TY  - INPR
A1  - Alsaedy, Ammar
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Normally solvable nonlinear boundary value problems
N2  - 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.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2(2013)11 
KW  - Nonlinear Laplace operator
KW  - boundary value problem
KW  - Dirichlet to Neumann operator
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-65077
SN  - 2193-6943
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
A1  - Shatalov, Victor
T1  - Nonstationary problems for equations of Borel-Fuchs type
N2  - 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.
T3  - Preprint - (1997) 11 
Y1  - 1997
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-24973
ER  - 
TY  - INPR
A1  - Läuter, Henning
A1  - Liero, Hannelore
T1  - Nonparametric estimation and testing in survival models
N2  - 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.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2004, 05 
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-51586
ER  - 
TY  - INPR
A1  - Schrohe, Elmar
T1  - Noncommutative residues, Dixmier's Trace, and heat trace expansions on manifolds with boundary
N2  - 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.
T3  - Preprint - (1999) 13 
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25486
ER  - 
TY  - JOUR
A1  - Piatnitski, Andrey
A1  - Zhizhina, Elena
T1  - Non-local convolution type parabolic equations with fractional and regular time derivative
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472024
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 65
EP  - 67
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Fedosov, Boris
T1  - Non-Abelian reduction in deformation quantization
N2  - 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).
T3  - Preprint - (1997) 26 
KW  - deformation quantization
KW  - Hamiltonian group action
KW  - moment map
KW  - classical and quantum reduction
Y1  - 1997
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25101
ER  - 
TY  - GEN
A1  - Dai Pra, Paolo
A1  - Louis, Pierre-Yves
A1  - Minelli, Ida
T1  - Monotonicity and complete monotonicity for continuous-time Markov chains
N2  - 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.
N2  - Nous étudions les notions de monotonie et de monotonie complète pour les processus de Markov (ou chaînes de Markov à temps continu) prenant leurs valeurs dans un espace partiellement ordonné. Ces deux notions ne sont pas équivalentes, comme c'est le cas lorsque le temps est discret. Cependant, nous établissons que pour certains ensembles partiellement ordonnés, l'équivalence a lieu en temps continu bien que n'étant pas vraie en temps discret.
KW  - Stochastik
KW  - continuous time Markov Chains
KW  - poset
KW  - monotonicity
KW  - coupling
Y1  - 2006
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-7665
ER  - 
TY  - INPR
A1  - Liu, Weian
T1  - Monotone method for nonlocal systems of first order
N2  - 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.
T3  - Preprint - (2005) 05 
KW  - System of nonlocal PDE of first order
KW  - comparison principle
KW  - monotone method
Y1  - 2005
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29791
ER  - 
TY  - GEN
A1  - Reich, Sebastian
T1  - Momentum conserving symplectic integrators
N2  - 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).
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 044 
Y1  - 1994
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-16824
ER  - 
TY  - INPR
A1  - Fedosov, Boris
T1  - Moduli spaces and deformation quantization in infinite dimensions
N2  - 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.
T3  - Preprint - (1998) 27 
KW  - moduli space of flat connections
KW  - gauge group
KW  - star-product
KW  - Weyl algebras bundle
KW  - symplectic reduction
Y1  - 1998
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25396
ER  - 
TY  - INPR
A1  - Shlapunov, Alexander
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Mixed problems with a parameter
N2  - 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.
T3  - Preprint - (2004) 02 
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26677
ER  - 
TY  - INPR
A1  - Tarkhanov, Nikolai Nikolaevich
A1  - Vasilevski, Nikolai
T1  - Microlocal analysis of the Bochner-Martinelli integral
N2  - 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 Szegö projection belongs to the strong closure of the algebra generated by the singular Bochner-Martinelli integral.
T3  - Preprint - (2005) 25 
Y1  - 2005
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30012
ER  - 
TY  - INPR
A1  - De Donno, G.
A1  - Schulze, Bert-Wolfgang
T1  - Meromorphic symbolic structures for boundary value problems on manifolds with edges
N2  - 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.
T3  - Preprint - (2003) 10 
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26570
ER  - 
TY  - INPR
A1  - Dines, Nicoleta
A1  - Schulze, Bert-Wolfgang
T1  - Mellin-edge representations of elliptic operators
N2  - 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.
T3  - Preprint - (2003) 18 
KW  - Pseudo-differential operators
KW  - edge algebra
KW  - ellipticity with interface conditions
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26627
ER  - 
TY  - JOUR
A1  - Jansen, Sabine
A1  - Tsagkarogiannis, Dimitrios
T1  - Mayer expansion for the Asakura-Oosawa model of colloid theory
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472109
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 127
EP  - 134
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Keller, Peter
T1  - Mathematical modeling of molecular motors
N2  - 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.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2 (2013) 1 
KW  - Markov chain
KW  - time duality
KW  - transition path theory
KW  - absorption
KW  - molecular motor
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-63045
ER  - 
TY  - INPR
A1  - Anders, Martin
T1  - Martingale, Amarts und das starke Gesetz der Grossen Zahlen
N2  - Aus dem Inhalt: Einleitung Kapitel 1. Starke Gesetze der Grossen Zahlen 1. SGGZ unter Wachstumsbedingungen an die p-ten Momente 2. SGGZ für identisch verteilte Zufallsvariablen 3. SGGZ für Prozesse mit *-mixing-Eigenschaft Kapitel 2. Einführung zu diskreten (Sub-,Super-)Martingalen 1. Vorhersagbarkeit 2. gestoppte (Sub-,Super-)Martingale 3. Upcrossings 4. Konvergenzsätze 5. Doob-Zerlegung 6. Eine äquivalente Definition eines (Sub-)Martingals Kapitel 3. Martingale und gleichgradige Integrierbarkeit 1. Gleichmäßige(-f¨ormige,-gradige) Integrierbarkeit 2. gleichgradig integrierbare Martingale Kapitel 4. Martingale und das SGGZ Kapitel 5.”reversed“ (Sub-,Super-)Martingale 1. Konvergenzsätze Kapitel 6. (Sub-,Super-)Martingale mit gerichteter Indexmenge 1. Äquivalente Formulierung eines (Sub-)Martingals 2. Konvergenzsätze Kapitel 7. Quasimartingale,Amarts und Semiamarts 1. Konvergenzsätze 2. Riesz-Zerlegung 3. Doob-Zerlegung Kapitel 8. Amarts und das SGGZ Kapitel 9.”reversed“ Amarts und Semiamarts 1. Konvergenzsätze 2.”Aufwärts“- gegen ”Abwärts“-Adaptiertheit 3. Riesz-Zerlegung 4. Stabilitätsanalyse Kapitel 10. Amarts mit gerichteter Indexmenge 1. Konvergenzsätze 2. Riesz-Zerlegung Anhang A. zur Existenz einer Folge unabhängiger Zufallsvariablen B. Konvergenz
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2009, 01 
Y1  - 2009
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49494
ER  - 
TY  - INPR
A1  - Hieber, Matthias
A1  - Schrohe, Elmar
T1  - Lρ spectral independence of elliptic operators via commutator estimates
N2  - 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 Hölder continuous coeffcients, Schrödinger operators, and certain elliptic operators in divergence form with real, but not necessarily symmetric, or complex coeffcients.
T3  - Preprint - (1997) 17 
KW  - Lφ spectrum
KW  - spectral independence
KW  - elliptic systems
Y1  - 1997
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25047
ER  - 
TY  - INPR
A1  - Galstian, Anahit
T1  - Lp - Lq decay estimates for the equation with exponentially growing coefficient
N2  - 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
T3  - Preprint - (2001) 24 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26079
ER  - 
TY  - INPR
A1  - Popivanov, Petăr R.
T1  - Lorenz transformations and creation of logarithmic singularities to the solutions of some nonstrictly hyperbolic semilinear systems with two space variables
T3  - Preprint - (2004) 07 
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26710
ER  - 
TY  - INPR
A1  - Krainer, Thomas
A1  - Schulze, Bert-Wolfgang
T1  - Long-time asymptotics with geometric singularities in the spatial variables
N2  - 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
T3  - Preprint - (2000) 17 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25824
ER  - 
TY  - INPR
A1  - Cattiaux, Patrick
A1  - Fradon, Myriam
A1  - Kulik, Alexei Michajlovič
A1  - Roelly, Sylvie
T1  - Long time behavior of stochastic hard ball systems
N2  - 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.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2(2013)15 
KW  - Stochastic differential equations
KW  - hard core interaction
KW  - reversible measure
KW  - normal reflection
KW  - local time
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-68388
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Localization problem in index theory of elliptic operators
N2  - 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.
T3  - Preprint - (2001) 34 
KW  - elliptic operators
KW  - index theory
KW  - surgery
KW  - relative index
KW  - manifold with singularities
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26175
ER  - 
TY  - INPR
A1  - Messina, Francesca
T1  - Local solvability for semilinear Fuchsian equations
N2  - 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
T3  - Preprint - (2001) 29 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26124
ER  - 
TY  - INPR
A1  - Brauer, Uwe
A1  - Karp, Lavi
T1  - Local existence of classical solutions for the Einstein-Euler system using weighted Sobolev spaces of fractional order
N2  - 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.
T3  - Preprint - (2006) 17 
Y1  - 2006
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30175
ER  - 
TY  - INPR
A1  - Witt, Ingo
T1  - Local asymptotic types
N2  - 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.
T3  - Preprint - (2002) 16 
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26346
ER  - 
TY  - GEN
A1  - Champagnat, Nicolas
A1  - Roelly, Sylvie
T1  - Limit theorems for conditioned multitype Dawson-Watanabe processes and Feller diffusions
N2  - 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 .
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 065 
KW  - multitype measure-valued branching processes
KW  - conditioned
KW  - critical and subcritical Dawson-Watanabe process
KW  - conditioned Feller diffusion
Y1  - 2008
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-18610
ER  - 
TY  - INPR
A1  - Champagnat, Nicolas
A1  - Roelly, Sylvie
T1  - Limit theorems for conditioned multitype Dawson-Watanabe processes
N2  - 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.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2007, 01 
Y1  - 2007
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49426
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Lefschetz theory on manifolds with edges : introduction
N2  - 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.
N2  - Ziel des Buches ist es, die Lefschetz-Theorie der Fixpunkte für elliptische Komplexe von Pseudodifferentialoperatoren auf Mannigfaltigkeiten mit Kanten zu gewinnen. Die allgemeine Lefschetz-Theorie enthält die Index-Theorie als Spezialfall, aber der Fall, den wir analysieren werden, ist viel leichter als das Index-Problem. Ergebnisse in dieser Richtung sind wünschenswert, einerseits aus innermathematischen Gründen, aber auch im Hinblick auf Anwendungen in den Naturwissenschaften.
T3  - Preprint - (1997) 08 
Y1  - 1997
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-24948
ER  - 
TY  - JOUR
A1  - Pechersky, Eugeny
A1  - Pirogov, Sergei
A1  - Yambartsev, Anatoly
T1  - Large emissions
BT  - Hawking-Penrose black hole model
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472049
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 77
EP  - 86
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Keverpütz, Claudia
A1  - Küppers, Bastian
T1  - Konsistente Lehr-Lern-Prozesse in der dualen IT-Ausbildung
JF  - Commentarii informaticae didacticae
N2  - 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 Prüfungswesen wird oft auf klassische Papierklausuren zurückgegriffen. Unterrichtseinheiten mit hohem Blended-Learning-Anteil ohne E-Prüfung werden dabei als „nicht konsistent“ wahrgenommen. In diesem Artikel wird eine empirische Studie dargelegt, die untersucht, welche Einflüsse aus der persönlichen Lernbiografie bei den Lehrenden in einer dualen IT-Ausbildung dazu führen können, die Möglichkeiten eines E-Assessments als summative Modulprüfung anzunehmen oder abzulehnen. Beispielhaft wurden in der dargelegten Studie Interviews mit Dozenten geführt und diese hinsichtlich der Verbindung zwischen Lernbiografie, Gestaltung der Didaktik der Lehr-Lern-Prozesse, Zufriedenheit und Veränderungsbereitschaft untersucht.
KW  - e-Learning
KW  - e-Assessment
KW  - Blended Learning
KW  - duale IT-Ausbildung
Y1  - 2018
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-416341
IS  - 12
SP  - 91
EP  - 100
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Prenov, B.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Kernel spikes of singular problems
N2  - 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.
T3  - Preprint - (2001) 36 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26195
ER  - 
TY  - INPR
A1  - Shlapunov, Alexander
T1  - Iterations of self-adjoint operators and their applications to elliptic systems
N2  - 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.
T3  - Preprint - (1999) 03 
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25401
ER  - 
TY  - INPR
A1  - Airapetyan, Ruben
A1  - Witt, Ingo
T1  - Isometric properties of the Hankel Transformation in weighted sobolev spaces
N2  - 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.
T3  - Preprint - (1997) 14 
Y1  - 1997
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25001
ER  - 
TY  - INPR
A1  - Levendorskii, Sergei Z.
A1  - Boyarchenko, Svetlana I.
T1  - Investment under uncertainty when shocks are non-gaussian
T3  - Preprint - (1998) 08 
Y1  - 1998
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25201
ER  - 
TY  - INPR
A1  - Fradon, Myriam
A1  - Roelly, Sylvie
T1  - Infinitely many Brownian globules with Brownian radii
N2  - 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.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2009, 07 
Y1  - 2009
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49552
ER  - 
TY  - INPR
A1  - Fradon, Myriam
A1  - Roelly, Sylvie
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.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2005, 02 
KW  - Stochastic Differential Equation
KW  - hard core potential
KW  - Canonical Gibbs measure
KW  - detailed balance equation
KW  - reversible measure
Y1  - 2005
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-51594
ER  - 
TY  - INPR
A1  - Savin, Anton
A1  - Sternin, Boris
T1  - Index defects in the theory of nonlocal boundary value problems and the η-invariant
N2  - 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 Poincaré duality in the K-theory of the corresponding manifolds with singularities.
T3  - Preprint - (2001) 31 
KW  - elliptic operator
KW  - boundary value problem
KW  - finiteness theorem
KW  - nonlocal problem
KW  - covering
KW  - relative η-invariant
KW  - index
KW  - modn-index
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26146
ER  - 
TY  - INPR
A1  - Louis, Pierre-Yves
T1  - Increasing Coupling of Probabilistic Cellular Automata
N2  - 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.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2004, 04 
KW  - stochastic ordering
KW  - Probabilistic Cellular Automata
KW  - monotone coupling
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-51578
ER  - 
TY  - INPR
A1  - Sadykov, Timour
T1  - Hypergeometric systems of differential equations and amoebas of rational functions
N2  - 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].
T3  - Preprint - (1999) 33 
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25665
ER  - 
TY  - INPR
A1  - Kytmanov, Alexander
A1  - Myslivets, Simona
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Holomorphic Lefschetz formula for manifolds with boundary
N2  - 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
T3  - Preprint - (2002) 17 
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26354
ER  - 
TY  - INPR
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Harmonic integrals on domains with edges
N2  - 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.
T3  - Preprint - (2004) 20 
KW  - domains with singularities
KW  - de Rham complex
KW  - Neumann problem
KW  - Hodge theory
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26800
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Volpato, A.
T1  - Green operators in the edge calculus
N2  - 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.
T3  - Preprint - (2004) 25 
KW  - operators on manifolds with edges
KW  - weighted spaces with asymptotics
KW  - Green and Mellin edge operators
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26846
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Shlapunov, Alexander
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Green integrals on manifolds with cracks
N2  - 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.
T3  - Preprint - (2000) 12 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25777
ER  - 
TY  - INPR
A1  - Witt, Ingo
T1  - Green formulae for cone differential operators
N2  - 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.
T3  - Preprint - (2003) 20 
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26633
ER  - 
TY  - INPR
A1  - Liero, Hannelore
T1  - Goodness of Fit Tests of L2-Type
N2  - 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.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2003, 15 
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-51494
ER  - 
TY  - INPR
A1  - Huicheng, Yin
A1  - Witt, Ingo
T1  - Global singularity structure of weak solutions to 3-D semilinear dispersive wave equations with discontinuous initial data
T3  - Preprint - (2002) 21 
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26395
ER  - 
TY  - INPR
A1  - Yin, Huicheng
T1  - Global existence of a shock for the supersonic flow past a curved wedge
N2  - 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.
T3  - Preprint - (2002) 08 
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26272
ER  - 
TY  - INPR
A1  - De-Xing, Kong
A1  - Hui, Yao
T1  - Global exact boundary controllability of a class of quasilinear hyperbolic systems of conservation laws II
N2  - 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.
T3  - Preprint - (2003) 08 
KW  - Quasilinear hyperbolic system
KW  - conservation laws
KW  - global exact boundary controllability
KW  - Cauchy problem
KW  - Goursat problem
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26565
ER  - 
TY  - INPR
A1  - Chen, Hua
A1  - Li, Wei-Xi
A1  - Xu, Chao-Jiang
T1  - Gevrey hypoellipticity for linear and non-linear Fokker-Planck equations
N2  - This paper studies the Gevrey regularity of weak solutions of a class of linear and semilinear Fokker-Planck equations.
T3  - Preprint - (2007) 07 
Y1  - 2007
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30283
ER  -