TY  - GEN
A1  - Benini, Marco
A1  - Schenkel, Alexander
T1  - Quantum field theories on categories fibered in groupoids
T2  - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - We introduce an abstract concept of quantum field theory on categories fibered in groupoids over the category of spacetimes. This provides us with a general and flexible framework to study quantum field theories defined on spacetimes with extra geometric structures such as bundles, connections and spin structures. Using right Kan extensions, we can assign to any such theory an ordinary quantum field theory defined on the category of spacetimes and we shall clarify under which conditions it satisfies the axioms of locally covariant quantum field theory. The same constructions can be performed in a homotopy theoretic framework by using homotopy right Kan extensions, which allows us to obtain first toy-models of homotopical quantum field theories resembling some aspects of gauge theories.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 895 
KW  - C-asterisk-algebra
KW  - observables
KW  - covariance
KW  - locality
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-431541
SN  - 1866-8372
IS  - 895
ER  - 
TY  - GEN
A1  - Karpuz, Eylem Guzel
A1  - Çevik, Ahmet Sinan
A1  - Koppitz, Jörg
A1  - Cangul, Ismail Naci
T1  - Some fixed-point results on (generalized) Bruck-Reilly ∗-extensions of monoids
T2  - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - In this paper, we determine necessary and sufficient conditions for Bruck-Reilly and generalized Bruck-Reilly ∗-extensions of arbitrary monoids to be regular, coregular and strongly π-inverse. These semigroup classes have applications in various field of mathematics, such as matrix theory, discrete mathematics and p-adic analysis (especially in operator theory). In addition, while regularity and coregularity have so many applications in the meaning of boundaries (again in operator theory), inverse monoids and Bruck-Reilly extensions contain a mixture fixed-point results of algebra, topology and geometry within the purposes of this journal.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 942 
KW  - Bruck-Reilly extension
KW  - generalized Bruck-Reilly ∗-extension
KW  - π -inverse monoid
KW  - regular monoid
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-432701
SN  - 1866-8372
IS  - 942
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  - GEN
A1  - Ascher, Uri M.
A1  - Chin, Hongsheng
A1  - Reich, Sebastian
T1  - Stabilization of DAEs and invariant manifolds
N2  - Many methods have been proposed for the stabilization of higher index differential-algebraic equations (DAEs). Such methods often involve constraint differentiation and problem stabilization, thus obtaining a stabilized index reduction. A popular method is Baumgarte stabilization, but the choice of parameters to make it robust is unclear in practice. Here we explain why the Baumgarte method may run into trouble. We then show how to improve it. We further develop a unifying theory for stabilization methods which includes many of the various techniques proposed in the literature. Our approach is to (i) consider stabilization of ODEs with invariants, (ii) discretize the stabilizing term in a simple way, generally different from the ODE discretization, and (iii) use orthogonal projections whenever possible. The best methods thus obtained are related to methods of coordinate projection. We discuss them and make concrete algorithmic suggestions.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 030 
Y1  - 1994
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-15625
ER  - 
TY  - GEN
A1  - Reich, Sebastian
T1  - Smoothed dynamics of highly oscillatory Hamiltonian systems
N2  - We consider the numerical treatment of Hamiltonian systems that contain a potential which grows large when the system deviates from the equilibrium value of the potential. Such systems arise, e.g., in molecular dynamics simulations and the spatial discretization of Hamiltonian partial differential equations. Since the presence of highly oscillatory terms in the solutions forces any explicit integrator to use very small step size, the numerical integration of such systems provides a challenging task. It has been suggested before to replace the strong potential by a holonomic constraint that forces the solutions to stay at the equilibrium value of the potential. This approach has, e.g., been successfully applied to the bond stretching in molecular dynamics simulations. In other cases, such as the bond-angle bending, this methods fails due to the introduced rigidity. Here we give a careful analysis of the analytical problem by means of a smoothing operator. This will lead us to the notion of the smoothed dynamics of a highly oscillatory Hamiltonian system. Based on our analysis, we suggest a new constrained formulation that maintains the flexibility of the system while at the same time suppressing the high-frequency components in the solutions and thus allowing for larger time steps. The new constrained formulation is Hamiltonian and can be discretized by the well-known SHAKE method.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 031 
Y1  - 1995
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-15639
ER  - 
TY  - GEN
A1  - Leimkuhler, Benedict
A1  - Reich, Sebastian
T1  - Symplectic integration of constrained Hamiltonian systems
N2  - A Hamiltonian system in potential form (formula in the original abstract) subject to smooth constraints on q can be viewed as a Hamiltonian system on a manifold, but numerical computations must be performed in Rn. In this paper methods which reduce "Hamiltonian differential algebraic equations" to ODEs in Euclidean space are examined. The authors study the construction of canonical parameterizations or local charts as well as methods based on the construction of ODE systems in the space in which the constraint manifold is embedded which preserve the constraint manifold as an invariant manifold. In each case, a Hamiltonian system of ordinary differential equations is produced. The stability of the constraint invariants and the behavior of the original Hamiltonian along solutions are investigated both numerically and analytically.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 032 
KW  - differential-algebraic equations
KW  - constrained Hamiltonian systems
KW  - canonical discretization schemes
KW  - symplectic methods
Y1  - 1994
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-15653
ER  - 
TY  - GEN
A1  - Ascher, Uri M.
A1  - Chin, Hongsheng
A1  - Petzold, Linda R.
A1  - Reich, Sebastian
T1  - Stabilization of constrained mechanical systems with DAEs and invariant manifolds
N2  - Many methods have been proposed for the simulation of constrained mechanical systems. The most obvious of these have mild instabilities and drift problems. Consequently, stabilization techniques have been proposed A popular stabilization method is Baumgarte's technique, but the choice of parameters to make it robust has been unclear in practice. Some of the simulation methods that have been proposed and used in computations are reviewed here, from a stability point of view. This involves concepts of differential-algebraic equation (DAE) and ordinary differential equation (ODE) invariants. An explanation of the difficulties that may be encountered using Baumgarte's method is given, and a discussion of why a further quest for better parameter values for this method will always remain frustrating is presented. It is then shown how Baumgarte's method can be improved. An efficient stabilization technique is proposed, which may employ explicit ODE solvers in case of nonstiff or highly oscillatory problems and which relates to coordinate projection methods. Examples of a two-link planar robotic arm and a squeezing mechanism illustrate the effectiveness of this new stabilization method.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 033 
Y1  - 1994
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-15698
ER  - 
TY  - GEN
A1  - Reich, Sebastian
T1  - Algebrodifferentialgleichungen und Vektorfelder auf Mannigfaltigkeiten
N2  - In diesem Beitrag wird der Zusammenhang zwischen Algebrodifferentialgleichungen (ADGL) und Vektorfeldern auf Mannigfaltigkeiten untersucht. Dazu wird zunächst der Begriff der regulären ADGL eingeführt, wobei unter eirter regulären ADGL eine ADGL verstanden wird, deren Lösungsmenge identisch mit der Lösungsmenge eines Vektorfeldes ist. Ausgehend von bekannten Aussagen über die Lösungsmenge eines Vektorfeldes werden analoge Aussagen für die Lösungsmenge einer regulären ADGL abgeleitet. Es wird eine Reduktionsmethode angegeben, die auf ein Kriterium für die Begularität einer ADGL und auf die Definition des Index einer nichtlinearen ADGL führt. Außerdem wird gezeigt, daß beliebige Vektorfelder durch reguläre ADGL so realisiert werden können, daß die Lösungsmenge des Vektorfeldes mit der der realisierenden ADGL identisch ist. Abschließend werden die für autonome ADGL gewonnenen Aussagen auf den Fall der nichtautonomen ADGL übertragen.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 160 
Y1  - 1980
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-47290
ER  - 
TY  - GEN
A1  - Reich, Sebastian
T1  - Differential-algebraic equations and applications in circuit theory
N2  - 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.
N2  - Die mathematische Modellierung technisch physikalischer Systeme wie elektrische Netzwerke, führt häufig auf ein System von Differentialgleichungen und nichtlinearen impliziten Gleichungen sogenannten Algebrodifferentialgleichungen (ADGL). Es zeigt sich, daß die numerischen und analytischen Eigenschaften von ADGL durch den Index des Problems charakterisiert werden können. Insbesondere können die bekannten Integrationsformeln von Gear im allgemeinen nur auf ADGL mit dem Index eins angewendet werden. In diesem Beitrag wird eine geometrische Interpretation von ADGL mit einem höheren Index gegeben sowie auf Probleme im Zusammenhang mit derartigen ADGL an Hand verschiedener Beispiele hingewiesen.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 156 
Y1  - 1992
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-46646
ER  - 
TY  - GEN
A1  - Ginoux, Nicolas
T1  - Dirac operators on Lagrangian submanifolds
N2  - We study a natural Dirac operator on a Lagrangian submanifold of a Kähler 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.
KW  - Dirac operators
KW  - Global Analysis
KW  - Spectral Geometry
KW  - Spin Geometry
KW  - Lagrangian submanifolds
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-5627
ER  - 
TY  - GEN
A1  - Ginoux, Nicolas
T1  - Remarques sur le spectre de l'opérateur de Dirac
T1  - Remarks on the spectrum of the Dirac operator
N2  - Nous décrivons un nouvelle famille d'exemples d'hypersurfaces de la sphère satisfaisant le cas d'égalité de la majoration extrinsèque de C. Bär de la plus petite valeur propre de l'opérateur de Dirac.
N2  - We describe a new family of examples of hypersurfaces in the sphere satisfying the limitingcase in C. Bär's extrinsic upper bound for the smallest eigenvalue of the Dirac operator.
KW  - 1st Eigenvalue
KW  - Submanifolds
KW  - Bounds
KW  - Space
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-5630
ER  - 
TY  - GEN
A1  - Ginoux, Nicolas
T1  - Une nouvelle estimation extrinsèque du spectre de l'opérateur de Dirac
T1  - A new extrinsic estimate for the spectrum of the Dirac operator
N2  - Nous établissons une nouvelle majoration optimale pour les plus petites valeurs propres de l'opérateur de Dirac sur une hypersurface compacte de l'espace hyperbolique.
N2  - We prove a new upper bound for the smallest eigenvalues of the Dirac operator on a compact hypersurface of the hyperbolic space.
KW  - bounds
KW  - Eigenvalues
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-5644
ER  - 
TY  - GEN
A1  - Roelly, Sylvie
A1  - Sortais, Michel
T1  - Space-time asymptotics of an infinite-dimensional diffusion having a long- range memory
N2  - We develop a cluster expansion in space-time for an infinite-dimensional system of interacting diffusions where the drift term of each diffusion depends on the whole past of the trajectory; these interacting diffusions arise when considering the Langevin dynamics of a ferromagnetic system submitted to a disordered external magnetic field.
KW  - Random Field Ising Model
KW  - Langevin Dynamics
KW  - Interacting Diffusion Processes
KW  - Space-Time Cluster Expansions
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6700
ER  - 
TY  - GEN
A1  - Roelly, Sylvie
A1  - Thieullen, Michèle
T1  - Duality formula for the bridges of a Brownian diffusion : application to gradient drifts
N2  - In this paper, we consider families of time Markov fields (or reciprocal classes) which have the same bridges as a Brownian diffusion. We characterize each class as the set of solutions of an integration by parts formula on the space of continuous paths C[0; 1]; R-d) Our techniques provide a characterization of gradient diffusions by a duality formula and, in case of reversibility, a generalization of a result of Kolmogorov.
KW  - reciprocal processes
KW  - stochastic bridge
KW  - mixture of bridges
KW  - integration by parts formula
KW  - Malliavin calculus
KW  - entropy
KW  - time reversal
Y1  - 2005
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6710
ER  - 
TY  - GEN
A1  - Louis, Pierre-Yves
T1  - Ergodicity of PCA
BT  - equivalence between spatial and temporal mixing conditions
N2  - 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.
KW  - Wahrscheinlichkeitstheorie
KW  - Wechselwirkende Teilchensysteme
KW  - Stochastische Zellulare Automaten
KW  - Interacting particle systems
KW  - Probabilistic Cellular Automata
KW  - ERgodicity of Markov Chains
KW  - Gibbs measures
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6589
ER  - 
TY  - GEN
A1  - Louis, Pierre-Yves
T1  - Increasing coupling for 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.
KW  - Wahrscheinlichkeitstheorie
KW  - stochastische Anordnung
KW  - stochastische Zellulare Automaten
KW  - Kopplung
KW  - stochastic ordering
KW  - Probabilistic Cellular Automata
KW  - monotone coupling
Y1  - 2005
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6593
ER  - 
TY  - GEN
A1  - Roelly, Sylvie
A1  - Dai Pra, Paolo
T1  - An existence result for infinite-dimensional Brownian diffusions with non- regular and non Markovian drift
N2  - We prove in this paper an existence result for infinite-dimensional stationary interactive Brownian diffusions. The interaction is supposed to be small in the norm ||.||∞ but otherwise is very general, being possibly non-regular and non-Markovian. Our method consists in using the characterization of such diffusions as space-time Gibbs fields so that we construct them by space-time cluster expansions in the small coupling parameter.
KW  - infinite-dimensional Brownian diffusion
KW  - space-time Gibbs field
KW  - cluster expansion
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6684
ER  - 
TY  - GEN
A1  - Nüsken, Nikolas
A1  - Reich, Sebastian
A1  - Rozdeba, Paul J.
T1  - State and parameter estimation from observed signal increments
T2  - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - The success of the ensemble Kalman filter has triggered a strong interest in expanding its scope beyond classical state estimation problems. In this paper, we focus on continuous-time data assimilation where the model and measurement errors are correlated and both states and parameters need to be identified. Such scenarios arise from noisy and partial observations of Lagrangian particles which move under a stochastic velocity field involving unknown parameters. We take an appropriate class of McKean–Vlasov equations as the starting point to derive ensemble Kalman–Bucy filter algorithms for combined state and parameter estimation. We demonstrate their performance through a series of increasingly complex multi-scale model systems.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 916 
KW  - parameter estimation
KW  - continuous-time data assimilation
KW  - ensemble Kalman filter
KW  - correlated noise
KW  - multi-scale diffusion processes
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-442609
SN  - 1866-8372
IS  - 916
ER  - 
TY  - GEN
A1  - Pornsawad, Pornsarp
A1  - Sungcharoen, Parada
A1  - Böckmann, Christine
T1  - Convergence rate of the modified Landweber method for solving inverse potential problems
T2  - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - In this paper, we present the convergence rate analysis of the modified Landweber method under logarithmic source condition for nonlinear ill-posed problems. The regularization parameter is chosen according to the discrepancy principle. The reconstructions of the shape of an unknown domain for an inverse potential problem by using the modified Landweber method are exhibited.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1034 
KW  - nonlinear operator
KW  - regularization
KW  - modified Landweber method
KW  - discrepancy principle
KW  - logarithmic source condition
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-471942
SN  - 1866-8372
IS  - 1034
ER  - 
TY  - GEN
A1  - Bandara, Menaka Lashitha
A1  - Rosén, Andreas
T1  - Riesz continuity of the Atiyah–Singer Dirac operator under perturbations of local boundary conditions
T2  - Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe
N2  - On a smooth complete Riemannian spin manifold with smooth compact boundary, we demonstrate that Atiyah-Singer Dirac operator in depends Riesz continuously on perturbations of local boundary conditions The Lipschitz bound for the map depends on Lipschitz smoothness and ellipticity of and bounds on Ricci curvature and its first derivatives as well as a lower bound on injectivity radius away from a compact neighbourhood of the boundary. More generally, we prove perturbation estimates for functional calculi of elliptic operators on manifolds with local boundary conditions.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 758 
KW  - boundary value problems
KW  - Dirac operator
KW  - functional calculus
KW  - real-variable harmonic analysis
KW  - Riesz continuity
KW  - spectral flow
Y1  - 2019
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-434078
SN  - 1866-8372
IS  - 758
SP  - 1253
EP  - 1284
ER  -