TY - BOOK A1 - Tarkhanov, Nikolai Nikolaevich T1 - Euler characteristic of Fredholm quasicomplexes T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2006 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Tarkhanov, Nikolai Nikolaevich T1 - Euler characteristic of Fredholm quasicomplexes N2 - By quasicomplexes are usually meant perturbations of complexes small in some sense. Of interest are not only perturbations within the category of complexes but also those going beyond this category. A sequence perturbed in this way is no longer a complex, and so it bears no cohomology. We show how to introduce Euler characteristic for small perturbations of Fredholm complexes. The paper is to appear in Funct. Anal. and its Appl., 2006. T3 - Preprint - (2006) 11 Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30117 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 - Schulze, Bert-Wolfgang A1 - Seiler, Jörg T1 - Edge operators with conditions of Toeplitz type N2 - Ellipticity of operators on a manifold with edges can be treated in the framework of a calculus of 2 X 2-block matrix operators with trace and potential operators on the edges. The picture is similar to the pseudodifferential analysis of boundary-value problems. The extra conditions satisfy an analogue of the Shapiro-Lopatinskij condition, provided a topological obstruction for the elliptic edge-degenerate operator in the upper left corner vanishes; this is an analogue of a condition of Atiyah and Bott in boundary-value problems. In general, however, we need global projection data, similarly to global boundary conditions, known for Dirac operators or other geometric operators. The present paper develops a new calculus with global projection data for operators on manifolds with edges. In particular, we show the Fredholm property in a suitable scale of spaces and construct parametrices within the calculus Y1 - 2006 ER - TY - BOOK A1 - Schulze, Bert-Wolfgang T1 - The structure of operators on manifolds with polyhedral singularities T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2006 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Schulze, Bert-Wolfgang T1 - Pseudo-differential calculus on Manifolds with geometric singularities T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2006 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Schulze, Bert-Wolfgang T1 - Elliptic differential operators on Manifolds with Edges T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2006 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Schulze, Bert-Wolfgang T1 - Pseudo-differential calculus on manifolds with geometric singularities N2 - Differential and pseudo-differential operators on a manifold with (regular) geometric singularities can be studied within a calculus, inspired by the concept of classical pseudo-differential operators on a C1 manifold. In the singular case the operators form an algebra with a principal symbolic hierarchy σ = (σj)0≤j≤k, with k being the order of the singularity and σk operator-valued for k ≥ 1. The symbols determine ellipticity and the nature of parametrices. It is typical in this theory that, similarly as in boundary value problems (which are special edge problems, where the edge is just the boundary), there are trace, potential and Green operators, associated with the various strata of the configuration. The operators, obtained from the symbols by various quantisations, act in weighted distribution spaces with multiple weights. We outline some essential elements of this calculus, give examples and also comment on new challenges and interesting problems of the recent development. T3 - Preprint - (2006) 20 Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30204 ER - TY - INPR A1 - Schulze, Bert-Wolfgang T1 - Elliptic differential operators on manifolds with edges N2 - On a manifold with edge we construct a specific class of (edgedegenerate) elliptic differential operators. The ellipticity refers to the principal symbolic structure σ = (σψ, σ^) of the edge calculus consisting of the interior and edge symbol, denoted by σψ and σ^, respectively. For our choice of weights the ellipticity will not require additional edge conditions of trace or potential type, and the operators will induce isomorphisms between the respective edge spaces. T3 - Preprint - (2006) 18 KW - Operators on manifolds with edge KW - ellipticity with respect to interior and edge symbols KW - weighted edge spaces Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30188 ER - TY - INPR A1 - Schulze, Bert-Wolfgang T1 - The structure of operators on manifolds with polyhedral singularities N2 - We discuss intuitive ideas and historical background of concepts in the analysis on configurations with singularities, here in connection with our iterative approach for higher singularities. T3 - Preprint - (2006) 05 Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30099 ER - TY - THES A1 - Schopka, Sven T1 - Noncommutative Einstein Manifolds Y1 - 2006 CY - Potsdam ER - TY - THES A1 - Rosenberger, Elke T1 - Asymptotic spectral analysis and tunnelling for a class of difference operators T1 - Asymptotische Spektralanalyse und Tunneleffekt für eine Klasse von Differenzen-Operatoren N2 - We analyze the asymptotic behavior in the limit epsilon to zero for a wide class of difference operators H_epsilon = T_epsilon + V_epsilon with underlying multi-well potential. They act on the square summable functions on the lattice (epsilon Z)^d. We start showing the validity of an harmonic approximation and construct WKB-solutions at the wells. Then we construct a Finslerian distance d induced by H and show that short integral curves are geodesics and d gives the rate for the exponential decay of Dirichlet eigenfunctions. In terms of this distance, we give sharp estimates for the interaction between the wells and construct the interaction matrix. N2 - Wir analysieren das asymptotische Verhalten im Grenzwert epsilon gegen null von einer weiten Klasse von Differenzen operatoren H_epsilon = T_epsilon + V_epsilon mit unterliegendem Potential. Sie wirken auf die quadrat-summierbaren Funktionen auf dem Gitter (epsilon Z)^d. Zunächst zeigen wir die Gültigkeit einer harmonischen Approximation und konstruieren WKB-Lösungen an den Töpfen. Dann konstruieren wir eine Finslersche Abstandsfunktion d, die durch H induziert wird und zeigen, daß kurze Integralkurven Geodäten sind und daß d die Rate des exponentiellen Abfallverhaltens von Dirichlet-Eigenfunktionen beschreibt. Bezügliche dieses Abstands geben wir scharfe Abschätzungen für die Wechselwirkung zwischen den Töpfen und konstruieren die Wechselwirkungs-Matrix. KW - Mathematische Physik KW - Operatortheorie KW - Generalized translation operator KW - Tunneleffekt KW - Spektraltheorie KW - Asymptotische Entwicklung KW - Semi-klasische Abschätzung KW - Finsler-Abstand KW - Pseudodifferentialoperatoren auf dem Torus KW - Kontinuumsgrenzwert KW - Differenzenoperator KW - tunneling KW - semi-classical spectral estimates KW - Finsler-distance KW - difference operator KW - scaled lattice Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-7393 ER - TY - INPR A1 - Roelly, Sylvie A1 - Fradon, Myriam T1 - Infinite system of Brownian balls : equilibrium measures are canonical Gibbs N2 - We consider a system of infinitely many hard balls in Rd undergoing Brownian motions and submitted to a smooth pair potential. It is modelized by an infinite-dimensional stochastic differential equation with a local time term. We prove that the set of all equilibrium measures, solution of a detailed balance equation, coincides with the set of canonical Gibbs measures associated to the hard core potential added to the smooth interaction potential. KW - Stochastic Differential Equation KW - hard core potential KW - Canonical Gibbs measure KW - detailed balance equation KW - reversible measure Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6720 ER - TY - JOUR A1 - Reich, Sebastian T1 - Linearly implicit time stepping methods for numerical weather prediction JF - BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians N2 - The efficient time integration of the dynamic core equations for numerical weather prediction (NWP) remains a key challenge. One of the most popular methods is currently provided by implementations of the semi-implicit semi-Lagrangian (SISL) method, originally proposed by Robert (J. Meteorol. Soc. Jpn., 1982). Practical implementations of the SISL method are, however, not without certain shortcomings with regard to accuracy, conservation properties and stability. Based on recent work by Gottwald, Frank and Reich (LNCSE, Springer, 2002), Frank, Reich, Staniforth, White and Wood (Atm. Sci. Lett., 2005) and Wood, Staniforth and Reich (Atm. Sci. Lett., 2006) we propose an alternative semi-Lagrangian implementation based on a set of regularized equations and the popular Stormer-Verlet time stepping method in the context of the shallow-water equations (SWEs). Ultimately, the goal is to develop practical implementations for the 3D Euler equations that overcome some or all shortcomings of current SISL implementations. KW - numerical weather prediction KW - linearly implicit time stepping methods KW - semi-Lagrangian method KW - Stormer-Verlet method KW - shallow-water equations Y1 - 2006 U6 - https://doi.org/10.1007/s10543-006-0065-0 SN - 0006-3835 VL - 46 SP - 607 EP - 616 PB - Springer CY - Dordrecht 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 - INPR A1 - Paneah, Boris T1 - Another approach to the stability of linear functional operators N2 - Contents: 1 Introduction. 2 The main notations and notions. 3 Statement of results 4 Proofs of the main results. T3 - Preprint - (2006) 13 Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30139 ER - TY - JOUR A1 - Meyerhöfer, Wolfram A1 - Rienits, Clara T1 - Evaluation des Referendariats im Land Brandenburg, Fachseminare Mathematik Y1 - 2006 SN - 3- 937786-08-2 ER - TY - JOUR A1 - Meyerhöfer, Wolfram T1 - Erkennen und Vorurteil : Antwort auf die Replik von Iffert Y1 - 2006 SN - 3- 937786-08-2 ER - TY - JOUR A1 - Meyerhöfer, Wolfram T1 - PISA und Co. als kulturindustrielle Phänomene Y1 - 2006 SN - 978-388120-428-6 ER - TY - JOUR A1 - Meyerhöfer, Wolfram T1 - Testen, Lernen und Gesellschaft : zwischen Autonomie und Heteronomie Y1 - 2006 SN - 978-388120-428-6 ER - TY - THES A1 - Martin, Calin-Iulian T1 - Operator Algebras and Complexes of Operators Manifolds with Corners Y1 - 2006 CY - Potsdam ER - TY - INPR A1 - Makhmudov, O. A1 - Niyozov, I. A1 - Tarkhanov, Nikolai Nikolaevich T1 - The cauchy problem of couple-stress elasticity N2 - We study the Cauchy problem for the oscillation equation of the couple-stress theory of elasticity in a bounded domain in R3. Both the displacement and stress are given on a part S of the boundary of the domain. This problem is densely solvable while data of compact support in the interior of S fail to belong to the range of the problem. Hence the problem is ill-posed which makes the standard calculi of Fourier integral operators inapplicable. If S is real analytic the Cauchy-Kovalevskaya theorem applies to guarantee the existence of a local solution. We invoke the special structure of the oscillation equation to derive explicit conditions of global solvability and an approximation solution. T3 - Preprint - (2006) 03 Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30078 ER - TY - BOOK A1 - Makhmudov, O. I. A1 - Niyozov, I. E. A1 - Tarkhanov, Nikolai Nikolaevich T1 - The cauchy problem of couple-stress elasticity T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2006 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Maergoiz, L. A1 - Tarkhanov, Nikolai Nikolaevich T1 - Optimal recovery from finite set in banach spaces of entire functions T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2006 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Maergoiz, L. A1 - Tarkhanov, Nikolai Nikolaevich T1 - Optimal recovery from a finite set in Banach spaces of entire functions N2 - We develop an approach to the problem of optimal recovery of continuous linear functionals in Banach spaces through information on a finite number of given functionals. The results obtained are applied to the problem of the best analytic continuation from a finite set in the complex space Cn, n ≥ 1, for classes of entire functions of exponential type which belong to the space Lp, 1 < p < 1, on the real subspace of Cn. These latter are known as Wiener classes. T3 - Preprint - (2006) 19 Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30199 ER - TY - INPR A1 - Läuter, Henning T1 - On approximate likelihood in survival models N2 - We give a common frame for different estimates in survival models. For models with nuisance parameters we approximate the profile likelihood and find estimates especially for the proportional hazard model. T3 - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2006, 04 KW - Approximate likelihood KW - profile likelihood KW - propor-tional hazard mode Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-51615 ER - TY - INPR A1 - Liero, Hannelore A1 - Liero, Matthias T1 - Testing the acceleration function in life time models N2 - The accelerated life time model is considered. First, test procedures for testing the parameter of a parametric acceleration function is investigated; this is done under the assumption of parametric and nonparametric baseline distribution. Further, based on nonparametric estimators for regression functions tests are proposed for checking whether a parametric acceleration function is appropriate to model the influence of the covariates. Resampling procedures are discussed for the realization of these methods. Simulations complete the considerations. T3 - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2006, 03 Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49405 ER - TY - INPR A1 - Liero, Hannelore T1 - A Note on : testing the Copula Based on Densities N2 - We consider the problem of testing whether the density of a mul- tivariate random variable can be expressed by a prespecified copula function and the marginal densities. The proposed test procedure is based on the asymptotic normality of the properly standardized integrated squared distance between a multivariate kernel density estimator and an estimator of its expectation under the hypothesis. The test of independence is a special case of this approach. T3 - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2006, 02 Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49393 ER - TY - JOUR A1 - Li, Xianhua A1 - Xu, Mingyao T1 - The primitive permutation groups of degree 2(a)center dot 3(b) N2 - In this paper, we give a complete classification of all finite simple groups with maximal subgroups of index n, where n = 2(a)center dot 3b for a, b >= 1. As a consequence, for such n, all primitive permutation groups of degree n are given. The motivation of this work comes also from a study of Cayley graphs of certain valency on a finite simple group Y1 - 2006 UR - http://www.springerlink.com/content/101192 U6 - https://doi.org/10.1007/s00013-005-1494-8 SN - 0003-889X ER - TY - THES A1 - Li, Xianhua T1 - Arithmetic properties and the characterization of finite groups Y1 - 2006 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 A1 - Kytmanov, Alexander M. A1 - Myslivets, Simona A1 - Tarkhanov, Nikolai Nikolaevich T1 - The bochner-martinelli integral on surfaces with singular points T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2006 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Krupchyk, K. A1 - Tarkhanov, Nikolai Nikolaevich A1 - Tuomela, J. T1 - Elliptic quasicomplexes in boutet de monvel algebra T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2006 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Krupchyk, K. A1 - Tarkhanov, Nikolai Nikolaevich A1 - Tuomela, J. T1 - Elliptic quasicomplexes in Boutet de Monvel algebra N2 - We consider quasicomplexes of Boutet de Monvel operators in Sobolev spaces on a smooth compact manifold with boundary. To each quasicomplex we associate two complexes of symbols. One complex is defined on the cotangent bundle of the manifold and the other on that of the boundary. The quasicomplex is elliptic if these symbol complexes are exact away from the zero sections. We prove that elliptic quasicomplexes are Fredholm. As a consequence of this result we deduce that a compatibility complex for an overdetermined elliptic boundary problem operator is also Fredholm. Moreover, we introduce the Euler characteristic for elliptic quasicomplexes of Boutet de Monvel operators. T3 - Preprint - (2006) 12 Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30122 ER - TY - JOUR A1 - Kirsche, Andreas A1 - Böckmann, Christine T1 - Pade iteration method for regularization JF - Applied mathematics and computation N2 - In this study we present iterative regularization methods using rational approximations, in particular, Pade approximants, which work well for ill-posed problems. We prove that the (k,j)-Pade method is a convergent and order optimal iterative regularization method in using the discrepancy principle of Morozov. Furthermore, we present a hybrid Pade method, compare it with other well-known methods and found that it is faster than the Landweber method. It is worth mentioning that this study is a completion of the paper [A. Kirsche, C. Bockmann, Rational approximations for ill-conditioned equation systems, Appl. Math. Comput. 171 (2005) 385-397] where this method was treated to solve ill-conditioned equation systems. (c) 2006 Elsevier Inc. All rights reserved. KW - Pade approximants KW - iterative regularization KW - ill-posed problem Y1 - 2006 U6 - https://doi.org/10.1016/j.amc.2006.01.011 SN - 0096-3003 VL - 180 IS - 2 SP - 648 EP - 663 PB - Elsevier CY - New York ER - TY - BOOK A1 - Karp, Lavi T1 - On null quadrature domains T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2006 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Karp, Lavi T1 - On null quadrature domains N2 - The characterization of null quadrature domains in Rn (n ≥ 3) has been an open problem throughout the past two and a half decades. A substantial contribution was done by Friedman and Sakai [10]; they showed that if the complement is bounded, then null quadrature domains are exactly the complement of ellip- soids. The first result with unbounded complements appeared in [15], there it is assumed the complement is contained in an infinitely cylinder. The aim of this paper is to show the relation between null quadrature domains and Newton's theorem on the gravitational force induced by homogeneous homoeoidal ellipsoids. We also succeed to make progress in the classification problem and we show that if the boundary of null quadrature domain is contained in a strip and the complement satisfies a certain capacity condition at infinity, then it must be a half-space or a complement of a strip. In addition, we present a Phragm¶en-Lindelöf type theorem which seems to be forgotten in the literature. T3 - Preprint - (2006) 15 Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30156 ER - TY - BOOK A1 - Kapanadze, David A1 - Schulze, Bert-Wolfgang A1 - Seiler, Jörg T1 - Operators with singular trace conditions on a manifold with edges T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2006 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Kapanadze, D. A1 - Schulze, Bert-Wolfgang A1 - Seiler, J. T1 - Operators with singular trace conditions on a manifold with edges N2 - We establish a new calculus of pseudodifferential operators on a manifold with smooth edges and study ellipticity with extra trace and potential conditions (as well as Green operators) at the edge. In contrast to the known scenario with conditions of that kind in integral form we admit in this paper ‘singular’ trace, potential and Green operators, which are related to the corresponding operators of positive type in Boutet de Monvel’s calculus for boundary value problems. T3 - Preprint - (2006) 01 Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30058 ER - TY - JOUR A1 - Jahnke, Thomas T1 - Zur Ideologie von PISA und Co Y1 - 2006 SN - 978-388120-428-6 ER - TY - JOUR A1 - Holschneider, Matthias A1 - Teschke, Gerd T1 - Existence and computation of optimally localized coherent states JF - Journal of mathematical physics N2 - This paper is concerned with localization properties of coherent states. Instead of classical uncertainty relations we consider "generalized" localization quantities. This is done by introducing measures on the reproducing kernel. In this context we may prove the existence of optimally localized states. Moreover, we provide a numerical scheme for deriving them. Y1 - 2006 U6 - https://doi.org/10.1063/1.2375031 SN - 0022-2488 SN - 1089-7658 VL - 47 IS - 3 SP - 211 EP - 214 PB - Elsevier CY - Melville ER - TY - THES A1 - Hohberger, Horst T1 - Semiclassical asymptotics for the scattering amplitude in the presence of focal points at infinity Y1 - 2006 CY - Potsdam ER - TY - THES A1 - Hohberger, Horst T1 - Semiclassical asymptotics for the scattering amplitude in the presence of focal points at infinity T1 - Semiklassische Asymptotik der Streuamplitude bei unendlich fernen Fokalpunkten N2 - We consider scattering in $\R^n$, $n\ge 2$, described by the Schr\"odinger operator $P(h)=-h^2\Delta+V$, where $V$ is a short-range potential. With the aid of Maslov theory, we give a geometrical formula for the semiclassical asymptotics as $h\to 0$ of the scattering amplitude $f(\omega_-,\omega_+;\lambda,h)$ $\omega_+\neq\omega_-$) which remains valid in the presence of focal points at infinity (caustics). Crucial for this analysis are precise estimates on the asymptotics of the classical phase trajectories and the relationship between caustics in euclidean phase space and caustics at infinity. N2 - Wir betrachten Streuung in $\R^n$, $n\ge 2$, beschrieben durch den Schr\"odinger operator $P(h)=-h^2\Delta+V$, wo $V$ ein kurzreichweitiges Potential ist. Mit Hilfe von Maslov Theorie erhalten wir eine geometrische Formel fuer die semiklassische Asymptotik ($h\to 0$) der Streuamplitude $f(\omega_-,\omega_+;\lambda,h)$ ($\omega_+\neq\omega_-$) welche auch bei Vorhandensein von Fokalpunkten bei Unendlich (Kaustiken) gueltig bleibt. KW - Mathematik KW - Physik KW - Streutheorie KW - Streuamplitude KW - Semiklassik KW - mathematics KW - physics KW - scattering theory KW - semiclassics KW - scattering amplitude Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-11574 ER - TY - INPR A1 - Harutyunyan, Gohar A1 - Schulze, Bert-Wolfgang T1 - Boundary value problems in weighted edge spaces N2 - We study elliptic boundary value problems in a wedge with additional edge conditions of trace and potential type. We compute the (difference of the) number of such conditions in terms of the Fredholm index of the principal edge symbol. The task will be reduced to the case of special opening angles, together with a homotopy argument. T3 - Preprint - (2006) 09 KW - Elliptic operators in domains with edges KW - boundary value problems KW - weighted edge spaces Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30104 ER - TY - JOUR A1 - Harutyunyan, Gohar A1 - Schulze, Bert-Wolfgang T1 - The Zaremba problem with singular interfaces as a corner boundary value problem JF - Potential analysis : an international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis N2 - We study mixed boundary value problems for an elliptic operator A on a manifold X with boundary Y, i.e., Au = f in int X, T (+/-) u = g(+/-) on int Y+/-, where Y is subdivided into subsets Y+/- with an interface Z and boundary conditions T+/- on Y+/- that are Shapiro-Lopatinskij elliptic up to Z from the respective sides. We assume that Z subset of Y is a manifold with conical singularity v. As an example we consider the Zaremba problem, where A is the Laplacian and T- Dirichlet, T+ Neumann conditions. The problem is treated as a corner boundary value problem near v which is the new point and the main difficulty in this paper. Outside v the problem belongs to the edge calculus as is shown in Bull. Sci. Math. ( to appear). With a mixed problem we associate Fredholm operators in weighted corner Sobolev spaces with double weights, under suitable edge conditions along Z {v} of trace and potential type. We construct parametrices within the calculus and establish the regularity of solutions. KW - Zaremba problem KW - corner Sobolev spaces with double weights KW - pseudo-differential boundary value problems Y1 - 2006 U6 - https://doi.org/10.1007/s11118-006-9020-6 SN - 0926-2601 VL - 25 SP - 327 EP - 369 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Harutjunjan, Gohar A1 - Schulze, Bert-Wolfgang T1 - The relative index for corner singularities N2 - We study pseudo-differential operators on a cylinder R x B where B has conical singularities. Configurations of that kind are the local model of corner singularities with cross section B. Operators in our calculus are assumed to have symbols a which are meromorphic in the complex covariable with values in the algebra of all cone operators on B. We show an explicit formula for solutions of the homogeneous equation if a is independent of the axial variable t is an element of R. Each non-bijectivity point of the symbol in the complex plane corresponds to a finite-dimensional space of solutions. Moreover, we give a relative index formula Y1 - 2006 UR - http://www.springerlink.com/content/300422 U6 - https://doi.org/10.1007/s00020-005-1367-3 SN - 0378-620X ER - TY - BOOK A1 - Harutjunjan, Gohar A1 - Schulze, Bert-Wolfgang T1 - Boundary value problems in weighted edge spaces T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2006 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Gosson, Maurice A. de A1 - Gosson, Serge M. de T1 - Extension of the Conley-Zehnder index, a product formula, and an application to the Weyl representation of metaplectic operators JF - Journal of mathematical physics N2 - The aim of this paper is to express the Conley-Zehnder index of a symplectic path in terms of an index due to Leray and which has been studied by one of us in a previous work. This will allow us to prove a formula for the Conley-Zehnder index of the product of two symplectic paths in terms of a symplectic Cayley transform. We apply our results to a rigorous study of the Weyl representation of metaplectic operators, which plays a crucial role in the understanding of semiclassical quantization of Hamiltonian systems exhibiting chaotic behavior. Y1 - 2006 U6 - https://doi.org/10.1063/1.239066 SN - 0022-2488 VL - 47 IS - 12 PB - American Institute of Physics CY - Melville ER - TY - BOOK A1 - Gosson, Maurice A. de T1 - Symplectic geometry, wigner-weyl-moyal calculus, and quantum mechanics, in phase space ; Part 1 T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2006 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Gosson, Maurice A. de T1 - Symplectic geometry, wigner-weyl-moyal calculus, and quantum mechanics, in phase space ; Part 2 T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2006 SN - 1437-739X PB - Univ. CY - Potsdam ER -