@phdthesis{Abed2010,
  author    = {Abed, Jamil},
  title     = {An iterative approach to operators on manifolds with singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-44757},
  school      = {Universit{\"a}t Potsdam},
  year      = {2010},
  abstract  = {We establish elements of a new approach to ellipticity and parametrices within operator algebras on manifolds with higher singularities, only based on some general axiomatic requirements on parameter-dependent operators in suitable scales of spaes. The idea is to model an iterative process with new generations of parameter-dependent operator theories, together with new scales of spaces that satisfy analogous requirements as the original ones, now on a corresponding higher level. The "full" calculus involves two separate theories, one near the tip of the corner and another one at the conical exit to infinity. However, concerning the conical exit to infinity, we establish here a new concrete calculus of edge-degenerate operators which can be iterated to higher singularities.},
  language  = {en}
}
@book{AbedSchulze2008,
  author    = {Abed, Jamil and Schulze, Bert-Wolfgang},
  title     = {Operators with Corner-degenerate Symbols},
  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     = {47 S.},
  year      = {2008},
  language  = {en}
}
@unpublished{AbedSchulze2009,
  author    = {Abed, Jamil and Schulze, Bert-Wolfgang},
  title     = {Edge-degenerate families of ΨDO's on an infinite cylinder},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30365},
  year      = {2009},
  abstract  = {We establish a parameter-dependent pseudo-differential calculus on an infinite cylinder, regarded as a manifold with conical exits to infinity. The parameters are involved in edge-degenerate form, and we formulate the operators in terms of operator-valued amplitude functions.},
  language  = {en}
}
@unpublished{AbedSchulze2008,
  author    = {Abed, Jamil and Schulze, Bert-Wolfgang},
  title     = {Operators with corner-degenerate symbols},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30299},
  year      = {2008},
  abstract  = {We establish elements of a new approch to ellipticity and parametrices within operator algebras on a manifold with higher singularities, only based on some general axiomatic requirements on parameter-dependent operators in suitable scales of spaces. The idea is to model an iterative process with new generations of parameter-dependent operator theories, together with new scales of spaces that satisfy analogous requirements as the original ones, now on a corresponding higher level. The "full" calculus is voluminous; so we content ourselves here with some typical aspects such as symbols in terms of order reducing families, classes of relevant examples, and operators near the conical exit to infinity.},
  language  = {en}
}
@article{AcevedoDeWiljesReich2017,
  author    = {Acevedo, Walter and De Wiljes, Jana and Reich, Sebastian},
  title     = {Second-order accurate ensemble transform particle filters},
  series = {SIAM journal on scientific computing},
  volume    = {39},
  journal   = {SIAM journal on scientific computing},
  number    = {5},
  publisher = {Society for Industrial and Applied Mathematics},
  address   = {Philadelphia},
  issn      = {1064-8275},
  doi       = {10.1137/16M1095184},
  pages     = {A1834 -- A1850},
  year      = {2017},
  abstract  = {Particle filters (also called sequential Monte Carlo methods) are widely used for state and parameter estimation problems in the context of nonlinear evolution equations. The recently proposed ensemble transform particle filter (ETPF) [S. Reich, SIAM T. Sci. Comput., 35, (2013), pp. A2013-A2014[ replaces the resampling step of a standard particle filter by a linear transformation which allows for a hybridization of particle filters with ensemble Kalman filters and renders the resulting hybrid filters applicable to spatially extended systems. However, the linear transformation step is computationally expensive and leads to an underestimation of the ensemble spread for small and moderate ensemble sizes. Here we address both of these shortcomings by developing second order accurate extensions of the ETPF. These extensions allow one in particular to replace the exact solution of a linear transport problem by its Sinkhorn approximation. It is also demonstrated that the nonlinear ensemble transform filter arises as a special case of our general framework. We illustrate the performance of the second-order accurate filters for the chaotic Lorenz-63 and Lorenz-96 models and a dynamic scene-viewing model. The numerical results for the Lorenz-63 and Lorenz-96 models demonstrate that significant accuracy improvements can be achieved in comparison to a standard ensemble Kalman filter and the ETPF for small to moderate ensemble sizes. The numerical results for the scene-viewing model reveal, on the other hand, that second-order corrections can lead to statistically inconsistent samples from the posterior parameter distribution.},
  language  = {en}
}
@article{AcevedoFallahReichetal.2017,
  author    = {Acevedo, Walter and Fallah, Bijan and Reich, Sebastian and Cubasch, Ulrich},
  title     = {Assimilation of pseudo-tree-ring-width observations into an atmospheric general circulation model},
  series = {Climate of the past : an interactive open access journal of the European Geosciences Union},
  volume    = {13},
  journal   = {Climate of the past : an interactive open access journal of the European Geosciences Union},
  publisher = {Copernicus},
  address   = {G{\"o}ttingen},
  issn      = {1814-9324},
  doi       = {10.5194/cp-13-545-2017},
  pages     = {545 -- 557},
  year      = {2017},
  abstract  = {Paleoclimate data assimilation (DA) is a promising technique to systematically combine the information from climate model simulations and proxy records. Here, we investigate the assimilation of tree-ring-width (TRW) chronologies into an atmospheric global climate model using ensemble Kalman filter (EnKF) techniques and a process-based tree-growth forward model as an observation operator. Our results, within a perfect-model experiment setting, indicate that the "online DA" approach did not outperform the "off-line" one, despite its considerable additional implementation complexity. On the other hand, it was observed that the nonlinear response of tree growth to surface temperature and soil moisture does deteriorate the operation of the time-averaged EnKF methodology. Moreover, for the first time we show that this skill loss appears significantly sensitive to the structure of the growth rate function, used to represent the principle of limiting factors (PLF) within the forward model. In general, our experiments showed that the error reduction achieved by assimilating pseudo-TRW chronologies is modulated by the magnitude of the yearly internal variability in themodel. This result might help the dendrochronology community to optimize their sampling efforts.},
  language  = {en}
}
@article{AcevedoReichCubasch2016,
  author    = {Acevedo, Walter and Reich, Sebastian and Cubasch, Ulrich},
  title     = {Towards the assimilation of tree-ring-width records using ensemble Kalman filtering techniques},
  series = {Climate dynamics : observational, theoretical and computational research on the climate system},
  volume    = {46},
  journal   = {Climate dynamics : observational, theoretical and computational research on the climate system},
  publisher = {Springer},
  address   = {New York},
  issn      = {0930-7575},
  doi       = {10.1007/s00382-015-2683-1},
  pages     = {1909 -- 1920},
  year      = {2016},
  abstract  = {This paper investigates the applicability of the Vaganov-Shashkin-Lite (VSL) forward model for tree-ring-width chronologies as observation operator within a proxy data assimilation (DA) setting. Based on the principle of limiting factors, VSL combines temperature and moisture time series in a nonlinear fashion to obtain simulated TRW chronologies. When used as observation operator, this modelling approach implies three compounding, challenging features: (1) time averaging, (2) "switching recording" of 2 variables and (3) bounded response windows leading to "thresholded response". We generate pseudo-TRW observations from a chaotic 2-scale dynamical system, used as a cartoon of the atmosphere-land system, and attempt to assimilate them via ensemble Kalman filtering techniques. Results within our simplified setting reveal that VSL's nonlinearities may lead to considerable loss of assimilation skill, as compared to the utilization of a time-averaged (TA) linear observation operator. In order to understand this undesired effect, we embed VSL's formulation into the framework of fuzzy logic (FL) theory, which thereby exposes multiple representations of the principle of limiting factors. DA experiments employing three alternative growth rate functions disclose a strong link between the lack of smoothness of the growth rate function and the loss of optimality in the estimate of the TA state. Accordingly, VSL's performance as observation operator can be enhanced by resorting to smoother FL representations of the principle of limiting factors. This finding fosters new interpretations of tree-ring-growth limitation processes.},
  language  = {en}
}
@book{AdamyanNeidhardt1996,
  author    = {Adamyan, Vadim M. and Neidhardt, Hagen},
  title     = {On the absolutely continuous subspace for non-selfadjoint operators},
  series = {Preprint / SFB 288, Differentialgeometrie und Quantenphysik},
  volume    = {207},
  journal   = {Preprint / SFB 288, Differentialgeometrie und Quantenphysik},
  address   = {Berlin},
  year      = {1996},
  language  = {en}
}
@book{AdamyanNeidhardt1996,
  author    = {Adamyan, Vadim M. and Neidhardt, Hagen},
  title     = {On the absolutely continuous subspace for contractions and dissipative operators},
  series = {Preprint / SFB 288, Differentialgeometrie und Quantenphysik},
  volume    = {205},
  journal   = {Preprint / SFB 288, Differentialgeometrie und Quantenphysik},
  address   = {Berlin},
  year      = {1996},
  language  = {en}
}
@article{AfshariMoeinSomogyvariValleyetal.2018,
  author    = {Afshari Moein, Mohammad J. and Somogyv{\´a}ri, M{\´a}rk and Valley, Beno{\^i}t and Jalali, Mohammadreza and L{\"o}w, Simon and Bayer, Peter},
  title     = {Fracture network characterization using stress-based tomography},
  series = {Journal of geophysical research : JGR},
  volume    = {123},
  journal   = {Journal of geophysical research : JGR},
  number    = {11},
  publisher = {American Geophysical Union},
  address   = {Washington},
  issn      = {2169-9313},
  doi       = {10.1029/2018JB016438},
  pages     = {9324 -- 9340},
  year      = {2018},
  abstract  = {Information on structural features of a fracture network at early stages of Enhanced Geothermal System development is mostly restricted to borehole images and, if available, outcrop data. However, using this information to image discontinuities in deep reservoirs is difficult. Wellbore failure data provides only some information on components of the in situ stress state and its heterogeneity. Our working hypothesis is that slip on natural fractures primarily controls these stress heterogeneities. Based on this, we introduce stress-based tomography in a Bayesian framework to characterize the fracture network and its heterogeneity in potential Enhanced Geothermal System reservoirs. In this procedure, first a random initial discrete fracture network (DFN) realization is generated based on prior information about the network. The observations needed to calibrate the DFN are based on local variations of the orientation and magnitude of at least one principal stress component along boreholes. A Markov Chain Monte Carlo sequence is employed to update the DFN iteratively by a fracture translation within the domain. The Markov sequence compares the simulated stress profile with the observed stress profiles in the borehole, evaluates each iteration with Metropolis-Hastings acceptance criteria, and stores acceptable DFN realizations in an ensemble. Finally, this obtained ensemble is used to visualize the potential occurrence of fractures in a probability map, indicating possible fracture locations and lengths. We test this methodology to reconstruct simple synthetic and more complex outcrop-based fracture networks and successfully image the significant fractures in the domain.},
  language  = {en}
}
@unpublished{AirapetyanWitt1997,
  author    = {Airapetyan, Ruben and Witt, Ingo},
  title     = {Isometric properties of the Hankel Transformation in weighted sobolev spaces},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25001},
  year      = {1997},
  abstract  = {It is shown that the Hankel transformation Hsub(v) acts in a class of weighted Sobolev spaces. Especially, the isometric mapping property of Hsub(v) which holds on L²(IRsub(+),rdr) is extended to spaces of arbitrary Sobolev order. The novelty in the approach consists in using techniques developed by B.-W. Schulze and others to treat the half-line Rsub(+) as a manifold with a conical singularity at r = 0. This is achieved by pointing out a connection between the Hankel transformation and the Mellin transformation.The procedure proposed leads at the same time to a short proof of the Hankel inversion formula. An application to the existence and higher regularity of solutions, including their asymptotics, to the 1-1-dimensional edge-degenerated wave equation is given.},
  language  = {en}
}
@book{AirapetyanWitt1997,
  author    = {Airapetyan, Ruben and Witt, Ingo},
  title     = {Isometric properties of the Hankel transformation in weighted Sobolev spaces},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1997, 14},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {19 S.},
  year      = {1997},
  language  = {en}
}
@book{AizenbergTarchanov1999,
  author    = {Aizenberg, Lev A. and Tarchanov, Nikolaj N.},
  title     = {A Bohr phenomenon for elliptic equations},
  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     = {24 S.},
  year      = {1999},
  language  = {en}
}
@book{AizenbergTarkhanov2005,
  author    = {Aizenberg, Lev A. and Tarkhanov, Nikolai Nikolaevich},
  title     = {Stable expansions in homogeneous polynomials},
  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     = {23 S.},
  year      = {2005},
  language  = {en}
}
@unpublished{AizenbergTarkhanov1999,
  author    = {Aizenberg, Lev A. and Tarkhanov, Nikolai Nikolaevich},
  title     = {A Bohr phenomenon for elliptic equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25547},
  year      = {1999},
  abstract  = {In 1914 Bohr proved that there is an r ∈ (0, 1) such that if a power series converges in the unit disk and its sum has modulus less than 1 then, for |z| < r, the sum of absolute values of its terms is again less than 1. Recently analogous results were obtained for functions of several variables. The aim of this paper is to comprehend the theorem of Bohr in the context of solutions to second order elliptic equations meeting the maximum principle.},
  language  = {en}
}
@unpublished{AizenbergTarkhanov2005,
  author    = {Aizenberg, Lev A. and Tarkhanov, Nikolai Nikolaevich},
  title     = {Stable expansions in homogeneous polynomials},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29925},
  year      = {2005},
  abstract  = {An expansion for a class of functions is called stable if the partial sums are bounded uniformly in the class. Stable expansions are of key importance in numerical analysis where functions are given up to certain error. We show that expansions in homogeneous functions are always stable on a small ball around the origin, and evaluate the radius of the largest ball with this property.},
  language  = {en}
}
@unpublished{AizenbergTarkhanov2014,
  author    = {Aizenberg, Lev A. and Tarkhanov, Nikolai Nikolaevich},
  title     = {An integral formula for the number of lattice points in a domain},
  volume    = {3},
  number    = {3},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-70453},
  pages     = {7},
  year      = {2014},
  abstract  = {Using the multidimensional logarithmic residue we show a simple formula for the difference between the number of integer points in a bounded domain of R^n and the volume of this domain. The difference proves to be the integral of an explicit differential form over the boundary of the domain.},
  language  = {en}
}
@article{AizingerKornGiorgettaetal.2015,
  author    = {Aizinger, Vadym and Korn, Peter and Giorgetta, Marco and Reich, Sebastian},
  title     = {Large-scale turbulence modelling via alpha-regularisation for atmospheric simulations},
  series = {Journal of turbulence},
  volume    = {16},
  journal   = {Journal of turbulence},
  number    = {4},
  publisher = {Routledge, Taylor \& Francis Group},
  address   = {Abingdon},
  issn      = {1468-5248},
  doi       = {10.1080/14685248.2014.991443},
  pages     = {367 -- 391},
  year      = {2015},
  abstract  = {We study the possibility of obtaining a computational turbulence model by means of non-dissipative regularisation of the compressible atmospheric equations for climate-type applications. We use an -regularisation (Lagrangian averaging) of the atmospheric equations. For the hydrostatic and compressible atmospheric equations discretised using a finite volume method on unstructured grids, deterministic and non-deterministic numerical experiments are conducted to compare the individual solutions and the statistics of the regularised equations to those of the original model. The impact of the regularisation parameter is investigated. Our results confirm the principal compatibility of -regularisation with atmospheric dynamics and encourage further investigations within atmospheric model including complex physical parametrisations.},
  language  = {en}
}
@article{AkhmatskayaBouRabeeReich2009,
  author    = {Akhmatskaya, Elena and Bou-Rabee, Nawaf and Reich, Sebastian},
  title     = {A comparison of generalized hybrid Monte Carlo methods with and without momentum flip},
  issn      = {0021-9991},
  doi       = {10.1016/j.jcp.2008.12.014},
  year      = {2009},
  abstract  = {The generalized hybrid Monte Carlo (GHMC) method combines Metropolis corrected constant energy simulations with a partial random refreshment step in the particle momenta. The standard detailed balance condition requires that momenta are negated upon rejection of a molecular dynamics proposal step. The implication is a trajectory reversal upon rejection, which is undesirable when interpreting GHMC as thermostated molecular dynamics. We show that a modified detailed balance condition can be used to implement GHMC without momentum flips. The same modification can be applied to the generalized shadow hybrid Monte Carlo (GSHMC) method. Numerical results indicate that GHMC/GSHMC implementations with momentum flip display a favorable behavior in terms of sampling efficiency, i.e., the traditional GHMC/GSHMC implementations with momentum flip got the advantage of a higher acceptance rate and faster decorrelation of Monte Carlo samples. The difference is more pronounced for GHMC. We also numerically investigate the behavior of the GHMC method as a Langevin-type thermostat. We find that the GHMC method without momentum flip interferes less with the underlying stochastic molecular dynamics in terms of autocorrelation functions and it to be preferred over the GHMC method with momentum flip. The same finding applies to GSHMC.},
  language  = {en}
}
@article{AkhmatskayaBouRabeeReich2009,
  author    = {Akhmatskaya, Elena and Bou-Rabee, Nawaf and Reich, Sebastian},
  title     = {Erratum to "A comparison of generalized hybrid Monte Carlo methods with and without momentum flip" [J. Comput. Phys. 228 (2009), S. 2256 - 2265]},
  issn      = {0021-9991},
  doi       = {10.1016/j.jcp.2009.06.039},
  year      = {2009},
  abstract  = {The generalized hybrid Monte Carlo (GHMC) method combines Metropolis corrected constant energy simulations with a partial random refreshment step in the particle momenta. The standard detailed balance condition requires that momenta are negated upon rejection of a molecular dynamics proposal step. The implication is a trajectory reversal upon rejection, which is undesirable when interpreting GHMC as thermostated molecular dynamics. We show that a modified detailed balance condition can be used to implement GHMC without momentum flips. The same modification can be applied to the generalized shadow hybrid Monte Carlo (GSHMC) method. Numerical results indicate that GHMC/GSHMC implementations with momentum flip display a favorable behavior in terms of sampling efficiency, i.e., the traditional GHMC/GSHMC implementations with momentum flip got the advantage of a higher acceptance rate and faster decorrelation of Monte Carlo samples. The difference is more pronounced for GHMC. We also numerically investigate the behavior of the GHMC method as a Langevin-type thermostat. We find that the GHMC method without momentum flip interferes less with the underlying stochastic molecular dynamics in terms of autocorrelation functions and it to be preferred over the GHMC method with momentum flip. The same finding applies to GSHMC.},
  language  = {en}
}
@phdthesis{AlSaedy2015,
  author    = {Al-Saedy, Ammar Jaffar Muhesin},
  title     = {Normally solvable lagrangian boundary value problems},
  school      = {Universit{\"a}t Potsdam},
  pages     = {110},
  year      = {2015},
  language  = {en}
}
@article{AlSaedyTarchanov2020,
  author    = {Al-Saedy, Ammar Jaffar Muhesin and Tarchanov, Nikolaj Nikolaevič},
  title     = {A degree theory for Lagrangian boundary value problems},
  series = {Žurnal Sibirskogo Federalʹnogo Universiteta = Journal of Siberian Federal University; mathematics \& physics},
  volume    = {13},
  journal   = {Žurnal Sibirskogo Federalʹnogo Universiteta = Journal of Siberian Federal University; mathematics \& physics},
  number    = {1},
  publisher = {Sibirskij Federalʹnyj Universitet},
  address   = {Krasnojarsk},
  issn      = {1997-1397},
  doi       = {10.17516/1997-1397-2020-13-1-5-25},
  pages     = {5 -- 25},
  year      = {2020},
  abstract  = {We study those nonlinear partial differential equations which appear as Euler-Lagrange equations of variational problems. On defining weak boundary values of solutions to such equations 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 Lagrangian problems.},
  language  = {en}
}
@article{AlbeverioBrascheNeidhardt1998,
  author    = {Albeverio, Sergio and Brasche, Johannes F. and Neidhardt, Hagen},
  title     = {On inverse spectral theory: mixed types of spectra.},
  year      = {1998},
  language  = {en}
}
@book{AlbeverioDemuthSchroheetal.2002,
  author    = {Albeverio, Sergio and Demuth, Michael and Schrohe, Elmar and Schulze, Bert-Wolfgang},
  title     = {Parabolicity, volterra calculus, and conical singularities : a volume of advances in partial differential equations},
  series = {Operator theory : advances and applications},
  volume    = {138},
  journal   = {Operator theory : advances and applications},
  publisher = {Birkh{\"a}user Verl.},
  address   = {Basel},
  isbn      = {3-7643-6906-x},
  pages     = {358 S.},
  year      = {2002},
  language  = {en}
}
@article{Alpers1994,
  author    = {Alpers, Karsten},
  title     = {{\"U}ber zweidimensionale diskrete Bewegungsgruppen der pseudoeuklidischen Ebene},
  year      = {1994},
  language  = {de}
}
@phdthesis{Alpers1995,
  author    = {Alpers, Karsten},
  title     = {Diskrete Bewegungsgruppen der pseudoeuklidischen Ebene},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {II, 107 S.},
  year      = {1995},
  language  = {de}
}
@book{AlpersDietzschEppetal.2004,
  author    = {Alpers, Karsten and Dietzsch, Volker and Epp, Thomas and Jahnke, Thomas and Janßen, Martin and Siekmann, Angelika and Simanowsky, Ursula and Wuttke, Hans},
  title     = {Mathematik : Analytische Geometrie lineare Algebra ; Orientierungswissen Stochastik ; Handreichungen f{\"u}r den Unterricht ; Gymnasiale Oberstufe ; NRW},
  series = {Orientierungswissen Stoachstik},
  journal   = {Orientierungswissen Stoachstik},
  publisher = {Cornelsen},
  address   = {Berlin},
  isbn      = {3-464-57282-x},
  pages     = {456 S.},
  year      = {2004},
  language  = {de}
}
@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}
}
@unpublished{AlsaedyTarkhanov2012,
  author    = {Alsaedy, Ammar and Tarkhanov, Nikolai Nikolaevich},
  title     = {The method of Fischer-Riesz equations for elliptic boundary value problems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-61792},
  year      = {2012},
  abstract  = {We develop the method of Fischer-Riesz equations for general boundary value problems elliptic in the sense of Douglis-Nirenberg. To this end we reduce them to a boundary problem for a (possibly overdetermined) first order system whose classical symbol has a left inverse. For such a problem there is a uniquely determined boundary value problem which is adjoint to the given one with respect to the Green formula. On using a well elaborated theory of approximation by solutions of the adjoint problem, we find the Cauchy data of solutions of our problem.},
  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{AlsaedyTarkhanov2014,
  author    = {Alsaedy, Ammar and Tarkhanov, Nikolai Nikolaevich},
  title     = {Normally solvable nonlinear boundary value problems},
  series = {Nonlinear analysis : theory, methods \& applications ; an international multidisciplinary journal},
  volume    = {95},
  journal   = {Nonlinear analysis : theory, methods \& applications ; an international multidisciplinary journal},
  publisher = {Elsevier},
  address   = {Oxford},
  issn      = {0362-546X},
  doi       = {10.1016/j.na.2013.09.024},
  pages     = {468 -- 482},
  year      = {2014},
  abstract  = {We investigate nonlinear problems which appear as Euler-Lagrange equations for a variational problem. They include in particular variational boundary value problems for nonlinear elliptic equations studied by F. Browder in the 1960s. We establish a solvability criterion of such problems and elaborate an efficient orthogonal projection method for constructing approximate solutions.},
  language  = {en}
}
@unpublished{AlsaedyTarkhanov2012,
  author    = {Alsaedy, Ammar and Tarkhanov, Nikolai Nikolaevich},
  title     = {Spectral projection for the dbar-Neumann problem},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-58616},
  year      = {2012},
  abstract  = {We show that the spectral kernel function of the dbar-Neumann problem on a non-compact strongly pseudoconvex manifold is smooth up to the boundary.},
  language  = {en}
}
@unpublished{AlsaedyTarkhanov2016,
  author    = {Alsaedy, Ammar and Tarkhanov, Nikolai Nikolaevich},
  title     = {A Hilbert boundary value problem for generalised Cauchy-Riemann equations},
  volume    = {5},
  number    = {1},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-86109},
  pages     = {21},
  year      = {2016},
  abstract  = {We elaborate a boundary Fourier method for studying an analogue of the Hilbert problem for analytic functions within the framework of generalised Cauchy-Riemann equations. The boundary value problem need not satisfy the Shapiro-Lopatinskij condition and so it fails to be Fredholm in Sobolev spaces. We show a solvability condition of the Hilbert problem, which looks like those for ill-posed problems, and construct an explicit formula for approximate solutions.},
  language  = {en}
}
@unpublished{AlsaedyTarkhanov2013,
  author    = {Alsaedy, Ammar and Tarkhanov, Nikolai Nikolaevich},
  title     = {Normally solvable nonlinear boundary value problems},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-65077},
  year      = {2013},
  abstract  = {We study a boundary value problem for an overdetermined elliptic system of nonlinear first order differential equations with linear boundary operators. Such a problem is solvable for a small set of data, and so we pass to its variational formulation which consists in minimising the discrepancy. The Euler-Lagrange equations for the variational problem are far-reaching analogues of the classical Laplace equation. Within the framework of Euler-Lagrange equations we specify an operator on the boundary whose zero set consists precisely of those boundary data for which the initial problem is solvable. The construction of such operator has much in common with that of the familiar Dirichlet to Neumann operator. In the case of linear problems we establish complete results.},
  language  = {en}
}
@article{AltundagBoeckmannTaseli2015,
  author    = {Altundag, H{\"u}seyin and B{\"o}ckmann, Christine and Taseli, Hasan},
  title     = {Inverse Sturm-Liouville problems with pseudospectral methods},
  series = {International journal of computer mathematics},
  volume    = {92},
  journal   = {International journal of computer mathematics},
  number    = {7},
  publisher = {Routledge, Taylor \& Francis Group},
  address   = {Abingdon},
  issn      = {0020-7160},
  doi       = {10.1080/00207160.2014.939646},
  pages     = {1373 -- 1384},
  year      = {2015},
  abstract  = {In this paper a technique to obtain a first approximation for singular inverse Sturm-Liouville problems with a symmetrical potential is introduced. The singularity, as a result of unbounded domain (-infinity, infinity), is treated by considering numerically the asymptotic limit of the associated problem on a finite interval (-L, L). In spite of this treatment, the problem has still an ill-conditioned structure unlike the classical regular ones and needs regularization techniques. Direct computation of eigenvalues in iterative solution procedure is made by means of pseudospectral methods. A fairly detailed description of the numerical algorithm and its applications to specific examples are presented to illustrate the accuracy and convergence behaviour of the proposed approach.},
  language  = {en}
}
@article{AmendolaBattagliaMayerCapozzielloetal.1992,
  author    = {Amendola, Luca and Battaglia Mayer, Alexandra and Capozziello, Salvatore and Gottl{\"o}ber, Stefan and M{\"u}ller, Volker and Occhionero, Franco and Schmidt, Hans-J{\"u}rgen},
  title     = {Generalized sixth-order gravity and inflation},
  series = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik},
  volume    = {1992, 04},
  journal   = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {7 S.},
  year      = {1992},
  language  = {en}
}
@article{AmezcuaIdeKalnayetal.2014,
  author    = {Amezcua, Javier and Ide, Kayo and Kalnay, Eugenia and Reich, Sebastian},
  title     = {Ensemble transform Kalman-Bucy filters},
  series = {Quarterly journal of the Royal Meteorological Society},
  volume    = {140},
  journal   = {Quarterly journal of the Royal Meteorological Society},
  number    = {680},
  publisher = {Wiley-Blackwell},
  address   = {Hoboken},
  issn      = {0035-9009},
  doi       = {10.1002/qj.2186},
  pages     = {995 -- 1004},
  year      = {2014},
  abstract  = {Two recent works have adapted the Kalman-Bucy filter into an ensemble setting. In the first formulation, the ensemble of perturbations is updated by the solution of an ordinary differential equation (ODE) in pseudo-time, while the mean is updated as in the standard Kalman filter. In the second formulation, the full ensemble is updated in the analysis step as the solution of single set of ODEs in pseudo-time. Neither requires matrix inversions except for the frequently diagonal observation error covariance. We analyse the behaviour of the ODEs involved in these formulations. We demonstrate that they stiffen for large magnitudes of the ratio of background error to observational error variance, and that using the integration scheme proposed in both formulations can lead to failure. A numerical integration scheme that is both stable and is not computationally expensive is proposed. We develop transform-based alternatives for these Bucy-type approaches so that the integrations are computed in ensemble space where the variables are weights (of dimension equal to the ensemble size) rather than model variables. Finally, the performance of our ensemble transform Kalman-Bucy implementations is evaluated using three models: the 3-variable Lorenz 1963 model, the 40-variable Lorenz 1996 model, and a medium complexity atmospheric general circulation model known as SPEEDY. The results from all three models are encouraging and warrant further exploration of these assimilation techniques.},
  language  = {en}
}
@unpublished{Anders2009,
  author    = {Anders, Martin},
  title     = {Martingale, Amarts und das starke Gesetz der Grossen Zahlen},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49494},
  year      = {2009},
  abstract  = {Aus dem Inhalt: Einleitung Kapitel 1. Starke Gesetze der Grossen Zahlen 1. SGGZ unter Wachstumsbedingungen an die p-ten Momente 2. SGGZ f{\"u}r identisch verteilte Zufallsvariablen 3. SGGZ f{\"u}r Prozesse mit *-mixing-Eigenschaft Kapitel 2. Einf{\"u}hrung zu diskreten (Sub-,Super-)Martingalen 1. Vorhersagbarkeit 2. gestoppte (Sub-,Super-)Martingale 3. Upcrossings 4. Konvergenzs{\"a}tze 5. Doob-Zerlegung 6. Eine {\"a}quivalente Definition eines (Sub-)Martingals Kapitel 3. Martingale und gleichgradige Integrierbarkeit 1. Gleichm{\"a}ßige(-f¨ormige,-gradige) Integrierbarkeit 2. gleichgradig integrierbare Martingale Kapitel 4. Martingale und das SGGZ Kapitel 5."reversed" (Sub-,Super-)Martingale 1. Konvergenzs{\"a}tze Kapitel 6. (Sub-,Super-)Martingale mit gerichteter Indexmenge 1. {\"A}quivalente Formulierung eines (Sub-)Martingals 2. Konvergenzs{\"a}tze Kapitel 7. Quasimartingale,Amarts und Semiamarts 1. Konvergenzs{\"a}tze 2. Riesz-Zerlegung 3. Doob-Zerlegung Kapitel 8. Amarts und das SGGZ Kapitel 9."reversed" Amarts und Semiamarts 1. Konvergenzs{\"a}tze 2."Aufw{\"a}rts"- gegen "Abw{\"a}rts"-Adaptiertheit 3. Riesz-Zerlegung 4. Stabilit{\"a}tsanalyse Kapitel 10. Amarts mit gerichteter Indexmenge 1. Konvergenzs{\"a}tze 2. Riesz-Zerlegung Anhang A. zur Existenz einer Folge unabh{\"a}ngiger Zufallsvariablen B. Konvergenz},
  language  = {de}
}
@inproceedings{AnderssonKeuneckeEseretal.2014,
  author    = {Andersson, H. and Keunecke, A. and Eser, A. and Huisinga, Wilhelm and Reinisch, W. and Kloft, Charlotte},
  title     = {Pharmacokinetic considerations for optimising dosing regimens of a potsdam univ infliximab in patients with Crohn's disease},
  series = {JOURNAL OF CROHNS \& COLITIS},
  volume    = {8},
  booktitle = {JOURNAL OF CROHNS \& COLITIS},
  publisher = {Oxford Univ. Press},
  address   = {Oxford},
  issn      = {1873-9946},
  doi       = {10.1016/S1873-9946(14)60086-6},
  pages     = {S44 -- S44},
  year      = {2014},
  language  = {en}
}
@article{AnderssonMetzger2010,
  author    = {Andersson, Lars and Metzger, Jan},
  title     = {Curvature estimates for stable marginally trapped surfaces},
  issn      = {0022-040X},
  year      = {2010},
  abstract  = {We derive local integral and sup-estimates for the curvature of stable marginally outer trapped surfaces in a sliced space-time. The estimates bound the shear of a marginally outer trapped surface in terms of the intrinsic and extrinsic curvature of a slice containing the surface. These estimates are well adapted to situations of physical interest, such as dynamical horizons.},
  language  = {en}
}
@phdthesis{Angwenyi2019,
  author    = {Angwenyi, David},
  title     = {Time-continuous state and parameter estimation with application to hyperbolic SPDEs},
  doi       = {10.25932/publishup-43654},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-436542},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xi, 101},
  year      = {2019},
  abstract  = {Data assimilation has been an active area of research in recent years, owing to its wide utility. At the core of data assimilation are filtering, prediction, and smoothing procedures. Filtering entails incorporation of measurements' information into the model to gain more insight into a given state governed by a noisy state space model. Most natural laws are governed by time-continuous nonlinear models. For the most part, the knowledge available about a model is incomplete; and hence uncertainties are approximated by means of probabilities. Time-continuous filtering, therefore, holds promise for wider usefulness, for it offers a means of combining noisy measurements with imperfect model to provide more insight on a given state. The solution to time-continuous nonlinear Gaussian filtering problem is provided for by the Kushner-Stratonovich equation. Unfortunately, the Kushner-Stratonovich equation lacks a closed-form solution. Moreover, the numerical approximations based on Taylor expansion above third order are fraught with computational complications. For this reason, numerical methods based on Monte Carlo methods have been resorted to. Chief among these methods are sequential Monte-Carlo methods (or particle filters), for they allow for online assimilation of data. Particle filters are not without challenges: they suffer from particle degeneracy, sample impoverishment, and computational costs arising from resampling. The goal of this thesis is to:— i) Review the derivation of Kushner-Stratonovich equation from first principles and its extant numerical approximation methods, ii) Study the feedback particle filters as a way of avoiding resampling in particle filters, iii) Study joint state and parameter estimation in time-continuous settings, iv) Apply the notions studied to linear hyperbolic stochastic differential equations. The interconnection between It{\^o} integrals and stochastic partial differential equations and those of Stratonovich is introduced in anticipation of feedback particle filters. With these ideas and motivated by the variants of ensemble Kalman-Bucy filters founded on the structure of the innovation process, a feedback particle filter with randomly perturbed innovation is proposed. Moreover, feedback particle filters based on coupling of prediction and analysis measures are proposed. They register a better performance than the bootstrap particle filter at lower ensemble sizes. We study joint state and parameter estimation, both by means of extended state spaces and by use of dual filters. Feedback particle filters seem to perform well in both cases. Finally, we apply joint state and parameter estimation in the advection and wave equation, whose velocity is spatially varying. Two methods are employed: Metropolis Hastings with filter likelihood and a dual filter comprising of Kalman-Bucy filter and ensemble Kalman-Bucy filter. The former performs better than the latter.},
  language  = {en}
}
@article{AntoniniAzzaliSkandalis2016,
  author    = {Antonini, Paolo and Azzali, Sara and Skandalis, Georges},
  title     = {Bivariant K-theory with R/Z-coefficients and rho classes of unitary representations},
  series = {Journal of functional analysis},
  volume    = {270},
  journal   = {Journal of functional analysis},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0022-1236},
  doi       = {10.1016/j.jfa.2015.06.017},
  pages     = {447 -- 481},
  year      = {2016},
  abstract  = {We construct equivariant KK-theory with coefficients in and R/Z as suitable inductive limits over II1-factors. We show that the Kasparov product, together with its usual functorial properties, extends to KK-theory with real coefficients. Let Gamma be a group. We define a Gamma-algebra A to be K-theoretically free and proper (KFP) if the group trace tr of Gamma acts as the unit element in KKR Gamma (A, A). We show that free and proper Gamma-algebras (in the sense of Kasparov) have the (KFP) property. Moreover, if Gamma is torsion free and satisfies the KK Gamma-form of the Baum-Connes conjecture, then every Gamma-algebra satisfies (KFP). If alpha : Gamma -> U-n is a unitary representation and A satisfies property (KFP), we construct in a canonical way a rho class rho(A)(alpha) is an element of KKR/Z1,Gamma (A A) This construction generalizes the Atiyah-Patodi-Singer K-theory class with R/Z-coefficients associated to alpha. (C) 2015 Elsevier Inc. All rights reserved.},
  language  = {en}
}
@article{AntonioukKiselevTarkhanov2015,
  author    = {Antoniouk, Alexandra Viktorivna and Kiselev, Oleg M. and Tarkhanov, Nikolai Nikolaevich},
  title     = {Asymptotic Solutions of the Dirichlet Problem for the Heat Equation at a Characteristic Point},
  series = {Ukrainian mathematical journal},
  volume    = {66},
  journal   = {Ukrainian mathematical journal},
  number    = {10},
  publisher = {Springer},
  address   = {New York},
  issn      = {0041-5995},
  doi       = {10.1007/s11253-015-1038-8},
  pages     = {1455 -- 1474},
  year      = {2015},
  abstract  = {The Dirichlet problem for the heat equation in a bounded domain aS, a"e (n+1) is characteristic because there are boundary points at which the boundary touches a characteristic hyperplane t = c, where c is a constant. For the first time, necessary and sufficient conditions on the boundary guaranteeing that the solution is continuous up to the characteristic point were established by Petrovskii (1934) under the assumption that the Dirichlet data are continuous. The appearance of Petrovskii's paper was stimulated by the existing interest to the investigation of general boundary-value problems for parabolic equations in bounded domains. We contribute to the study of this problem by finding a formal solution of the Dirichlet problem for the heat equation in a neighborhood of a cuspidal characteristic boundary point and analyzing its asymptotic behavior.},
  language  = {en}
}
@unpublished{AntonioukKiselevStepanenkoetal.2012,
  author    = {Antoniouk, Alexandra Viktorivna and Kiselev, Oleg and Stepanenko, Vitaly and Tarkhanov, Nikolai Nikolaevich},
  title     = {Asymptotic solutions of the Dirichlet problem for the heat equation at a characteristic point},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-61987},
  year      = {2012},
  abstract  = {The Dirichlet problem for the heat equation in a bounded domain is characteristic, for there are boundary points at which the boundary touches a characteristic hyperplane t = c, c being a constant. It was I.G. Petrovskii (1934) who first found necessary and sufficient conditions on the boundary which guarantee that the solution is continuous up to the characteristic point, provided that the Dirichlet data are continuous. This paper initiated standing interest in studying general boundary value problems for parabolic equations in bounded domains. We contribute to the study by constructing a formal solution of the Dirichlet problem for the heat equation in a neighbourhood of a characteristic boundary point and showing its asymptotic character.},
  language  = {en}
}
@phdthesis{Arworn1999,
  author    = {Arworn, Srichan},
  title     = {Groupoids of hypersubstitutions and G-solid varieties},
  address   = {Potsdam},
  pages     = {80 S.},
  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{ArwornDenecke1999,
  author    = {Arworn, Srichan and Denecke, Klaus-Dieter},
  title     = {Left-edges solid varieties of differential groupoids},
  year      = {1999},
  language  = {en}
}
@article{ArwornDenecke1997,
  author    = {Arworn, Srichan and Denecke, Klaus-Dieter},
  title     = {Groupoids of hypersubstitutions and G-solid varieties},
  year      = {1997},
  language  = {en}
}
@article{ArwornDenecke1997,
  author    = {Arworn, Srichan and Denecke, Klaus-Dieter},
  title     = {A new methods to study subvariety lattices of semigroup varieties},
  year      = {1997},
  language  = {en}
}
@article{ArwornDenecke2001,
  author    = {Arworn, Srichan and Denecke, Klaus-Dieter},
  title     = {Tree Transformations defined by Hypersubstitutions},
  issn      = {1509 - 9415},
  year      = {2001},
  language  = {en}
}