TY - JOUR A1 - Rodríguez Zuluaga, Juan A1 - Stolle, Claudia A1 - Yamazaki, Yosuke A1 - Xiong, Chao A1 - England, Scott L. T1 - A synoptic-scale wavelike structure in the nighttime equatorial ionization anomaly JF - Earth and Space Science : ESS N2 - Both ground- and satellite-based airglow imaging have significantly contributed to understanding the low-latitude ionosphere, especially the morphology and dynamics of the equatorial ionization anomaly (EIA). The NASA Global-scale Observations of the Limb and Disk (GOLD) mission focuses on far-ultraviolet airglow images from a geostationary orbit at 47.5 degrees W. This region is of particular interest at low magnetic latitudes because of the high magnetic declination (i.e., about -20 degrees) and proximity of the South Atlantic magnetic anomaly. In this study, we characterize an exciting feature of the nighttime EIA using GOLD observations from October 5, 2018 to June 30, 2020. It consists of a wavelike structure of a few thousand kilometers seen as poleward and equatorward displacements of the EIA-crests. Initial analyses show that the synoptic-scale structure is symmetric about the dip equator and appears nearly stationary with time over the night. In quasi-dipole coordinates, maxima poleward displacements of the EIA-crests are seen at about +/- 12 degrees latitude and around 20 and 60 degrees longitude (i.e., in geographic longitude at the dip equator, about 53 degrees W and 14 degrees W). The wavelike structure presents typical zonal wavelengths of about 6.7 x 10(3) km and 3.3 x 10(3) km. The structure's occurrence and wavelength are highly variable on a day-to-day basis with no apparent dependence on geomagnetic activity. In addition, a cluster or quasi-periodic wave train of equatorial plasma depletions (EPDs) is often detected within the synoptic-scale structure. We further outline the difference in observing these EPDs from FUV images and in situ measurements during a GOLD and Swarm mission conjunction. KW - equatorial ionization anomaly KW - equatorial ionosphere KW - equatorial plasma bubbles KW - wave structure KW - forcing from below Y1 - 2021 U6 - https://doi.org/10.1029/2020EA001529 SN - 2333-5084 VL - 8 IS - 2 PB - American Geophysical Union CY - Malden, Mass. ER - TY - JOUR A1 - Staniforth, Andrew A1 - Wood, Nigel A1 - Reich, Sebastian T1 - A time-staggered semi-Lagrangian discretization of the rotating shallow-water equations JF - Quarterly journal of the Royal Meteorological Society N2 - A time-staggered semi-Lagrangian discretization of the rotating shallow-water equations is proposed and analysed. Application of regularization to the geopotential field used in the momentum equations leads to an unconditionally stable scheme. The analysis, together with a fully nonlinear example application, suggests that this approach is a promising, efficient, and accurate alternative to traditional schemes. KW - regularization KW - temporal discretization Y1 - 2006 U6 - https://doi.org/10.1256/qj.06.30 SN - 0035-9009 VL - 132 IS - 621C SP - 3107 EP - 3116 PB - Wiley CY - Weinheim ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - A two-dimensional representation of four-dimensional graviational waves Y1 - 1998 ER - TY - JOUR A1 - Klotzek, Benno T1 - About newer results to the discontinuous motion groups of different degrees with respect to different geometries Y1 - 1999 ER - TY - JOUR A1 - Klotzek, Benno T1 - About newer results to the discontinuous motion groups of different degrees with respect to different geometries Y1 - 1999 ER - TY - JOUR A1 - Klotzek, Benno T1 - About the geometry of normed space Y1 - 1999 ER - TY - JOUR A1 - Hermann, Andreas A1 - Humbert, Emmanuel T1 - About the mass of certain second order elliptic operators JF - Advances in mathematics N2 - Let (M, g) be a closed Riemannian manifold of dimension n >= 3 and let f is an element of C-infinity (M), such that the operator P-f := Delta g + f is positive. If g is flat near some point p and f vanishes around p, we can define the mass of P1 as the constant term in the expansion of the Green function of P-f at p. In this paper, we establish many results on the mass of such operators. In particular, if f := n-2/n(n-1)s(g), i.e. if P-f is the Yamabe operator, we show the following result: assume that there exists a closed simply connected non-spin manifold M such that the mass is non-negative for every metric g as above on M, then the mass is non-negative for every such metric on every closed manifold of the same dimension as M. (C) 2016 Elsevier Inc. All rights reserved. KW - Yamabe operator KW - Surgery KW - Positive mass theorem Y1 - 2016 U6 - https://doi.org/10.1016/j.aim.2016.03.008 SN - 0001-8708 SN - 1090-2082 VL - 294 SP - 596 EP - 633 PB - Elsevier CY - San Diego ER - TY - JOUR A1 - Edlund, Helena A1 - Grisic, Ana-Marija A1 - Steenholdt, Casper A1 - Ainsworth, Mark Andrew A1 - Brynskov, Torn A1 - Huisinga, Wilhelm A1 - Kloft, Charlotte T1 - Absence of Relationship Between Crohn's Disease Activity Index or C-Reactive Protein and Infliximab Exposure Calls for Objective Crohn's Disease Activity Measures for the Evaluation of Treatment Effects at Treatment Failure JF - Therapeutic drug monitoring : official journal of the International Association of Therapeutic Drug Monitoring and Clinical Toxicology N2 - Background: Circulating infliximab (IFX) concentrations correlate with clinical outcomes, forming the basis of the IFX concentration monitoring in patients with Crohn's disease. This study aims to investigate and refine the exposure-response relationship by linking the disease activity markers "Crohn's disease activity index" (CDAI) and C-reactive protein (CRP) to IFX exposure. In addition, we aim to explore the correlations between different disease markers and exposure metrics. Methods: Data from 47 Crohn's disease patients of a randomized controlled trial were analyzed post hoc. All patients had secondary treatment failure at inclusion and had received intensified IFX of 5 mg/kg every 4 weeks for up to 20 weeks. Graphical analyses were performed to explore exposure-response relationships. Metrics of exposure included area under the concentration-time curve (AUC) and trough concentrations (Cmin). Disease activity was measured by CDAI and CRP values, their change from baseline/last visit, and response/remission outcomes at week 12. Results: Although trends toward lower Cmin and lower AUC in nonresponders were observed, neither CDAI nor CRP showed consistent trends of lower disease activity with higher IFX exposure across the 30 evaluated relationships. As can be expected, Cmin and AUC were strongly correlated with each other. Contrarily, the disease activity markers were only weakly correlated with each other. Conclusions: No significant relationship between disease activity, as evaluated by CDAI or CRP, and IFX exposure was identified. AUC did not add benefit compared with Cmin. These findings support the continued use of Cmin and call for stringent objective disease activity (bio-)markers (eg, endoscopy) to form the basis of personalized IFX therapy for Crohn's disease patients with IFX treatment failure. Y1 - 2019 U6 - https://doi.org/10.1097/FTD.0000000000000590 SN - 0163-4356 SN - 1536-3694 VL - 41 IS - 2 SP - 235 EP - 242 PB - Lippincott Williams & Wilkins CY - Philadelphia ER - TY - BOOK A1 - Baumgärtel, Hellmut T1 - Actions of finite abelian groups on abelian C*-algebras Z: Second cohomology and description by C*-extensions F ) Z T3 - Preprint / SFB 288, Differentialgeometrie und Quantenphysik Y1 - 1999 VL - 383 CY - Berlin ER - TY - JOUR A1 - Carpentier, Alexandra A1 - Klopp, Olga A1 - Löffler, Matthias A1 - Nickl, Richard T1 - Adaptive confidence sets for matrix completion JF - Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability N2 - In the present paper, we study the problem of existence of honest and adaptive confidence sets for matrix completion. We consider two statistical models: the trace regression model and the Bernoulli model. In the trace regression model, we show that honest confidence sets that adapt to the unknown rank of the matrix exist even when the error variance is unknown. Contrary to this, we prove that in the Bernoulli model, honest and adaptive confidence sets exist only when the error variance is known a priori. In the course of our proofs, we obtain bounds for the minimax rates of certain composite hypothesis testing problems arising in low rank inference. KW - adaptivity KW - confidence sets KW - low rank recovery KW - matrix completion KW - minimax hypothesis testing KW - unknown variance Y1 - 2018 U6 - https://doi.org/10.3150/17-BEJ933 SN - 1350-7265 SN - 1573-9759 VL - 24 IS - 4A SP - 2429 EP - 2460 PB - International Statistical Institute CY - Voorburg ER - TY - BOOK A1 - Junker, W. A1 - Schrohe, Elmar T1 - Adiabatic vacuum states on general spacetime manifolds : definition, construction and physical properties T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2001 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - THES A1 - Waltz, Christine T1 - Adjungierte Polynomideale und duale Typen auf Banachräumen und ihre Anwendung Y1 - 1994 ER - TY - JOUR A1 - Gunther, U. A1 - Zhuk, Alexandre A1 - Bezerra, Valdir B. A1 - Romero, C. T1 - AdS and stabilized extra dimensions in multi-dimensional gravitational models with nonlinear scalar curvature terms R-1 and R-4 N2 - We study multi-dimensional gravitational models with scalar curvature nonlinearities of types R-1 and R-4. It is assumed that the corresponding higher dimensional spacetime manifolds undergo a spontaneous compactification to manifolds with a warped product structure. Special attention has been paid to the stability of the extra-dimensional factor spaces. It is shown that for certain parameter regions the systems allow for a freezing stabilization of these spaces. In particular, we find for the R-1 model that configurations with stabilized extra dimensions do not provide a late-time Acceleration (they are AdS), whereas the solution branch which allows. for accelerated expansion (the dS branch) is incompatible with stabilized factor spaces. In the case of the R-4 model, we obtain that the stability region in parameter space depends on the total dimension D = dim(M) of the higher dimensional spacetime M. Tor D > 8 the stability region consists of a single (absolutely stable) sector which is shielded from a conformal singularity (and an antigravity sector beyond it) by a potential barrier of infinite height and width. This sector is smoothly connected with the stability region of a curvature-linear model. For D < 8 an additional (metastable) sector exists Which is separated from the conformal singularity by a potential barrier of finite height and width so that systems in this sector are prone to collapse into the conformal singularity. This second sector is not smoothly connected with the first (absolutely stable) one. Several limiting cases and the possibility of inflation are discussed for the R-4 model Y1 - 2005 SN - 0264-9381 ER - TY - BOOK A1 - Schulze, Bert-Wolfgang A1 - Demuth, Michael A1 - Albeverio, Sergio A1 - Schrohe, Elmar T1 - Advances in Partial differential equations Y1 - 2001 PB - Birkhäuser CY - Basel ER - TY - JOUR A1 - Böckmann, Christine A1 - Wandinger, Ulla A1 - Ansmann, Albert A1 - Bösenberg, Jens A1 - Amiridis, Vassilis A1 - Boselli, Antonella A1 - Delaval, Arnaud A1 - De Tomasi, Ferdinando de A1 - Frioud, Max A1 - Grigorov, Ivan Videnov A1 - Hagard, Arne A1 - Horvat, Matej A1 - Iarlori, Marco A1 - Komguem, Leonce A1 - Kreipl, Stephan A1 - Larchevque, Gilles A1 - Matthias, Volker A1 - Papayannis, Alexandros A1 - Pappalardo, GGelsomina A1 - Rocadenbosch, Francesc A1 - Rodrigues, Jose António A1 - Schneider, Johannes A1 - Shcherbakov, Valery A1 - Wiegner, Matthias T1 - Aerosol lidar intercomparison in the framework of the EARLINET project : 2. Aerosol backscatter algorithms N2 - An intercomparison of aerosol backscatter lidar algorithms was performed in 2001 within the framework of the European Aerosol Research Lidar Network to Establish an Aerosol Climatology (EARLINET). The objective of this research was to test the correctness of the algorithms and the influence of the lidar ratio used by the various lidar teams involved in the EARLINET for calculation of backscatter-coefficient profiles from the lidar signals. The exercise consisted of processing synthetic lidar signals of various degrees of difficulty. One of these profiles contained height- dependent lidar ratios to test the vertical influence of those profiles on the various retrieval algorithms. Furthermore, a realistic incomplete overlap of laser beam and receiver field of view was introduced to remind the teams to take great care in the nearest range to the lidar. The intercomparison was performed in three stages with increasing knowledge on the input parameters. First, only the lidar signals were distributed; this is the most realistic stage. Afterward the lidar ratio profiles and the reference values at calibration height were provided. The unknown height- dependent lidar ratio had the largest influence on the retrieval, whereas the unknown reference value was of minor importance. These results show the necessity of making additional independent measurements, which can provide us with a suitable approximation of the lidar ratio. The final stage proves in general, that the data evaluation schemes of the different groups of lidar systems work well. (C) 2004 Optical Society of America Y1 - 2004 SN - 0003-6935 ER - TY - JOUR A1 - Garbuno-Inigo, Alfredo A1 - Nüsken, Nikolas A1 - Reich, Sebastian T1 - Affine invariant interacting Langevin dynamics for Bayesian inference JF - SIAM journal on applied dynamical systems N2 - We propose a computational method (with acronym ALDI) for sampling from a given target distribution based on first-order (overdamped) Langevin dynamics which satisfies the property of affine invariance. The central idea of ALDI is to run an ensemble of particles with their empirical covariance serving as a preconditioner for their underlying Langevin dynamics. ALDI does not require taking the inverse or square root of the empirical covariance matrix, which enables application to high-dimensional sampling problems. The theoretical properties of ALDI are studied in terms of nondegeneracy and ergodicity. Furthermore, we study its connections to diffusion on Riemannian manifolds and Wasserstein gradient flows. Bayesian inference serves as a main application area for ALDI. In case of a forward problem with additive Gaussian measurement errors, ALDI allows for a gradient-free approximation in the spirit of the ensemble Kalman filter. A computational comparison between gradient-free and gradient-based ALDI is provided for a PDE constrained Bayesian inverse problem. KW - Langevin dynamics KW - interacting particle systems KW - Bayesian inference KW - gradient flow KW - multiplicative noise KW - affine invariance KW - gradient-free Y1 - 2020 U6 - https://doi.org/10.1137/19M1304891 SN - 1536-0040 VL - 19 IS - 3 SP - 1633 EP - 1658 PB - Society for Industrial and Applied Mathematics CY - Philadelphia ER - TY - JOUR A1 - Klein, Markus A1 - Rosenberger, Elke T1 - Agmon estimates for the difference of exact and approximate Dirichlet eigenfunctions for difference operators JF - Asymptotic analysis N2 - We analyze a general class of difference operators H-epsilon = T-epsilon + V-epsilon on l(2)(((epsilon)Z)(d)), where V-epsilon is a multi-well potential and epsilon is a small parameter. We construct approximate eigenfunctions in neighbourhoods of the different wells and give weighted l(2)-estimates for the difference of these and the exact eigenfunctions of the associated Dirichlet-operators. Y1 - 2016 U6 - https://doi.org/10.3233/ASY-151343 SN - 0921-7134 SN - 1875-8576 VL - 97 SP - 61 EP - 89 PB - IOS Press CY - Amsterdam ER - TY - INPR A1 - Klein, Markus A1 - Léonard, Christian A1 - Rosenberger, Elke T1 - Agmon-type estimates for a class of jump processes N2 - In the limit we analyze the generators of families of reversible jump processes in the n-dimensional space associated with a class of symmetric non-local Dirichlet forms and show exponential decay of the eigenfunctions. The exponential rate function is a Finsler distance, given as solution of certain eikonal equation. Fine results are sensitive to the rate functions being twice differentiable or just Lipschitz. Our estimates are similar to the semiclassical Agmon estimates for differential operators of second order. They generalize and strengthen previous results on the lattice. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1 (2012) 6 KW - finsler distance KW - decay of eigenfunctions KW - jump process KW - Dirichlet form Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-56995 ER - TY - JOUR A1 - Klein, Markus A1 - Leonard, Christian A1 - Rosenberger, Elke T1 - Agmon-type estimates for a class of jump processes JF - Mathematische Nachrichten N2 - In the limit 0 we analyse the generators H of families of reversible jump processes in Rd associated with a class of symmetric non-local Dirichlet-forms and show exponential decay of the eigenfunctions. The exponential rate function is a Finsler distance, given as solution of a certain eikonal equation. Fine results are sensitive to the rate function being C2 or just Lipschitz. Our estimates are analogous to the semiclassical Agmon estimates for differential operators of second order. They generalize and strengthen previous results on the lattice Zd. Although our final interest is in the (sub)stochastic jump process, technically this is a pure analysis paper, inspired by PDE techniques. KW - Decay of eigenfunctions KW - semiclassical Agmon estimate KW - Finsler distance KW - jump process KW - Dirichlet-form Y1 - 2014 U6 - https://doi.org/10.1002/mana.201200324 SN - 0025-584X SN - 1522-2616 VL - 287 IS - 17-18 SP - 2021 EP - 2039 PB - Wiley-VCH CY - Weinheim ER - TY - BOOK A1 - Denecke, Klaus-Dieter T1 - Algebra und Diskrete Mathematik für Informatiker N2 - Algebra und Diskrete Mathematik gehören zu den wesentlichen Grundlagen der Informatik. Sie sind unverzichtbare Werkzeuge eines jeden Informatikers und spielen daher auch im Studium eine zentrale Rolle. Das Lehrbuch vermittelt anschaulich und leicht nachvollziehbar die wichtigsten algebraischen Grundlagen der Informatik bis hin zur Gleichungstheorie der Universellen Algebra. Zahlreiche Übungsaufgaben und ihre Lösungen helfen dem Leser, den Stoff zu verstehen Y1 - 2003 PB - Teubner CY - Stuttgart u.a. ER - TY - JOUR A1 - Guo, Li A1 - Paycha, Sylvie A1 - Zhang, Bin T1 - Algebraic Birkhoff factorization and the Euler–Maclaurin formula on cones JF - Duke mathematical journal N2 - We equip the space of lattice cones with a coproduct which makes it a cograded, coaugmented, connnected coalgebra. The exponential generating sum and exponential generating integral on lattice cones can be viewed as linear maps on this space with values in the space of meromorphic germs with linear poles at zero. We investigate the subdivision properties-reminiscent of the inclusion-exclusion principle for the cardinal on finite sets-of such linear maps and show that these properties are compatible with the convolution quotient of maps on the coalgebra. Implementing the algebraic Birkhoff factorization procedure on the linear maps under consideration, we factorize the exponential generating sum as a convolution quotient of two maps, with each of the maps in the factorization satisfying a subdivision property. A direct computation shows that the polar decomposition of the exponential generating sum on a smooth lattice cone yields an Euler-Maclaurin formula. The compatibility with subdivisions of the convolution quotient arising in the algebraic Birkhoff factorization then yields the Euler-Maclaurin formula for any lattice cone. This provides a simple formula for the interpolating factor by means of a projection formula. Y1 - 2017 U6 - https://doi.org/10.1215/00127094-3715303 SN - 0012-7094 SN - 1547-7398 VL - 166 IS - 3 SP - 537 EP - 571 PB - Duke Univ. Press CY - Durham ER - TY - JOUR A1 - Gräter, Joachim T1 - Algebraic elements in division rings Y1 - 1996 ER - TY - THES A1 - Sareeto, Apatsara T1 - Algebraic properties of a subsemigroup of the symmetric inverse semigroup Y1 - 2024 ER - TY - THES A1 - Lledó, Fernando T1 - Algebraic properties of massless free nets Y1 - 1998 CY - Potsdam ER - TY - THES A1 - Sarasit, Napaporn T1 - Algebraic properties of sets of terms Y1 - 2011 CY - Potsdam ER - TY - BOOK A1 - Denecke, Klaus-Dieter A1 - Todorov, Kalco T1 - Algebraische Grundlagen der Arithmetik T3 - Berliner Studienreihe zur Mathematik Y1 - 1994 VL - 4 PB - Heldermann CY - Berlin ER - TY - THES A1 - Srithus, Ratana T1 - Algebras derived by hypersubstitutions Y1 - 2008 ER - TY - JOUR A1 - Chajada, I. A1 - Denecke, Klaus-Dieter A1 - Halas, R. T1 - Algebras induced by hypersubstitutions Y1 - 1999 ER - TY - JOUR A1 - Koppitz, Jörg T1 - All 2-solid varieties of semigroups Y1 - 2000 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Hounnon, Hippolyte T1 - All solid varieties of semirings Y1 - 2003 ER - TY - BOOK A1 - Denecke, Klaus-Dieter A1 - Todorov, Kalco T1 - Allgemeine Algebra und Anwendungen Y1 - 1996 PB - Shaker CY - Aachen ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Allgemeine Relativitätstheorie Y1 - 2000 ER - TY - JOUR A1 - Junek, Heinz A1 - Braunß, Hans-Andreas A1 - Botelho, Geraldo T1 - Almost p-summing polynomials and multilinear mappings N2 - For several applications it is very useful to classify the linear or non-linear mappings by their summability properties. Absolutely summing operators and polynomials are prominent and classical examples of such setting. Here we are interested in the larger class of almost summing polynomials and we investigate their connections to other related notions of summability. Y1 - 2001 ER - TY - BOOK A1 - Schulze, Bert-Wolfgang T1 - An algebra of boundary value problems not requiring Shapiro-Lopatinskij conditions T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 1999 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - THES A1 - Dorschfeldt, Christoph T1 - An algebra of mellin pseudo-differential operators near corner singularities Y1 - 1995 CY - Potsdam ER - TY - BOOK A1 - Maniccia, L. A1 - Schulze, Bert-Wolfgang T1 - An algebra of meromorphic corner symbols T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2002 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Clavier, Pierre J. A1 - Guo, Li A1 - Paycha, Sylvie A1 - Zhang, Bin T1 - An algebraic formulation of the locality principle in renormalisation JF - European Journal of Mathematics N2 - We study the mathematical structure underlying the concept of locality which lies at the heart of classical and quantum field theory, and develop a machinery used to preserve locality during the renormalisation procedure. Viewing renormalisation in the framework of Connes and Kreimer as the algebraic Birkhoff factorisation of characters on a Hopf algebra with values in a Rota-Baxter algebra, we build locality variants of these algebraic structures, leading to a locality variant of the algebraic Birkhoff factorisation. This provides an algebraic formulation of the conservation of locality while renormalising. As an application in the context of the Euler-Maclaurin formula on lattice cones, we renormalise the exponential generating function which sums over the lattice points in a lattice cone. As a consequence, for a suitable multivariate regularisation, renormalisation from the algebraic Birkhoff factorisation amounts to composition by a projection onto holomorphic multivariate germs. KW - Locality KW - Renormalisation KW - Algebraic Birkhoff factorisation KW - Partial algebra KW - Hopf algebra KW - Rota-Baxter algebra KW - Multivariate meromorphic functions KW - Lattice cones Y1 - 2019 U6 - https://doi.org/10.1007/s40879-018-0255-8 SN - 2199-675X SN - 2199-6768 VL - 5 IS - 2 SP - 356 EP - 394 PB - Springer CY - Cham ER - TY - BOOK A1 - Schmidt, Hans-Jürgen T1 - An alternate Hamiltonian formulation of fourth-order theories Y1 - 1995 CY - Potsdam ER - TY - BOOK A1 - Schmidt, Hans-Jürgen T1 - An alternate Hamiltonian formulation of fourth-order theories T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1994 VL - 1994, 12 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Baumgärtel, Hellmut T1 - An Application of the DR-Duality Theory for Compact Groups to Endomorphism Categories of C*-Algebras with Nontrivial Center Y1 - 2001 ER - TY - BOOK A1 - Kytmanov, Alexander M. A1 - Myslivets, Simona A1 - Tarkhanov, Nikolai Nikolaevich T1 - An Asymptotic expansion of the Bochner-Martinelli integral T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgrupe Partielle Differentialgleichun Y1 - 2001 SN - 1437-339X PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Baake, Ellen A1 - Baake, Michael A1 - Bovier, Anton A1 - Klein, Markus T1 - An asymptotic maximum principle for essentially linear evolution models N2 - Recent work on mutation-selection models has revealed that, under specific assumptions on the fitness function and the mutation rates, asymptotic estimates for the leading eigenvalue of the mutation-reproduction matrix may be obtained through a low-dimensional maximum principle in the limit N --> infinity (where N, or N-d with d greater than or equal to 1, is proportional to the number of types). In order to extend this variational principle to a larger class of models, we consider here a family of reversible matrices of asymptotic dimension N-d and identify conditions under which the high-dimensional Rayleigh-Ritz variational problem may be reduced to a low-dimensional one that yields the leading eigenvalue up to an error term of order 1/N. For a large class of mutation-selection models, this implies estimates for the mean fitness, as well as a concentration result for the ancestral distribution of types Y1 - 2005 SN - 0303-6812 ER - TY - JOUR A1 - Mera, Azal Jaafar Musa A1 - Tarkhanov, Nikolai T1 - An elliptic equation of finite index in a domain JF - Boletin de la Sociedad Matemática Mexicana N2 - We give an example of first order elliptic equation for a complex-valued function in a plane domain which has a finite number of linearly independent solutions for any right-hand side. No boundary value conditions are thus required. KW - elliptic equation KW - Fredholm operator KW - index Y1 - 2022 U6 - https://doi.org/10.1007/s40590-022-00442-7 SN - 1405-213X SN - 2296-4495 VL - 28 IS - 2 PB - Springer International CY - New York [u.a.] ER - TY - JOUR A1 - Bergemann, Kay A1 - Reich, Sebastian T1 - An ensemble Kalman-Bucy filter for continuous data assimilation JF - Meteorologische Zeitschrift N2 - The ensemble Kalman filter has emerged as a promising filter algorithm for nonlinear differential equations subject to intermittent observations. In this paper, we extend the well-known Kalman-Bucy filter for linear differential equations subject to continous observations to the ensemble setting and nonlinear differential equations. The proposed filter is called the ensemble Kalman-Bucy filter and its performance is demonstrated for a simple mechanical model (Langevin dynamics) subject to incremental observations of its velocity. Y1 - 2012 U6 - https://doi.org/10.1127/0941-2948/2012/0307 SN - 0941-2948 VL - 21 IS - 3 SP - 213 EP - 219 PB - Schweizerbart CY - Stuttgart ER - TY - GEN A1 - Roelly, Sylvie A1 - Dai Pra, Paolo T1 - An existence result for infinite-dimensional Brownian diffusions with non- regular and non Markovian drift N2 - We prove in this paper an existence result for infinite-dimensional stationary interactive Brownian diffusions. The interaction is supposed to be small in the norm ||.||∞ but otherwise is very general, being possibly non-regular and non-Markovian. Our method consists in using the characterization of such diffusions as space-time Gibbs fields so that we construct them by space-time cluster expansions in the small coupling parameter. KW - infinite-dimensional Brownian diffusion KW - space-time Gibbs field KW - cluster expansion Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6684 ER - TY - JOUR A1 - Houdebert, Pierre A1 - Zass, Alexander T1 - An explicit Dobrushin uniqueness region for Gibbs point processes with repulsive interactions JF - Journal of applied probability / Applied Probability Trust N2 - We present a uniqueness result for Gibbs point processes with interactions that come from a non-negative pair potential; in particular, we provide an explicit uniqueness region in terms of activity z and inverse temperature beta. The technique used relies on applying to the continuous setting the classical Dobrushin criterion. We also present a comparison to the two other uniqueness methods of cluster expansion and disagreement percolation, which can also be applied for this type of interaction. KW - Gibbs point process KW - DLR equations KW - uniqueness KW - Dobrushin criterion; KW - cluster expansion KW - disagreement percolation Y1 - 2022 U6 - https://doi.org/10.1017/jpr.2021.70 SN - 0021-9002 SN - 1475-6072 VL - 59 IS - 2 SP - 541 EP - 555 PB - Cambridge Univ. Press CY - Cambridge ER - TY - JOUR A1 - Hanke, Timo T1 - An explicit example of a noncrossed product division algebra N2 - The paper presents an explicit example of a noncrossed product division algebra of index and exponent 8 over the field Q(s) (t). It is an iterated twisted function field in two variables D (x, sigma) (y, tau) over a quaternion division algebra D which is defined over the number field Q(root3, root-7). The automorphisms sigma and tau are computed by solving relative norm equations in extensions of number fields. The example is explicit in the sense that its structure constants are known. Moreover, it is pointed out that the same arguments also yield another example, this time over the field Q((s)) ((t)), given by an iterated twisted Laurent series ring D((x, sigma)) ((y, tau)) over the same quaternion division algebra D. (C) 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Y1 - 2004 SN - 0025-584X ER - TY - INPR A1 - Dereudre, David A1 - Mazzonetto, Sara A1 - Roelly, Sylvie T1 - An explicit representation of the transition densities of the skew Brownian motion with drift and two semipermeable barriers N2 - In this paper we obtain an explicit representation of the transition density of the one-dimensional skew Brownian motion with (a constant drift and) two semipermeable barriers. Moreover we propose a rejection method to simulate this density in an exact way. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015) 9 KW - skew Brownian motion KW - semipermeable barriers KW - distorted Brownian motion KW - local time KW - rejection sampling KW - exact simulation Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-80613 SN - 2193-6943 VL - 4 IS - 9 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Makhmudov, Olimdjan A1 - Tarkhanov, Nikolai Nikolaevich T1 - An extremal problem related to analytic continuation N2 - We show that the usual variational formulation of the problem of analytic continuation from an arc on the boundary of a plane domain does not lead to a relaxation of this overdetermined problem. To attain such a relaxation, we bound the domain of the functional, thus changing the Euler equations. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 2 (2013) 4 KW - Extremal problem KW - Euler equations KW - p-Laplace operator KW - mixed problems Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-63634 ER - TY - JOUR A1 - Keller, Matthias A1 - Pinchover, Yehuda A1 - Pogorzelski, Felix T1 - An improved discrete hardy inequality JF - The American mathematical monthly : an official publication of the Mathematical Association of America N2 - In this note, we prove an improvement of the classical discrete Hardy inequality. Our improved Hardy-type inequality holds with a weight w which is strictly greater than the classical Hardy weight w(H)(n) : 1/(2n)(2), where N. KW - Primary 26D15 Y1 - 2018 U6 - https://doi.org/10.1080/00029890.2018.1420995 SN - 0002-9890 SN - 1930-0972 VL - 125 IS - 4 SP - 347 EP - 350 PB - Taylor & Francis Group CY - Philadelphia ER - TY - INPR A1 - Fedchenko, Dmitry A1 - Tarkhanov, Nikolai Nikolaevich T1 - An index formula for Toeplitz operators N2 - We prove a Fedosov index formula for the index of Toeplitz operators connected with the Hardy space of solutions to an elliptic system of first order partial differential equations in a bounded domain of Euclidean space with infinitely differentiable boundary. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3(2014)12 KW - Toeplitz operators KW - Fredholm property KW - index Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-72499 SN - 2193-6943 VL - 3 IS - 12 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Fedchenko, Dmitri A1 - Tarkhanov, Nikolai Nikolaevich T1 - An index formula for Toeplitz operators JF - Complex variables and elliptic equations N2 - We prove a Fedosov index formula for the index of Toeplitz operators connected with the Hardy space of solutions to an elliptic system of first-order partial differential equations in a bounded domain in R-n with smooth boundary. KW - Toeplitz operators KW - Fredholm property KW - index KW - Primary: 47B35 KW - Secondary: 47L80 Y1 - 2015 U6 - https://doi.org/10.1080/17476933.2015.1050007 SN - 1747-6933 SN - 1747-6941 VL - 60 IS - 12 SP - 1764 EP - 1787 PB - Routledge, Taylor & Francis Group CY - Abingdon ER - TY - JOUR A1 - Bär, Christian A1 - Strohmaier, Alexander T1 - An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary JF - American Journal of Mathematics N2 - We show that the Dirac operator on a compact globally hyperbolic Lorentzian spacetime with spacelike Cauchy boundary is a Fredholm operator if appropriate boundary conditions are imposed. We prove that the index of this operator is given by the same expression as in the index formula of Atiyah-Patodi-Singer for Riemannian manifolds with boundary. The index is also shown to equal that of a certain operator constructed from the evolution operator and a spectral projection on the boundary. In case the metric is of product type near the boundary a Feynman parametrix is constructed. Y1 - 2019 U6 - https://doi.org/10.1353/ajm.2019.0037 SN - 0002-9327 SN - 1080-6377 VL - 141 IS - 5 SP - 1421 EP - 1455 PB - Johns Hopkins Univ. Press CY - Baltimore ER - TY - INPR A1 - Aizenberg, Lev A. A1 - Tarkhanov, Nikolai Nikolaevich T1 - An integral formula for the number of lattice points in a domain N2 - 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. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 3 KW - logarithmic residue KW - lattice point Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-70453 SN - 2193-6943 VL - 3 IS - 3 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Baumgärtel, Hellmut T1 - An inverse problem for superselection structures on C*-algebras with nontrivial center Y1 - 1999 ER - TY - THES A1 - Abed, Jamil T1 - An iterative approach to operators on manifolds with singularities T1 - Ein iterativer Zugang zu Operatoren auf Mannigfaltigkeiten mit Singularitäten N2 - 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. N2 - Wir führen einen neuen Zugang ein zu Elliptizität und Parametrices in Operatorenalgebren auf Mannigfaltigkeiten mit höheren Singularitäten, nur basierend auf allgemeinen axiomatischen Voraussetzungen über parameter-abhängige Operatoren in geeigneten Skalen von Räumen. Die Idee besteht darin, ein iteratives Verfahren zu modellieren mit neuen Generationen von parameter-abhängigen Operatortheorien, zusammen mit neuen Skalen von Räumen, die analoge Voraussetzungen erfüllen wie die ursprünglichen Objekte, jetzt auf dem entsprechenden höheren Niveau. Der „volle“ Kalkül besteht aus zwei separaten Theorien, eine nahe der Spitze der Ecke und eine andere am konischen Ausgang nach Unendlich. Allerdings, bezüglich des konischen Ausgangs nach Unendlich, bauen wir hier einen neuen konkreten Kalkül von kanten-entarteten Operatoren auf, der für höhere Singularitäten iteriert werden kann. KW - Pseudo-Differentialoperatoren KW - kanten- und ecken-entartete Symbole KW - Elliptizität KW - Parametrices KW - höhere Singularitäten KW - Pseudo-differential operators KW - edge- and corner-degenerate symbols KW - ellipticity KW - parametrices KW - higher singularities Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-44757 ER - TY - JOUR A1 - Carpentier, Alexandra A1 - Kim, Arlene K. H. T1 - An iterative hard thresholding estimator for low rank matrix recovery with explicit limiting distribution JF - Statistica Sinica N2 - We consider the problem of low rank matrix recovery in a stochastically noisy high-dimensional setting. We propose a new estimator for the low rank matrix, based on the iterative hard thresholding method, that is computationally efficient and simple. We prove that our estimator is optimal in terms of the Frobenius risk and in terms of the entry-wise risk uniformly over any change of orthonormal basis, allowing us to provide the limiting distribution of the estimator. When the design is Gaussian, we prove that the entry-wise bias of the limiting distribution of the estimator is small, which is of interest for constructing tests and confidence sets for low-dimensional subsets of entries of the low rank matrix. KW - High dimensional statistical inference KW - inverse problem KW - limiting distribution KW - low rank matrix recovery KW - numerical methods KW - uncertainty quantification Y1 - 2018 U6 - https://doi.org/10.5705/ss.202016.0103 SN - 1017-0405 SN - 1996-8507 VL - 28 IS - 3 SP - 1371 EP - 1393 PB - Statistica Sinica, Institute of Statistical Science, Academia Sinica CY - Taipei ER - TY - INPR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - An open mapping theorem for the Navier-Stokes equations N2 - We consider the Navier-Stokes equations in the layer R^n x [0,T] over R^n with finite T > 0. Using the standard fundamental solutions of the Laplace operator and the heat operator, we reduce the Navier-Stokes equations to a nonlinear Fredholm equation of the form (I+K) u = f, where K is a compact continuous operator in anisotropic normed Hölder spaces weighted at the point at infinity with respect to the space variables. Actually, the weight function is included to provide a finite energy estimate for solutions to the Navier-Stokes equations for all t in [0,T]. On using the particular properties of the de Rham complex we conclude that the Fréchet derivative (I+K)' is continuously invertible at each point of the Banach space under consideration and the map I+K is open and injective in the space. In this way the Navier-Stokes equations prove to induce an open one-to-one mapping in the scale of Hölder spaces. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 5 (2016)10 KW - Navier-Stokes equations KW - weighted Hölder spaces KW - integral representation method Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-98687 SN - 2193-6943 VL - 5 IS - 10 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Shlapunov, Alexander A1 - Tarchanov, Nikolaj Nikolaevič T1 - An open mapping theorem for the Navier-Stokes type equations associated with the de Rham complex over R-n JF - Siberian electronic mathematical reports = Sibirskie ėlektronnye matematičeskie izvestija N2 - We consider an initial problem for the Navier-Stokes type equations associated with the de Rham complex over R-n x[0, T], n >= 3, with a positive time T. We prove that the problem induces an open injective mappings on the scales of specially constructed function spaces of Bochner-Sobolev type. In particular, the corresponding statement on the intersection of these classes gives an open mapping theorem for smooth solutions to the Navier-Stokes equations. KW - Navier-Stokes equations KW - de Rham complex KW - open mapping theorem Y1 - 2021 U6 - https://doi.org/10.33048/semi.2021.18.108 SN - 1813-3304 VL - 18 IS - 2 SP - 1433 EP - 1466 PB - Institut Matematiki Imeni S. L. Soboleva CY - Novosibirsk ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. A1 - Satalov, Viktor E. T1 - An operator algebra on manifolds with cusp type singularities Y1 - 1998 ER - TY - JOUR A1 - Bölling, Reinhard T1 - An unknown photograph of Kovalevskaja Y1 - 1998 SN - 0343-6993 ER - TY - BOOK A1 - Junek, Heinz T1 - Analysis : Funktionen - Folgen - Reihen Y1 - 1998 SN - 3-519-00212-4 U6 - https://doi.org/10.1007/978-3-322-84791-1 PB - Vieweg+Teubner Verlag CY - Wiesbaden ER - TY - GEN A1 - Wiljes, Jana de A1 - Tong, Xin T. T1 - Analysis of a localised nonlinear ensemble Kalman Bucy filter with complete and accurate observations T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - Concurrent observation technologies have made high-precision real-time data available in large quantities. Data assimilation (DA) is concerned with how to combine this data with physical models to produce accurate predictions. For spatial-temporal models, the ensemble Kalman filter with proper localisation techniques is considered to be a state-of-the-art DA methodology. This article proposes and investigates a localised ensemble Kalman Bucy filter for nonlinear models with short-range interactions. We derive dimension-independent and component-wise error bounds and show the long time path-wise error only has logarithmic dependence on the time range. The theoretical results are verified through some simple numerical tests. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1221 KW - data assimilation KW - stability and accuracy KW - dimension independent bound KW - localisation KW - high dimensional KW - filter KW - nonlinear Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-540417 SN - 1866-8372 VL - 33 IS - 9 SP - 4752 EP - 4782 PB - IOP Publ. CY - Bristol ER - TY - JOUR A1 - Wiljes, Jana de A1 - Tong, Xin T. T1 - Analysis of a localised nonlinear ensemble Kalman Bucy filter with complete and accurate observations JF - Nonlinearity N2 - Concurrent observation technologies have made high-precision real-time data available in large quantities. Data assimilation (DA) is concerned with how to combine this data with physical models to produce accurate predictions. For spatial-temporal models, the ensemble Kalman filter with proper localisation techniques is considered to be a state-of-the-art DA methodology. This article proposes and investigates a localised ensemble Kalman Bucy filter for nonlinear models with short-range interactions. We derive dimension-independent and component-wise error bounds and show the long time path-wise error only has logarithmic dependence on the time range. The theoretical results are verified through some simple numerical tests. KW - data assimilation KW - stability and accuracy KW - dimension independent bound KW - localisation KW - high dimensional KW - filter KW - nonlinear Y1 - 2020 U6 - https://doi.org/10.1088/1361-6544/ab8d14 SN - 0951-7715 SN - 1361-6544 VL - 33 IS - 9 SP - 4752 EP - 4782 PB - IOP Publ. CY - Bristol ER - TY - JOUR A1 - Böckmann, Christine A1 - Biele, Jens A1 - Neuber, Roland T1 - Analysis of multi-wavelength lidar data by inversion with mollifier method Y1 - 1998 ER - TY - JOUR A1 - Schindler, Daniel A1 - Moldenhawer, Ted A1 - Stange, Maike A1 - Lepro, Valentino A1 - Beta, Carsten A1 - Holschneider, Matthias A1 - Huisinga, Wilhelm T1 - Analysis of protrusion dynamics in amoeboid cell motility by means of regularized contour flows JF - PLoS Computational Biology : a new community journal N2 - Amoeboid cell motility is essential for a wide range of biological processes including wound healing, embryonic morphogenesis, and cancer metastasis. It relies on complex dynamical patterns of cell shape changes that pose long-standing challenges to mathematical modeling and raise a need for automated and reproducible approaches to extract quantitative morphological features from image sequences. Here, we introduce a theoretical framework and a computational method for obtaining smooth representations of the spatiotemporal contour dynamics from stacks of segmented microscopy images. Based on a Gaussian process regression we propose a one-parameter family of regularized contour flows that allows us to continuously track reference points (virtual markers) between successive cell contours. We use this approach to define a coordinate system on the moving cell boundary and to represent different local geometric quantities in this frame of reference. In particular, we introduce the local marker dispersion as a measure to identify localized membrane expansions and provide a fully automated way to extract the properties of such expansions, including their area and growth time. The methods are available as an open-source software package called AmoePy, a Python-based toolbox for analyzing amoeboid cell motility (based on time-lapse microscopy data), including a graphical user interface and detailed documentation. Due to the mathematical rigor of our framework, we envision it to be of use for the development of novel cell motility models. We mainly use experimental data of the social amoeba Dictyostelium discoideum to illustrate and validate our approach.
Author summary Amoeboid motion is a crawling-like cell migration that plays an important key role in multiple biological processes such as wound healing and cancer metastasis. This type of cell motility results from expanding and simultaneously contracting parts of the cell membrane. From fluorescence images, we obtain a sequence of points, representing the cell membrane, for each time step. By using regression analysis on these sequences, we derive smooth representations, so-called contours, of the membrane. Since the number of measurements is discrete and often limited, the question is raised of how to link consecutive contours with each other. In this work, we present a novel mathematical framework in which these links are described by regularized flows allowing a certain degree of concentration or stretching of neighboring reference points on the same contour. This stretching rate, the so-called local dispersion, is used to identify expansions and contractions of the cell membrane providing a fully automated way of extracting properties of these cell shape changes. We applied our methods to time-lapse microscopy data of the social amoeba Dictyostelium discoideum. Y1 - 2021 U6 - https://doi.org/10.1371/journal.pcbi.1009268 SN - 1553-734X SN - 1553-7358 VL - 17 IS - 8 PB - PLoS CY - San Fransisco ER - TY - JOUR A1 - Chang, Der-Chen A1 - Khalil, Sara A1 - Schulze, Bert-Wolfgang T1 - Analysis on regular corner spaces JF - The journal of geometric analysis N2 - We establish a new approach of treating elliptic boundary value problems (BVPs) on manifolds with boundary and regular corners, up to singularity order 2. Ellipticity and parametrices are obtained in terms of symbols taking values in algebras of BVPs on manifolds of corresponding lower singularity orders. Those refer to Boutet de Monvel's calculus of operators with the transmission property, see Boutet de Monvel (Acta Math 126:11-51, 1971) for the case of smooth boundary. On corner configuration operators act in spaces with multiple weights. We mainly study the case of upper left entries in the respective 2 x 2 operator block-matrices of such a calculus. Green operators in the sense of Boutet de Monvel (Acta Math 126:11-51, 1971) analogously appear in singular cases, and they are complemented by contributions of Mellin type. We formulate a result on ellipticity and the Fredholm property in weighted corner spaces, with parametrices of analogous kind. KW - Boutet de Monvel's calculus KW - Pseudo-differential operators KW - Singular cones KW - Mellin symbols with values in the edge calculus KW - Parametrices of elliptic operators KW - Kegel space Y1 - 2021 U6 - https://doi.org/10.1007/s12220-021-00614-3 SN - 1050-6926 SN - 1559-002X VL - 31 IS - 9 SP - 9199 EP - 9240 PB - Springer CY - New York ER - TY - INPR A1 - Elin, Mark A1 - Shoikhet, David A1 - Tarkhanov, Nikolai Nikolaevich T1 - Analytic semigroups of holomorphic mappings and composition operators N2 - In this paper we study the problem of analytic extension in parameter for a semigroup of holomorphic self-mappings of the unit ball in a complex Banach space and its relation to the linear continuous semigroup of composition operators. We also provide a brief review around this topic. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015) 6 KW - nonlinear semigroup KW - composition operator Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-77914 SN - 2193-6943 VL - 4 IS - 6 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Elin, Mark A1 - Shoikhet, David A1 - Tarkhanov, Nikolai Nikolaevich T1 - Analytic Semigroups of Holomorphic Mappings and Composition Operators JF - Computational Methods and Function Theory N2 - In this manuscript we provide a review on the classical and resent results related to the problem of analytic extension in parameter for a semigroup of holomorphic self-mappings of the unit ball in a complex Banach space and its relation to the linear continuous semigroup of composition operators. KW - Non-linear semigroups KW - Composition operators KW - Analytic extension KW - Holomorphic mappings Y1 - 2017 U6 - https://doi.org/10.1007/s40315-017-0227-x SN - 1617-9447 SN - 2195-3724 VL - 18 IS - 2 SP - 269 EP - 294 PB - Springer CY - Heidelberg ER - TY - BOOK A1 - Klotzek, Benno T1 - Analytische Geometrie und lineare Algebra Y1 - 1997 SN - 3-8171-1532-6 PB - Deutsch CY - Thun, Frankfurt am Main ER - TY - JOUR A1 - Bartl, Peter T1 - Anforderungen an und Integration von Workflow-Management-Systemen in öffentlichen Verwaltungen JF - Preprint / Universität Potsdam, Institut für Informatik Y1 - 1997 SN - 0946-7580 VL - 1997, 03 PB - Inst. für Informatik CY - Potsdam ER - TY - BOOK A1 - Tarkhanov, Nikolai Nikolaevich T1 - Anisotropic edge problems T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2002 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Buchholz, Thilo A1 - Schulze, Bert-Wolfgang T1 - Anisotropic edges pseudo-differential operators withdiscrete asymptotics Y1 - 1997 ER - TY - BOOK A1 - Paneah, Boris T1 - Another approach to the stability of linear functional operators T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2006 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Bomanson, Jori A1 - Janhunen, Tomi A1 - Schaub, Torsten A1 - Gebser, Martin A1 - Kaufmann, Benjamin T1 - Answer Set Programming Modulo Acyclicity JF - Fundamenta informaticae N2 - Acyclicity constraints are prevalent in knowledge representation and applications where acyclic data structures such as DAGs and trees play a role. Recently, such constraints have been considered in the satisfiability modulo theories (SMT) framework, and in this paper we carry out an analogous extension to the answer set programming (ASP) paradigm. The resulting formalism, ASP modulo acyclicity, offers a rich set of primitives to express constraints related to recursive structures. In the technical results of the paper, we relate the new generalization with standard ASP by showing (i) how acyclicity extensions translate into normal rules, (ii) how weight constraint programs can be instrumented by acyclicity extensions to capture stability in analogy to unfounded set checking, and (iii) how the gap between supported and stable models is effectively closed in the presence of such an extension. Moreover, we present an efficient implementation of acyclicity constraints by incorporating a respective propagator into the state-of-the-art ASP solver CLASP. The implementation provides a unique combination of traditional unfounded set checking with acyclicity propagation. In the experimental part, we evaluate the interplay of these orthogonal checks by equipping logic programs with supplementary acyclicity constraints. The performance results show that native support for acyclicity constraints is a worthwhile addition, furnishing a complementary modeling construct in ASP itself as well as effective means for translation-based ASP solving. Y1 - 2016 U6 - https://doi.org/10.3233/FI-2016-1398 SN - 0169-2968 SN - 1875-8681 VL - 147 SP - 63 EP - 91 PB - IOS Press CY - Amsterdam ER - TY - GEN A1 - Quaisser, Erhard T1 - Antoni, C. ; Dalena, A., Discrete applied mathematics, 66 (1996), S. 75 - 79 BT - Discrete applied mathematics Y1 - 1996 ER - TY - BOOK A1 - Nazajkinskij, Vladimir E. A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. T1 - Applications of noncommutative analysis to operator algebras on singular manifolds T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2000 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - THES A1 - Le, Tuan Anh T1 - Applying realistic mathematics education in Vietnam : teaching middle school geometry T1 - Der Einsatz von ‘Realistic Mathematics Education’ in Vietnam : Geometrieunterricht an Mittelschulen N2 - Since 1971, the Freudenthal Institute has developed an approach to mathematics education named Realistic Mathematics Education (RME). The philosophy of RME is based on Hans Freudenthal’s concept of ‘mathematics as a human activity’. Prof. Hans Freudenthal (1905-1990), a mathematician and educator, believes that ‘ready-made mathematics’ should not be taught in school. By contrast, he urges that students should be offered ‘realistic situations’ so that they can rediscover from informal to formal mathematics. Although mathematics education in Vietnam has some achievements, it still encounters several challenges. Recently, the reform of teaching methods has become an urgent task in Vietnam. It appears that Vietnamese mathematics education lacks necessary theoretical frameworks. At first sight, the philosophy of RME is suitable for the orientation of the teaching method reform in Vietnam. However, the potential of RME for mathematics education as well as the ability of applying RME to teaching mathematics is still questionable in Vietnam. The primary aim of this dissertation is to research into abilities of applying RME to teaching and learning mathematics in Vietnam and to answer the question “how could RME enrich Vietnamese mathematics education?”. This research will emphasize teaching geometry in Vietnamese middle school. More specifically, the dissertation will implement the following research tasks: • Analyzing the characteristics of Vietnamese mathematics education in the ‘reformed’ period (from the early 1980s to the early 2000s) and at present; • Implementing a survey of 152 middle school teachers’ ideas from several Vietnamese provinces and cities about Vietnamese mathematics education; • Analyzing RME, including Freudenthal’s viewpoints for RME and the characteristics of RME; • Discussing how to design RME-based lessons and how to apply these lessons to teaching and learning in Vietnam; • Experimenting RME-based lessons in a Vietnamese middle school; • Analyzing the feedback from the students’ worksheets and the teachers’ reports, including the potentials of RME-based lessons for Vietnamese middle school and the difficulties the teachers and their students encountered with RME-based lessons; • Discussing proposals for applying RME-based lessons to teaching and learning mathematics in Vietnam, including making suggestions for teachers who will apply these lessons to their teaching and designing courses for in-service teachers and teachers-in training. This research reveals that although teachers and students may encounter some obstacles while teaching and learning with RME-based lesson, RME could become a potential approach for mathematics education and could be effectively applied to teaching and learning mathematics in Vietnamese school. N2 - Seit 1971 wurde an dem renommierten Freudenthal Institut in Utrecht ein als Realistic Mathematics Education (RME) bezeichneter mathematikdidaktischer Ansatz entwickelt. Die Philosophie von RME beruht auf Hans Freudenthals Auffassung von Mathematik als menschlicher Aktivität. Der Mathematiker und Didaktiker Prof. Hans Freudenthal (1905 – 1990) plädierte dafür, dass Mathematik an den Schulen nicht als Fertigprodukt unterrichtet werden sollte. Im Gegensatz dazu forderte er, den Schülern an ‚realistischen’ Situationen nicht-formale und formale Mathematik wieder entdecken zu lassen. Obwohl die mathematische Schulbildung in Vietnam in den letzten Jahrzehnten schon einige Fortschritte gemacht hat, steht sie noch vor großen Herausforderungen. Derzeit ist die Reform der Unterrichtsmethoden eine dringliche Aufgabe in Vietnam. Augenscheinlich ermangelt es der Mathematikdidaktik in Vietnam an dem dazu notwendigen theoretischen Rahmen. Die Philosophie von RME eignet sich grundsätzlich als Orientierung für die Reform der Unterrichtsmethoden in Vietnam. Allerdings ist die Potenz von RME für die mathematische Schulbildung in Vietnam und die Möglichkeiten, RME im Mathematikunterricht anzuwenden, noch zu klären. Das Hauptziel dieser Arbeit war zu erforschen, wie RME beim Mathematik-Lernen und -Lehren in Vietnam eingesetzt werden kann und die Frage zu beantworten: Wie kann RME den Mathematikunterricht in Vietnam bereichern? Dazu wurde insbesondere der Geometrieunterricht in der Sekundarstufe I betrachtet. Im Einzelnen beinhaltet die Untersuchung: • eine Analyse der vietnamesischen Mathematikdidaktik in der ‘Reformperiode’ (etwa von 1980 bis 2000) • die Konzeption, Durchführung und Auswertung einer Befragung von 152 Mittelschullehrern aus verschiedenen vietnamesischen Provinzen und Städten zum Mathematikunterricht in Vietnam • eine Analyse von RME einschließlich der Freudenthalschen Sicht von RME und der Charakteristika von RME • die Diskussion, wie man RME-basierten Unterrichtseinheiten gestalten und diese in den Mathematikunterricht in Vietnam integrieren kann • Test solcher Einheiten in vietnamesischen Mittelschulen • Analyse der Rückmeldungen anhand der Schülerarbeitsblätter und der Lehrerberichte • Diskussion der Chancen und Probleme von RME-basierten Unterrichtseinheiten im Geometrieunterricht vietnamesischer Mittelschulen • Diskussion von Vorschläge zur Entwicklung und zum Einsatz RME- basierter Unterrichtseinheiten in Vietnam, einschließlich von Hinweisen für Lehrende und der Konzeption von Ausbildungs- und Fortbildungskursen zu RME Die Untersuchung zeigt, dass – obwohl Lehrer wie Schüler zunächst einige Hindernisse beim Lehren und Lernen mit RME- basierten Unterrichtseinheiten zu bewältigen haben werden – RME ein mächtiger mathematikdidaktischer Ansatz ist, der wirkungsvoll im Lehren und Lernen von Mathematik in vietnamesischen Schulen angewandt werden kann. KW - Didaktik der Mathematik KW - Vietnam KW - Geometrieunterricht KW - Sekundarstufe I KW - Realistic Mathematics Education KW - Vietnam KW - middle school KW - geometry Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13480 ER - TY - BOOK ED - Gil, Juan ED - Grieser, Daniel ED - Lesch, Matthias T1 - Approaches to singular analysis : a volume of advances in partial differential equations T3 - Operator theory : advances and applications Y1 - 2001 SN - 3-7643-6518-8 U6 - https://doi.org/10.1007/978-3-0348-8253-8 VL - 125 PB - Birkhäuser Basel CY - Basel ER - TY - JOUR A1 - Junek, Heinz A1 - Braunß, Hans-Andreas A1 - Plewnia, Eckart T1 - Approximation numbers for polynomials N2 - Approximation numbers of linear operators are a very useful tool in order to understand the structure and the numerical behaviour of the operators. In this paper, this concept is extended to polynomials on Banach spaces and the approximation numbers of diagonal polynomials are estimated. As a main tool the rank of polynomials as a graduation of finite type polynomials is introduced and studied. Y1 - 2000 ER - TY - THES A1 - Brademann, Sylke T1 - Approximationsideale homogener Polynome und holomorpher Funktionen Y1 - 1993 ER - TY - THES A1 - Plewnia, Eckart T1 - Approximationstheorie homogener Polynome auf Banachräumen Y1 - 1997 ER - TY - JOUR A1 - Jahnke, Thomas T1 - Arbeitsaufträge - nicht nur - zum Einstieg Y1 - 2001 ER - TY - BOOK A1 - Schulze, Bert-Wolfgang A1 - Schrohe, Elmar T1 - Arbeitsgruppe "Partielle Differentialgleichungen und Komplexe Analysis" (seit 1992) T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1997 VL - 1997, 12 PB - Univ. CY - Potsdam ER - TY - THES A1 - Trappmann, Henryk T1 - Arborescent numbers : higher arithmetic operations and division trees T1 - Baumartige Zahlen : höhere arithmetische Operationen und Divisionsbäume N2 - The overall program "arborescent numbers" is to similarly perform the constructions from the natural numbers (N) to the positive fractional numbers (Q+) to positive real numbers (R+) beginning with (specific) binary trees instead of natural numbers. N can be regarded as the associative binary trees. The binary trees B and the left-commutative binary trees P allow the hassle-free definition of arbitrary high arithmetic operations (hyper ... hyperpowers). To construct the division trees the algebraic structure "coppice" is introduced which is a group with an addition over which the multiplication is right-distributive. Q+ is the initial associative coppice. The present work accomplishes one step in the program "arborescent numbers". That is the construction of the arborescent equivalent(s) of the positive fractional numbers. These equivalents are the "division binary trees" and the "fractional trees". A representation with decidable word problem for each of them is given. The set of functions f:R1->R1 generated from identity by taking powers is isomorphic to P and can be embedded into a coppice by taking inverses. N2 - Baumartige Zahlen und höhere arithmetische Operationen Von Schülern und Laienmathematikern wird oft die Frage gestellt, warum nach den Operationen Addition (1. Stufe), Multiplikation (2. Stufe), Potenzieren (3. Stufe) keine Operationen der 4. oder höheren Stufen betrachtet werden. Jede Operation der nächsthöheren Stufe ist die Wiederholung der vorhergehenden Operation, z.B. n * x = x + x + ... + x x^n = x * x * ... * x Das offensichtliche Problem mit der Wiederholung des Potenzierens besteht darin, dass das Potenzieren nicht assoziativ ist und es somit mehrere Klammerungsmöglichkeiten für die Wiederholung dieser Operation gibt. Wählt man eine spezifische Klammerungsmöglichkeit aus, z.B. x^^n = (x^(x^(x^(......)))), gibt es jedoch wieder verschiedene Möglichkeiten, diese Operation auf rationale oder reelle n fortzusetzen. In der Tat kann man im Internet verschiedene solcher Fortsetzungen beschrieben finden und keine scheint besonders ausgezeichnet zu sein. Das ganze Dilemma der verschiedenen Klammerungen kann man jedoch überwinden, in dem man den Zahlenbereich abstrakter macht. So dass statt nur der Anzahl auch eine Klammerungsstruktur in einer Zahl kodiert wird. Die ganz natürliche Verallgemeinerung der natürlichen Zahlen in dieser Hinsicht sind die Binärbäume. Und in der Tat lassen sich die 4. und höhere Operationen in einer eindeutigen Weise auf den Binärbäumen erklären. Vielmehr stellt sich sogar heraus, dass die Binärbäume zu viel Information mit sich tragen, wenn es nur darum geht, die höheren Operationen zu definieren. Es gibt eine Spezialisierung der Binärbäume, die aber allgemeiner als die natürlichen Zahlen (die die assoziative Spezialisierung der Binärbäume sind) ist, und die die passende Informationsmenge zur Definition der höheren Operationen kodiert. Dies sind die so genannten linkskommutativen Binärbäume. Es stellt sich heraus, dass die (linkskommutativen) Binärbäume viele Eigenschaften der natürlichen Zahlen teilen, so z.B. die Assoziativität der Multiplikation (die Operation der 2. Stufe) und eine eindeutige Primzahlzerlegung. Dies motiviert die Frage, ob man die Erweiterungskonstruktionen der Zahlen: „natürliche Zahlen zu gebrochenen Zahlen“ (macht die Multiplikation umkehrbar) „gebrochene Zahlen zu positiven reellen Zahlen“ (macht das Potenzieren umkehrbar und erlaubt Grenzwertbildung) auch ausgehend von (linkskommutativen) Binärbäumen vornehmen kann. In der vorliegenden Arbeit wird (neben unzähligen anderen Resultaten) gezeigt, dass die Zahlenbereichserweiterung „natürliche Zahlen zu gebrochenen Zahlen“ auch analog für (linkskommutative) Binärbäume möglich ist. Das Ergebnis dieser Konstruktion sind die Divisionsbinärbäume (bzw. die gebrochenen Bäume). Letztere lassen sich unerwartet in der Form von Brüchen darstellen, sind jedoch als Verallgemeinerung der gebrochenen Zahlen sehr viel komplexer als dieser. (Das kann man live nachprüfen mit dem dafür erstellten Online-Rechner für gebrochene Bäume (auf englisch): http://math.eretrandre.org/cgi-bin/ftc/ftc.pl ) Damit wird ein Programm „baumartige Zahlen“ gestartet, indem es darum geht, auch die Erweiterung „gebrochene Zahlen zu positiven reellen Zahlen“ für die Divisionsbinärbäume (bzw. die gebrochenen Bäume) durchzuführen, wobei die höheren Operationen auf dieser Erweiterung definiert werden könnten und umkehrbar sein müssten. Ob dies wirklich möglich ist, ist derzeit unklar (neben diversen anderen direkt aus der Dissertation sich ergebenden Fragen) und eröffnet damit ein enorm umfangreiches Feld für weitere Forschungen. KW - Tetration KW - höhere Operationen KW - strukturierte Zahlen KW - Divisionsbäume KW - tetration KW - higher operations KW - structured numbers KW - division trees Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-15247 ER - TY - JOUR A1 - Schanner, Maximilian A1 - Korte, Monika A1 - Holschneider, Matthias T1 - ArchKalmag14k: A kalman-filter based global geomagnetic model for the holocene JF - Journal of geophysical research : Solid earth N2 - We propose a global geomagnetic field model for the last 14 thousand years, based on thermoremanent records. We call the model ArchKalmag14k. ArchKalmag14k is constructed by modifying recently proposed algorithms, based on space-time correlations. Due to the amount of data and complexity of the model, the full Bayesian posterior is numerically intractable. To tackle this, we sequentialize the inversion by implementing a Kalman-filter with a fixed time step. Every step consists of a prediction, based on a degree dependent temporal covariance, and a correction via Gaussian process regression. Dating errors are treated via a noisy input formulation. Cross correlations are reintroduced by a smoothing algorithm and model parameters are inferred from the data. Due to the specific statistical nature of the proposed algorithms, the model comes with space and time-dependent uncertainty estimates. The new model ArchKalmag14k shows less variation in the large-scale degrees than comparable models. Local predictions represent the underlying data and agree with comparable models, if the location is sampled well. Uncertainties are bigger for earlier times and in regions of sparse data coverage. We also use ArchKalmag14k to analyze the appearance and evolution of the South Atlantic anomaly together with reverse flux patches at the core-mantle boundary, considering the model uncertainties. While we find good agreement with earlier models for recent times, our model suggests a different evolution of intensity minima prior to 1650 CE. In general, our results suggest that prior to 6000 BCE the data is not sufficient to support global models. Y1 - 2022 U6 - https://doi.org/10.1029/2021JB023166 SN - 2169-9313 SN - 2169-9356 VL - 127 IS - 2 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Wessel, Walter T1 - Are all complete plane multimaps but one bounded by Euler only? Y1 - 1995 ER - TY - THES A1 - Li, Xianhua T1 - Arithmetic properties and the characterization of finite groups Y1 - 2006 CY - Potsdam ER - TY - BOOK ED - Gil, Juan ED - Krainer, Thomas ED - Witt, Ingo T1 - Aspects of Boundary Problems in Analysis and Geometry : advances in partial differential equations T3 - Operator Theory : Advances and Applications Y1 - 2004 SN - 3-7643-7069-6 VL - 151 PB - Birkhäuser CY - Basel ER - TY - JOUR A1 - Acevedo, Walter A1 - Fallah, Bijan A1 - Reich, Sebastian A1 - Cubasch, Ulrich T1 - Assimilation of pseudo-tree-ring-width observations into an atmospheric general circulation model JF - Climate of the past : an interactive open access journal of the European Geosciences Union N2 - 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. Y1 - 2017 U6 - https://doi.org/10.5194/cp-13-545-2017 SN - 1814-9324 SN - 1814-9332 VL - 13 SP - 545 EP - 557 PB - Copernicus CY - Göttingen ER - TY - BOOK A1 - Witt, Ingo T1 - Asymptotic algebras T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2001 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Fang, Daoyuan A1 - Xu, Jiang T1 - Asymptotic behavior of solutions to multidimensional nonisentropic hydrodynamic model for semiconductors T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2005 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Chen, Hua A1 - Yu, Chun T1 - Asymptotic behaviour of the trace for schrödinger operator on fractal drums T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2001 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Finner, Helmut A1 - Roters, Markus T1 - Asymptotic comparison of step-down and step-up multiple test procedures based on exchangeable test statistics Y1 - 1998 ER - TY - JOUR A1 - Finner, Helmut A1 - Roters, Markus T1 - Asymptotic comparison of the critical values of step-down and step-up multiple comparison procedures Y1 - 1999 ER - TY - JOUR A1 - Klein, Markus A1 - Rosenberger, Elke T1 - Asymptotic eigenfunctions for a class of difference operators JF - Asymptotic analysis N2 - We analyze a general class of difference operators H(epsilon) = T(epsilon) + V(epsilon) on l(2)((epsilon Z)(d)), where V(epsilon) is a one-well potential and epsilon is a small parameter. We construct formal asymptotic expansions of WKB-type for eigenfunctions associated with the low lying eigenvalues of H(epsilon). These are obtained from eigenfunctions or quasimodes for the operator H(epsilon), acting on L(2)(R(d)), via restriction to the lattice (epsilon Z)(d). KW - difference operator KW - tunneling KW - WKB-expansion KW - quasimodes Y1 - 2011 U6 - https://doi.org/10.3233/ASY-2010-1025 SN - 0921-7134 VL - 73 IS - 1-2 SP - 1 EP - 36 PB - IOS Press CY - Amsterdam ER - TY - JOUR A1 - Ludewig, Matthias A1 - Rosenberger, Elke T1 - Asymptotic eigenfunctions for Schrödinger operators on a vector bundle JF - Reviews in mathematical physics N2 - In the limit (h) over bar -> 0, we analyze a class of Schrödinger operators H-(h) over bar = (h) over bar L-2 + (h) over barW + V .id(epsilon) acting on sections of a vector bundle epsilon over a Riemannian manifold M where L is a Laplace type operator, W is an endomorphism field and the potential energy V has a non-degenerate minimum at some point p is an element of M. We construct quasimodes of WKB-type near p for eigenfunctions associated with the low-lying eigenvalues of H-(h) over bar. These are obtained from eigenfunctions of the associated harmonic oscillator H-p,H-(h) over bar at p, acting on smooth functions on the tangent space. KW - Semi-classical analysis KW - WKB approximation KW - Schrödinger operators KW - semi-classical limit Y1 - 2020 U6 - https://doi.org/10.1142/S0129055X20500208 SN - 0129-055X SN - 1793-6659 VL - 32 IS - 7 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Debussche, Arnaud A1 - Hoegele, Michael A1 - Imkeller, Peter T1 - Asymptotic exit times JF - Lecture notes in mathematics : a collection of informal reports and seminars JF - Lecture Notes in Mathematics Y1 - 2013 SN - 978-3-319-00828-8; 978-3-319-00827-1 U6 - https://doi.org/10.1007/978-3-319-00828-8_5 SN - 0075-8434 VL - 2085 SP - 87 EP - 120 PB - Springer CY - Berlin ER - TY - INPR A1 - Ly, Ibrahim A1 - Tarkhanov, Nikolai Nikolaevich T1 - Asymptotic expansions at nonsymmetric cuspidal points N2 - We study asymptotics of solutions to the Dirichlet problem in a domain whose boundary contains a nonsymmetric conical point. We establish a complete asymptotic expansion of solutions near the singular point. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015) 7 KW - the Dirichlet problem KW - singular point KW - asymptotic expansion Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-78199 SN - 2193-6943 VL - 4 IS - 7 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Ly, Ibrahim A1 - Tarkhanov, Nikolaj Nikolaevič T1 - Asymptotic expansions at nonsymmetric cuspidal points JF - Mathematical notes N2 - We study the asymptotics of solutions to the Dirichlet problem in a domain X subset of R3 whose boundary contains a singular point O. In a small neighborhood of this point, the domain has the form {z > root x(2) + y(4)}, i.e., the origin is a nonsymmetric conical point at the boundary. So far, the behavior of solutions to elliptic boundary-value problems has not been studied sufficiently in the case of nonsymmetric singular points. This problem was posed by V.A. Kondrat'ev in 2000. We establish a complete asymptotic expansion of solutions near the singular point. KW - Dirichlet problem KW - singular points KW - asymptotic expansions Y1 - 2020 U6 - https://doi.org/10.1134/S0001434620070238 SN - 0001-4346 SN - 1573-8876 VL - 108 IS - 1-2 SP - 219 EP - 228 PB - Springer Science CY - New York ER -