TY - INPR A1 - Weske, Mathias A1 - Rinderle-Ma, Stefanie A1 - Toumani, Farouk A1 - Wolf, Karsten T1 - Special section on BPM 2011 conference. - Special Issue T2 - Information systems Y1 - 2013 U6 - https://doi.org/10.1016/j.is.2013.01.003 SN - 0306-4379 VL - 38 IS - 4 SP - 545 EP - 546 PB - Elsevier CY - Oxford ER - TY - INPR A1 - Wallenta, Daniel T1 - A Lefschetz fixed point formula for elliptic quasicomplexes N2 - In a recent paper with N. Tarkhanov, the Lefschetz number for endomorphisms (modulo trace class operators) of sequences of trace class curvature was introduced. We show that this is a well defined, canonical extension of the classical Lefschetz number and establish the homotopy invariance of this number. Moreover, we apply the results to show that the Lefschetz fixed point formula holds for geometric quasiendomorphisms of elliptic quasicomplexes. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 2(2013)12 KW - Perturbed complexes KW - curvature KW - Lefschetz number KW - fixed point formula Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-67016 ER - TY - INPR A1 - Vasiliev, Serguei A1 - Tarkhanov, Nikolai Nikolaevich T1 - Construction of series of perfect lattices by layer superposition N2 - We construct a new series of perfect lattices in n dimensions by the layer superposition method of Delaunay-Barnes. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 5 (2016)11 KW - lattice packing and covering KW - polyhedra and polytopes KW - regular figures KW - division of spaces Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-100591 SN - 2193-6943 VL - 5 IS - 11 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Tarkhanov, Nikolai Nikolaevich A1 - Wallenta, Daniel T1 - The Lefschetz number of sequences of trace class curvature N2 - For a sequence of Hilbert spaces and continuous linear operators the curvature is defined to be the composition of any two consecutive operators. This is modeled on the de Rham resolution of a connection on a module over an algebra. Of particular interest are those sequences for which the curvature is "small" at each step, e.g., belongs to a fixed operator ideal. In this context we elaborate the theory of Fredholm sequences and show how to introduce the Lefschetz number. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1 (2012) 3 KW - Perturbed complexes KW - curvature KW - Lefschetz number Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-56969 ER - TY - INPR A1 - Tarkhanov, Nikolai Nikolaevich T1 - A spectral theorem for deformation quantisation N2 - We present a construction of the eigenstate at a noncritical level of the Hamiltonian function. Moreover, we evaluate the contributions of Morse critical points to the spectral decomposition. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015) 4 KW - star product KW - WKB method KW - spectral theorem Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-72425 SN - 2193-6943 VL - 4 IS - 4 PB - Universitätsverlag Potsdam CY - Potsdam 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 - Sultanov, Oskar A1 - Kalyakin, Leonid A1 - Tarkhanov, Nikolai Nikolaevich T1 - Elliptic perturbations of dynamical systems with a proper node N2 - The paper is devoted to asymptotic analysis of the Dirichlet problem for a second order partial differential equation containing a small parameter multiplying the highest order derivatives. It corresponds to a small perturbation of a dynamical system having a stationary solution in the domain. We focus on the case where the trajectories of the system go into the domain and the stationary solution is a proper node. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 4 KW - dynamical system KW - singular perturbation KW - asymptotic methods Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-70460 SN - 2193-6943 VL - 3 IS - 4 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - An open mapping theorem for the Navier-Stokes equations N2 - We consider the Navier-Stokes equations in the layer R^n x [0,T] over R^n with finite T > 0. Using the standard fundamental solutions of the Laplace operator and the heat operator, we reduce the Navier-Stokes equations to a nonlinear Fredholm equation of the form (I+K) u = f, where K is a compact continuous operator in anisotropic normed Hölder spaces weighted at the point at infinity with respect to the space variables. Actually, the weight function is included to provide a finite energy estimate for solutions to the Navier-Stokes equations for all t in [0,T]. On using the particular properties of the de Rham complex we conclude that the Fréchet derivative (I+K)' is continuously invertible at each point of the Banach space under consideration and the map I+K is open and injective in the space. In this way the Navier-Stokes equations prove to induce an open one-to-one mapping in the scale of Hölder spaces. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 5 (2016)10 KW - Navier-Stokes equations KW - weighted Hölder spaces KW - integral representation method Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-98687 SN - 2193-6943 VL - 5 IS - 10 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - Golusin-Krylov Formulas in Complex Analysis T2 - Preprints des Instituts für Mathematik der Universität Potsdam N2 - This is a brief survey of a constructive technique of analytic continuation related to an explicit integral formula of Golusin and Krylov (1933). It goes far beyond complex analysis and applies to the Cauchy problem for elliptic partial differential equations as well. As started in the classical papers, the technique is elaborated in generalised Hardy spaces also called Hardy-Smirnov spaces. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 6 (2017) 2 KW - analytic continuation KW - integral formulas KW - Cauchy problem Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-102774 VL - 6 IS - 2 PB - Universitätsverlag Potsdam CY - Potsdam 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 - TY - INPR A1 - Roelly, Sylvie A1 - Vallois, Pierre T1 - Convoluted Brownian motion BT - a semimartingale approach N2 - In this paper we analyse semimartingale properties of a class of Gaussian periodic processes, called convoluted Brownian motions, obtained by convolution between a deterministic function and a Brownian motion. A classical example in this class is the periodic Ornstein-Uhlenbeck process. We compute their characteristics and show that in general, they are neither Markovian nor satisfy a time-Markov field property. Nevertheless, by enlargement of filtration and/or addition of a one-dimensional component, one can in some case recover the Markovianity. We treat exhaustively the case of the bidimensional trigonometric convoluted Brownian motion and the higher-dimensional monomial convoluted Brownian motion. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 5 (2016) 9 KW - periodic Gaussian process KW - periodic Ornstein-Uhlenbeck process KW - Markov-field property KW - enlargement of filtration Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-96339 SN - 2193-6943 VL - 5 IS - 9 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Roelly, Sylvie A1 - Fradon, Myriam T1 - Infinite system of Brownian balls : equilibrium measures are canonical Gibbs N2 - We consider a system of infinitely many hard balls in Rd undergoing Brownian motions and submitted to a smooth pair potential. It is modelized by an infinite-dimensional stochastic differential equation with a local time term. We prove that the set of all equilibrium measures, solution of a detailed balance equation, coincides with the set of canonical Gibbs measures associated to the hard core potential added to the smooth interaction potential. KW - Stochastic Differential Equation KW - hard core potential KW - Canonical Gibbs measure KW - detailed balance equation KW - reversible measure Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6720 ER - TY - 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 - Rafler, Mathias T1 - Martin-Dynkin Boundaries of the Bose Gas N2 - The Ginibre gas is a Poisson point process defined on a space of loops related to the Feynman-Kac representation of the ideal Bose gas. Here we study thermodynamic limits of different ensembles via Martin-Dynkin boundary technique and show, in which way infinitely long loops occur. This effect is the so-called Bose-Einstein condensation. T3 - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2008, 03 KW - Martin-Dynkin boundary KW - Bose-Einstein condensation KW - Point process KW - Loop space KW - Gibbs state Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-51667 ER - TY - INPR A1 - Pornsawad, Pornsarp A1 - Böckmann, Christine T1 - Modified iterative Runge-Kutta-type methods for nonlinear ill-posed problems N2 - This work is devoted to the convergence analysis of a modified Runge-Kutta-type iterative regularization method for solving nonlinear ill-posed problems under a priori and a posteriori stopping rules. The convergence rate results of the proposed method can be obtained under Hölder-type source-wise condition if the Fréchet derivative is properly scaled and locally Lipschitz continuous. Numerical results are achieved by using the Levenberg-Marquardt and Radau methods. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 7 KW - ill-posed problems KW - Runge-Kutta methods KW - regularization methods KW - Hölder-type source condition KW - stopping rules Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-70834 SN - 2193-6943 VL - 3 IS - 7 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Polkovnikov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - A Riemann-Hilbert problem for the Moisil-Teodorescu system N2 - In a bounded domain with smooth boundary in R^3 we consider the stationary Maxwell equations for a function u with values in R^3 subject to a nonhomogeneous condition (u,v)_x = u_0 on the boundary, where v is a given vector field and u_0 a function on the boundary. We specify this problem within the framework of the Riemann-Hilbert boundary value problems for the Moisil-Teodorescu system. This latter is proved to satisfy the Shapiro-Lopaniskij condition if an only if the vector v is at no point tangent to the boundary. The Riemann-Hilbert problem for the Moisil-Teodorescu system fails to possess an adjoint boundary value problem with respect to the Green formula, which satisfies the Shapiro-Lopatinskij condition. We develop the construction of Green formula to get a proper concept of adjoint boundary value problem. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 6 (2017) 3 KW - Dirac operator KW - Riemann-Hilbert problem KW - Fredholm operators Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-397036 VL - 6 IS - 3 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 - 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 - 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 - 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 -