@article{FernandesKoppitzMusunthia2019, author = {Fernandes, Vitor H. and Koppitz, J{\"o}rg and Musunthia, Tiwadee}, title = {The Rank of the Semigroup of All Order-Preserving Transformations on a Finite Fence}, series = {Bulletin of the Malaysian Mathematical Sciences Society volume}, volume = {42}, journal = {Bulletin of the Malaysian Mathematical Sciences Society volume}, number = {5}, publisher = {Malaysian mathematical sciences sciences soc}, address = {Pulau Punang}, issn = {0126-6705}, doi = {10.1007/s40840-017-0598-1}, pages = {2191 -- 2211}, year = {2019}, abstract = {A zig-zag (or fence) order is a special partial order on a (finite) set. In this paper, we consider the semigroup TFn of all order-preserving transformations on an n-element zig-zag-ordered set. We determine the rank of TFn and provide a minimal generating set for TFn. Moreover, a formula for the number of idempotents in TFn is given.}, language = {en} } @article{BeniniCapoferriDappiaggi2017, author = {Benini, Marco and Capoferri, Matteo and Dappiaggi, Claudio}, title = {Hadamard States for Quantum Abelian Duality}, series = {Annales de l'Institut Henri Poincar{\´e}}, volume = {18}, journal = {Annales de l'Institut Henri Poincar{\´e}}, publisher = {Springer}, address = {Basel}, issn = {1424-0637}, doi = {10.1007/s00023-017-0593-y}, pages = {3325 -- 3370}, year = {2017}, abstract = {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.}, language = {en} } @article{ShcherbakovZhuangZoelleretal.2019, author = {Shcherbakov, Robert and Zhuang, Jiancang and Z{\"o}ller, Gert and Ogata, Yosihiko}, title = {Forecasting the magnitude of the largest expected earthquake}, series = {Nature Communications}, volume = {10}, journal = {Nature Communications}, publisher = {Nature Publishing Group}, address = {London}, issn = {2041-1723}, doi = {10.1038/s41467-019-11958-4}, pages = {11}, year = {2019}, abstract = {The majority of earthquakes occur unexpectedly and can trigger subsequent sequences of events that can culminate in more powerful earthquakes. This self-exciting nature of seismicity generates complex clustering of earthquakes in space and time. Therefore, the problem of constraining the magnitude of the largest expected earthquake during a future time interval is of critical importance in mitigating earthquake hazard. We address this problem by developing a methodology to compute the probabilities for such extreme earthquakes to be above certain magnitudes. We combine the Bayesian methods with the extreme value theory and assume that the occurrence of earthquakes can be described by the Epidemic Type Aftershock Sequence process. We analyze in detail the application of this methodology to the 2016 Kumamoto, Japan, earthquake sequence. We are able to estimate retrospectively the probabilities of having large subsequent earthquakes during several stages of the evolution of this sequence.}, language = {en} } @article{ConfortiKosenkovaRoelly2019, author = {Conforti, Giovanni and Kosenkova, Tetiana and Roelly, Sylvie}, title = {Conditioned Point Processes with Application to Levy Bridges}, series = {Journal of theoretical probability}, volume = {32}, journal = {Journal of theoretical probability}, number = {4}, publisher = {Springer}, address = {New York}, issn = {0894-9840}, doi = {10.1007/s10959-018-0863-8}, pages = {2111 -- 2134}, year = {2019}, abstract = {Our first result concerns a characterization by means of a functional equation of Poisson point processes conditioned by the value of their first moment. It leads to a generalized version of Mecke's formula. En passant, it also allows us to gain quantitative results about stochastic domination for Poisson point processes under linear constraints. Since bridges of a pure jump L{\´e}vy process in Rd with a height a can be interpreted as a Poisson point process on space-time conditioned by pinning its first moment to a, our approach allows us to characterize bridges of L{\´e}vy processes by means of a functional equation. The latter result has two direct applications: First, we obtain a constructive and simple way to sample L{\´e}vy bridge dynamics; second, it allows us to estimate the number of jumps for such bridges. We finally show that our method remains valid for linearly perturbed L{\´e}vy processes like periodic Ornstein-Uhlenbeck processes driven by L{\´e}vy noise.}, language = {en} } @article{SalamatZoellerAmini2019, author = {Salamat, Mona and Z{\"o}ller, Gert and Amini, Morteza}, title = {Prediction of the Maximum Expected Earthquake Magnitude in Iran:}, series = {Pure and applied geophysics}, volume = {176}, journal = {Pure and applied geophysics}, number = {8}, publisher = {Springer}, address = {Basel}, issn = {0033-4553}, doi = {10.1007/s00024-019-02141-3}, pages = {3425 -- 3438}, year = {2019}, abstract = {This paper concerns the problem of predicting the maximum expected earthquake magnitude μ in a future time interval Tf given a catalog covering a time period T in the past. Different studies show the divergence of the confidence interval of the maximum possible earthquake magnitude m_{ max } for high levels of confidence (Salamat et al. 2017). Therefore, m_{ max } should be better replaced by μ (Holschneider et al. 2011). In a previous study (Salamat et al. 2018), μ is estimated for an instrumental earthquake catalog of Iran from 1900 onwards with a constant level of completeness ( {m0 = 5.5} ). In the current study, the Bayesian methodology developed by Z{\"o}ller et al. (2014, 2015) is applied for the purpose of predicting μ based on the catalog consisting of both historical and instrumental parts. The catalog is first subdivided into six subcatalogs corresponding to six seismotectonic zones, and each of those zone catalogs is subsequently subdivided according to changes in completeness level and magnitude uncertainty. For this, broad and small error distributions are considered for historical and instrumental earthquakes, respectively. We assume that earthquakes follow a Poisson process in time and Gutenberg-Richter law in the magnitude domain with a priori unknown a and b values which are first estimated by Bayes' theorem and subsequently used to estimate μ. Imposing different values of m_{ max } for different seismotectonic zones namely Alborz, Azerbaijan, Central Iran, Zagros, Kopet Dagh and Makran, the results show considerable probabilities for the occurrence of earthquakes with Mw ≥ 7.5 in short Tf , whereas for long Tf, μ is almost equal to m_{ max }}, language = {en} } @article{StaniforthWoodReich2006, author = {Staniforth, Andrew and Wood, Nigel and Reich, Sebastian}, title = {A time-staggered semi-Lagrangian discretization of the rotating shallow-water equations}, series = {Quarterly journal of the Royal Meteorological Society}, volume = {132}, journal = {Quarterly journal of the Royal Meteorological Society}, number = {621C}, publisher = {Wiley}, address = {Weinheim}, issn = {0035-9009}, doi = {10.1256/qj.06.30}, pages = {3107 -- 3116}, year = {2006}, abstract = {A time-staggered semi-Lagrangian discretization of the rotating shallow-water equations is proposed and analysed. Application of regularization to the geopotential field used in the momentum equations leads to an unconditionally stable scheme. The analysis, together with a fully nonlinear example application, suggests that this approach is a promising, efficient, and accurate alternative to traditional schemes.}, language = {en} } @article{KirscheBoeckmann2006, author = {Kirsche, Andreas and B{\"o}ckmann, Christine}, title = {Pade iteration method for regularization}, series = {Applied mathematics and computation}, volume = {180}, journal = {Applied mathematics and computation}, number = {2}, publisher = {Elsevier}, address = {New York}, issn = {0096-3003}, doi = {10.1016/j.amc.2006.01.011}, pages = {648 -- 663}, year = {2006}, abstract = {In this study we present iterative regularization methods using rational approximations, in particular, Pade approximants, which work well for ill-posed problems. We prove that the (k,j)-Pade method is a convergent and order optimal iterative regularization method in using the discrepancy principle of Morozov. Furthermore, we present a hybrid Pade method, compare it with other well-known methods and found that it is faster than the Landweber method. It is worth mentioning that this study is a completion of the paper [A. Kirsche, C. Bockmann, Rational approximations for ill-conditioned equation systems, Appl. Math. Comput. 171 (2005) 385-397] where this method was treated to solve ill-conditioned equation systems. (c) 2006 Elsevier Inc. All rights reserved.}, language = {en} } @article{Junek2020, author = {Junek, Heinz}, title = {Zyklizit{\"a}t in Raum, zeit und geist : {\"u}ber Pflasterungen, Rollkurven, Dezimalbr{\"u}che, Schwingungen, Wellen, Iteration und Neuronale Netze}, series = {Zyklizit{\"a}t \& Rhythmik: eine multidisziplin{\"a}re Vorlesungsreihe}, journal = {Zyklizit{\"a}t \& Rhythmik: eine multidisziplin{\"a}re Vorlesungsreihe}, publisher = {trafo}, address = {Berlin}, isbn = {978-3-86464-169-5}, pages = {85 -- 103}, year = {2020}, language = {de} } @article{Reich2006, author = {Reich, Sebastian}, title = {Linearly implicit time stepping methods for numerical weather prediction}, series = {BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians}, volume = {46}, journal = {BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians}, publisher = {Springer}, address = {Dordrecht}, issn = {0006-3835}, doi = {10.1007/s10543-006-0065-0}, pages = {607 -- 616}, year = {2006}, abstract = {The efficient time integration of the dynamic core equations for numerical weather prediction (NWP) remains a key challenge. One of the most popular methods is currently provided by implementations of the semi-implicit semi-Lagrangian (SISL) method, originally proposed by Robert (J. Meteorol. Soc. Jpn., 1982). Practical implementations of the SISL method are, however, not without certain shortcomings with regard to accuracy, conservation properties and stability. Based on recent work by Gottwald, Frank and Reich (LNCSE, Springer, 2002), Frank, Reich, Staniforth, White and Wood (Atm. Sci. Lett., 2005) and Wood, Staniforth and Reich (Atm. Sci. Lett., 2006) we propose an alternative semi-Lagrangian implementation based on a set of regularized equations and the popular Stormer-Verlet time stepping method in the context of the shallow-water equations (SWEs). Ultimately, the goal is to develop practical implementations for the 3D Euler equations that overcome some or all shortcomings of current SISL implementations.}, language = {en} } @article{BaerStrohmaier2019, author = {B{\"a}r, Christian and Strohmaier, Alexander}, title = {An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary}, series = {American Journal of Mathematics}, volume = {141}, journal = {American Journal of Mathematics}, number = {5}, publisher = {Johns Hopkins Univ. Press}, address = {Baltimore}, issn = {0002-9327}, doi = {10.1353/ajm.2019.0037}, pages = {1421 -- 1455}, year = {2019}, abstract = {We show that the Dirac operator on a compact globally hyperbolic Lorentzian spacetime with spacelike Cauchy boundary is a Fredholm operator if appropriate boundary conditions are imposed. We prove that the index of this operator is given by the same expression as in the index formula of Atiyah-Patodi-Singer for Riemannian manifolds with boundary. The index is also shown to equal that of a certain operator constructed from the evolution operator and a spectral projection on the boundary. In case the metric is of product type near the boundary a Feynman parametrix is constructed.}, language = {en} } @article{Lewandowski2022, author = {Lewandowski, Max}, title = {Hadamard states for bosonic quantum field theory on globally hyperbolic spacetimes}, series = {Journal of mathematical physics}, volume = {63}, journal = {Journal of mathematical physics}, number = {1}, publisher = {American Institute of Physics}, address = {Melville}, issn = {0022-2488}, doi = {10.1063/5.0055753}, pages = {34}, year = {2022}, abstract = {According to Radzikowski's celebrated results, bisolutions of a wave operator on a globally hyperbolic spacetime are of the Hadamard form iff they are given by a linear combination of distinguished parametrices i2(G˜aF-G˜F+G˜A-G˜R) in the sense of Duistermaat and H{\"o}rmander [Acta Math. 128, 183-269 (1972)] and Radzikowski [Commun. Math. Phys. 179, 529 (1996)]. Inspired by the construction of the corresponding advanced and retarded Green operator GA, GR as done by B{\"a}r, Ginoux, and Pf{\"a}ffle {Wave Equations on Lorentzian Manifolds and Quantization [European Mathematical Society (EMS), Z{\"u}rich, 2007]}, we construct the remaining two Green operators GF, GaF locally in terms of Hadamard series. Afterward, we provide the global construction of i2(G˜aF-G˜F), which relies on new techniques such as a well-posed Cauchy problem for bisolutions and a patching argument using Čech cohomology. This leads to global bisolutions of the Hadamard form, each of which can be chosen to be a Hadamard two-point-function, i.e., the smooth part can be adapted such that, additionally, the symmetry and the positivity condition are exactly satisfied.}, language = {en} } @article{StolleMichaelisRauberg2016, author = {Stolle, Claudia and Michaelis, Ingo and Rauberg, Jan}, title = {The role of high-resolution geomagnetic field models for investigating ionospheric currents at low Earth orbit satellites}, series = {Earth, planets and space}, volume = {68}, journal = {Earth, planets and space}, publisher = {Springer}, address = {Heidelberg}, issn = {1880-5981}, doi = {10.1186/s40623-016-0494-1}, pages = {10}, year = {2016}, abstract = {Low Earth orbiting geomagnetic satellite missions, such as the Swarm satellite mission, are the only means to monitor and investigate ionospheric currents on a global scale and to make in situ measurements of F region currents. High-precision geomagnetic satellite missions are also able to detect ionospheric currents during quiet-time geomagnetic conditions that only have few nanotesla amplitudes in the magnetic field. An efficient method to isolate the ionospheric signals from satellite magnetic field measurements has been the use of residuals between the observations and predictions from empirical geomagnetic models for other geomagnetic sources, such as the core and lithospheric field or signals from the quiet-time magnetospheric currents. This study aims at highlighting the importance of high-resolution magnetic field models that are able to predict the lithospheric field and that consider the quiet-time magnetosphere for reliably isolating signatures from ionospheric currents during geomagnetically quiet times. The effects on the detection of ionospheric currents arising from neglecting the lithospheric and magnetospheric sources are discussed on the example of four Swarm orbits during very quiet times. The respective orbits show a broad range of typical scenarios, such as strong and weak ionospheric signal (during day- and nighttime, respectively) superimposed over strong and weak lithospheric signals. If predictions from the lithosphere or magnetosphere are not properly considered, the amplitude of the ionospheric currents, such as the midlatitude Sq currents or the equatorial electrojet (EEJ), is modulated by 10-15 \% in the examples shown. An analysis from several orbits above the African sector, where the lithospheric field is significant, showed that the peak value of the signatures of the EEJ is in error by 5 \% in average when lithospheric contributions are not considered, which is in the range of uncertainties of present empirical models of the EEJ.}, language = {en} } @article{ChajadaDeneckeHalas1999, author = {Chajada, I. and Denecke, Klaus-Dieter and Halas, R.}, title = {Algebras induced by hypersubstitutions}, year = {1999}, language = {en} } @phdthesis{ArwornDenecke1999, author = {Arworn, Srichan and Denecke, Klaus-Dieter}, title = {Sets of hypersubstitutions and set-solid varieties}, year = {1999}, language = {en} } @article{DeneckeKoppitz1999, author = {Denecke, Klaus-Dieter and Koppitz, J{\"o}rg}, title = {Normal forms of hypersubstitutions}, year = {1999}, language = {en} } @article{DeneckeLeeratanavalee1999, author = {Denecke, Klaus-Dieter and Leeratanavalee, Sorasak}, title = {Weak hypersubstitutions and weakly derived algebras}, year = {1999}, language = {en} } @article{ArwornDenecke1999, author = {Arworn, Srichan and Denecke, Klaus-Dieter}, title = {Left-edges solid varieties of differential groupoids}, year = {1999}, language = {en} } @article{DeneckeMruczek2000, author = {Denecke, Klaus-Dieter and Mruczek, Krysztyna}, title = {P-compatible Hypersubstitutions}, year = {2000}, language = {en} } @book{ArwornDeneckePoeschel1998, author = {Arworn, Srichan and Denecke, Klaus-Dieter and P{\"o}schel, Reinhard}, title = {Closure operators on complete lattices}, series = {Preprint MATH-ALG / Technische Universit{\"a}t Dresden}, volume = {1998, 05}, journal = {Preprint MATH-ALG / Technische Universit{\"a}t Dresden}, publisher = {Techn. Univ.}, address = {Dresden}, year = {1998}, language = {en} } @article{DeneckeKoppitz1998, author = {Denecke, Klaus-Dieter and Koppitz, J{\"o}rg}, title = {Finite monoids of hypersubstitutions of type € = (2)}, year = {1998}, language = {en} }