@unpublished{BagdonavičiusLevulieneNikulinetal.2004, author = {Bagdonavičius, Vilijandas B. and Levuliene, Ruta and Nikulin, Mikhail S. and Zdorova-Cheminade, Olga}, title = {Tests for homogeneity of survival distributions against non-location alternatives and analysis of the gastric cancer data}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51527}, year = {2004}, abstract = {The two and k-sample tests of equality of the survival distributions against the alternatives including cross-effects of survival functions, proportional and monotone hazard ratios, are given for the right censored data. The asymptotic power against approaching alternatives is investigated. The tests are applied to the well known chemio and radio therapy data of the Gastrointestinal Tumor Study Group. The P-values for both proposed tests are much smaller then in the case of other known tests. Differently from the test of Stablein and Koutrouvelis the new tests can be applied not only for singly but also to randomly censored data.}, language = {en} } @unpublished{BagderinaTarkhanov2013, author = {Bagderina, Yulia Yu. and Tarkhanov, Nikolai Nikolaevich}, title = {Differential invariants of a class of Lagrangian systems with two degrees of freedom}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-63129}, year = {2013}, abstract = {We consider systems of Euler-Lagrange equations with two degrees of freedom and with Lagrangian being quadratic in velocities. For this class of equations the generic case of the equivalence problem is solved with respect to point transformations. Using Lie's infinitesimal method we construct a basis of differential invariants and invariant differentiation operators for such systems. We describe certain types of Lagrangian systems in terms of their invariants. The results are illustrated by several examples.}, language = {en} } @article{BaerenzungHolschneiderWichtetal.2020, author = {Baerenzung, Julien and Holschneider, Matthias and Wicht, Johannes and Lesur, Vincent and Sanchez, Sabrina}, title = {The Kalmag model as a candidate for IGRF-13}, series = {Earth, planets and space}, volume = {72}, journal = {Earth, planets and space}, number = {1}, publisher = {Springer}, address = {New York}, issn = {1880-5981}, doi = {10.1186/s40623-020-01295-y}, pages = {13}, year = {2020}, abstract = {We present a new model of the geomagnetic field spanning the last 20 years and called Kalmag. Deriving from the assimilation of CHAMP and Swarm vector field measurements, it separates the different contributions to the observable field through parameterized prior covariance matrices. To make the inverse problem numerically feasible, it has been sequentialized in time through the combination of a Kalman filter and a smoothing algorithm. The model provides reliable estimates of past, present and future mean fields and associated uncertainties. The version presented here is an update of our IGRF candidates; the amount of assimilated data has been doubled and the considered time window has been extended from [2000.5, 2019.74] to [2000.5, 2020.33].}, language = {en} } @article{BachocBlanchardNeuvial2018, author = {Bachoc, Francois and Blanchard, Gilles and Neuvial, Pierre}, title = {On the post selection inference constant under restricted isometry properties}, series = {Electronic journal of statistics}, volume = {12}, journal = {Electronic journal of statistics}, number = {2}, publisher = {Institute of Mathematical Statistics}, address = {Cleveland}, issn = {1935-7524}, doi = {10.1214/18-EJS1490}, pages = {3736 -- 3757}, year = {2018}, abstract = {Uniformly valid confidence intervals post model selection in regression can be constructed based on Post-Selection Inference (PoSI) constants. PoSI constants are minimal for orthogonal design matrices, and can be upper bounded in function of the sparsity of the set of models under consideration, for generic design matrices. In order to improve on these generic sparse upper bounds, we consider design matrices satisfying a Restricted Isometry Property (RIP) condition. We provide a new upper bound on the PoSI constant in this setting. This upper bound is an explicit function of the RIP constant of the design matrix, thereby giving an interpolation between the orthogonal setting and the generic sparse setting. We show that this upper bound is asymptotically optimal in many settings by constructing a matching lower bound.}, language = {en} } @article{AzzaliPaycha2020, author = {Azzali, Sara and Paycha, Sylvie}, title = {Spectral zeta-invariants lifted to coverings}, series = {Transactions of the American Mathematical Society}, volume = {373}, journal = {Transactions of the American Mathematical Society}, number = {9}, publisher = {American Mathematical Society}, address = {Providence, RI}, issn = {0002-9947}, doi = {10.1090/tran/8067}, pages = {6185 -- 6226}, year = {2020}, abstract = {The canonical trace and the Wodzicki residue on classical pseudo-differential operators on a closed manifold are characterised by their locality and shown to be preserved under lifting to the universal covering as a result of their local feature. As a consequence, we lift a class of spectral zeta-invariants using lifted defect formulae which express discrepancies of zeta-regularised traces in terms of Wodzicki residues. We derive Atiyah's L-2-index theorem as an instance of the Z(2)-graded generalisation of the canonical lift of spectral zeta-invariants and we show that certain lifted spectral zeta-invariants for geometric operators are integrals of Pontryagin and Chern forms.}, language = {en} } @article{AyanbayevKlebanovLieetal.2021, author = {Ayanbayev, Birzhan and Klebanov, Ilja and Lie, Han Cheng and Sullivan, Tim J.}, title = {Gamma-convergence of Onsager-Machlup functionals}, series = {Inverse problems : an international journal of inverse problems, inverse methods and computerised inversion of data}, volume = {38}, journal = {Inverse problems : an international journal of inverse problems, inverse methods and computerised inversion of data}, number = {2}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {0266-5611}, doi = {10.1088/1361-6420/ac3f82}, pages = {35}, year = {2021}, abstract = {We derive Onsager-Machlup functionals for countable product measures on weighted l(p) subspaces of the sequence space R-N. Each measure in the product is a shifted and scaled copy of a reference probability measure on R that admits a sufficiently regular Lebesgue density. We study the equicoercivity and Gamma-convergence of sequences of Onsager-Machlup functionals associated to convergent sequences of measures within this class. We use these results to establish analogous results for probability measures on separable Banach or Hilbert spaces, including Gaussian, Cauchy, and Besov measures with summability parameter 1 <= p <= 2. Together with part I of this paper, this provides a basis for analysis of the convergence of maximum a posteriori estimators in Bayesian inverse problems and most likely paths in transition path theory.}, language = {en} } @article{AyanbayevKlebanovLietal.2021, author = {Ayanbayev, Birzhan and Klebanov, Ilja and Li, Han Cheng and Sullivan, Tim J.}, title = {Gamma-convergence of Onsager-Machlup functionals}, series = {Inverse problems : an international journal of inverse problems, inverse methods and computerised inversion of data}, volume = {38}, journal = {Inverse problems : an international journal of inverse problems, inverse methods and computerised inversion of data}, number = {2}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {0266-5611}, doi = {10.1088/1361-6420/ac3f81}, pages = {32}, year = {2021}, abstract = {The Bayesian solution to a statistical inverse problem can be summarised by a mode of the posterior distribution, i.e. a maximum a posteriori (MAP) estimator. The MAP estimator essentially coincides with the (regularised) variational solution to the inverse problem, seen as minimisation of the Onsager-Machlup (OM) functional of the posterior measure. An open problem in the stability analysis of inverse problems is to establish a relationship between the convergence properties of solutions obtained by the variational approach and by the Bayesian approach. To address this problem, we propose a general convergence theory for modes that is based on the Gamma-convergence of OM functionals, and apply this theory to Bayesian inverse problems with Gaussian and edge-preserving Besov priors. Part II of this paper considers more general prior distributions.}, language = {en} } @inproceedings{AudinDucourtiouxOuedraogoetal.2017, author = {Audin, Mich{\`e}le and Ducourtioux, Catherine and Ou{\´e}draogo, Fran{\c{c}}oise and Schulz, Ren{\´e} and Delgado, Julio and Ruzhansky, Michael and Lebeau, Gilles}, title = {Integral Fourier operators}, editor = {Paycha, Sylvie}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-413-5}, issn = {2199-4951}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-402657}, pages = {xxi, 229}, year = {2017}, abstract = {This volume of contributions based on lectures delivered at a school on Fourier Integral Operators held in Ouagadougou, Burkina Faso, 14-26 September 2015, provides an introduction to Fourier Integral Operators (FIO) for a readership of Master and PhD students as well as any interested layperson. Considering the wide spectrum of their applications and the richness of the mathematical tools they involve, FIOs lie the cross-road of many a field. This volume offers the necessary background, whether analytic or geometric, to get acquainted with FIOs, complemented by more advanced material presenting various aspects of active research in that area.}, language = {en} } @misc{AscherChinReich1994, author = {Ascher, Uri M. and Chin, Hongsheng and Reich, Sebastian}, title = {Stabilization of DAEs and invariant manifolds}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-15625}, year = {1994}, abstract = {Many methods have been proposed for the stabilization of higher index differential-algebraic equations (DAEs). Such methods often involve constraint differentiation and problem stabilization, thus obtaining a stabilized index reduction. A popular method is Baumgarte stabilization, but the choice of parameters to make it robust is unclear in practice. Here we explain why the Baumgarte method may run into trouble. We then show how to improve it. We further develop a unifying theory for stabilization methods which includes many of the various techniques proposed in the literature. Our approach is to (i) consider stabilization of ODEs with invariants, (ii) discretize the stabilizing term in a simple way, generally different from the ODE discretization, and (iii) use orthogonal projections whenever possible. The best methods thus obtained are related to methods of coordinate projection. We discuss them and make concrete algorithmic suggestions.}, language = {en} } @misc{AscherChinPetzoldetal.1994, author = {Ascher, Uri M. and Chin, Hongsheng and Petzold, Linda R. and Reich, Sebastian}, title = {Stabilization of constrained mechanical systems with DAEs and invariant manifolds}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-15698}, year = {1994}, abstract = {Many methods have been proposed for the simulation of constrained mechanical systems. The most obvious of these have mild instabilities and drift problems. Consequently, stabilization techniques have been proposed A popular stabilization method is Baumgarte's technique, but the choice of parameters to make it robust has been unclear in practice. Some of the simulation methods that have been proposed and used in computations are reviewed here, from a stability point of view. This involves concepts of differential-algebraic equation (DAE) and ordinary differential equation (ODE) invariants. An explanation of the difficulties that may be encountered using Baumgarte's method is given, and a discussion of why a further quest for better parameter values for this method will always remain frustrating is presented. It is then shown how Baumgarte's method can be improved. An efficient stabilization technique is proposed, which may employ explicit ODE solvers in case of nonstiff or highly oscillatory problems and which relates to coordinate projection methods. Examples of a two-link planar robotic arm and a squeezing mechanism illustrate the effectiveness of this new stabilization method.}, 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{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{AndjelkovicSimevskiChenetal.2022, author = {Andjelkovic, Marko and Simevski, Aleksandar and Chen, Junchao and Schrape, Oliver and Stamenkovic, Zoran and Krstić, Miloš and Ilic, Stefan and Ristic, Goran and Jaksic, Aleksandar and Vasovic, Nikola and Duane, Russell and Palma, Alberto J. and Lallena, Antonio M. and Carvajal, Miguel A.}, title = {A design concept for radiation hardened RADFET readout system for space applications}, series = {Microprocessors and microsystems}, volume = {90}, journal = {Microprocessors and microsystems}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0141-9331}, doi = {10.1016/j.micpro.2022.104486}, pages = {18}, year = {2022}, abstract = {Instruments for measuring the absorbed dose and dose rate under radiation exposure, known as radiation dosimeters, are indispensable in space missions. They are composed of radiation sensors that generate current or voltage response when exposed to ionizing radiation, and processing electronics for computing the absorbed dose and dose rate. Among a wide range of existing radiation sensors, the Radiation Sensitive Field Effect Transistors (RADFETs) have unique advantages for absorbed dose measurement, and a proven record of successful exploitation in space missions. It has been shown that the RADFETs may be also used for the dose rate monitoring. In that regard, we propose a unique design concept that supports the simultaneous operation of a single RADFET as absorbed dose and dose rate monitor. This enables to reduce the cost of implementation, since the need for other types of radiation sensors can be minimized or eliminated. For processing the RADFET's response we propose a readout system composed of analog signal conditioner (ASC) and a self-adaptive multiprocessing system-on-chip (MPSoC). The soft error rate of MPSoC is monitored in real time with embedded sensors, allowing the autonomous switching between three operating modes (high-performance, de-stress and fault-tolerant), according to the application requirements and radiation conditions.}, 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} } @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} } @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} } @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{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} } @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} } @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} } @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} } @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} } @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} } @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{OPUS4-41720, title = {Mathematik mit digitalen Medien - konkret}, series = {Lernen, Lehren und Forschen mit digitalen Medien in der Primarstufe ; 4}, journal = {Lernen, Lehren und Forschen mit digitalen Medien in der Primarstufe ; 4}, editor = {Ladel, Silke and Kortenkamp, Ulrich and Etzold, Heiko}, publisher = {WTM-Verlag}, address = {M{\"u}nster}, isbn = {978-3-95987-078-8}, publisher = {Universit{\"a}t Potsdam}, year = {2018}, abstract = {Neue Medien" war {\"u}ber viele Jahre hinweg das Codewort f{\"u}r Computer, die den Einzug in den Schulunterricht schaffen sollten - wenn es nach den Bef{\"u}rwortern ging. Die Widerst{\"a}nde, gerade in der Grundschule, waren groß und vielf{\"a}ltig. Es ist verst{\"a}ndlich, dass kurz nach der spielerischen Heranf{\"u}hrung an Bildung im Kindergarten, in einer Zeit, in der die Sch{\"u}lerinnen und Sch{\"u}ler auch das soziale Miteinander ein{\"u}ben m{\"u}ssen und auch fein- und grobmotorische F{\"a}higkeiten erwerben sollen, das vereinzelnde Sitzen vor einem Bildschirm nicht zu den obersten Priorit{\"a}ten geh{\"o}rt - und auch unserer Meinung nach nicht geh{\"o}ren sollte. In den letzten Jahren hat sich der Begriff der neuen Medien aber ver{\"a}ndert, und das, was bisher damit verbunden wurde, ist mit der „Digitalisierung" nicht nur des Schulunterrichts, sondern des ganzen Lebens, zu einem Dreh- und Angelpunkt der Bildung geworden. Statt klobigen Computern mit Bildschirmen, die das Miteinander schon {\"u}ber die Ausstattung der Computerr{\"a}ume in die falsche Bahn lenken, haben mobile Ger{\"a}te in der Hand der Sch{\"u}lerinnen und Sch{\"u}ler {\"u}bernommen. Diese k{\"o}nnen nun gemeinsam an einem Ger{\"a}t arbeiten, sie k{\"o}nnen direkt mit den Bildschirminhalten interagieren, sie k{\"o}nnen die Kameras, Mikrophone und Sensoren nutzen, um authentische Daten zu erfassen und zu verarbeiten, sie k{\"o}nnen auch außerhalb des Klassenraums oder der Schule damit arbeiten und haben inzwischen fast jederzeit das ganze Wissen des Internets mit dabei. Schwerpunkt dieses Bandes ist daher der Umgang mit Tablets und den darauf laufenden „Apps" im Mathematikunterricht. In f{\"u}nf Beitr{\"a}gen werden konkrete Unterrichtsvorschl{\"a}ge gemacht, die als Blaupausen f{\"u}r App-gest{\"u}tzten Unterricht dienen k{\"o}nnen. Erg{\"a}nzt wird dieser Band durch einen allgemeinen Leitfaden zur Beurteilung von Apps f{\"u}r den Mathematikunterricht samt Beispielen.}, language = {de} } @inproceedings{OPUS4-41526, title = {Beitr{\"a}ge zum Mathematikunterricht 2017}, editor = {Kortenkamp, Ulrich and Kuzle, Ana}, publisher = {WTM-Verlag}, address = {M{\"u}nster}, isbn = {978-3-95987-072-6}, year = {2018}, language = {de} } @book{OPUS4-43561, title = {Implementation research on problem solving in school settings}, series = {Ars inveniendi et dejudicandi ; 13}, journal = {Ars inveniendi et dejudicandi ; 13}, editor = {Kuzle, Ana and Rott, Benjamin and Gebel, Inga}, publisher = {WTM-Verlag}, address = {M{\"u}nster}, isbn = {978-3-95987-116-7}, pages = {IV, 220}, year = {2019}, language = {en} }