, for all x,y in the domain of α. In this paper, we study the semigroup PFIn of all partial fence-preserving injections of Xn and its subsemigroup IFn={α∈PFIn:α−1∈PFIn}. Clearly, IFn is an inverse semigroup and contains all regular elements of PFIn. We characterize the Green’s relations for the semigroup IFn. Further, we prove that the semigroup IFn is generated by its elements with rank ≥n−2. Moreover, for n∈2N, we find the least generating set and calculate the rank of IFn.
KW  - Finite transformation semigroup
KW  - fence-preserving transformations
KW  - inverse semigroup
KW  - Green´s Relations
KW  - generators
KW  - rank
Y1  - 2017
U6  - https://doi.org/10.1142/S0219498817502231
SN  - 0219-4988
SN  - 1793-6829
VL  - 16
IS  - 12
PB  - World Scientific
CY  - Singapore
ER  - 
TY  - JOUR
A1  - Benini, Marco
A1  - Capoferri, Matteo
A1  - Dappiaggi, Claudio
T1  - Hadamard States for Quantum Abelian Duality
JF  - Annales de l'Institut Henri Poincaré
N2  - Abelian duality is realized naturally by combining differential cohomology and locally covariant quantum field theory. This leads to a -algebra of observables, which encompasses the simultaneous discretization of both magnetic and electric fluxes. We discuss the assignment of physically well-behaved states on this algebra and the properties of the associated GNS triple. We show that the algebra of observables factorizes as a suitable tensor product of three -algebras: the first factor encodes dynamical information, while the other two capture topological data corresponding to electric and magnetic fluxes. On the former factor and in the case of ultra-static globally hyperbolic spacetimes with compact Cauchy surfaces, we exhibit a state whose two-point correlation function has the same singular structure of a Hadamard state. Specifying suitable counterparts also on the topological factors, we obtain a state for the full theory, ultimately implementing Abelian duality transformations as Hilbert space isomorphisms.
Y1  - 2017
U6  - https://doi.org/10.1007/s00023-017-0593-y
SN  - 1424-0637
SN  - 1424-0661
VL  - 18
SP  - 3325
EP  - 3370
PB  - Springer
CY  - Basel
ER  - 
TY  - JOUR
A1  - Lesur, Vincent
A1  - Wardinski, Ingo
A1  - Bärenzung, Julien
A1  - Holschneider, Matthias
T1  - On the frequency spectra of the core magnetic field Gauss coefficients
JF  - Physics of the earth and planetary interiors
N2  - From monthly mean observatory data spanning 1957-2014, geomagnetic field secular variation values were calculated by annual differences. Estimates of the spherical harmonic Gauss coefficients of the core field secular variation were then derived by applying a correlation based modelling. Finally, a Fourier transform was applied to the time series of the Gauss coefficients. This process led to reliable temporal spectra of the Gauss coefficients up to spherical harmonic degree 5 or 6, and down to periods as short as 1 or 2 years depending on the coefficient. We observed that a k(-2) slope, where k is the frequency, is an acceptable approximation for these spectra, with possibly an exception for the dipole field. The monthly estimates of the core field secular variation at the observatory sites also show that large and rapid variations of the latter happen. This is an indication that geomagnetic jerks are frequent phenomena and that significant secular variation signals at short time scales - i.e. less than 2 years, could still be extracted from data to reveal an unexplored part of the core dynamics.
KW  - Geomagnetism
KW  - Core field
KW  - Secular variation rate of change
KW  - Geomagnetic jerks
KW  - Correlation based modelling
Y1  - 2017
U6  - https://doi.org/10.1016/j.pepi.2017.05.017
SN  - 0031-9201
SN  - 1872-7395
VL  - 276
SP  - 145
EP  - 158
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Gerlach, Moritz Reinhardt
A1  - Glück, Jochen
T1  - On a convergence theorem for semigroups of positive integral operators
JF  - Comptes Rendus Mathematique
N2  - We give a new and very short proof of a theorem of Greiner asserting that a positive and contractive -semigroup on an -space is strongly convergent in case it has a strictly positive fixed point and contains an integral operator. Our proof is a streamlined version of a much more general approach to the asymptotic theory of positive semigroups developed recently by the authors. Under the assumptions of Greiner's theorem, this approach becomes particularly elegant and simple. We also give an outlook on several generalisations of this result.
Y1  - 2017
U6  - https://doi.org/10.1016/j.crma.2017.07.017
SN  - 1631-073X
SN  - 1778-3569
VL  - 355
SP  - 973
EP  - 976
PB  - Elsevier
CY  - Paris
ER  - 
TY  - JOUR
A1  - Brungs, Hans H.
A1  - Gräter, Joachim
T1  - On central extensions of SL(2, F) admitting left-orderings
JF  - Journal of Algebra
N2  - For an arbitrary euclidean field F we introduce a central extension (G(F), Phi) of SL(2, F) admitting a left-ordering and study its algebraic properties. The elements of G(F) are order preserving bijections of the convex hull of Q in F. If F = R then G(F) is isomorphic to the classical universal covering group of the Lie group SL(2, R). Among other results we show that G(F) is a perfect group which possesses a rank 1 cone of exceptional type. We also prove that its centre is an infinite cyclic group and investigate its normal subgroups.
KW  - Universal covering group
KW  - Central extensions of groups
KW  - Perfect groups
KW  - Ordered fields
KW  - Left-ordered groups
KW  - Order-preserving bijections
KW  - Euclidean fields
Y1  - 2017
U6  - https://doi.org/10.1016/j.jalgebra.2017.05.025
SN  - 0021-8693
SN  - 1090-266X
VL  - 486
SP  - 288
EP  - 327
PB  - Elsevier
CY  - San Diego
ER  - 
TY  - JOUR
A1  - Zöller, Gert
A1  - Ullah, Shahid
A1  - Bindi, Dino
A1  - Parolai, Stefano
A1  - Mikhailova, Natalya
T1  - The largest expected earthquake magnitudes in Central Asia
BT  - statistical inference from an earthquake catalogue with uncertain magnitudes
JF  - Seismicity, fault rupture and earthquake hazards in slowly deforming regions
N2  - The knowledge of the largest expected earthquake magnitude in a region is one of the key issues in probabilistic seismic hazard calculations and the estimation of worst-case scenarios. Earthquake catalogues are the most informative source of information for the inference of earthquake magnitudes. We analysed the earthquake catalogue for Central Asia with respect to the largest expected magnitudes m(T) in a pre-defined time horizon T-f using a recently developed statistical methodology, extended by the explicit probabilistic consideration of magnitude errors. For this aim, we assumed broad error distributions for historical events, whereas the magnitudes of recently recorded instrumental earthquakes had smaller errors. The results indicate high probabilities for the occurrence of large events (M >= 8), even in short time intervals of a few decades. The expected magnitudes relative to the assumed maximum possible magnitude are generally higher for intermediate-depth earthquakes (51-300 km) than for shallow events (0-50 km). For long future time horizons, for example, a few hundred years, earthquakes with M >= 8.5 have to be taken into account, although, apart from the 1889 Chilik earthquake, it is probable that no such event occurred during the observation period of the catalogue.
Y1  - 2017
SN  - 978-1-86239-745-3
SN  - 978-1-86239-964-8
U6  - https://doi.org/10.1144/SP432.3
SN  - 0305-8719
VL  - 432
SP  - 29
EP  - 40
PB  - The Geological Society
CY  - London
ER  - 
TY  - CHAP
A1  - Audin, Michèle
A1  - Ducourtioux, Catherine
A1  - Ouédraogo, Françoise
A1  - Schulz, René
A1  - Delgado, Julio
A1  - Ruzhansky, Michael
A1  - Lebeau, Gilles
ED  - Paycha, Sylvie
T1  - Integral Fourier operators
T1  - Fourier Integraloperatoren
BT  - proceedings of a summer school, Ouagadougou 14–25 September 2015
BT  - Akten einer Sommerschule, Ouagadougou, Burkina Faso, 14-26. September 2015
N2  - This volume of contributions  based on lectures  delivered at a school on Fourier Integral Operators
held in Ouagadougou, Burkina Faso, 14–26 September 2015, provides an introduction to Fourier Integral Operators (FIO) for a readership of Master and PhD students as well as any interested layperson. Considering the wide
spectrum of their applications and the richness of the mathematical tools they involve, FIOs lie the cross-road of many a field. This volume  offers
the necessary background, whether analytic or geometric, to get acquainted with FIOs, complemented by more advanced material presenting various aspects of active research in that area.
N2  - Dieser Band basiert auf Vorlesungen, die in einer Schule über Fourier Integraloperatoren in Ouagadougou, Burkina Faso, 14. - 26. September 2015 gehalten wurden. Es bietet eine Einführung in die Fourier Integraloperatoren (FIO) und richtet sich sowohl an Masterstudierende und Promovenden als auch an interessierte Laien. Aufgrund der Breite des Spektrums ihrer Anwendungen und der Vielfalt der mathematischen Werkzeuge, die sie ins Spiel bringen, liegen FIO an der Grenze zwischen mehreren Gebieten. Dieses Band bietet sowohl die analytisch und  geometrisch nötigen Kenntnisse, um sich mit dem Begriff der FIO vertraut zu machen als auch fortgeschrittenes Material für einen Einblick in verschiedene Aspekte der gegenwärtigen Forschung dieses Gebietes an.
T3  - Lectures in pure and applied mathematics - 3 
KW  - pseudodifferentiale Operatoren
KW  - Fourier Integraloperatoren
KW  - Lagrange Distributionen
KW  - microlokale Analysis
KW  - pseudodifferential operators
KW  - integral Fourier operators
KW  - Lagrangian submanifolds
KW  - microlocal analysis
Y1  - 2017
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-402657
SN  - 978-3-86956-413-5
SN  - 2199-4951
SN  - 2199-496X
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Kolasinski, Slawomir
A1  - Menne, Ulrich
T1  - Decay rates for the quadratic and super-quadratic tilt-excess of integral varifolds
JF  - Nonlinear Differential Equations and Applications NoDEA
N2  - This paper concerns integral varifolds of arbitrary dimension in an open subset of Euclidean space satisfying integrability conditions on their first variation. Firstly, the study of pointwise power decay rates almost everywhere of the quadratic tilt-excess is completed by establishing the precise decay rate for two-dimensional integral varifolds of locally bounded first variation. In order to obtain the exact decay rate, a coercive estimate involving a height-excess quantity measured in Orlicz spaces is established. Moreover, counter-examples to pointwise power decay rates almost everywhere of the super-quadratic tilt-excess are obtained. These examples are optimal in terms of the dimension of the varifold and the exponent of the integrability condition in most cases, for example if the varifold is not two-dimensional. These examples also demonstrate that within the scale of Lebesgue spaces no local higher integrability of the second fundamental form, of an at least two-dimensional curvature varifold, may be deduced from boundedness of its generalised mean curvature vector. Amongst the tools are Cartesian products of curvature varifolds.
KW  - Integral varifold
KW  - First variation
KW  - Generalised mean curvature vector
KW  - Quadratic tilt-excess
KW  - Super-quadratic tilt-excess
KW  - Orlicz space height-excess
KW  - Curvature varifold
KW  - Second fundamental form
KW  - Cartesian product of varifolds
Y1  - 2017
U6  - https://doi.org/10.1007/s00030-017-0436-z
SN  - 1021-9722
SN  - 1420-9004
VL  - 24
PB  - Springer
CY  - Basel
ER  - 
TY  - JOUR
A1  - Taghvaei, Amirhossein
A1  - de Wiljes, Jana
A1  - Mehta, Prashant G.
A1  - Reich, Sebastian
T1  - Kalman filter and its modern extensions for the continuous-time nonlinear filtering problem
JF  - Journal of dynamic systems measurement and control
N2  - This paper is concerned with the filtering problem in continuous time. Three algorithmic solution approaches for this problem are reviewed: (i) the classical Kalman-Bucy filter, which provides an exact solution for the linear Gaussian problem; (ii) the ensemble Kalman-Bucy filter (EnKBF), which is an approximate filter and represents an extension of the Kalman-Bucy filter to nonlinear problems; and (iii) the feedback particle filter (FPF), which represents an extension of the EnKBF and furthermore provides for a consistent solution in the general nonlinear, non-Gaussian case. The common feature of the three algorithms is the gain times error formula to implement the update step (to account for conditioning due to the observations) in the filter. In contrast to the commonly used sequential Monte Carlo methods, the EnKBF and FPF avoid the resampling of the particles in the importance sampling update step. Moreover, the feedback control structure provides for error correction potentially leading to smaller simulation variance and improved stability properties. The paper also discusses the issue of nonuniqueness of the filter update formula and formulates a novel approximation algorithm based on ideas from optimal transport and coupling of measures. Performance of this and other algorithms is illustrated for a numerical example.
Y1  - 2017
U6  - https://doi.org/10.1115/1.4037780
SN  - 0022-0434
SN  - 1528-9028
VL  - 140
IS  - 3
PB  - ASME
CY  - New York
ER  -