@unpublished{AlsaedyTarkhanov2013, author = {Alsaedy, Ammar and Tarkhanov, Nikolai Nikolaevich}, title = {Normally solvable nonlinear boundary value problems}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-65077}, year = {2013}, abstract = {We study a boundary value problem for an overdetermined elliptic system of nonlinear first order differential equations with linear boundary operators. Such a problem is solvable for a small set of data, and so we pass to its variational formulation which consists in minimising the discrepancy. The Euler-Lagrange equations for the variational problem are far-reaching analogues of the classical Laplace equation. Within the framework of Euler-Lagrange equations we specify an operator on the boundary whose zero set consists precisely of those boundary data for which the initial problem is solvable. The construction of such operator has much in common with that of the familiar Dirichlet to Neumann operator. In the case of linear problems we establish complete results.}, language = {en} } @unpublished{SchulzeSterninShatalov1997, author = {Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor}, title = {Nonstationary problems for equations of Borel-Fuchs type}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-24973}, year = {1997}, abstract = {In the paper, the nonstationary problems for equations of Borel-Fuchs type are investigated. The asymptotic expansion are obtained for different orders of degeneration of operators in question. The approach to nonstationary problems based on the asymptotic theory on abstract algebras is worked out.}, language = {en} } @unpublished{LaeuterLiero2004, author = {L{\"a}uter, Henning and Liero, Hannelore}, title = {Nonparametric estimation and testing in survival models}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51586}, year = {2004}, abstract = {The aim of this paper is to demonstrate that nonparametric smoothing methods for estimating functions can be an useful tool in the analysis of life time data. After stating some basic notations we will present a data example. Applying standard parametric methods to these data we will see that this approach fails - basic features of the underlying functions are not reflected by their estimates. Our proposal is to use nonparametric estimation methods. These methods are explained in section 2. Nonparametric approaches are better in the sense that they are more flexible, and misspecifications of the model are avoided. But, parametric models have the advantage that the parameters can be interpreted. So, finally, we will formulate a test procedure to check whether a parametric or a nonparametric model is appropriate.}, language = {en} } @unpublished{Schrohe1999, author = {Schrohe, Elmar}, title = {Noncommutative residues, Dixmier's Trace, and heat trace expansions on manifolds with boundary}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25486}, year = {1999}, abstract = {For manifolds with boundary, we define an extension of Wodzicki's noncommutative residue to boundary value problems in Boutet de Monvel's calculus. We show that this residue can be recovered with the help of heat kernel expansions and explore its relation to Dixmier's trace.}, language = {en} } @article{PiatnitskiZhizhina2020, author = {Piatnitski, Andrey and Zhizhina, Elena}, title = {Non-local convolution type parabolic equations with fractional and regular time derivative}, series = {Lectures in pure and applied mathematics}, journal = {Lectures in pure and applied mathematics}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-485-2}, issn = {2199-4951}, doi = {10.25932/publishup-47202}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-472024}, pages = {65 -- 67}, year = {2020}, language = {en} } @unpublished{Fedosov1997, author = {Fedosov, Boris}, title = {Non-Abelian reduction in deformation quantization}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25101}, year = {1997}, abstract = {We consider a G-invariant star-product algebra A on a symplectic manifold (M,ω) obtained by a canonical construction of deformation quantization. Under assumptions of the classical Marsden-Weinstein theorem we define a reduction of the algebra A with respect to the G-action. The reduced algebra turns out to be isomorphic to a canonical star-product algebra on the reduced phase space B. In other words, we show that the reduction commutes with the canonical G-invariant deformation quantization. A similar statement in the framework of geometric quantization is known as the Guillemin-Sternberg conjecture (by now completely proved).}, language = {en} } @misc{DaiPraLouisMinelli2006, author = {Dai Pra, Paolo and Louis, Pierre-Yves and Minelli, Ida}, title = {Monotonicity and complete monotonicity for continuous-time Markov chains}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-7665}, year = {2006}, abstract = {We analyze the notions of monotonicity and complete monotonicity for Markov Chains in continuous-time, taking values in a finite partially ordered set. Similarly to what happens in discrete-time, the two notions are not equivalent. However, we show that there are partially ordered sets for which monotonicity and complete monotonicity coincide in continuous time but not in discrete-time.}, subject = {Stochastik}, language = {en} } @unpublished{Liu2005, author = {Liu, Weian}, title = {Monotone method for nonlocal systems of first order}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29791}, year = {2005}, abstract = {In this paper, the monotone method is extended to the initial-boundary value problems of nonlocal PDE system of first order, both quasi-monotone and non-monotone. A comparison principle is established, and a monotone scheme is given.}, language = {en} } @misc{Reich1994, author = {Reich, Sebastian}, title = {Momentum conserving symplectic integrators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-16824}, year = {1994}, abstract = {In this paper, we show that symplectic partitioned Runge-Kutta methods conserve momentum maps corresponding to linear symmetry groups acting on the phase space of Hamiltonian differential equations by extended point transformation. We also generalize this result to constrained systems and show how this conservation property relates to the symplectic integration of Lie-Poisson systems on certain submanifolds of the general matrix group GL(n).}, language = {en} } @unpublished{Fedosov1998, author = {Fedosov, Boris}, title = {Moduli spaces and deformation quantization in infinite dimensions}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25396}, year = {1998}, abstract = {We construct a deformation quantization on an infinite-dimensional symplectic space of regular connections on an SU(2)-bundle over a Riemannian surface of genus g ≥ 2. The construction is based on the normal form thoerem representing the space of connections as a fibration over a finite-dimensional moduli space of flat connections whose fibre is a cotangent bundle of the infinite-dimensional gauge group. We study the reduction with respect to the gauge groupe both for classical and quantum cases and show that our quantization commutes with reduction.}, language = {en} } @unpublished{ShlapunovTarkhanov2004, author = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich}, title = {Mixed problems with a parameter}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26677}, year = {2004}, abstract = {Let X be a smooth n -dimensional manifold and D be an open connected set in X with smooth boundary ∂D. Perturbing the Cauchy problem for an elliptic system Au = f in D with data on a closed set Γ ⊂ ∂D we obtain a family of mixed problems depending on a small parameter ε > 0. Although the mixed problems are subject to a non-coercive boundary condition on ∂D\Γ in general, each of them is uniquely solvable in an appropriate Hilbert space DT and the corresponding family {uε} of solutions approximates the solution of the Cauchy problem in DT whenever the solution exists. We also prove that the existence of a solution to the Cauchy problem in DT is equivalent to the boundedness of the family {uε}. We thus derive a solvability condition for the Cauchy problem and an effective method of constructing its solution. Examples for Dirac operators in the Euclidean space Rn are considered. In the latter case we obtain a family of mixed boundary problems for the Helmholtz equation.}, language = {en} } @unpublished{TarkhanovVasilevski2005, author = {Tarkhanov, Nikolai Nikolaevich and Vasilevski, Nikolai}, title = {Microlocal analysis of the Bochner-Martinelli integral}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30012}, year = {2005}, abstract = {In order to characterise the C*-algebra generated by the singular Bochner-Martinelli integral over a smooth closed hypersurfaces in Cn, we compute its principal symbol. We show then that the Szeg{\"o} projection belongs to the strong closure of the algebra generated by the singular Bochner-Martinelli integral.}, language = {en} } @unpublished{DeDonnoSchulze2003, author = {De Donno, G. and Schulze, Bert-Wolfgang}, title = {Meromorphic symbolic structures for boundary value problems on manifolds with edges}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26570}, year = {2003}, abstract = {We investigate the ideal of Green and Mellin operators with asymtotics for a manifold with edge-corner singularities and boundary which belongs to the structure of parametrices of elliptic boundary value problems on a configuration with corners whose base manifolds have edges.}, language = {en} } @unpublished{DinesSchulze2003, author = {Dines, Nicoleta and Schulze, Bert-Wolfgang}, title = {Mellin-edge representations of elliptic operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26627}, year = {2003}, abstract = {We construct a class of elliptic operators in the edge algebra on a manifold M with an embedded submanifold Y interpreted as an edge. The ellipticity refers to a principal symbolic structure consisting of the standard interior symbol and an operator-valued edge symbol. Given a differential operator A on M for every (sufficiently large) s we construct an associated operator As in the edge calculus. We show that ellipticity of A in the usual sense entails ellipticity of As as an edge operator (up to a discrete set of reals s). Parametrices P of A then correspond to parametrices Ps of As, interpreted as Mellin-edge representations of P.}, language = {en} } @article{JansenTsagkarogiannis2020, author = {Jansen, Sabine and Tsagkarogiannis, Dimitrios}, title = {Mayer expansion for the Asakura-Oosawa model of colloid theory}, series = {Lectures in pure and applied mathematics}, journal = {Lectures in pure and applied mathematics}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-485-2}, issn = {2199-4951}, doi = {10.25932/publishup-47210}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-472109}, pages = {127 -- 134}, year = {2020}, language = {en} } @unpublished{Keller2013, author = {Keller, Peter}, title = {Mathematical modeling of molecular motors}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-63045}, year = {2013}, abstract = {Amongst the many complex processes taking place in living cells, transport of cargoes across the cytosceleton is fundamental to cell viability and activity. To move cargoes between the different cell parts, cells employ Molecular Motors. The motors operate by transporting cargoes along the so-called cellular micro-tubules, namely rope-like structures that connect, for instance, the cell-nucleus and outer membrane. We introduce a new Markov Chain, the killed Quasi-Random-Walk, for such transport molecules and derive properties like the maximal run length and time. Furthermore we introduce permuted balance, which is a more flexible extension of the ordinary reversibility and introduce the notion of Time Duality, which compares certain passage times pathwise. We give a number of sufficient conditions for Time Duality based on the geometry of the transition graph. Both notions are closely related to properties of the killed Quasi-Random-Walk.}, language = {en} } @unpublished{Anders2009, author = {Anders, Martin}, title = {Martingale, Amarts und das starke Gesetz der Grossen Zahlen}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49494}, year = {2009}, abstract = {Aus dem Inhalt: Einleitung Kapitel 1. Starke Gesetze der Grossen Zahlen 1. SGGZ unter Wachstumsbedingungen an die p-ten Momente 2. SGGZ f{\"u}r identisch verteilte Zufallsvariablen 3. SGGZ f{\"u}r Prozesse mit *-mixing-Eigenschaft Kapitel 2. Einf{\"u}hrung zu diskreten (Sub-,Super-)Martingalen 1. Vorhersagbarkeit 2. gestoppte (Sub-,Super-)Martingale 3. Upcrossings 4. Konvergenzs{\"a}tze 5. Doob-Zerlegung 6. Eine {\"a}quivalente Definition eines (Sub-)Martingals Kapitel 3. Martingale und gleichgradige Integrierbarkeit 1. Gleichm{\"a}ßige(-f¨ormige,-gradige) Integrierbarkeit 2. gleichgradig integrierbare Martingale Kapitel 4. Martingale und das SGGZ Kapitel 5."reversed" (Sub-,Super-)Martingale 1. Konvergenzs{\"a}tze Kapitel 6. (Sub-,Super-)Martingale mit gerichteter Indexmenge 1. {\"A}quivalente Formulierung eines (Sub-)Martingals 2. Konvergenzs{\"a}tze Kapitel 7. Quasimartingale,Amarts und Semiamarts 1. Konvergenzs{\"a}tze 2. Riesz-Zerlegung 3. Doob-Zerlegung Kapitel 8. Amarts und das SGGZ Kapitel 9."reversed" Amarts und Semiamarts 1. Konvergenzs{\"a}tze 2."Aufw{\"a}rts"- gegen "Abw{\"a}rts"-Adaptiertheit 3. Riesz-Zerlegung 4. Stabilit{\"a}tsanalyse Kapitel 10. Amarts mit gerichteter Indexmenge 1. Konvergenzs{\"a}tze 2. Riesz-Zerlegung Anhang A. zur Existenz einer Folge unabh{\"a}ngiger Zufallsvariablen B. Konvergenz}, language = {de} } @unpublished{HieberSchrohe1997, author = {Hieber, Matthias and Schrohe, Elmar}, title = {Lρ spectral independence of elliptic operators via commutator estimates}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25047}, year = {1997}, abstract = {Let {Tsub(p) : q1 ≤ p ≤ q2} be a family of consistent Csub(0) semigroups on Lφ(Ω) with q1, q2 ∈ [1, ∞)and Ω ⊆ IRn open. We show that certain commutator conditions on Tφ and on the resolvent of its generator Aφ ensure the φ independence of the spectrum of Aφ for φ ∈ [q1, q2]. Applications include the case of Petrovskij correct systems with H{\"o}lder continuous coeffcients, Schr{\"o}dinger operators, and certain elliptic operators in divergence form with real, but not necessarily symmetric, or complex coeffcients.}, language = {en} } @unpublished{Galstian2001, author = {Galstian, Anahit}, title = {Lp - Lq decay estimates for the equation with exponentially growing coefficient}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26079}, year = {2001}, abstract = {Contents: 1 Introduction 1 Representation formulas 2 Consideration in the pseudodifferential zone: e up(t) |ξ| ≤ 1 3 Consideration in he hyperbolic zone: e up(t) |ξ| ≥ 1}, language = {en} } @unpublished{Popivanov2004, author = {Popivanov, Petăr R.}, title = {Lorenz transformations and creation of logarithmic singularities to the solutions of some nonstrictly hyperbolic semilinear systems with two space variables}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26710}, year = {2004}, language = {en} } @unpublished{KrainerSchulze2000, author = {Krainer, Thomas and Schulze, Bert-Wolfgang}, title = {Long-time asymptotics with geometric singularities in the spatial variables}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25824}, year = {2000}, abstract = {Content: Introduction 1 Anisotropic operators in a cylinder with a conical base 1.1 Manifolds with conical singularities and opertors of Fuchs type 1.2 Typical operators and symbol structures 2 Weighted wedge Sobolev spaces and edge asymptotics 2.1 Discrete edge asymptotics 2.2 Continuos edge asymptotics with discrete limit at infinity 2.3 Calculus with operator valued symbols 3 Corner asymptotics at infinity 3.1 The structure of singular functions 3.2 Operators with trace and potential conditions 3.3 Asymptotics and (anisotropic) elliptic regularity}, language = {en} } @unpublished{CattiauxFradonKuliketal.2013, author = {Cattiaux, Patrick and Fradon, Myriam and Kulik, Alexei Michajlovič and Roelly, Sylvie}, title = {Long time behavior of stochastic hard ball systems}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-68388}, year = {2013}, abstract = {We study the long time behavior of a system of two or three Brownian hard balls living in the Euclidean space of dimension at least two, submitted to a mutual attraction and to elastic collisions.}, language = {en} } @unpublished{NazaikinskiiSchulzeSternin2001, author = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris}, title = {Localization problem in index theory of elliptic operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26175}, year = {2001}, abstract = {This is a survey of recent results concerning the general index locality principle, associated surgery, and their applications to elliptic operators on smooth manifolds and manifolds with singularities as well as boundary value problems. The full version of the paper is submitted for publication in Russian Mathematical Surveys.}, language = {en} } @unpublished{Messina2001, author = {Messina, Francesca}, title = {Local solvability for semilinear Fuchsian equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26124}, year = {2001}, abstract = {Contents: 1 Introduction 2 Differential operators on manifolds with conical singularities 3 When H up(s,y) (B) is an algebra 4 Statement of the main result 5 Proof of the theorem}, language = {en} } @unpublished{BrauerKarp2006, author = {Brauer, Uwe and Karp, Lavi}, title = {Local existence of classical solutions for the Einstein-Euler system using weighted Sobolev spaces of fractional order}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30175}, year = {2006}, abstract = {We prove the existence of a class of local in time solutions, including static solutions, of the Einstein-Euler system. This result is the relativistic generalisation of a similar result for the Euler-Poisson system obtained by Gamblin [8]. As in his case the initial data of the density do not have compact support but fall off at infinity in an appropriate manner. An essential tool in our approach is the construction and use of weighted Sobolev spaces of fractional order. Moreover, these new spaces allow us to improve the regularity conditions for the solutions of evolution equations. The details of this construction, the properties of these spaces and results on elliptic and hyperbolic equations will be presented in a forthcoming article.}, language = {en} } @unpublished{Witt2002, author = {Witt, Ingo}, title = {Local asymptotic types}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26346}, year = {2002}, abstract = {The local theory of asymptotic types is elaborated. It appears as coordinate-free version of part of GOHBERG-SIGAL's theory of the inversion of finitely meromorphic, operator-valued functions at a point.}, language = {en} } @misc{ChampagnatRoelly2008, author = {Champagnat, Nicolas and Roelly, Sylvie}, title = {Limit theorems for conditioned multitype Dawson-Watanabe processes and Feller diffusions}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-18610}, year = {2008}, abstract = {A multitype Dawson-Watanabe process is conditioned, in subcritical and critical cases, on non-extinction in the remote future. On every finite time interval, its distribution is absolutely continuous with respect to the law of the unconditioned process. A martingale problem characterization is also given. Several results on the long time behavior of the conditioned mass process - the conditioned multitype Feller branching diffusion - are then proved. The general case is first considered, where the mutation matrix which models the interaction between the types, is irreducible. Several two-type models with decomposable mutation matrices are analyzed too .}, language = {en} } @unpublished{ChampagnatRoelly2007, author = {Champagnat, Nicolas and Roelly, Sylvie}, title = {Limit theorems for conditioned multitype Dawson-Watanabe processes}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49426}, year = {2007}, abstract = {A multitype Dawson-Watanabe process is conditioned, in subcritical and critical cases, on non-extinction in the remote future. On every nite time interval, its distribution law is absolutely continuous with respect to the law of the unconditioned process. A martingale problem characterization is also given. The explicit form of the Laplace functional of the conditioned process is used to obtain several results on the long time behaviour of the mass of the conditioned and unconditioned processes. The general case is considered first, where the mutation matrix which modelizes the interaction between the types, is irreducible. Several two-type models with decomposable mutation matrices are also analysed.}, language = {en} } @unpublished{SchulzeTarkhanov1997, author = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {Lefschetz theory on manifolds with edges : introduction}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-24948}, year = {1997}, abstract = {The aim of this book is to develop the Lefschetz fixed point theory for elliptic complexes of pseudodifferential operators on manifolds with edges. The general Lefschetz theory contains the index theory as a special case, while the case to be studied is much more easier than the index problem. The main topics are: - The calculus of pseudodifferential operators on manifolds with edges, especially symbol structures (inner as well as edge symbols). - The concept of ellipticity, parametrix constructions, elliptic regularity in Sobolev spaces. - Hodge theory for elliptic complexes of pseudodifferential operators on manifolds with edges. - Development of the algebraic constructions for these complexes, such as homotopy, tensor products, duality. - A generalization of the fixed point formula of Atiyah and Bott for the case of simple fixed points. - Development of the fixed point formula also in the case of non-simple fixed points, provided that the complex consists of diferential operarators only. - Investigation of geometric complexes (such as, for instance, the de Rham complex and the Dolbeault complex). Results in this direction are desirable because of both purely mathe matical reasons and applications in natural sciences.}, language = {en} } @article{PecherskyPirogovYambartsev2020, author = {Pechersky, Eugeny and Pirogov, Sergei and Yambartsev, Anatoly}, title = {Large emissions}, series = {Lectures in pure and applied mathematics}, journal = {Lectures in pure and applied mathematics}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-485-2}, issn = {2199-4951}, doi = {10.25932/publishup-47204}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-472049}, pages = {77 -- 86}, year = {2020}, language = {en} } @article{KeverpuetzKueppers2018, author = {Keverp{\"u}tz, Claudia and K{\"u}ppers, Bastian}, title = {Konsistente Lehr-Lern-Prozesse in der dualen IT-Ausbildung}, series = {Commentarii informaticae didacticae}, journal = {Commentarii informaticae didacticae}, number = {12}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-416341}, pages = {91 -- 100}, year = {2018}, abstract = {In der dualen IT-Ausbildung als Verbindung von beruflicher und akademischer Qualifikation werden die berufstypischen Werkzeuge, wie z. B. Laptops, ebenso in den Lehr-Lern-Prozessen der akademischen Unterrichtseinheiten eingesetzt. Im Pr{\"u}fungswesen wird oft auf klassische Papierklausuren zur{\"u}ckgegriffen. Unterrichtseinheiten mit hohem Blended-Learning-Anteil ohne E-Pr{\"u}fung werden dabei als „nicht konsistent" wahrgenommen. In diesem Artikel wird eine empirische Studie dargelegt, die untersucht, welche Einfl{\"u}sse aus der pers{\"o}nlichen Lernbiografie bei den Lehrenden in einer dualen IT-Ausbildung dazu f{\"u}hren k{\"o}nnen, die M{\"o}glichkeiten eines E-Assessments als summative Modulpr{\"u}fung anzunehmen oder abzulehnen. Beispielhaft wurden in der dargelegten Studie Interviews mit Dozenten gef{\"u}hrt und diese hinsichtlich der Verbindung zwischen Lernbiografie, Gestaltung der Didaktik der Lehr-Lern-Prozesse, Zufriedenheit und Ver{\"a}nderungsbereitschaft untersucht.}, language = {de} } @unpublished{PrenovTarkhanov2001, author = {Prenov, B. and Tarkhanov, Nikolai Nikolaevich}, title = {Kernel spikes of singular problems}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26195}, year = {2001}, abstract = {Function spaces with asymptotics is a usual tool in the analysis on manifolds with singularities. The asymptotics are singular ingredients of the kernels of pseudodifferential operators in the calculus. They correspond to potentials supported by the singularities of the manifold, and in this form asymptotics can be treated already on smooth configurations. This paper is aimed at describing refined asymptotics in the Dirichlet problem in a ball. The beauty of explicit formulas highlights the structure of asymptotic expansions in the calculi on singular varieties.}, language = {en} } @unpublished{Shlapunov1999, author = {Shlapunov, Alexander}, title = {Iterations of self-adjoint operators and their applications to elliptic systems}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25401}, year = {1999}, abstract = {Let Hsub(0), Hsub(1) be Hilbert spaces and L : Hsub(0) -> Hsub(1) be a linear bounded operator with ||L|| ≤ 1. Then L*L is a bounded linear self-adjoint non-negative operator in the Hilbert space Hsub(0) and one can use the Neumann series ∑∞sub(v=0)(I - L*L)v L*f in order to study solvability of the operator equation Lu = f. In particular, applying this method to the ill-posed Cauchy problem for solutions to an elliptic system Pu = 0 of linear PDE's of order p with smooth coefficients we obtain solvability conditions and representation formulae for solutions of the problem in Hardy spaces whenever these solutions exist. For the Cauchy-Riemann system in C the summands of the Neumann series are iterations of the Cauchy type integral. We also obtain similar results 1) for the equation Pu = f in Sobolev spaces, 2) for the Dirichlet problem and 3) for the Neumann problem related to operator P*P if P is a homogeneous first order operator and its coefficients are constant. In these cases the representations involve sums of series whose terms are iterations of integro-differential operators, while the solvability conditions consist of convergence of the series together with trivial necessary conditions.}, language = {en} } @unpublished{AirapetyanWitt1997, author = {Airapetyan, Ruben and Witt, Ingo}, title = {Isometric properties of the Hankel Transformation in weighted sobolev spaces}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25001}, year = {1997}, abstract = {It is shown that the Hankel transformation Hsub(v) acts in a class of weighted Sobolev spaces. Especially, the isometric mapping property of Hsub(v) which holds on L²(IRsub(+),rdr) is extended to spaces of arbitrary Sobolev order. The novelty in the approach consists in using techniques developed by B.-W. Schulze and others to treat the half-line Rsub(+) as a manifold with a conical singularity at r = 0. This is achieved by pointing out a connection between the Hankel transformation and the Mellin transformation.The procedure proposed leads at the same time to a short proof of the Hankel inversion formula. An application to the existence and higher regularity of solutions, including their asymptotics, to the 1-1-dimensional edge-degenerated wave equation is given.}, language = {en} } @unpublished{LevendorskiiBoyarchenko1998, author = {Levendorskii, Sergei Z. and Boyarchenko, Svetlana I.}, title = {Investment under uncertainty when shocks are non-gaussian}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25201}, year = {1998}, language = {en} } @unpublished{FradonRoelly2009, author = {Fradon, Myriam and Roelly, Sylvie}, title = {Infinitely many Brownian globules with Brownian radii}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49552}, year = {2009}, abstract = {We consider an infinite system of non overlaping globules undergoing Brownian motions in R3. The term globules means that the objects we are dealing with are spherical, but with a radius which is random and time-dependent. The dynamics is modelized by an infinitedimensional Stochastic Differential Equation with local time. Existence and uniqueness of a strong solution is proven for such an equation with fixed deterministic initial condition. We also find a class of reversible measures.}, language = {en} } @unpublished{FradonRoelly2005, author = {Fradon, Myriam and Roelly, Sylvie}, title = {Infinite system of Brownian Balls: Equilibrium measures are canonical Gibbs}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51594}, year = {2005}, abstract = {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.}, language = {en} } @unpublished{SavinSternin2001, author = {Savin, Anton and Sternin, Boris}, title = {Index defects in the theory of nonlocal boundary value problems and the η-invariant}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26146}, year = {2001}, abstract = {The paper deals with elliptic theory on manifolds with boundary represented as a covering space. We compute the index for a class of nonlocal boundary value problems. For a nontrivial covering, the index defect of the Atiyah-Patodi-Singer boundary value problem is computed. We obtain the Poincar{\´e} duality in the K-theory of the corresponding manifolds with singularities.}, language = {en} } @unpublished{Louis2004, author = {Louis, Pierre-Yves}, title = {Increasing Coupling of Probabilistic Cellular Automata}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51578}, year = {2004}, abstract = {We give a necessary and sufficient condition for the existence of an increasing coupling of N (N >= 2) synchronous dynamics on S-Zd (PCA). Increasing means the coupling preserves stochastic ordering. We first present our main construction theorem in the case where S is totally ordered; applications to attractive PCAs are given. When S is only partially ordered, we show on two examples that a coupling of more than two synchronous dynamics may not exist. We also prove an extension of our main result for a particular class of partially ordered spaces.}, language = {en} } @unpublished{Sadykov1999, author = {Sadykov, Timour}, title = {Hypergeometric systems of differential equations and amoebas of rational functions}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25665}, year = {1999}, abstract = {We study the approach to the theory of hypergeometric functions in several variables via a generalization of the Horn system of differential equations. A formula for the dimension of its solution space is given. Using this formula we construct an explicit basis in the space of holomorphic solutions to the generalized Horn system under some assumptions on its parameters. These results are applied to the problem of describing the complement of the amoeba of a rational function, which was posed in [12].}, language = {en} } @unpublished{KytmanovMyslivetsTarkhanov2002, author = {Kytmanov, Alexander and Myslivets, Simona and Tarkhanov, Nikolai Nikolaevich}, title = {Holomorphic Lefschetz formula for manifolds with boundary}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26354}, year = {2002}, abstract = {The classical Lefschetz fixed point formula expresses the number of fixed points of a continuous map f : M -> M in terms of the transformation induced by f on the cohomology of M. In 1966 Atiyah and Bott extended this formula to elliptic complexes over a compact closed manifold. In particular, they presented a holomorphic Lefschtz formula for compact complex manifolds without boundary, a result, in the framework of algebraic geometry due to Eichler (1957) for holomorphic curves. On compact complex manifolds with boundary the Dolbeault complex is not elliptic, hence the Atiyah-Bott theory is no longer applicable. To get rid of the difficulties related to the boundary behaviour of the Dolbeault cohomology, Donelli and Fefferman (1986) derived a fixed point formula for the Bergman metric. The purpose of this paper is to present a holomorphic Lefschtz formula on a compact complex manifold with boundary}, language = {en} } @unpublished{Tarkhanov2004, author = {Tarkhanov, Nikolai Nikolaevich}, title = {Harmonic integrals on domains with edges}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26800}, year = {2004}, abstract = {We study the Neumann problem for the de Rham complex in a bounded domain of Rn with singularities on the boundary. The singularities may be general enough, varying from Lipschitz domains to domains with cuspidal edges on the boundary. Following Lopatinskii we reduce the Neumann problem to a singular integral equation of the boundary. The Fredholm solvability of this equation is then equivalent to the Fredholm property of the Neumann problem in suitable function spaces. The boundary integral equation is explicitly written and may be treated in diverse methods. This way we obtain, in particular, asymptotic expansions of harmonic forms near singularities of the boundary.}, language = {en} } @unpublished{SchulzeVolpato2004, author = {Schulze, Bert-Wolfgang and Volpato, A.}, title = {Green operators in the edge calculus}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26846}, year = {2004}, abstract = {Green operators on manifolds with edges are known to be an ingredient of parametrices of elliptic (edge-degenerate) operators. They play a similar role as corresponding operators in boundary value problems. Close to edge singularities the Green operators have a very complex asymptotic behaviour. We give a new characterisation of Green edge symbols in terms of kernels with discrete and continuous asymptotics in the axial variable of local model cones.}, language = {en} } @unpublished{SchulzeShlapunovTarkhanov2000, author = {Schulze, Bert-Wolfgang and Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich}, title = {Green integrals on manifolds with cracks}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25777}, year = {2000}, abstract = {We prove the existence of a limit in Hm(D) of iterations of a double layer potential constructed from the Hodge parametrix on a smooth compact manifold with boundary, X, and a crack S ⊂ ∂D, D being a domain in X. Using this result we obtain formulas for Sobolev solutions to the Cauchy problem in D with data on S, for an elliptic operator A of order m ≥ 1, whenever these solutions exist. This representation involves the sum of a series whose terms are iterations of the double layer potential. A similar regularisation is constructed also for a mixed problem in D.}, language = {en} } @unpublished{Witt2003, author = {Witt, Ingo}, title = {Green formulae for cone differential operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26633}, year = {2003}, abstract = {Green formulae for elliptic cone differential operators are established. This is achieved by an accurate description of the maximal domain of an elliptic cone differential operator and its formal adjoint; thereby utilizing the concept of a discrete asymptotic type. From this description, the singular coefficients replacing the boundary traces in classical Green formulas are deduced.}, language = {en} } @unpublished{Liero2003, author = {Liero, Hannelore}, title = {Goodness of Fit Tests of L2-Type}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51494}, year = {2003}, abstract = {We give a survey on procedures for testing functions which are based on quadratic deviation measures. The following problems are considered: Testing whether a density function lies in a parametric class of functions, whether continuous random variables are independent; testing cell probabilities and independence in sparse data sets; testing the parametric fit of a regression homoscedasticity in a regression model and testing the hazard rate in survival models with censoring and with and without covariates.}, language = {en} } @unpublished{HuichengWitt2002, author = {Huicheng, Yin and Witt, Ingo}, title = {Global singularity structure of weak solutions to 3-D semilinear dispersive wave equations with discontinuous initial data}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26395}, year = {2002}, language = {en} } @unpublished{Yin2002, author = {Yin, Huicheng}, title = {Global existence of a shock for the supersonic flow past a curved wedge}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26272}, year = {2002}, abstract = {This note is devoted to the study on the global existence of a shock wave for the supersonic flow past a curved wedge. When the curved wedge is a small perturbation of a straight wedge and the angle of the wedge is less than some critical value, wwe show that a shock attached at the wedge will exist globally.}, language = {en} } @unpublished{DeXingHui2003, author = {De-Xing, Kong and Hui, Yao}, title = {Global exact boundary controllability of a class of quasilinear hyperbolic systems of conservation laws II}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26565}, year = {2003}, abstract = {In this paper, by a new constructive method, the authors reprove the global exact boundary controllability of a class of quasilinear hyperbolic systems of conservation laws with linearly degenerate fields. It is shown that the system with nonlinear boundary conditions is globally exactly boundary controllable in the class of piecewise C¹ functions. In particular, the authors give the optimal control time of the system. Finally, a new application is also given.}, language = {en} } @unpublished{ChenLiXu2007, author = {Chen, Hua and Li, Wei-Xi and Xu, Chao-Jiang}, title = {Gevrey hypoellipticity for linear and non-linear Fokker-Planck equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30283}, year = {2007}, abstract = {This paper studies the Gevrey regularity of weak solutions of a class of linear and semilinear Fokker-Planck equations.}, language = {en} } @unpublished{GilKrainerMendoza2004, author = {Gil, Juan B. and Krainer, Thomas and Mendoza, Gerardo A.}, title = {Geometry and spectra of closed extensions of elliptic cone operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26815}, year = {2004}, abstract = {We study the geometry of the set of closed extensions of index 0 of an elliptic cone operator and its model operator in connection with the spectra of the extensions, and give a necessary and sufficient condition for the existence of rays of minimal growth for such operators.}, language = {en} } @unpublished{Yagdjian2001, author = {Yagdjian, Karen}, title = {Geometric optics for the nonlinear hyperbolic systems of Kirchhoff-type}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26059}, year = {2001}, abstract = {Contents: 1 Introduction 2 Main result 3 Construction of the asymptotic solutions 3.1 Derivation of the equations for the profiles 3.2 Exsistence of the principal profile 3.3 Determination of Usub(2) and the remaining profiles 4 Stability of the samll global solutions. Justification of One Phase Nonlinear Geometric Optics for the Kirchhoff-type equations 4.1 Stability of the global solutions to the Kirchhoff-type symmetric hyperbolic systems 4.2 The nonlinear system of ordinary differential equations with the parameter 4.3 Some energies estimates 4.4 The dependence of the solution W(t, ξ) on the function s(t) 4.5 The oscillatory integrals of the bilinear forms of the solutions 4.6 Estimates for the basic bilinear form Γsub(s)(t) 4.7 Contraction mapping 4.8 Stability of the global solution 4.9 Justification of One Phase Nonlinear Geometric Optics for the Kirchhoff-type equations}, language = {en} } @unpublished{KrupchykTarkhanovTuomela2005, author = {Krupchyk, K. and Tarkhanov, Nikolai Nikolaevich and Tuomela, J.}, title = {Generalised elliptic boundary problems}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29994}, year = {2005}, abstract = {For elliptic systems of differential equations on a manifold with boundary, we prove the Fredholm property of a class of boundary problems which do not satisfy the Shapiro-Lopatinskii property. We name these boundary problems generalised elliptic, for they preserve the main properties of elliptic boundary problems. Moreover, they reduce to systems of pseudodifferential operators on the boundary which are generalised elliptic in the sense of Saks (1997).}, language = {en} } @unpublished{LyTarkhanov2013, author = {Ly, Ibrahim and Tarkhanov, Nikolai Nikolaevich}, title = {Generalised Beltrami equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-67416}, year = {2013}, abstract = {We enlarge the class of Beltrami equations by developping a stability theory for the sheaf of solutions of an overdetermined elliptic system of first order homogeneous partial differential equations with constant coefficients in the Euclidean space.}, language = {en} } @unpublished{Rafler2009, author = {Rafler, Mathias}, title = {Gaussian loop- and polya processes : a point process approach}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51638}, year = {2009}, abstract = {Zuf{\"a}llige Punktprozesse beschreiben eine (zuf{\"a}llige) zeitliche Abfolge von Ereignissen oder eine (zuf{\"a}llige) r{\"a}umliche Anordnung von Objekten. Deren wichtigster Vertreter ist der Poissonprozess. Der Poissonprozess zum Intensit{\"a}tsmaß, das Lebesgue-Maß ordnet jedem Gebiet sein Volumen zu, erzeugt lokal, d.h in einem beschr{\"a}nkten Gebiet B, gerade eine mit dem Volumen von B poissonverteilte Anzahl von Punkten, die identisch und unabh{\"a}ngig voneinander in B plaziert werden; im Mittel ist diese Anzahl (B). Ersetzt man durch ein Vielfaches a, so wird diese Anzahl mit dem a-fachen Mittelwert erzeugt. Poissonprozesse, die im gesamten Raum unendlich viele Punkte realisieren, enthalten bereits in einer einzigen Stichprobe gen{\"u}gend Informationen, um Statistik betreiben zu k{\"o}nnen: Bedingt man lokal bzgl. der Anzahl der Teilchen einer Stichprobe, so fragt man nach allen Punktprozessen, die eine solche Beobachtung h{\"a}tten liefern k{\"o}nnen. Diese sind Limespunktprozesse zu dieser Beobachtung. Kommt mehr als einer in Frage, spricht man von einem Phasen{\"u}bergang. Da die Menge dieser Limespunktprozesse konvex ist, fragt man nach deren Extremalpunkten, dem Rand. Im ersten Teil wird ein Poissonprozess f{\"u}r ein physikalisches Teilchenmodell f{\"u}r Bosonen konstruiert. Dieses erzeugt sogenannte Loops, das sind geschlossene Polygonz{\"u}ge, die dadurch charakterisiert sind, dass man an einem Ort mit einem Punkt startet, den mit einem normalverteilten Schritt l{\"a}uft und dabei nach einer gegebenen, aber zuf{\"a}lligen Anzahl von Schritten zum Ausgangspunkt zur{\"u}ckkehrt. F{\"u}r verschiedene Beobachtungen von Stichproben werden zugeh{\"o}rige Limespunktprozesse diskutiert. Diese Beobachtungen umfassen etwa das Z{\"a}hlen der Loops gem{\"a}aß ihrer L{\"a}nge, das Z{\"a}hlen der Loops insgesamt, oder das Z{\"a}hlen der von den Loops gemachten Schritte. Jede Wahl zieht eine charakteristische Struktur der invarianten Punktprozesse nach sich. In allen hiesigen F{\"a}llen wird ein charakteristischer Phasen{\"u}bergang gezeigt und Extremalpunkte werden als spezielle Poissonprozesse identifiziert. Insbesondere wird gezeigt, wie die Wahl der Beobachtung die L{\"a}nge der Loops beeinflusst. Geometrische Eigenschaften dieser Poissonprozesse sind der Gegenstand des zweiten Teils der Arbeit. Die Technik der Palmschen Verteilungen eines Punktprozesses erlaubt es, unter den unendlich vielen Loops einer Realisierung den typischen Loop herauszupicken, dessen Geometrie dann untersucht wird. Eigenschaften sind unter anderem die euklidische L{\"a}nge eines Schrittes oder, nimmt man mehrere aufeinander folgende Schritte, das Volumen des von ihnen definierten Simplex. Weiterhin wird gezeigt, dass der Schwerpunkt eines typischen Loops normalverteilt ist mit einer festen Varianz. Der dritte und letzte Teil befasst sich mit der Konstruktion, den Eigenschaften und der Statistik eines neuartigen Punktprozesses, der Polyascher Summenprozess genannt wird. Seine Konstruktion verallgemeinert das Prinzip der Polyaschen Urne: Im Gegensatz zum Poissonprozess, der alle Punkte unabh{\"a}ngig und vor allem identisch verteilt, werden hier die Punkte nacheinander derart verteilt, dass der Ort, an dem ein Punkt plaziert wird, eine Belohnung auf die Wahrscheinlichkeit bekommt, nach der nachfolgende Punkte verteilt werden. Auf diese Weise baut der Polyasche Summenprozess "T{\"u}rmchen", indem sich verschiedene Punkte am selben Ort stapeln. Es wird gezeigt, dass dennoch grundlegende Eigenschaften mit denjenigen des Poissonprozesses {\"u}bereinstimmen, dazu geh{\"o}ren unendliche Teilbarkeit sowie Unabh{\"a}ngigkeit der Zuw{\"a}chse. Zudem werden sein Laplace-Funktional sowie seine Palmsche Verteilung bestimmt. Letztere zeigt, dass die H{\"o}he der T{\"u}rmchen gerade geometrisch verteilt ist. Abschließend werden wiederum Statistiken, nun f{\"u}r den Summenprozess, diskutiert. Je nach Art der Beobachtung von der Stichprobe, etwa Anzahl, Gesamth{\"o}he der T{\"u}rmchen oder beides, gibt es in jedem der drei F{\"a}lle charakteristische Limespunktprozesse und es stellt sich heraus, dass die zugeh{\"o}rigen Extremalverteilungen wiederum Polyasche Summenprozesse sind.}, language = {en} } @article{RoepkeLarischSchroeder2018, author = {R{\"o}pke, Ren{\´e} and Larisch, Kathrin and Schroeder, Ulrik}, title = {F{\"o}rderung {\"u}berfachlicher Kompetenzen in praktischen Software- Engineering-Veranstaltungen der RWTH Aachen}, series = {Commentarii informaticae didacticae}, journal = {Commentarii informaticae didacticae}, number = {12}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-416334}, pages = {79 -- 89}, year = {2018}, abstract = {Im Rahmen eines Informatikstudiums wird neben theoretischen Grundlagen und Programmierf{\"a}higkeiten auch gezielt vermittelt, wie moderne Software in der Praxis entwickelt wird. Dabei wird oftmals eine Form der Projektarbeit gew{\"a}hlt, um Studierenden m{\"o}glichst realit{\"a}tsnahe Erfahrungen zu erm{\"o}glichen. Die Studierenden entwickeln einzeln oder in kleineren Teams Softwareprodukte f{\"u}r ausgew{\"a}hlte Problemstellungen. Neben fachlichen Inhalte stehen durch gruppendynamische Prozesse auch {\"u}berfachliche Kompetenzen im Fokus. Dieser Beitrag pr{\"a}sentiert eine Interviewstudie mit Dozierenden von Softwareprojektpraktika an der RWTH Aachen und konzentriert sich auf die Ausgestaltung der Veranstaltungen sowie F{\"o}rderung von {\"u}berfachlichen Kompetenzen nach einem Kompetenzprofil f{\"u}r Softwareingenieure.}, language = {de} } @unpublished{YagdjianGalstian2007, author = {Yagdjian, Karen and Galstian, Anahit}, title = {Fundamental solutions for wave equation in de Sitter model of universe}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30271}, year = {2007}, abstract = {In this article we construct the fundamental solutions for the wave equation arising in the de Sitter model of the universe. We use the fundamental solutions to represent solutions of the Cauchy problem and to prove the Lp - Lq-decay estimates for the solutions of the equation with and without a source term.}, language = {en} } @unpublished{CoriascoPanarese2000, author = {Coriasco, Sandro and Panarese, Paolo}, title = {Fourier integral operators defined by classical symbols with exit behaviour}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25896}, year = {2000}, abstract = {We continue the investigation of the calculus of Fourier Integral Operators (FIOs) in the class of symbols with exit behaviour (SG symbols). Here we analyse what happens when one restricts the choice of amplitude and phase functions to the subclass of the classical SG symbols. It turns out that the main composition theorem, obtained in the environment of general SG classes, has a "classical" counterpart. As an application, we study the Cauchy problem for classical hyperbolic operators of order (1, 1); for such operators we refine the known results about the analogous problem for general SG hyperbolic operators. The material contained here will be used in a forthcoming paper to obtain a Weyl formula for a class of operators defined on manifolds with cylindrical ends, improving the results obtained in [9].}, language = {en} } @unpublished{Yin2002, author = {Yin, Huicheng}, title = {Formation and construction of a shock wave for 3-D compressible Euler equations with spherical initial data}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26263}, year = {2002}, abstract = {In this paper, the problem on formation and construction of a shock wave for three dimensional compressible Euler equations with the small perturbed spherical initial data is studied. If the given smooth initial data satisfies certain nondegenerate condition, then from the results in [20], we know that there exists a unique blowup point at the blowup time such that the first order derivates of smooth solution blow up meanwhile the solution itself is still continuous at the blowup point. From the blowup point, we construct a weak entropy solution which is not uniformly Lipschitz continuous on two sides of shock curve, moreover the strength of the constructed shock is zero at the blowup point and then gradually increases. Additionally, some detailed and precise estimates on the solution are obtained in the neighbourhood of the blowup point.}, language = {en} } @unpublished{ShlapunovTarkhanov2007, author = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich}, title = {Formal Poincar{\´e} lemma}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30231}, year = {2007}, abstract = {We show how the multiple application of the formal Cauchy-Kovalevskaya theorem leads to the main result of the formal theory of overdetermined systems of partial differential equations. Namely, any sufficiently regular system Au = f with smooth coefficients on an open set U ⊂ Rn admits a solution in smooth sections of a bundle of formal power series, provided that f satisfies a compatibility condition in U.}, language = {en} } @unpublished{Gosson2005, author = {Gosson, Maurice A. de}, title = {Extended Weyl calculus and application to the phase-space Schr{\"o}dinger equation}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29879}, year = {2005}, abstract = {We show that the Schr¨odinger equation in phase space proposed by Torres-Vega and Frederick is canonical in the sense that it is a natural consequence of the extendedWeyl calculus obtained by letting the Heisenberg group act on functions (or half-densities) defined on phase space. This allows us, in passing, to solve rigorously the TF equation for all quadratic Hamiltonians.}, language = {en} } @unpublished{GalstianYagdjian1997, author = {Galstian, Anahit and Yagdjian, Karen}, title = {Exponential function of pseudo-differential operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-24982}, year = {1997}, abstract = {The paper is devoted to the construction of the exponential function of a matrix pseudo-differential operator which do not satisfy any of the known theorems (see, Sec.8 Ch.VIII and Sec.2 Ch.XI of [17]). The applications to the construction of the fundamental solution for the Cauchy problem for the hyperbolic operators with the characteristics of variable multiplicity are given, too.}, language = {en} } @article{FredeKnobelsdorf2018, author = {Frede, Christiane and Knobelsdorf, Maria}, title = {Explorative Datenanalyse der Studierendenperformance in der Theoretischen Informatik}, series = {Commentarii informaticae didacticae}, journal = {Commentarii informaticae didacticae}, number = {10}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-416378}, pages = {135 -- 149}, year = {2018}, abstract = {In diesem Artikel werden die Ergebnisse einer explorativen Datenanalyse {\"u}ber die Studierendenperformance in Klausur- und Hausaufgaben eines Einf{\"u}hrungskurses der Theoretischen Informatik vorgestellt. Da bisher empirisch wenig untersucht ist, welche Probleme Studierenden in den Einf{\"u}hrungskursen haben und die Durchfallquoten in diesen Kursen sehr hoch sind, soll auf diesem Weg ein {\"U}berblick gegeben werden. Die Ergebnisse zeigen, dass alle Studierenden unabh{\"a}ngig von ihrer Klausurnote die niedrigste Performance in den Klausur- und Hausaufgaben aufweisen, in denen formale Beweise gefordert sind. Dieses Ergebnis st{\"a}rkt die Vermutung, dass didaktische Ans{\"a}tze und Maßnahmen sich insbesondere auf das Erlernen formaler Beweismethoden fokussieren sollten, um Informatik-Studierende nachhaltiger dabei zu unterst{\"u}tzen, in Theoretischer Informatik erfolgreich zu sein.}, language = {de} } @unpublished{BoeckmannNiebsch1998, author = {B{\"o}ckmann, Christine and Niebsch, Jenny}, title = {Examination of the nonlinear LIDAR-operator : the influence of inhomogeneous absorbing spheres on the operator}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14725}, year = {1998}, abstract = {The determination of the atmospheric aerosol size distribution is an inverse illposed problem. The shape and the material composition of the air-carried particles are two substantial model parameters. Present evaluation algorithms only used an approximation with spherical homogeneous particles. In this paper we propose a new numerically efficient recursive algorithm for inhomogeneous multilayered coated and absorbing particles. Numerical results of real existing particles show that the influence of the two parameters on the model is very important and therefore cannot be ignored.}, language = {en} } @unpublished{SchulzeTarkhanov1998, author = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {Euler solutions of pseudodifferential equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25211}, year = {1998}, abstract = {We consider a homogeneous pseudodifferential equation on a cylinder C = IR x X over a smooth compact closed manifold X whose symbol extends to a meromorphic function on the complex plane with values in the algebra of pseudodifferential operators over X. When assuming the symbol to be independent on the variable t element IR, we show an explicit formula for solutions of the equation. Namely, to each non-bijectivity point of the symbol in the complex plane there corresponds a finite-dimensional space of solutions, every solution being the residue of a meromorphic form manufactured from the inverse symbol. In particular, for differential equations we recover Euler's theorem on the exponential solutions. Our setting is model for the analysis on manifolds with conical points since C can be thought of as a 'stretched' manifold with conical points at t = -infinite and t = infinite.}, language = {en} } @unpublished{Tarkhanov2006, author = {Tarkhanov, Nikolai Nikolaevich}, title = {Euler characteristic of Fredholm quasicomplexes}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30117}, year = {2006}, abstract = {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.}, language = {en} } @unpublished{SavinSternin2000, author = {Savin, Anton and Sternin, Boris}, title = {Eta-invariant and Pontrjagin duality in K-theory}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25747}, year = {2000}, abstract = {The topological significance of the spectral Atiyah-Patodi-Singer η-invariant is investigated. We show that twice the fractional part of the invariant is computed by the linking pairing in K-theory with the orientation bundle of the manifold. The Pontrjagin duality implies the nondegeneracy of the linking form. An example of a nontrivial fractional part for an even-order operator is presented.}, language = {en} } @unpublished{SavinSternin2000, author = {Savin, Anton and Sternin, Boris}, title = {Eta invariant and parity conditions}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25869}, year = {2000}, abstract = {We give a formula for the η-invariant of odd order operators on even-dimensional manifolds, and for even order operators on odd-dimensional manifolds. Geometric second order operators are found with nontrivial η-invariants. This solves a problem posed by P. Gilkey.}, language = {en} } @unpublished{Penisson2010, author = {P{\´e}nisson, Sophie}, title = {Estimation of the infection parameter in the different phases of an epidemic modeled by a branching process}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49607}, year = {2010}, abstract = {The aim of this paper is to build and compare estimators of the infection parameter in the different phases of an epidemic (growth and extinction phases). The epidemic is modeled by a Markovian process of order d > 1 (allowing non-Markovian life spans), and can be written as a multitype branching process. We propose three estimators suitable for the different classes of criticality of the process, in particular for the subcritical case corresponding to the extinction phase. We prove their consistency and asymptotic normality for two asymptotics, when the number of ancestors (resp. number of generations) tends to infinity. We illustrate the asymptotic properties with simulated examples, and finally use our estimators to study the infection intensity in the extinction phase of the BSE epidemic in Great-Britain.}, language = {en} } @unpublished{Laeuter2003, author = {L{\"a}uter, Henning}, title = {Estimation in partly parametric additive Cox models}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51509}, year = {2003}, abstract = {The dependence between survival times and covariates is described e.g. by proportional hazard models. We consider partly parametric Cox models and discuss here the estimation of interesting parameters. We represent the ma- ximum likelihood approach and extend the results of Huang (1999) from linear to nonlinear parameters. Then we investigate the least squares esti- mation and formulate conditions for the a.s. boundedness and consistency of these estimators.}, language = {en} } @book{Liero2010, author = {Liero, Hannelore}, title = {Estimation and testing the effect of covariates in accelerated life time models under censoring}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-52823}, publisher = {Universit{\"a}t Potsdam}, year = {2010}, abstract = {The accelerated lifetime model is considered. To test the influence of the covariate we transform the model in a regression model. Since censoring is allowed this approach leads to a goodness-of-fit problem for regression functions under censoring. So nonparametric estimation of regression functions under censoring is investigated, a limit theorem for a L2-distance is stated and a test procedure is formulated. Finally a Monte Carlo procedure is proposed.}, language = {en} } @misc{Louis2004, author = {Louis, Pierre-Yves}, title = {Ergodicity of PCA}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-6589}, year = {2004}, abstract = {For a general attractive Probabilistic Cellular Automata on S-Zd, we prove that the (time-) convergence towards equilibrium of this Markovian parallel dynamics, exponentially fast in the uniform norm, is equivalent to a condition (A). This condition means the exponential decay of the influence from the boundary for the invariant measures of the system restricted to finite boxes. For a class of reversible PCA dynamics on {1,+1}(Zd), wit a naturally associated Gibbsian potential rho, we prove that a (spatial-) weak mixing condition (WM) for rho implies the validity of the assumption (A); thus exponential (time-) ergodicity of these dynamics towards the unique Gibbs measure associated to rho hods. On some particular examples we state that exponential ergodicity holds as soon as there is no phase transition.}, subject = {Wahrscheinlichkeitstheorie}, language = {en} } @article{StrieweKramer2018, author = {Striewe, Michael and Kramer, Matthias}, title = {Empirische Untersuchungen von L{\"u}ckentext-Items zur Beherrschung der Syntax einer Programmiersprache}, series = {Commentarii informaticae didacticae}, journal = {Commentarii informaticae didacticae}, number = {12}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-416353}, pages = {101 -- 115}, year = {2018}, abstract = {L{\"u}ckentext-Items auf der Basis von Programmcode k{\"o}nnen eingesetzt werden, um Kenntnisse in der Syntax einer Programmiersprache zu pr{\"u}fen, ohne dazu komplexe Programmieraufgaben zu stellen, deren Bearbeitung weitere Kompetenzen erfordert. Der vorliegende Beitrag dokumentiert den Einsatz von insgesamt zehn derartigen Items in einer universit{\"a}ren Erstsemestervorlesung zur Programmierung mit Java. Es werden sowohl Erfahrungen mit der Konstruktion der Items als auch empirische Daten aus dem Einsatz diskutiert. Der Beitrag zeigt dadurch insbesondere die Herausforderungen bei der Konstruktion valider Instrumente zur Kompetenzmessung in der Programmierausbildung auf. Die begrenzten und teilweise vorl{\"a}ufigen Ergebnisse zur Qualit{\"a}t der erzeugten Items legen trotzdem nahe, dass Erstellung und Einsatz entsprechender Items m{\"o}glich ist und einen Beitrag zur Kompetenzmessung leisten kann.}, language = {de} } @unpublished{SchulzeTarkhanov1999, author = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {Ellipticity and parametrices on manifolds with caspidal edges}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25411}, year = {1999}, language = {en} } @unpublished{SchroheSeiler1999, author = {Schrohe, Elmar and Seiler, J{\"o}rg}, title = {Ellipticity and invertibility in the cone algebra on Lp-Sobolev spaces}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25621}, year = {1999}, abstract = {Given a manifold B with conical singularities, we consider the cone algebra with discrete asymptotics, introduced by Schulze, on a suitable scale of Lp-Sobolev spaces. Ellipticity is proven to be equivalent to the Fredholm property in these spaces, it turns out to be independent of the choice of p. We then show that the cone algebra is closed under inversion: whenever an operator is invertible between the associated Sobolev spaces, its inverse belongs to the calculus. We use these results to analyze the behaviour of these operators on Lp(B).}, language = {en} } @unpublished{NazaikinskiiSavinSchulzeetal.2003, author = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris}, title = {Elliptic theory on manifolds with nonisolated singularities : V. Index formulas for elliptic problems on manifolds with edges}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26500}, year = {2003}, abstract = {For elliptic problems on manifolds with edges, we construct index formulas in form of a sum of homotopy invariant contributions of the strata (the interior of the manifold and the edge). Both terms are the indices of elliptic operators, one of which acts in spaces of sections of finite-dimensional vector bundles on a compact closed manifold and the other in spaces of sections of infinite-dimensional vector bundles over the edge.}, language = {en} } @unpublished{NazaikinskiiSavinSchulzeetal.2002, author = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris}, title = {Elliptic theory on manifolds with nonisolated singularities : IV. Obstructions to elliptic problems on manifolds with edges}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26415}, year = {2002}, abstract = {The obstruction to the existence of Fredholm problems for elliptic differentail operators on manifolds with edges is a topological invariant of the operator. We give an explicit general formula for this invariant. As an application we compute this obstruction for geometric operators.}, language = {en} } @unpublished{NazaikinskiiSavinSchulzeetal.2002, author = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris}, title = {Elliptic theory on manifolds with nonisolated singularities : III. The spectral flow of families of conormal symbols}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26386}, year = {2002}, abstract = {When studyind elliptic operators on manifolds with nonisolated singularities one naturally encounters families of conormal symbols (i.e. operators elliptic with parameter p ∈ IR in the sense of Agranovich-Vishik) parametrized by the set of singular points. For homotopies of such families we define the notion of spectral flow, which in this case is an element of the K-group of the parameter space. We prove that the spectral flow is equal to the index of some family of operators on the infinite cone.}, language = {en} } @unpublished{NazaikinskiiSavinSchulzeetal.2002, author = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris}, title = {Elliptic theory on manifolds with nonisolated singularities : II. Products in elliptic theory on manifolds with edges}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26335}, year = {2002}, abstract = {Exterior tensor products of elliptic operators on smooth manifolds and manifolds with conical singularities are used to obtain examples of elliptic operators on manifolds with edges that do not admit well-posed edge boundary and coboundary conditions.}, language = {en} } @unpublished{NazaikinskiiSavinSchulzeetal.2002, author = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris}, title = {Elliptic theory on manifolds with nonisolated singularities : I. The index of families of cone-degenerate operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26327}, year = {2002}, abstract = {We study the index problem for families of elliptic operators on manifolds with conical singularities. The relative index theorem concerning changes of the weight line is obtained. AN index theorem for families whose conormal symbols satisfy some symmetry conditions is derived.}, language = {en} } @unpublished{KrupchykTarkhanovTuomela2006, author = {Krupchyk, K. and Tarkhanov, Nikolai Nikolaevich and Tuomela, J.}, title = {Elliptic quasicomplexes in Boutet de Monvel algebra}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30122}, year = {2006}, abstract = {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.}, language = {en} } @unpublished{KytmanovMyslivetsSchulzeetal.2001, author = {Kytmanov, Aleksandr and Myslivets, Simona and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {Elliptic problems for the Dolbeault complex}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25979}, year = {2001}, abstract = {The inhomogeneous ∂-equations is an inexhaustible source of locally unsolvable equations, subelliptic estimates and other phenomena in partial differential equations. Loosely speaking, for the anaysis on complex manifolds with boundary nonelliptic problems are typical rather than elliptic ones. Using explicit integral representations we assign a Fredholm complex to the Dolbeault complex over an arbitrary bounded domain in C up(n).}, language = {en} } @unpublished{SchulzeSavinSternin1999, author = {Schulze, Bert-Wolfgang and Savin, Anton and Sternin, Boris}, title = {Elliptic operators in subspaces and the eta invariant}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25496}, year = {1999}, abstract = {The paper deals with the calculation of the fractional part of the η-invariant for elliptic self-adjoint operators in topological terms. The method used to obtain the corresponding formula is based on the index theorem for elliptic operators in subspaces obtained in [1], [2]. It also utilizes K-theory with coefficients Zsub(n). In particular, it is shown that the group K(T*M,Zsub(n)) is realized by elliptic operators (symbols) acting in appropriate subspaces.}, language = {en} } @unpublished{SavinSchulzeSternin2000, author = {Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris}, title = {Elliptic operators in subspaces}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25701}, year = {2000}, abstract = {We construct elliptic theory in the subspaces, determined by pseudodifferential projections. The finiteness theorem as well as index formula are obtained for elliptic operators acting in the subspaces. Topological (K-theoretic) aspects of the theory are studied in detail.}, language = {en} } @unpublished{SavinSternin1999, author = {Savin, Anton and Sternin, Boris}, title = {Elliptic operators in odd subspaces}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25478}, year = {1999}, abstract = {An elliptic theory is constructed for operators acting in subspaces defined via even pseudodifferential projections. Index formulas are obtained for operators on compact manifolds without boundary and for general boundary value problems. A connection with Gilkey's theory of η-invariants is established.}, language = {en} } @unpublished{SavinSternin1999, author = {Savin, Anton and Sternin, Boris}, title = {Elliptic operators in even subspaces}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25461}, year = {1999}, abstract = {An elliptic theory is constructed for operators acting in subspaces defined via even pseudodifferential projections. Index formulas are obtained for operators on compact manifolds without boundary and for general boundary value problems. A connection with Gilkey's theory of η-invariants is established.}, language = {en} } @unpublished{Schulze2006, author = {Schulze, Bert-Wolfgang}, title = {Elliptic differential operators on manifolds with edges}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30188}, year = {2006}, abstract = {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.}, language = {en} } @unpublished{SchulzeTarkhanov1998, author = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {Elliptic complexes of pseudodifferential operators on manifolds with edges}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25257}, year = {1998}, abstract = {On a compact closed manifold with edges live pseudodifferential operators which are block matrices of operators with additional edge conditions like boundary conditions in boundary value problems. They include Green, trace and potential operators along the edges, act in a kind of Sobolev spaces and form an algebra with a wealthy symbolic structure. We consider complexes of Fr{\´e}chet spaces whose differentials are given by operators in this algebra. Since the algebra in question is a microlocalization of the Lie algebra of typical vector fields on a manifold with edges, such complexes are of great geometric interest. In particular, the de Rham and Dolbeault complexes on manifolds with edges fit into this framework. To each complex there correspond two sequences of symbols, one of the two controls the interior ellipticity while the other sequence controls the ellipticity at the edges. The elliptic complexes prove to be Fredholm, i.e., have a finite-dimensional cohomology. Using specific tools in the algebra of pseudodifferential operators we develop a Hodge theory for elliptic complexes and outline a few applications thereof.}, language = {en} } @unpublished{Krainer2005, author = {Krainer, Thomas}, title = {Elliptic boundary problems on manifolds with polycylindrical ends}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29912}, year = {2005}, abstract = {We investigate general Shapiro-Lopatinsky elliptic boundary value problems on manifolds with polycylindrical ends. This is accomplished by compactifying such a manifold to a manifold with corners of in general higher codimension, and we then deal with boundary value problems for cusp differential operators. We introduce an adapted Boutet de Monvel's calculus of pseudodifferential boundary value problems, and construct parametrices for elliptic cusp operators within this calculus. Fredholm solvability and elliptic regularity up to the boundary and up to infinity for boundary value problems on manifolds with polycylindrical ends follows.}, language = {en} } @article{SchmitzMoldt2018, author = {Schmitz, Dennis and Moldt, Daniel}, title = {Ein Lehr- und Lernkonzept f{\"u}r die Softwareentwicklung im Team}, series = {Commentarii informaticae didacticae}, journal = {Commentarii informaticae didacticae}, number = {12}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-416324}, pages = {63 -- 78}, year = {2018}, abstract = {Um beim Berufseinstieg erfolgreich als Informatiker wirken zu k{\"o}nnen, reicht es oft nicht aus nur separierte Kenntnisse {\"u}ber technische und theoretische Grundlagen, Programmiersprachen, Werkzeuge und Selbst- und Zeitmanagement zu besitzen. Vielmehr sollten Absolventen diese Kenntnisse praktisch miteinander verzahnt einsetzen k{\"o}nnen. An der Universit{\"a}t wird Studierenden leider selten die M{\"o}glichkeit geboten, diese verschiedenen Bereiche der Informatik miteinander integriert auszu{\"u}ben. Daf{\"u}r entwickeln wir seit {\"u}ber zwei Dekaden ein Lehr- und Lernkonzept zur Unterst{\"u}tzung praktischer Softwareentwicklungsveranstaltungen und setzen dieses um. Dadurch bieten wir angehenden SoftwareentwicklerInnen und ProjektmanagerInnen eine Umgebung, in der sie neues, praktisch relevantes Wissen erwerben k{\"o}nnen, sich selbst praktisch erproben und ihr Wissen konkret einsetzen k{\"o}nnen. Hier legen wir einen Schwerpunkt auf das Arbeiten im Team. Das hier vorgestellte Konzept kann auf {\"a}hnliche Lehrveranstaltungen {\"u}bertragen und aufgrund seiner Modularisierung ver{\"a}ndert und erweitert werden.}, language = {de} } @unpublished{AbedSchulze2009, author = {Abed, Jamil and Schulze, Bert-Wolfgang}, title = {Edge-degenerate families of ΨDO's on an infinite cylinder}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30365}, year = {2009}, abstract = {We establish a parameter-dependent pseudo-differential calculus on an infinite cylinder, regarded as a manifold with conical exits to infinity. The parameters are involved in edge-degenerate form, and we formulate the operators in terms of operator-valued amplitude functions.}, language = {en} } @unpublished{SchroheSchulze1999, author = {Schrohe, Elmar and Schulze, Bert-Wolfgang}, title = {Edge-degenerate boundary value problems on cones}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25436}, year = {1999}, abstract = {We consider edge-degenerate families of pseudodifferential boundary value problems on a semi-infinite cylinder and study the behavior of their push-forwards as the cylinder is blown up to a cone near infinity. We show that the transformed symbols belong to a particularly convenient symbol class. This result has applications in the Fredholm theory of boundary value problems on manifolds with edges.}, language = {en} } @unpublished{SchulzeWei2008, author = {Schulze, Bert-Wolfgang and Wei, Y.}, title = {Edge-boundary problems with singular trace conditions}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30317}, year = {2008}, abstract = {The ellipticity of boundary value problems on a smooth manifold with boundary relies on a two-component principal symbolic structure (σψ; σ∂), consisting of interior and boundary symbols. In the case of a smooth edge on manifolds with boundary we have a third symbolic component, namely the edge symbol σ∧, referring to extra conditions on the edge, analogously as boundary conditions. Apart from such conditions in integral form' there may exist singular trace conditions, investigated in [6] on closed' manifolds with edge. Here we concentrate on the phenomena in combination with boundary conditions and edge problem.}, language = {en} } @unpublished{DinesLiuSchulze2004, author = {Dines, Nicoleta and Liu, X. and Schulze, Bert-Wolfgang}, title = {Edge quantisation of elliptic operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26838}, year = {2004}, abstract = {The ellipticity of operators on a manifold with edge is defined as the bijectivity of the components of a principal symbolic hierarchy σ = (σψ, σ∧), where the second component takes value in operators on the infinite model cone of the local wedges. In general understanding of edge problems there are two basic aspects: Quantisation of edge-degenerate operators in weighted Sobolev spaces, and verifying the elliptcity of the principal edge symbol σ∧ which includes the (in general not explicitly known) number of additional conditions on the edge of trace and potential type. We focus here on these queations and give explicit answers for a wide class of elliptic operators that are connected with the ellipticity of edge boundary value problems and reductions to the boundary. In particular, we study the edge quantisation and ellipticity for Dirichlet-Neumann operators with respect to interfaces of some codimension on a boundary. We show analogues of the Agranovich-Dynin formula for edge boundary value problems, and we establish relations of elliptic operators for different weights, via the spectral flow of the underlying conormal symbols.}, language = {en} } @unpublished{CoriascoSchulze2002, author = {Coriasco, Sandro and Schulze, Bert-Wolfgang}, title = {Edge problems on configurations with model cones of different dimensions}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26438}, year = {2002}, abstract = {Elliptic equations on configurations W = W1 ∪ ... ∪ Wn with edge Y and components Wj of different dimension can be treated in the frame of pseudo-differential analysis on manifolds with geometric singularities, here, edges. Starting from edge-degenerate operators on Wj, j = 1, ..., N, we construct an algebra with extra "transmission" conditions on Y that satisfy an analogue of the Shapiro-Lopatinskij condition. Ellipticity refers to a two-component symbolic hierarchy with an interior and an edge part; the latter one is operator-valued, operating on the union of different dimensional model cones. We construct parametrices within our calculus, where exchange of information between the various components is encoded in Green and Mellin operators that are smoothing on W\Y. Moreover, we obtain regularity of solutions in weighted edge spaces with asymptotics.}, language = {en} } @unpublished{Paneah2002, author = {Paneah, Boris}, title = {Dynamic methods in the general theory of cauchy type functional equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26295}, year = {2002}, abstract = {Contents: 1 Introduction. Denfitions and Discussions 2 Solvability of the Cauchy Type Functional Equations 2.1 The Case of a P-configuration 2.2 The Case of a Z-configuration 2.3 Multiplicative Cauchy type functional equations 3 Problems in Analysis Reducing to Cauchy Type Functional Equations 3.1 Some problems in Integral Geometry and Cauchy Functional Equations 3.2 First Boundary Problem for Hyperbolic Differential Equations and Cauchy Type Functional Equations 4 Functional Equations Determining Polynomials}, language = {en} } @unpublished{ShlapunovTarkhanov2001, author = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich}, title = {Duality by reproducing kernels}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26095}, year = {2001}, abstract = {Let A be a determined or overdetermined elliptic differential operator on a smooth compact manifold X. Write Ssub(A)(D) for the space of solutions to thesystem Au = 0 in a domain D ⊂ X. Using reproducing kernels related to various Hilbert structures on subspaces of Ssub(A)(D) we show explicit identifications of the dual spaces. To prove the "regularity" of reproducing kernels up to the boundary of D we specify them as resolution operators of abstract Neumann problems. The matter thus reduces to a regularity theorem for the Neumann problem, a well-known example being the ∂-Neumann problem. The duality itself takes place only for those domains D which possess certain convexity properties with respect to A.}, language = {en} } @misc{Ginoux2004, author = {Ginoux, Nicolas}, title = {Dirac operators on Lagrangian submanifolds}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-5627}, year = {2004}, abstract = {We study a natural Dirac operator on a Lagrangian submanifold of a K{\"a}hler manifold. We first show that its square coincides with the Hodge - de Rham Laplacian provided the complex structure identifies the Spin structures of the tangent and normal bundles of the submanifold. We then give extrinsic estimates for the eigenvalues of that operator and discuss some examples.}, language = {en} } @misc{Reich1992, author = {Reich, Sebastian}, title = {Differential-algebraic equations and applications in circuit theory}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-46646}, year = {1992}, abstract = {Technical and physical systems, especially electronic circuits, are frequently modeled as a system of differential and nonlinear implicit equations. In the literature such systems of equations are called differentialalgebraic equations (DAEs). It turns out that the numerical and analytical properties of a DAE depend on an integer called the index of the problem. For example, the well-known BDF method of Gear can be applied, in general, to a DAE only if the index does not exceed one. In this paper we give a geometric interpretation of higherindex DAEs and indicate problems arising in connection with such DAEs by means of several examples.}, language = {en} } @unpublished{NazaikinskiiSavinSchulzeetal.2004, author = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris}, title = {Differential operators on manifolds with singularities : analysis and topology : Chapter 7: The index problem on manifolds with singularities}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26700}, year = {2004}, abstract = {Contents: Chapter 7: The Index Problemon Manifolds with Singularities Preface 7.1. The Simplest Index Formulas 7.1.1. General properties of the index 7.1.2. The index of invariant operators on the cylinder 7.1.3. Relative index formulas 7.1.4. The index of general operators on the cylinder 7.1.5. The index of operators of the form 1 + G with a Green operator G 7.1.6. The index of operators of the form 1 + G on manifolds with edges 7.1.7. The index on bundles with smooth base and fiber having conical points 7.2. The Index Problem for Manifolds with Isolated Singularities 7.2.1. Statement of the index splitting problem 7.2.2. The obstruction to the index splitting 7.2.3. Computation of the obstruction in topological terms 7.2.4. Examples. Operators with symmetries 7.3. The Index Problem for Manifolds with Edges 7.3.1. The index excision property 7.3.2. The obstruction to the index splitting 7.4. Bibliographical Remarks}, language = {en} }