@unpublished{KytmanovMyslivetsTarkhanov2004,
  author    = {Kytmanov, Aleksandr and Myslivets, Simona and Tarkhanov, Nikolai Nikolaevich},
  title     = {Zeta-function of a nonlinear system},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26795},
  year      = {2004},
  abstract  = {Given a system of entire functions in Cn with at most countable set of common zeros, we introduce the concept of zeta-function associated with the system. Under reasonable assumptions on the system, the zeta-function is well defined for all s ∈ Zn with sufficiently large components. Using residue theory we get an integral representation for the zeta-function which allows us to construct an analytic extension of the zeta-function to an infinite cone in Cn.},
  language  = {en}
}
@article{FigariTeta2020,
  author    = {Figari, Rodolfo and Teta, Alessandro},
  title     = {Zero-range hamiltonians for three quantum particles},
  series = {Lectures in pure and applied mathematics},
  journal   = {Lectures in pure and applied mathematics},
  number    = {6},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  isbn      = {978-3-86956-485-2},
  issn      = {2199-4951},
  doi       = {10.25932/publishup-47218},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-472189},
  pages     = {175 -- 184},
  year      = {2020},
  language  = {en}
}
@article{Hermann2014,
  author    = {Hermann, Andreas},
  title     = {Zero sets of eigenspinors for generic metrics},
  series = {Communications in analysis and geometry},
  volume    = {22},
  journal   = {Communications in analysis and geometry},
  number    = {2},
  publisher = {International Press of Boston},
  address   = {Somerville},
  issn      = {1019-8385},
  pages     = {177 -- 218},
  year      = {2014},
  abstract  = {Let M be a closed connected spin manifold of dimension 2 or 3 with a fixed orientation and a fixed spin structure. We prove that for a generic Riemannian metric on M the non-harmonic eigenspinors of the Dirac operator are nowhere zero. The proof is based on a transversality theorem and the unique continuation property of the Dirac operator.},
  language  = {en}
}
@article{DzhunushalievSchmidt2000,
  author    = {Dzhunushaliev, Vladimir and Schmidt, Hans-J{\"u}rgen},
  title     = {Wormholes and Flux Tubes in the 7D Gravity on the Principal Bundle with SU(2) Gauge Group as the Extra Dimensions},
  year      = {2000},
  language  = {en}
}
@article{Schrohe1997,
  author    = {Schrohe, Elmar},
  title     = {Wodzicki{\"i}s noncommutative residue and trace for operator algebras on manifolds with conical singularities},
  year      = {1997},
  language  = {en}
}
@misc{Schrohe1998,
  author    = {Schrohe, Elmar},
  title     = {Wloka, J. T. [u.a.], Boundary value problems for eliptic systems},
  year      = {1998},
  language  = {en}
}
@article{YenvonSpechtLinetal.2022,
  author    = {Yen, Ming-Hsuan and von Specht, Sebastian and Lin, Yen-Yu and Cotton, Fabrice and Ma, Kuo-Fong},
  title     = {Within- and between-event variabilities of strong-velocity pulses of moderate earthquakes within dense seismic arrays},
  series = {Bulletin of the Seismological Society of America},
  volume    = {112},
  journal   = {Bulletin of the Seismological Society of America},
  number    = {1},
  publisher = {Seismological Society of America},
  address   = {El Cerito, Calif.},
  issn      = {0037-1106},
  doi       = {10.1785/0120200376},
  pages     = {361 -- 380},
  year      = {2022},
  abstract  = {Ground motion with strong-velocity pulses can cause significant damage to buildings and structures at certain periods; hence, knowing the period and velocity amplitude of such pulses is critical for earthquake structural engineering. However, the physical factors relating the scaling of pulse periods with magnitude are poorly understood. In this study, we investigate moderate but damaging earthquakes (M-w 6-7) and characterize ground- motion pulses using the method of Shahi and Baker (2014) while considering the potential static-offset effects. We confirm that the within-event variability of the pulses is large. The identified pulses in this study are mostly from strike-slip-like earthquakes. We further perform simulations using the freq uency-wavenumber algorithm to investigate the causes of the variability of the pulse periods within and between events for moderate strike-slip earthquakes. We test the effect of fault dips, and the impact of the asperity locations and sizes. The simulations reveal that the asperity properties have a high impact on the pulse periods and amplitudes at nearby stations. Our results emphasize the importance of asperity characteristics, in addition to earthquake magnitudes for the occurrence and properties of pulses produced by the forward directivity effect. We finally quantify and discuss within- and between-event variabilities of pulse properties at short distances.},
  language  = {en}
}
@unpublished{BaerPfaeffle2012,
  author    = {B{\"a}r, Christian and Pf{\"a}ffle, Frank},
  title     = {Wiener measures on Riemannian manifolds and the Feynman-Kac formula},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-59998},
  year      = {2012},
  abstract  = {This is an introduction to Wiener measure and the Feynman-Kac formula on general Riemannian manifolds for Riemannian geometers with little or no background in stochastics. We explain the construction of Wiener measure based on the heat kernel in full detail and we prove the Feynman-Kac formula for Schr{\"o}dinger operators with bounded potentials. We also consider normal Riemannian coverings and show that projecting and lifting of paths are inverse operations which respect the Wiener measure.},
  language  = {en}
}
@book{Schmidt1994,
  author    = {Schmidt, Hans-J{\"u}rgen},
  title     = {Why do all the curvature invariants of a gravitational wave vanish?},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1994, 03},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {7 Bl.},
  year      = {1994},
  language  = {en}
}
@article{Schmidt1996,
  author    = {Schmidt, Hans-J{\"u}rgen},
  title     = {Why do all the curvature invariants of a gravitational wave vanish?},
  year      = {1996},
  language  = {en}
}
@article{Paycha2018,
  author    = {Paycha, Sylvie},
  title     = {When the market wins over research and higher education},
  series = {Sustainable Futures for Higher Education : the Making of Knowledge Makers},
  volume    = {7},
  journal   = {Sustainable Futures for Higher Education : the Making of Knowledge Makers},
  publisher = {Springer},
  address   = {Cham},
  isbn      = {978-3-319-96035-7},
  issn      = {2364-6799},
  doi       = {10.1007/978-3-319-96035-7_2},
  pages     = {23 -- 28},
  year      = {2018},
  abstract  = {In this chapter, an overview of systematic eradication of basic science foci in European universities in the last two decades is given. This happens under the slogan of optimisation of the university education to the needs and demands of the society. It is pointed out that reliance on "market demands" brings with it long-term deficiencies in the maintenance of basic and advanced knowledge construction in societies necessary for long-term future technological advances. University policies that claim improvement of higher education towards more immediate efficiency may end up with the opposite effect of affecting its quality and long term expected positive impact on society.},
  language  = {en}
}
@article{LykovMalyshev2020,
  author    = {Lykov, Alexander and Malyshev, Vadim},
  title     = {When bounded chaos becomes unbounded},
  series = {Lectures in pure and applied mathematics},
  journal   = {Lectures in pure and applied mathematics},
  number    = {6},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  isbn      = {978-3-86956-485-2},
  issn      = {2199-4951},
  doi       = {10.25932/publishup-47206},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-472060},
  pages     = {97 -- 106},
  year      = {2020},
  language  = {en}
}
@unpublished{ManicciaMughetti2001,
  author    = {Maniccia, L. and Mughetti, M.},
  title     = {Weyl calculus for a class of subelliptic operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26038},
  year      = {2001},
  abstract  = {Weyl-H{\"o}rmander calculus is used to get a parametrix in OPS¹-m sub(½, ½)(Ω)for a class of subelliptic pseudodifferential operators in OPS up(m)sub(1, 0)(Ω) with real non-negative principal symbol.},
  language  = {en}
}
@book{ManicciaMughetti2001,
  author    = {Maniccia, L. and Mughetti, M.},
  title     = {Weyl calculus for a class of subelliptic operators},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {15 S.},
  year      = {2001},
  language  = {en}
}
@unpublished{BrauerKarp2008,
  author    = {Brauer, Uwe and Karp, Lavi},
  title     = {Well-posedness of Einstein-Euler systems in asymptotically flat spacetimes},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30347},
  year      = {2008},
  abstract  = {We prove a local in time existence and uniqueness theorem of classical solutions of the coupled Einstein{Euler system, and therefore establish the well posedness of this system. We use the condition that the energy density might vanish or tends to zero at infinity and that the pressure is a certain function of the energy density, conditions which are used to describe simplified stellar models. In order to achieve our goals we are enforced, by the complexity of the problem, to deal with these equations in a new type of weighted Sobolev spaces of fractional order. Beside their construction, we develop tools for PDEs and techniques for hyperbolic and elliptic equations in these spaces. The well posedness is obtained in these spaces.},
  language  = {en}
}
@article{RungrottheeraSchulze2014,
  author    = {Rungrottheera, Wannarut and Schulze, Bert-Wolfgang},
  title     = {Weighted spaces on corner manifolds},
  series = {Complex variables and elliptic equations},
  volume    = {59},
  journal   = {Complex variables and elliptic equations},
  number    = {12},
  publisher = {Routledge, Taylor \& Francis Group},
  address   = {Abingdon},
  issn      = {1747-6933},
  doi       = {10.1080/17476933.2013.876416},
  pages     = {1706 -- 1738},
  year      = {2014},
  abstract  = {We study spaces on manifolds with double weights and iterated discrete and continuous asymptotics, and their relationship with corner pseudo-differential operators.},
  language  = {en}
}
@article{Boelling1998,
  author    = {B{\"o}lling, Reinhard},
  title     = {Weierstraß and some members of his circle : Kovalevskaja, Fuchs, Schwarz, Schottky},
  isbn      = {3-7643-5943- 9},
  year      = {1998},
  language  = {en}
}
@article{GlebovKiselevTarkhanov2010,
  author    = {Glebov, Sergei and Kiselev, Oleg and Tarkhanov, Nikolai Nikolaevich},
  title     = {Weakly nonlinear dispersive waves under parametric resonance perturbation},
  issn      = {0022-2526},
  doi       = {10.1111/j.1467-9590.2009.00460.x},
  year      = {2010},
  abstract  = {We consider a solution of the nonlinear Klein-Gordon equation perturbed by a parametric driver. The frequency of parametric perturbation varies slowly and passes through a resonant value, which leads to a solution change. We obtain a new connection formula for the asymptotic solution before and after the resonance.},
  language  = {en}
}
@article{Menne2016,
  author    = {Menne, Ulrich},
  title     = {Weakly Differentiable Functions on Varifolds},
  series = {Indiana University mathematics journal},
  volume    = {65},
  journal   = {Indiana University mathematics journal},
  publisher = {Indiana University, Department of Mathematics},
  address   = {Bloomington},
  issn      = {0022-2518},
  doi       = {10.1512/iumj.2016.65.5829},
  pages     = {977 -- 1088},
  year      = {2016},
  abstract  = {The present paper is intended to provide the basis for the study of weakly differentiable functions on rectifiable varifolds with locally bounded first variation. The concept proposed here is defined by means of integration-by-parts identities for certain compositions with smooth functions. In this class, the idea of zero boundary values is realised using the relative perimeter of superlevel sets. Results include a variety of Sobolev Poincare-type embeddings, embeddings into spaces of continuous and sometimes Holder-continuous functions, and point wise differentiability results both of approximate and integral type as well as coarea formulae. As a prerequisite for this study, decomposition properties of such varifolds and a relative isoperimetric inequality are established. Both involve a concept of distributional boundary of a set introduced for this purpose. As applications, the finiteness of the geodesic distance associated with varifolds with suitable summability of the mean curvature and a characterisation of curvature varifolds are obtained.},
  language  = {en}
}
@article{DeneckeLeeratanavalee1999,
  author    = {Denecke, Klaus-Dieter and Leeratanavalee, Sorasak},
  title     = {Weak hypersubstitutions and weakly derived algebras},
  year      = {1999},
  language  = {en}
}
@phdthesis{Leeratanavalee2002,
  author    = {Leeratanavalee, Sorasak},
  title     = {Weak Hypersubstitutions},
  pages     = {105 S.},
  year      = {2002},
  language  = {en}
}
@unpublished{AlsaedyTarkhanov2015,
  author    = {Alsaedy, Ammar and Tarkhanov, Nikolai Nikolaevich},
  title     = {Weak boundary values of solutions of Lagrangian problems},
  volume    = {4},
  number    = {2},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72617},
  pages     = {24},
  year      = {2015},
  abstract  = {We define weak boundary values of solutions to those nonlinear differential equations which appear as Euler-Lagrange equations of variational problems. As a result we initiate the theory of Lagrangian boundary value problems in spaces of appropriate smoothness. We also analyse if the concept of mapping degree of current importance applies to the study of Lagrangian problems.},
  language  = {en}
}
@article{LouisMaassRiederetal.1994,
  author    = {Louis, Alfred K. and Maaß, Peter and Rieder, Andreas and Stark, H.-G.},
  title     = {Wavelets and digital image processing},
  year      = {1994},
  language  = {en}
}
@article{HaynPanetDiamentetal.2012,
  author    = {Hayn, Michael and Panet, I. and Diament, M. and Holschneider, Matthias and Mandea, Mioara and Davaille, A.},
  title     = {Wavelet-based directional analysis of the gravity field evidence for large-scale undulations},
  series = {Geophysical journal international},
  volume    = {189},
  journal   = {Geophysical journal international},
  number    = {3},
  publisher = {Oxford Univ. Press},
  address   = {Oxford},
  issn      = {0956-540X},
  doi       = {10.1111/j.1365-246X.2012.05455.x},
  pages     = {1430 -- 1456},
  year      = {2012},
  abstract  = {In the eighties, the analysis of satellite altimetry data leads to the major discovery of gravity lineations in the oceans, with wavelengths between 200 and 1400 km. While the existence of the 200 km scale undulations is widely accepted, undulations at scales larger than 400 km are still a matter of debate. In this paper, we revisit the topic of the large-scale geoid undulations over the oceans in the light of the satellite gravity data provided by the GRACE mission, considerably more precise than the altimetry data at wavelengths larger than 400 km. First, we develop a dedicated method of directional Poisson wavelet analysis on the sphere with significance testing, in order to detect and characterize directional structures in geophysical data on the sphere at different spatial scales. This method is particularly well suited for potential field analysis. We validate it on a series of synthetic tests, and then apply it to analyze recent gravity models, as well as a bathymetry data set independent from gravity. Our analysis confirms the existence of gravity undulations at large scale in the oceans, with characteristic scales between 600 and 2000 km. Their direction correlates well with present-day plate motion over the Pacific ocean, where they are particularly clear, and associated with a conjugate direction at 1500 km scale. A major finding is that the 2000 km scale geoid undulations dominate and had never been so clearly observed previously. This is due to the great precision of GRACE data at those wavelengths. Given the large scale of these undulations, they are most likely related to mantle processes. Taking into account observations and models from other geophysical information, as seismological tomography, convection and geochemical models and electrical conductivity in the mantle, we conceive that all these inputs indicate a directional fabric of the mantle flows at depth, reflecting how the history of subduction influences the organization of lower mantle upwellings.},
  language  = {en}
}
@article{Maass1994,
  author    = {Maaß, Peter},
  title     = {Wavelet galerkin methods for inverse problems},
  year      = {1994},
  language  = {en}
}
@phdthesis{Hayn2010,
  author    = {Hayn, Michael},
  title     = {Wavelet analysis and spline modeling of geophysical data on the sphere},
  address   = {Potsdam},
  pages     = {95 S. : graph. Darst.},
  year      = {2010},
  language  = {en}
}
@article{MaassRamlau1996,
  author    = {Maaß, Peter and Ramlau, Ronny},
  title     = {Wavelet accelerated iteration methods for hyperthermia treatment planning},
  year      = {1996},
  language  = {en}
}
@book{BaerGinouxPfaeffle2007,
  author    = {B{\"a}r, Christian and Ginoux, Nicolas and Pf{\"a}ffle, Frank},
  title     = {Wave equations on lorentzian manifolds and quantization},
  publisher = {European Math. Society},
  address   = {Z{\"u}rich},
  isbn      = {978-3-03719-037-1},
  pages     = {194 S.},
  year      = {2007},
  language  = {en}
}
@article{ChangMahmoudiSchulze2018,
  author    = {Chang, Der-Chen and Mahmoudi, Mahdi Hedayat and Schulze, Bert-Wolfgang},
  title     = {Volterra operators in the edge-calculus},
  series = {Analysis and Mathematical Physics},
  volume    = {8},
  journal   = {Analysis and Mathematical Physics},
  number    = {4},
  publisher = {Springer},
  address   = {Basel},
  issn      = {1664-2368},
  doi       = {10.1007/s13324-018-0238-4},
  pages     = {551 -- 570},
  year      = {2018},
  abstract  = {We study the Volterra property of a class of anisotropic pseudo-differential operators on R x B for a manifold B with edge Y and time-variable t. This exposition belongs to a program for studying parabolicity in such a situation. In the present consideration we establish non-smoothing elements in a subalgebra with anisotropic operator-valued symbols of Mellin type with holomorphic symbols in the complex Mellin covariable from the cone theory, where the covariable t of t extends to symbolswith respect to t to the lower complex v half-plane. The resulting space ofVolterra operators enlarges an approach of Buchholz (Parabolische Pseudodifferentialoperatoren mit operatorwertigen Symbolen. Ph. D. thesis, Universitat Potsdam, 1996) by necessary elements to a new operator algebra containing Volterra parametrices under an appropriate condition of anisotropic ellipticity. Our approach avoids some difficulty in choosing Volterra quantizations in the edge case by generalizing specific achievements from the isotropic edge-calculus, obtained by Seiler (Pseudodifferential calculus on manifolds with non-compact edges, Ph. D. thesis, University of Potsdam, 1997), see also Gil et al. (in: Demuth et al (eds) Mathematical research, vol 100. Akademic Verlag, Berlin, pp 113-137, 1997; Osaka J Math 37: 221-260, 2000).},
  language  = {en}
}
@unpublished{BuchholzSchulze1998,
  author    = {Buchholz, Thilo and Schulze, Bert-Wolfgang},
  title     = {Volterra operators and parabolicity : anisotropic pseudo-differential operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25231},
  year      = {1998},
  abstract  = {Parabolic equations on manifolds with singularities require a new calculus of anisotropic pseudo-differential operators with operator-valued symbols. The paper develops this theory along the lines of sn abstract wedge calculus with strongly continuous groups of isomorphisms on the involved Banach spaces. The corresponding pseodo-diferential operators are continuous in anisotropic wedge Sobolev spaces, and they form an alegbra. There is then introduced the concept of anisotropic parameter-dependent ellipticity, based on an order reduction variant of the pseudo-differential calculus. The theory is appled to a class of parabolic differential operators, and it is proved the invertibility in Sobolev spaces with exponential weights at infinity in time direction.},
  language  = {en}
}
@book{BuchholzSchulze1998,
  author    = {Buchholz, Thilo and Schulze, Bert-Wolfgang},
  title     = {Volterra operators and parabolicity : anisotropic pseudo-differential operators},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1998, 11},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {57 S.},
  year      = {1998},
  language  = {en}
}
@unpublished{LiuYangLu2002,
  author    = {Liu, Weian and Yang, Yin and Lu, Gang},
  title     = {Viscosity solutions of fully nonlinear parabolic systems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26215},
  year      = {2002},
  abstract  = {In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in [2] and [3].},
  language  = {en}
}
@book{Weian2002,
  author    = {Weian, Liu},
  title     = {Viscosity Solutions of Fully Nonlinea Parabolic Systems},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {31 S.},
  year      = {2002},
  language  = {en}
}
@article{JansenKunaTsagkarogiannis2020,
  author    = {Jansen, Sabine and Kuna, Tobias and Tsagkarogiannis, Dimitrios},
  title     = {Virial inversion for inhomogeneous systems},
  series = {Lectures in pure and applied mathematics},
  journal   = {Lectures in pure and applied mathematics},
  number    = {6},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  isbn      = {978-3-86956-485-2},
  issn      = {2199-4951},
  doi       = {10.25932/publishup-47211},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-472111},
  pages     = {135 -- 144},
  year      = {2020},
  language  = {en}
}
@article{Ludewig2014,
  author    = {Ludewig, Matthias},
  title     = {Vector fields with a non-degenerate source},
  series = {Journal of geometry and physics},
  volume    = {79},
  journal   = {Journal of geometry and physics},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0393-0440},
  doi       = {10.1016/j.geomphys.2014.01.014},
  pages     = {59 -- 76},
  year      = {2014},
  abstract  = {We discuss the solution theory of operators of the form del(x) + A, acting on smooth sections of a vector bundle with connection del over a manifold M, where X is a vector field having a critical point with positive linearization at some point p is an element of M. As an operator on a suitable space of smooth sections Gamma(infinity)(U, nu), it fulfills a Fredholm alternative, and the same is true for the adjoint operator. Furthermore, we show that the solutions depend smoothly on the data del, X and A.},
  language  = {en}
}
@article{ZolotovProkhorovNamgaladzeetal.2011,
  author    = {Zolotov, O. V. and Prokhorov, Boris E. and Namgaladze, Alexander A. and Martynenko, O. V.},
  title     = {Variations in the total electron content of the ionosphere during preparation of earthquakes},
  series = {Russian journal of physical chemistry : B, Focus on physics},
  volume    = {5},
  journal   = {Russian journal of physical chemistry : B, Focus on physics},
  number    = {3},
  publisher = {Pleiades Publ.},
  address   = {New York},
  issn      = {1990-7931},
  doi       = {10.1134/S1990793111030146},
  pages     = {435 -- 438},
  year      = {2011},
  abstract  = {The morphological features in the deviations of the total electron content (TEC) of the ionosphere from the background undisturbed state as possible precursors of the earthquake of January 12, 2010 (21:53 UT (16:53 LT), 18.46A degrees N, 72.5A degrees W, 7.0 M) in Haiti are analyzed. To identify these features, global and regional differential TEC maps based on global 2-h TEC maps provided by NASA in the IONEX format were plotted. For the considered earthquake, long-lived disturbances, presumably of seismic origin, were localized in the near-epicenter area and were accompanied by similar effects in the magnetoconjugate region. Both decreases and increases in the local TEC over the period from 22 UT of January 10 to 08 UT of January 12, 2010 were observed. The horizontal dimensions of the anomalies were similar to 40A degrees in longitude and similar to 20A degrees in latitude, with the magnitude of TEC disturbances reaching similar to 40\% relative to the background near the epicenter and more than 50\% in the magnetoconjugate area. No significant geomagnetic disturbances within January 1-12, 2010 were observed, i.e., the detected TEC anomalies were manifestations of interplay between processes in the lithosphere-atmosphere-ionosphere system.},
  language  = {en}
}
@phdthesis{Hanisch2011,
  author    = {Hanisch, Florian},
  title     = {Variational problems on supermanifolds},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-59757},
  school      = {Universit{\"a}t Potsdam},
  year      = {2011},
  abstract  = {In this thesis, we discuss the formulation of variational problems on supermanifolds. Supermanifolds incorporate bosonic as well as fermionic degrees of freedom. Fermionic fields take values in the odd part of an appropriate Grassmann algebra and are thus showing an anticommutative behaviour. However, a systematic treatment of these Grassmann parameters requires a description of spaces as functors, e.g. from the category of Grassmann algberas into the category of sets (or topological spaces, manifolds). After an introduction to the general ideas of this approach, we use it to give a description of the resulting supermanifolds of fields/maps. We show that each map is uniquely characterized by a family of differential operators of appropriate order. Moreover, we demonstrate that each of this maps is uniquely characterized by its component fields, i.e. by the coefficients in a Taylor expansion w.r.t. the odd coordinates. In general, the component fields are only locally defined. We present a way how to circumvent this limitation. In fact, by enlarging the supermanifold in question, we show that it is possible to work with globally defined components. We eventually use this formalism to study variational problems. More precisely, we study a super version of the geodesic and a generalization of harmonic maps to supermanifolds. Equations of motion are derived from an energy functional and we show how to decompose them into components. Finally, in special cases, we can prove the existence of critical points by reducing the problem to equations from ordinary geometric analysis. After solving these component equations, it is possible to show that their solutions give rise to critical points in the functor spaces of fields.},
  language  = {en}
}
@unpublished{Alsaedy2016,
  author    = {Alsaedy, Ammar},
  title     = {Variational primitive of a differential form},
  volume    = {5},
  number    = {4},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-89223},
  pages     = {8},
  year      = {2016},
  abstract  = {In this paper we specify the Dirichlet to Neumann operator related to the Cauchy problem for the gradient operator with data on a part of the boundary. To this end, we consider a nonlinear relaxation of this problem which is a mixed boundary problem of Zaremba type for the p-Laplace equation.},
  language  = {en}
}
@article{MalemShinitskiOjedaOpper2022,
  author    = {Malem-Shinitski, Noa and Ojeda, Cesar and Opper, Manfred},
  title     = {Variational bayesian inference for nonlinear hawkes process with gaussian process self-effects},
  series = {Entropy},
  volume    = {24},
  journal   = {Entropy},
  number    = {3},
  publisher = {MDPI},
  address   = {Basel},
  issn      = {1099-4300},
  doi       = {10.3390/e24030356},
  pages     = {22},
  year      = {2022},
  abstract  = {Traditionally, Hawkes processes are used to model time-continuous point processes with history dependence. Here, we propose an extended model where the self-effects are of both excitatory and inhibitory types and follow a Gaussian Process. Whereas previous work either relies on a less flexible parameterization of the model, or requires a large amount of data, our formulation allows for both a flexible model and learning when data are scarce. We continue the line of work of Bayesian inference for Hawkes processes, and derive an inference algorithm by performing inference on an aggregated sum of Gaussian Processes. Approximate Bayesian inference is achieved via data augmentation, and we describe a mean-field variational inference approach to learn the model parameters. To demonstrate the flexibility of the model we apply our methodology on data from different domains and compare it to previously reported results.},
  language  = {en}
}
@phdthesis{Beinrucker2015,
  author    = {Beinrucker, Andre},
  title     = {Variable selection in high dimensional data analysis with applications},
  school      = {Universit{\"a}t Potsdam},
  pages     = {VII, 107},
  year      = {2015},
  language  = {en}
}
@article{DeneckeWismath2003,
  author    = {Denecke, Klaus-Dieter and Wismath, Shelly},
  title     = {Valuations of Terms},
  year      = {2003},
  abstract  = {Let tau be a type of algebras. There are several commonly used measurements of the complexity of terms of type tau, including the depth or height of a term and the number of variable symbols appearing in a term. In this paper we formalize these various measurements, by defining a complexity or valuation mapping on terms. A valuation of terms is thus a mapping from the absolutely free term algebra of type tau into another algebra of the same type on which an order relation is defined. We develop the interconnections between such term valuations and the equational theory of Universal Algebra. The collection of all varieties of a given type forms a complete lattice which is very complex and difficult to study; valuations of terms offer a new method to study complete sublattices of this lattice},
  language  = {en}
}
@article{DeneckeWismath2003,
  author    = {Denecke, Klaus-Dieter and Wismath, Shelly},
  title     = {Valuations and Hypersubstitutions},
  year      = {2003},
  language  = {en}
}
@article{CanforaSchmidt2003,
  author    = {Canfora, Fabrizio and Schmidt, Hans-J{\"u}rgen},
  title     = {Vacuum solutions which cannot be written in diagonal form},
  year      = {2003},
  abstract  = {A vacuum solution of the Einstein gravitational field equation is shown to follow from a general ansatz but fails to follow from it if the symmetric matrix in it is assumed to be in diagonal form.},
  language  = {en}
}
@phdthesis{Vu2014,
  author    = {Vu, Dinh Phuong},
  title     = {Using video study to investigate eighth-grade mathematics classrooms in Vietnam},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72464},
  school      = {Universit{\"a}t Potsdam},
  pages     = {273},
  year      = {2014},
  abstract  = {The International Project for the Evaluation of Educational Achievement (IEA) was formed in the 1950s (Postlethwaite, 1967). Since that time, the IEA has conducted many studies in the area of mathematics, such as the First International Mathematics Study (FIMS) in 1964, the Second International Mathematics Study (SIMS) in 1980-1982, and a series of studies beginning with the Third International Mathematics and Science Study (TIMSS) which has been conducted every 4 years since 1995. According to Stigler et al. (1999), in the FIMS and the SIMS, U.S. students achieved low scores in comparison with students in other countries (p. 1). The TIMSS 1995 "Videotape Classroom Study" was therefore a complement to the earlier studies conducted to learn "more about the instructional and cultural processes that are associated with achievement" (Stigler et al., 1999, p. 1). The TIMSS Videotape Classroom Study is known today as the TIMSS Video Study. From the findings of the TIMSS 1995 Video Study, Stigler and Hiebert (1999) likened teaching to "mountain ranges poking above the surface of the water," whereby they implied that we might see the mountaintops, but we do not see the hidden parts underneath these mountain ranges (pp. 73-78). By watching the videotaped lessons from Germany, Japan, and the United States again and again, they discovered that "the systems of teaching within each country look similar from lesson to lesson. At least, there are certain recurring features [or patterns] that typify many of the lessons within a country and distinguish the lessons among countries" (pp. 77-78). They also discovered that "teaching is a cultural activity," so the systems of teaching "must be understood in relation to the cultural beliefs and assumptions that surround them" (pp. 85, 88). From this viewpoint, one of the purposes of this dissertation was to study some cultural aspects of mathematics teaching and relate the results to mathematics teaching and learning in Vietnam. Another research purpose was to carry out a video study in Vietnam to find out the characteristics of Vietnamese mathematics teaching and compare these characteristics with those of other countries. In particular, this dissertation carried out the following research tasks: - Studying the characteristics of teaching and learning in different cultures and relating the results to mathematics teaching and learning in Vietnam - Introducing the TIMSS, the TIMSS Video Study and the advantages of using video study in investigating mathematics teaching and learning - Carrying out the video study in Vietnam to identify the image, scripts and patterns, and the lesson signature of eighth-grade mathematics teaching in Vietnam - Comparing some aspects of mathematics teaching in Vietnam and other countries and identifying the similarities and differences across countries - Studying the demands and challenges of innovating mathematics teaching methods in Vietnam - lessons from the video studies Hopefully, this dissertation will be a useful reference material for pre-service teachers at education universities to understand the nature of teaching and develop their teaching career.},
  language  = {en}
}
@article{SamarasNicolaeBoeckmannetal.2015,
  author    = {Samaras, Stefanos and Nicolae, Doina and B{\"o}ckmann, Christine and Vasilescu, Jeni and Binietoglou, Ioannis and Labzovskii, Lev and Toanca, Florica and Papayannis, Alexandros},
  title     = {Using Raman-lidar-based regularized microphysical retrievals and Aerosol Mass Spectrometer measurements for the characterization of biomass burning aerosols},
  series = {Journal of computational physics},
  volume    = {299},
  journal   = {Journal of computational physics},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0021-9991},
  doi       = {10.1016/j.jcp.2015.06.045},
  pages     = {156 -- 174},
  year      = {2015},
  abstract  = {In this work we extract the microphysical properties of aerosols for a collection of measurement cases with low volume depolarization ratio originating from fire sources captured by the Raman lidar located at the National Institute of Optoelectronics (INOE) in Bucharest. Our algorithm was tested not only for pure smoke but also for mixed smoke and urban aerosols of variable age and growth. Applying a sensitivity analysis on initial parameter settings of our retrieval code was proved vital for producing semi-automatized retrievals with a hybrid regularization method developed at the Institute of Mathematics of Potsdam University. A direct quantitative comparison of the retrieved microphysical properties with measurements from a Compact Time of Flight Aerosol Mass Spectrometer (CToF-AMS) is used to validate our algorithm. Microphysical retrievals performed with sun photometer data are also used to explore our results. Focusing on the fine mode we observed remarkable similarities between the retrieved size distribution and the one measured by the AMS. More complicated atmospheric structures and the factor of absorption appear to depend more on particle radius being subject to variation. A good correlation was found between the aerosol effective radius and particle age, using the ratio of lidar ratios (LR: aerosol extinction to backscatter ratios) as an indicator for the latter. Finally, the dependence on relative humidity of aerosol effective radii measured on the ground and within the layers aloft show similar patterns. (C) 2015 Elsevier Inc. All rights reserved.},
  language  = {en}
}
@article{KretschmerCoumouDongesetal.2016,
  author    = {Kretschmer, Marlene and Coumou, Dim and Donges, Jonathan and Runge, Jakob},
  title     = {Using Causal Effect Networks to Analyze Different Arctic Drivers of Midlatitude Winter Circulation},
  series = {Journal of climate},
  volume    = {29},
  journal   = {Journal of climate},
  publisher = {American Meteorological Soc.},
  address   = {Boston},
  issn      = {0894-8755},
  doi       = {10.1175/JCLI-D-15-0654.1},
  pages     = {4069 -- 4081},
  year      = {2016},
  abstract  = {In recent years, the Northern Hemisphere midlatitudes have suffered from severe winters like the extreme 2012/13 winter in the eastern United States. These cold spells were linked to a meandering upper-tropospheric jet stream pattern and a negative Arctic Oscillation index (AO). However, the nature of the drivers behind these circulation patterns remains controversial. Various studies have proposed different mechanisms related to changes in the Arctic, most of them related to a reduction in sea ice concentrations or increasing Eurasian snow cover. Here, a novel type of time series analysis, called causal effect networks (CEN), based on graphical models is introduced to assess causal relationships and their time delays between different processes. The effect of different Arctic actors on winter circulation on weekly to monthly time scales is studied, and robust network patterns are found. Barents and Kara sea ice concentrations are detected to be important external drivers of the midlatitude circulation, influencing winter AO via tropospheric mechanisms and through processes involving the stratosphere. Eurasia snow cover is also detected to have a causal effect on sea level pressure in Asia, but its exact role on AO remains unclear. The CEN approach presented in this study overcomes some difficulties in interpreting correlation analyses, complements model experiments for testing hypotheses involving teleconnections, and can be used to assess their validity. The findings confirm that sea ice concentrations in autumn in the Barents and Kara Seas are an important driver of winter circulation in the midlatitudes.},
  language  = {en}
}
@phdthesis{Butkote2009,
  author    = {Butkote, Runglawan},
  title     = {Universal-algebraic and Semigroup-theoretical Properties of Boolean Operations},
  address   = {Potsdam},
  pages     = {123 S.},
  year      = {2009},
  language  = {en}
}
@book{DeneckeWismath2009,
  author    = {Denecke, Klaus-Dieter and Wismath, Shelly L.},
  title     = {Universal Algebra and Coalgebra},
  publisher = {World Scientific Publ. Co},
  address   = {Singapore},
  isbn      = {978-981-283745-5},
  pages     = {278 S.},
  year      = {2009},
  language  = {en}
}
@book{DeneckeWismath2002,
  author    = {Denecke, Klaus-Dieter and Wismath, Shelly},
  title     = {Universal algebra and applications in theoretical computer science},
  publisher = {Chapman \& Hall/CRC},
  address   = {Boca Raton},
  isbn      = {1-584-88254-9},
  pages     = {383 S.},
  year      = {2002},
  language  = {en}
}
@unpublished{Tarkhanov2005,
  author    = {Tarkhanov, Nikolai Nikolaevich},
  title     = {Unitary solutions of partial differential equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29852},
  year      = {2005},
  abstract  = {We give an explicit construction of a fundamental solution for an arbitrary non-degenerate partial differential equation with smooth coefficients.},
  language  = {en}
}