TY - INPR A1 - Bühler, Markus J. A1 - Rabu, Pierre A1 - Taubert, Andreas T1 - Advanced hybrid materials - design and applications T2 - European journal of inorganic chemistry : a journal of ChemPubSoc Europe Y1 - 2012 U6 - https://doi.org/10.1002/ejic.201201263 SN - 1434-1948 IS - 32 SP - 5092 EP - 5093 PB - Wiley-VCH CY - Weinheim ER - TY - INPR A1 - Michaelis, Beatrice A1 - Dietze, Gabriele A1 - Yekani, Elahe Haschemi T1 - The queerness of things not queer - entgrenzungen - Affekte und Materialitäten - Interventionen T2 - Feministische Studien : Zeitschrift für interdisziplinäre Frauen- und Geschlechterforschung Y1 - 2012 SN - 0723-5186 VL - 30 IS - 2 SP - 184 EP - 197 PB - Lucius & Lucius CY - Stuttgart ER - TY - INPR A1 - Eckstein, Lars T1 - ‘We’re destroyed if we mix. And we’re destroyed if we don’t’ BT - indigeneity in the modern World system and the politics of Tricksterese in Pauline Melville’s The Ventriloquist’s Tale Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-85529 ER - TY - INPR A1 - Murr, Rüdiger T1 - Reciprocal classes of Markov processes : an approach with duality formulae N2 - In this work we are concerned with the characterization of certain classes of stochastic processes via duality formulae. First, we introduce a new formulation of a characterization of processes with independent increments, which is based on an integration by parts formula satisfied by infinitely divisible random vectors. Then we focus on the study of the reciprocal classes of Markov processes. These classes contain all stochastic processes having the same bridges, and thus similar dynamics, as a reference Markov process. We start with a resume of some existing results concerning the reciprocal classes of Brownian diffusions as solutions of duality formulae. As a new contribution, we show that the duality formula satisfied by elements of the reciprocal class of a Brownian diffusion has a physical interpretation as a stochastic Newton equation of motion. In the context of pure jump processes we derive the following new results. We will analyze the reciprocal classes of Markov counting processes and characterize them as a group of stochastic processes satisfying a duality formula. This result is applied to time-reversal of counting processes. We are able to extend some of these results to pure jump processes with different jump-sizes, in particular we are able to compare the reciprocal classes of Markov pure jump processes through a functional equation between the jump-intensities. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)26 KW - Duality formula KW - reciprocal class KW - Levy process KW - infinite divisibility KW - counting process KW - Malliavin calculus Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-63018 ER - TY - INPR A1 - Antoniouk, Alexandra Viktorivna A1 - Kiselev, Oleg A1 - Stepanenko, Vitaly A1 - Tarkhanov, Nikolai Nikolaevich T1 - Asymptotic solutions of the Dirichlet problem for the heat equation at a characteristic point N2 - The Dirichlet problem for the heat equation in a bounded domain is characteristic, for there are boundary points at which the boundary touches a characteristic hyperplane t = c, c being a constant. It was I.G. Petrovskii (1934) who first found necessary and sufficient conditions on the boundary which guarantee that the solution is continuous up to the characteristic point, provided that the Dirichlet data are continuous. This paper initiated standing interest in studying general boundary value problems for parabolic equations in bounded domains. We contribute to the study by constructing a formal solution of the Dirichlet problem for the heat equation in a neighbourhood of a characteristic boundary point and showing its asymptotic character. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)25 KW - Heat equation KW - the first boundary value problem KW - characteristic boundary point KW - cusp Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-61987 ER - TY - INPR A1 - Alsaedy, Ammar A1 - Tarkhanov, Nikolai Nikolaevich T1 - The method of Fischer-Riesz equations for elliptic boundary value problems N2 - We develop the method of Fischer-Riesz equations for general boundary value problems elliptic in the sense of Douglis-Nirenberg. To this end we reduce them to a boundary problem for a (possibly overdetermined) first order system whose classical symbol has a left inverse. For such a problem there is a uniquely determined boundary value problem which is adjoint to the given one with respect to the Green formula. On using a well elaborated theory of approximation by solutions of the adjoint problem, we find the Cauchy data of solutions of our problem. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)24 KW - Boundary value problems for first order systems KW - Green formula KW - Fischer-Riesz equations KW - regularisation Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-61792 ER - TY - INPR A1 - Dyachenko, Evgueniya A1 - Tarkhanov, Nikolai Nikolaevich T1 - Degeneration of boundary layer at singular points N2 - We study the Dirichlet problem in a bounded plane domain for the heat equation with small parameter multiplying the derivative in t. The behaviour of solution at characteristic points of the boundary is of special interest. The behaviour is well understood if a characteristic line is tangent to the boundary with contact degree at least 2. We allow the boundary to not only have contact of degree less than 2 with a characteristic line but also a cuspidal singularity at a characteristic point. We construct an asymptotic solution of the problem near the characteristic point to describe how the boundary layer degenerates. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)23 KW - Heat equation KW - Dirichlet problem KW - characteristic points KW - boundary layer Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-60135 ER - TY - INPR A1 - Bär, Christian T1 - Some properties of solutions to weakly hypoelliptic equations N2 - A linear differential operator L is called weakly hypoelliptic if any local solution u of Lu = 0 is smooth. We allow for systems, i.e. the coefficients may be matrices, not necessarily of square size. This is a huge class of important operators which covers all elliptic, overdetermined elliptic, subelliptic and parabolic equations. We extend several classical theorems from complex analysis to solutions of any weakly hypoelliptic equation: the Montel theorem providing convergent subsequences, the Vitali theorem ensuring convergence of a given sequence, and Riemann's first removable singularity theorem. In the case of constant coefficients we show that Liouville's theorem holds, any bounded solution must be constant and any L^p solution must vanish. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)22 KW - Hypoelliptic operators KW - hypoelliptic estimate KW - Montel theorem KW - Vitali theorem KW - Liouville theorem Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-60064 ER - TY - INPR A1 - Bär, Christian T1 - Renormalized integrals and a path integral formula for the heat kernel on a manifold N2 - We introduce renormalized integrals which generalize conventional measure theoretic integrals. One approximates the integration domain by measure spaces and defines the integral as the limit of integrals over the approximating spaces. This concept is implicitly present in many mathematical contexts such as Cauchy's principal value, the determinant of operators on a Hilbert space and the Fourier transform of an L^p function. We use renormalized integrals to define a path integral on manifolds by approximation via geodesic polygons. The main part of the paper is dedicated to the proof of a path integral formula for the heat kernel of any self-adjoint generalized Laplace operator acting on sections of a vector bundle over a compact Riemannian manifold. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)21 KW - Renormalized integral KW - path integral KW - Feynman-Kac formula KW - generalized Laplace operator KW - Riemannian manifold Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-60052 ER - TY - INPR A1 - Pfäffle, Frank A1 - Stephan, Christoph A. T1 - Chiral asymmetry and the spectral action N2 - We consider orthogonal connections with arbitrary torsion on compact Riemannian manifolds. For the induced Dirac operators, twisted Dirac operators and Dirac operators of Chamseddine-Connes type we compute the spectral action. In addition to the Einstein-Hilbert action and the bosonic part of the Standard Model Lagrangian we find the Holst term from Loop Quantum Gravity, a coupling of the Holst term to the scalar curvature and a prediction for the value of the Barbero-Immirzi parameter. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)20 Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-60046 ER - TY - INPR A1 - Pfäffle, Frank A1 - Stephan, Christoph A. T1 - The Holst action by the spectral action principle N2 - We investigate the Holst action for closed Riemannian 4-manifolds with orthogonal connections. For connections whose torsion has zero Cartan type component we show that the Holst action can be recovered from the heat asymptotics for the natural Dirac operator acting on left-handed spinor fields. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)19 Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-60032 ER - TY - INPR A1 - Bär, Christian A1 - Ballmann, Werner T1 - Boundary value problems for elliptic differential operators of first order N2 - We study boundary value problems for linear elliptic differential operators of order one. The underlying manifold may be noncompact, but the boundary is assumed to be compact. We require a symmetry property of the principal symbol of the operator along the boundary. This is satisfied by Dirac type operators, for instance. We provide a selfcontained introduction to (nonlocal) elliptic boundary conditions, boundary regularity of solutions, and index theory. In particular, we simplify and generalize the traditional theory of elliptic boundary value problems for Dirac type operators. We also prove a related decomposition theorem, a general version of Gromov and Lawson's relative index theorem and a generalization of the cobordism theorem. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)18 KW - Elliptic operators KW - elliptic boundary conditions KW - completeness KW - coercivity KW - boundary regularity Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-60023 ER - TY - INPR A1 - Bär, Christian A1 - Pfäffle, Frank T1 - Wiener measures on Riemannian manifolds and the Feynman-Kac formula N2 - This is an introduction to Wiener measure and the Feynman-Kac formula on general Riemannian manifolds for Riemannian geometers with little or no background in stochastics. We explain the construction of Wiener measure based on the heat kernel in full detail and we prove the Feynman-Kac formula for Schrödinger operators with bounded potentials. We also consider normal Riemannian coverings and show that projecting and lifting of paths are inverse operations which respect the Wiener measure. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)17 KW - Wiener measure KW - conditional Wiener measure KW - Brownian motion KW - Brownian bridge KW - Riemannian manifold Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-59998 ER - TY - INPR A1 - Pfäffle, Frank A1 - Stephan, Christoph A. T1 - On gravity, torsion and the spectral action principle N2 - We consider compact Riemannian spin manifolds without boundary equipped with orthogonal connections. We investigate the induced Dirac operators and the associated commutative spectral triples. In case of dimension four and totally anti-symmetric torsion we compute the Chamseddine-Connes spectral action, deduce the equations of motions and discuss critical points. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)16 Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-59989 SN - 2193-6943 ER - TY - INPR A1 - Bär, Christian A1 - Ginoux, Nicolas T1 - Classical and quantum fields on Lorentzian manifolds N2 - We construct bosonic and fermionic locally covariant quantum fields theories on curved backgrounds for large classes of fields. We investigate the quantum field and n-point functions induced by suitable states. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)15 KW - Wave operator KW - Dirac-type operator KW - globally hyperbolic spacetime KW - Green's operator KW - CCR-algebra Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-59973 ER - TY - INPR A1 - Nehring, Benjamin T1 - Construction of point processes for classical and quantum gases N2 - We propose a new construction of point processes, which generalizes the class of infinitely divisible point processes. Examples are the quantum Boson and Fermion gases as well as the classical Gibbs point processes, where the interaction is given by a stable and regular pair potential. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)14 KW - Gibbs point processes KW - permanental- KW - determinantal point processes KW - cluster expansion KW - Lévy measure KW - infinitely divisible point processes Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-59648 ER - TY - INPR A1 - Rattana, Amornrat A1 - Böckmann, Christine T1 - Matrix methods for computing Eigenvalues of Sturm-Liouville problems of order four N2 - This paper examines and develops matrix methods to approximate the eigenvalues of a fourth order Sturm-Liouville problem subjected to a kind of fixed boundary conditions, furthermore, it extends the matrix methods for a kind of general boundary conditions. The idea of the methods comes from finite difference and Numerov's method as well as boundary value methods for second order regular Sturm-Liouville problems. Moreover, the determination of the correction term formulas of the matrix methods are investigated in order to obtain better approximations of the problem with fixed boundary conditions since the exact eigenvalues for q = 0 are known in this case. Finally, some numerical examples are illustrated. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)13 KW - Finite difference method KW - Numerov's method KW - Boundary value methods KW - Fourth order Sturm-Liouville problem KW - Eigenvalues Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-59279 ER - TY - INPR A1 - Alsaedy, Ammar A1 - Tarkhanov, Nikolai Nikolaevich T1 - Spectral projection for the dbar-Neumann problem N2 - We show that the spectral kernel function of the dbar-Neumann problem on a non-compact strongly pseudoconvex manifold is smooth up to the boundary. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)12 KW - dbar-Neumann problem KW - strongly pseudoconvex domains KW - spectral kernel function Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-58616 SN - 2193-6943 ER - TY - INPR A1 - Tarkhanov, Nikolai Nikolaevich T1 - A simple numerical approach to the Riemann hypothesis N2 - The Riemann hypothesis is equivalent to the fact the the reciprocal function 1/zeta (s) extends from the interval (1/2,1) to an analytic function in the quarter-strip 1/2 < Re s < 1 and Im s > 0. Function theory allows one to rewrite the condition of analytic continuability in an elegant form amenable to numerical experiments. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1 (2012) 9 Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-57645 SN - 2193-6943 ER - TY - INPR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - On completeness of root functions of Sturm-Liouville problems with discontinuous boundary operators N2 - We consider a Sturm-Liouville boundary value problem in a bounded domain D of R^n. By this is meant that the differential equation is given by a second order elliptic operator of divergent form in D and the boundary conditions are of Robin type on bD. The first order term of the boundary operator is the oblique derivative whose coefficients bear discontinuities of the first kind. Applying the method of weak perturbation of compact self-adjoint operators and the method of rays of minimal growth, we prove the completeness of root functions related to the boundary value problem in Lebesgue and Sobolev spaces of various types. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)11 KW - Sturm-Liouville problems KW - discontinuous Robin condition KW - root functions KW - Lipschitz domains Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-57759 SN - 2193-6943 ER -