@unpublished{Zessin2010, author = {Zessin, Hans}, title = {Classical Symmetric Point Processes : Lectures held at ICIMAF, La Habana, Cuba, 2010}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49619}, year = {2010}, abstract = {The aim of these lectures is a reformulation and generalization of the fundamental investigations of Alexander Bach [2, 3] on the concept of probability in the work of Boltzmann [6] in the language of modern point process theory. The dominating point of view here is its subordination under the disintegration theory of Krickeberg [14]. This enables us to make Bach's consideration much more transparent. Moreover the point process formulation turns out to be the natural framework for the applications to quantum mechanical models.}, language = {en} } @unpublished{Zehmisch2008, author = {Zehmisch, Ren{\´e}}, title = {{\"U}ber Waldidentit{\"a}ten der Brownschen Bewegung}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49469}, year = {2008}, abstract = {Aus dem Inhalt: 1 Abraham Wald (1902-1950) 2 Einf{\"u}hrung der Grundbegriffe. Einige technische bekannte Ergebnisse 2.1 Martingal und Doob-Ungleichung 2.2 Brownsche Bewegung und spezielle Martingale 2.3 Gleichgradige Integrierbarkeit von Prozessen 2.4 Gestopptes Martingal 2.5 Optionaler Stoppsatz von Doob 2.6 Lokales Martingal 2.7 Quadratische Variation 2.8 Die Dichte der ersten einseitigen {\"U}berschreitungszeit der Brown- schen Bewegung 2.9 Waldidentit{\"a}ten f{\"u}r die {\"U}berschreitungszeiten der Brownschen Bewegung 3 Erste Waldidentit{\"a}t 3.1 Burkholder, Gundy und Davis Ungleichungen der gestoppten Brown- schen Bewegung 3.2 Erste Waldidentit{\"a}t f{\"u}r die Brownsche Bewegung 3.3 Verfeinerungen der ersten Waldidentit{\"a}t 3.4 St{\"a}rkere Verfeinerung der ersten Waldidentit{\"a}t f{\"u}r die Brown- schen Bewegung 3.5 Verfeinerung der ersten Waldidentit{\"a}t f{\"u}r spezielle Stoppzeiten der Brownschen Bewegung 3.6 Beispiele f{\"u}r lokale Martingale f{\"u}r die Verfeinerung der ersten Waldidentit{\"a}t 3.7 {\"U}berschreitungszeiten der Brownschen Bewegung f{\"u}r nichtlineare Schranken 4 Zweite Waldidentit{\"a}t 4.1 Zweite Waldidentit{\"a}t f{\"u}r die Brownsche Bewegung 4.2 Anwendungen der ersten und zweitenWaldidentit{\"a}t f{\"u}r die Brown- schen Bewegung 5 Dritte Waldidentit{\"a}t 5.1 Dritte Waldidentit{\"a}t f{\"u}r die Brownsche Bewegung 5.2 Verfeinerung der dritten Waldidentit{\"a}t 5.3 Eine wichtige Voraussetzung f{\"u}r die Verfeinerung der drittenWal- didentit{\"a}t 5.4 Verfeinerung der dritten Waldidentit{\"a}t f{\"u}r spezielle Stoppzeiten der Brownschen Bewegung 6 Waldidentit{\"a}ten im Mehrdimensionalen 6.1 Erste Waldidentit{\"a}t im Mehrdimensionalen 6.2 Zweite Waldidentit{\"a}t im Mehrdimensionalen 6.3 Dritte Waldidentit{\"a}t im Mehrdimensionalen 7 Appendix}, language = {de} } @unpublished{YinHua2007, author = {Yin, Yang and Hua, Chen}, title = {On chemotaxis systems with saturation growth}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30254}, year = {2007}, abstract = {In this paper, we discuss the global existence of solutions for Chemotaxis models with saturation growth. If the coe±cients of the equations are all positive smooth T-periodic functions, then the problem has a positive T-periodic solution, and meanwhile we discuss here the stability problems for the T-periodic solutions.}, language = {en} } @unpublished{Yin2002, author = {Yin, Huicheng}, title = {Formation and construction of a shock wave for 3-D compressible Euler equations with spherical initial data}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26263}, year = {2002}, abstract = {In this paper, the problem on formation and construction of a shock wave for three dimensional compressible Euler equations with the small perturbed spherical initial data is studied. If the given smooth initial data satisfies certain nondegenerate condition, then from the results in [20], we know that there exists a unique blowup point at the blowup time such that the first order derivates of smooth solution blow up meanwhile the solution itself is still continuous at the blowup point. From the blowup point, we construct a weak entropy solution which is not uniformly Lipschitz continuous on two sides of shock curve, moreover the strength of the constructed shock is zero at the blowup point and then gradually increases. Additionally, some detailed and precise estimates on the solution are obtained in the neighbourhood of the blowup point.}, language = {en} } @unpublished{Yin2002, author = {Yin, Huicheng}, title = {Global existence of a shock for the supersonic flow past a curved wedge}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26272}, year = {2002}, abstract = {This note is devoted to the study on the global existence of a shock wave for the supersonic flow past a curved wedge. When the curved wedge is a small perturbation of a straight wedge and the angle of the wedge is less than some critical value, wwe show that a shock attached at the wedge will exist globally.}, language = {en} } @unpublished{YihongLi2001, author = {Yihong, Du and Li, Ma}, title = {Some remarks related to De Giorgi's conjecture}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26027}, year = {2001}, abstract = {For several classes of functions including the special case f(u) = u - u³, we obtain boundedness and symmetry results for solutions of the problem -Δu = f(u) defined on R up(n). Our results complement a number of recent results related to a conjecture of De Giorgi.}, language = {en} } @unpublished{YagdjianGalstian2007, author = {Yagdjian, Karen and Galstian, Anahit}, title = {Fundamental solutions for wave equation in de Sitter model of universe}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30271}, year = {2007}, abstract = {In this article we construct the fundamental solutions for the wave equation arising in the de Sitter model of the universe. We use the fundamental solutions to represent solutions of the Cauchy problem and to prove the Lp - Lq-decay estimates for the solutions of the equation with and without a source term.}, language = {en} } @unpublished{Yagdjian2001, author = {Yagdjian, Karen}, title = {Geometric optics for the nonlinear hyperbolic systems of Kirchhoff-type}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26059}, year = {2001}, abstract = {Contents: 1 Introduction 2 Main result 3 Construction of the asymptotic solutions 3.1 Derivation of the equations for the profiles 3.2 Exsistence of the principal profile 3.3 Determination of Usub(2) and the remaining profiles 4 Stability of the samll global solutions. Justification of One Phase Nonlinear Geometric Optics for the Kirchhoff-type equations 4.1 Stability of the global solutions to the Kirchhoff-type symmetric hyperbolic systems 4.2 The nonlinear system of ordinary differential equations with the parameter 4.3 Some energies estimates 4.4 The dependence of the solution W(t, ξ) on the function s(t) 4.5 The oscillatory integrals of the bilinear forms of the solutions 4.6 Estimates for the basic bilinear form Γsub(s)(t) 4.7 Contraction mapping 4.8 Stability of the global solution 4.9 Justification of One Phase Nonlinear Geometric Optics for the Kirchhoff-type equations}, language = {en} } @unpublished{XiaochunWitt2002, author = {Xiaochun, Liu and Witt, Ingo}, title = {Pseudodifferential calculi on the half-line respecting prescribed asymptotic types}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26255}, year = {2002}, abstract = {Contents: 1. Introduction 2. Preliminaries 3. Basic Elements of the Calculus 4. Further Elements of the Calculus}, language = {en} } @unpublished{XiaochunWitt2001, author = {Xiaochun, Liu and Witt, Ingo}, title = {Asymptotic expansions for bounded solutions to semilinear Fuchsian equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25912}, year = {2001}, abstract = {It is shown that bounded solutions to semilinear elliptic Fuchsian equations obey complete asymptoic expansions in terms of powers and logarithms in the distance to the boundary. For that purpose, Schuze's notion of asymptotic type for conormal asymptotics close to a conical point is refined. This in turn allows to perform explicit calculations on asymptotic types - modulo the resolution of the spectral problem for determining the singular exponents in the asmptotic expansions.}, language = {en} } @unpublished{XiaochunSchulze2004, author = {Xiaochun, Liu and Schulze, Bert-Wolfgang}, title = {Boundary value problems in edge representation}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26746}, year = {2004}, abstract = {Edge representations of operators on closed manifolds are known to induce large classes of operators that are elliptic on specific manifolds with edges, cf. [9]. We apply this idea to the case of boundary value problems. We establish a correspondence between standard ellipticity and ellipticity with respect to the principal symbolic hierarchy of the edge algebra of boundary value problems, where an embedded submanifold on the boundary plays the role of an edge. We first consider the case that the weight is equal to the smoothness and calculate the dimensions of kernels and cokernels of the associated principal edge symbols. Then we pass to elliptic edge operators for arbitrary weights and construct the additional edge conditions by applying relative index results for conormal symbols.}, language = {en} } @unpublished{Witt2003, author = {Witt, Ingo}, title = {Green formulae for cone differential operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26633}, year = {2003}, abstract = {Green formulae for elliptic cone differential operators are established. This is achieved by an accurate description of the maximal domain of an elliptic cone differential operator and its formal adjoint; thereby utilizing the concept of a discrete asymptotic type. From this description, the singular coefficients replacing the boundary traces in classical Green formulas are deduced.}, language = {en} } @unpublished{Witt2002, author = {Witt, Ingo}, title = {Local asymptotic types}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26346}, year = {2002}, abstract = {The local theory of asymptotic types is elaborated. It appears as coordinate-free version of part of GOHBERG-SIGAL's theory of the inversion of finitely meromorphic, operator-valued functions at a point.}, language = {en} } @unpublished{Witt2002, author = {Witt, Ingo}, title = {A calculus for a class of finitely degenerate pseudodifferential operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26246}, year = {2002}, abstract = {For a class of degenerate pseudodifferential operators, local parametrices are constructed. This is done in the framework of a pseudodifferential calculus upon adding conditions of trace and potential type, respectively, along the boundary on which the operators degenerate.}, language = {en} } @unpublished{Witt2001, author = {Witt, Ingo}, title = {Asymptotic algebras}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26069}, year = {2001}, abstract = {The concept of asymptotic type that primarily appears in singular and asymptotic analysis is developed. Especially, asymptotic algebras are introduced.}, language = {en} } @unpublished{Witt1999, author = {Witt, Ingo}, title = {On the factorization of meromorphic Mellin symbols}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25427}, year = {1999}, abstract = {It is prooved that mermorphic, parameter-dependet elliptic Mellin symbols can be factorized in a particular way. The proof depends on the availability of logarithms of pseudodifferential operators. As a byproduct, we obtain a characterization of the group generated by pseudodifferential operators admitting a logarithm. The factorization has applications to the theory os pseudodifferential operators on spaces with conical singularities, e.g., to the index theory and the construction of various sub-calculi of the cone calculus.}, language = {en} } @unpublished{WeskeRinderleMaToumanietal.2013, author = {Weske, Mathias and Rinderle-Ma, Stefanie and Toumani, Farouk and Wolf, Karsten}, title = {Special section on BPM 2011 conference. - Special Issue}, series = {Information systems}, volume = {38}, journal = {Information systems}, number = {4}, publisher = {Elsevier}, address = {Oxford}, issn = {0306-4379}, doi = {10.1016/j.is.2013.01.003}, pages = {545 -- 546}, year = {2013}, language = {en} } @unpublished{WenyiTianbo2005, author = {Wenyi, Chen and Tianbo, Wang}, title = {The hypoellipticity of differential forms on closed manifolds}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29803}, year = {2005}, abstract = {In this paper we consider the hypo-ellipticity of differential forms on a closed manifold.The main results show that there are some topological obstruct for the existence of the differential forms with hypoellipticity.}, language = {de} } @unpublished{Wallenta2013, author = {Wallenta, Daniel}, title = {A Lefschetz fixed point formula for elliptic quasicomplexes}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-67016}, year = {2013}, abstract = {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.}, language = {en} } @unpublished{Voss2010, author = {Voss, Carola Regine}, title = {Harness-Prozesse}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49651}, year = {2010}, abstract = {Harness-Prozesse finden in der Forschung immer mehr Anwendung. Vor allem gewinnen Harness-Prozesse in stetiger Zeit an Bedeutung. Grundlegende Literatur zu diesem Thema ist allerdings wenig vorhanden. In der vorliegenden Arbeit wird die vorhandene Grundlagenliteratur zu Harness-Prozessen in diskreter und stetiger Zeit aufgearbeitet und Beweise ausgef{\"u}hrt, die bisher nur skizziert waren. Ziel dessen ist die Existenz einer Zerlegung von Harness-Prozessen {\"u}ber Z beziehungsweise R+ nachzuweisen.}, language = {de} }