@unpublished{KytmanovMyslivetsTarkhanov2004, author = {Kytmanov, Aleksandr and Myslivets, Simona and Tarkhanov, Nikolai Nikolaevich}, title = {Zeta-function of a nonlinear system}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26795}, year = {2004}, abstract = {Given a system of entire functions in Cn with at most countable set of common zeros, we introduce the concept of zeta-function associated with the system. Under reasonable assumptions on the system, the zeta-function is well defined for all s ∈ Zn with sufficiently large components. Using residue theory we get an integral representation for the zeta-function which allows us to construct an analytic extension of the zeta-function to an infinite cone in Cn.}, language = {en} } @article{FigariTeta2020, author = {Figari, Rodolfo and Teta, Alessandro}, title = {Zero-range hamiltonians for three quantum particles}, series = {Lectures in pure and applied mathematics}, journal = {Lectures in pure and applied mathematics}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-485-2}, issn = {2199-4951}, doi = {10.25932/publishup-47218}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-472189}, pages = {175 -- 184}, year = {2020}, language = {en} } @unpublished{BaerPfaeffle2012, author = {B{\"a}r, Christian and Pf{\"a}ffle, Frank}, title = {Wiener measures on Riemannian manifolds and the Feynman-Kac formula}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-59998}, year = {2012}, abstract = {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 Schr{\"o}dinger 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.}, language = {en} } @article{LykovMalyshev2020, author = {Lykov, Alexander and Malyshev, Vadim}, title = {When bounded chaos becomes unbounded}, series = {Lectures in pure and applied mathematics}, journal = {Lectures in pure and applied mathematics}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-485-2}, issn = {2199-4951}, doi = {10.25932/publishup-47206}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-472060}, pages = {97 -- 106}, year = {2020}, language = {en} } @unpublished{ManicciaMughetti2001, author = {Maniccia, L. and Mughetti, M.}, title = {Weyl calculus for a class of subelliptic operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26038}, year = {2001}, abstract = {Weyl-H{\"o}rmander calculus is used to get a parametrix in OPS¹-m sub(½, ½)(Ω)for a class of subelliptic pseudodifferential operators in OPS up(m)sub(1, 0)(Ω) with real non-negative principal symbol.}, language = {en} } @unpublished{BrauerKarp2008, author = {Brauer, Uwe and Karp, Lavi}, title = {Well-posedness of Einstein-Euler systems in asymptotically flat spacetimes}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30347}, year = {2008}, abstract = {We prove a local in time existence and uniqueness theorem of classical solutions of the coupled Einstein{Euler system, and therefore establish the well posedness of this system. We use the condition that the energy density might vanish or tends to zero at infinity and that the pressure is a certain function of the energy density, conditions which are used to describe simplified stellar models. In order to achieve our goals we are enforced, by the complexity of the problem, to deal with these equations in a new type of weighted Sobolev spaces of fractional order. Beside their construction, we develop tools for PDEs and techniques for hyperbolic and elliptic equations in these spaces. The well posedness is obtained in these spaces.}, language = {en} } @unpublished{AlsaedyTarkhanov2015, author = {Alsaedy, Ammar and Tarkhanov, Nikolai Nikolaevich}, title = {Weak boundary values of solutions of Lagrangian problems}, volume = {4}, number = {2}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72617}, pages = {24}, year = {2015}, abstract = {We define weak boundary values of solutions to those nonlinear differential equations which appear as Euler-Lagrange equations of variational problems. As a result we initiate the theory of Lagrangian boundary value problems in spaces of appropriate smoothness. We also analyse if the concept of mapping degree of current importance applies to the study of Lagrangian problems.}, language = {en} } @unpublished{BuchholzSchulze1998, author = {Buchholz, Thilo and Schulze, Bert-Wolfgang}, title = {Volterra operators and parabolicity : anisotropic pseudo-differential operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25231}, year = {1998}, abstract = {Parabolic equations on manifolds with singularities require a new calculus of anisotropic pseudo-differential operators with operator-valued symbols. The paper develops this theory along the lines of sn abstract wedge calculus with strongly continuous groups of isomorphisms on the involved Banach spaces. The corresponding pseodo-diferential operators are continuous in anisotropic wedge Sobolev spaces, and they form an alegbra. There is then introduced the concept of anisotropic parameter-dependent ellipticity, based on an order reduction variant of the pseudo-differential calculus. The theory is appled to a class of parabolic differential operators, and it is proved the invertibility in Sobolev spaces with exponential weights at infinity in time direction.}, language = {en} } @unpublished{LiuYangLu2002, author = {Liu, Weian and Yang, Yin and Lu, Gang}, title = {Viscosity solutions of fully nonlinear parabolic systems}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26215}, year = {2002}, abstract = {In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in [2] and [3].}, language = {en} } @article{JansenKunaTsagkarogiannis2020, author = {Jansen, Sabine and Kuna, Tobias and Tsagkarogiannis, Dimitrios}, title = {Virial inversion for inhomogeneous systems}, series = {Lectures in pure and applied mathematics}, journal = {Lectures in pure and applied mathematics}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-485-2}, issn = {2199-4951}, doi = {10.25932/publishup-47211}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-472111}, pages = {135 -- 144}, year = {2020}, language = {en} } @phdthesis{Hanisch2011, author = {Hanisch, Florian}, title = {Variational problems on supermanifolds}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-59757}, school = {Universit{\"a}t Potsdam}, year = {2011}, abstract = {In this thesis, we discuss the formulation of variational problems on supermanifolds. Supermanifolds incorporate bosonic as well as fermionic degrees of freedom. Fermionic fields take values in the odd part of an appropriate Grassmann algebra and are thus showing an anticommutative behaviour. However, a systematic treatment of these Grassmann parameters requires a description of spaces as functors, e.g. from the category of Grassmann algberas into the category of sets (or topological spaces, manifolds). After an introduction to the general ideas of this approach, we use it to give a description of the resulting supermanifolds of fields/maps. We show that each map is uniquely characterized by a family of differential operators of appropriate order. Moreover, we demonstrate that each of this maps is uniquely characterized by its component fields, i.e. by the coefficients in a Taylor expansion w.r.t. the odd coordinates. In general, the component fields are only locally defined. We present a way how to circumvent this limitation. In fact, by enlarging the supermanifold in question, we show that it is possible to work with globally defined components. We eventually use this formalism to study variational problems. More precisely, we study a super version of the geodesic and a generalization of harmonic maps to supermanifolds. Equations of motion are derived from an energy functional and we show how to decompose them into components. Finally, in special cases, we can prove the existence of critical points by reducing the problem to equations from ordinary geometric analysis. After solving these component equations, it is possible to show that their solutions give rise to critical points in the functor spaces of fields.}, language = {en} } @unpublished{Alsaedy2016, author = {Alsaedy, Ammar}, title = {Variational primitive of a differential form}, volume = {5}, number = {4}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-89223}, pages = {8}, year = {2016}, abstract = {In this paper we specify the Dirichlet to Neumann operator related to the Cauchy problem for the gradient operator with data on a part of the boundary. To this end, we consider a nonlinear relaxation of this problem which is a mixed boundary problem of Zaremba type for the p-Laplace equation.}, language = {en} } @phdthesis{Vu2014, author = {Vu, Dinh Phuong}, title = {Using video study to investigate eighth-grade mathematics classrooms in Vietnam}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72464}, school = {Universit{\"a}t Potsdam}, pages = {273}, year = {2014}, abstract = {The International Project for the Evaluation of Educational Achievement (IEA) was formed in the 1950s (Postlethwaite, 1967). Since that time, the IEA has conducted many studies in the area of mathematics, such as the First International Mathematics Study (FIMS) in 1964, the Second International Mathematics Study (SIMS) in 1980-1982, and a series of studies beginning with the Third International Mathematics and Science Study (TIMSS) which has been conducted every 4 years since 1995. According to Stigler et al. (1999), in the FIMS and the SIMS, U.S. students achieved low scores in comparison with students in other countries (p. 1). The TIMSS 1995 "Videotape Classroom Study" was therefore a complement to the earlier studies conducted to learn "more about the instructional and cultural processes that are associated with achievement" (Stigler et al., 1999, p. 1). The TIMSS Videotape Classroom Study is known today as the TIMSS Video Study. From the findings of the TIMSS 1995 Video Study, Stigler and Hiebert (1999) likened teaching to "mountain ranges poking above the surface of the water," whereby they implied that we might see the mountaintops, but we do not see the hidden parts underneath these mountain ranges (pp. 73-78). By watching the videotaped lessons from Germany, Japan, and the United States again and again, they discovered that "the systems of teaching within each country look similar from lesson to lesson. At least, there are certain recurring features [or patterns] that typify many of the lessons within a country and distinguish the lessons among countries" (pp. 77-78). They also discovered that "teaching is a cultural activity," so the systems of teaching "must be understood in relation to the cultural beliefs and assumptions that surround them" (pp. 85, 88). From this viewpoint, one of the purposes of this dissertation was to study some cultural aspects of mathematics teaching and relate the results to mathematics teaching and learning in Vietnam. Another research purpose was to carry out a video study in Vietnam to find out the characteristics of Vietnamese mathematics teaching and compare these characteristics with those of other countries. In particular, this dissertation carried out the following research tasks: - Studying the characteristics of teaching and learning in different cultures and relating the results to mathematics teaching and learning in Vietnam - Introducing the TIMSS, the TIMSS Video Study and the advantages of using video study in investigating mathematics teaching and learning - Carrying out the video study in Vietnam to identify the image, scripts and patterns, and the lesson signature of eighth-grade mathematics teaching in Vietnam - Comparing some aspects of mathematics teaching in Vietnam and other countries and identifying the similarities and differences across countries - Studying the demands and challenges of innovating mathematics teaching methods in Vietnam - lessons from the video studies Hopefully, this dissertation will be a useful reference material for pre-service teachers at education universities to understand the nature of teaching and develop their teaching career.}, language = {en} } @unpublished{Tarkhanov2005, author = {Tarkhanov, Nikolai Nikolaevich}, title = {Unitary solutions of partial differential equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29852}, year = {2005}, abstract = {We give an explicit construction of a fundamental solution for an arbitrary non-degenerate partial differential equation with smooth coefficients.}, language = {en} } @unpublished{SchulzeQin2005, author = {Schulze, Bert-Wolfgang and Qin, Yuming}, title = {Uniform compact attractors for a nonlinear non-autonomous equation of viscoelasticity}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29892}, year = {2005}, abstract = {In this paper we establish the regularity, exponential stability of global (weak) solutions and existence of uniform compact attractors of semiprocesses, which are generated by the global solutions, of a two-parameter family of operators for the nonlinear 1-d non-autonomous viscoelasticity. We employ the properties of the analytic semigroup to show the compactness for the semiprocess generated by the global solutions.}, language = {en} } @unpublished{KleinRosenberger2012, author = {Klein, Markus and Rosenberger, Elke}, title = {Tunneling for a class of difference operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-56989}, year = {2012}, abstract = {We analyze a general class of difference operators containing a multi-well potential and a small parameter. We decouple the wells by introducing certain Dirichlet operators on regions containing only one potential well, and we treat the eigenvalue problem as a small perturbation of these comparison problems. We describe tunneling by a certain interaction matrix similar to the analysis for the Schr{\"o}dinger operator, and estimate the remainder, which is exponentially small and roughly quadratic compared with the interaction matrix.}, language = {en} } @article{Zagrebnov2020, author = {Zagrebnov, Valentin}, title = {Trotter product formula on Hilbert and Banach spaces for operator-norm convergence}, series = {Lectures in pure and applied mathematics}, journal = {Lectures in pure and applied mathematics}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-485-2}, issn = {2199-4951}, doi = {10.25932/publishup-47197}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-471971}, pages = {23 -- 34}, year = {2020}, language = {en} } @unpublished{GairingHoegeleKosenkova2016, author = {Gairing, Jan and H{\"o}gele, Michael and Kosenkova, Tetiana}, title = {Transportation distances and noise sensitivity of multiplicative L{\´e}vy SDE with applications}, volume = {5}, number = {2}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-86693}, pages = {24}, year = {2016}, abstract = {This article assesses the distance between the laws of stochastic differential equations with multiplicative L{\´e}vy noise on path space in terms of their characteristics. The notion of transportation distance on the set of L{\´e}vy kernels introduced by Kosenkova and Kulik yields a natural and statistically tractable upper bound on the noise sensitivity. This extends recent results for the additive case in terms of coupling distances to the multiplicative case. The strength of this notion is shown in a statistical implementation for simulations and the example of a benchmark time series in paleoclimate.}, language = {en} } @unpublished{Schulze2003, author = {Schulze, Bert-Wolfgang}, title = {Toeplitz operators, and ellipticity of boundary value problems with global projection conditions}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26510}, year = {2003}, abstract = {Ellipticity of (pseudo-) differential operators A on a compact manifold X with boundary (or with edges) Y is connected with boundary (or edge) conditions of trace and potential type, formulated in terms of global projections on Y together with an additional symbolic structure. This gives rise to operator block matrices A with A in the upper left corner. We study an algebra of such operators, where ellipticity is equivalent to the Fredhom property in suitable scales of spaces: Sobolev spaces on X plus closed subspaces of Sobolev spaces on Y which are the range of corresponding pseudo-differential projections. Moreover, we express parametrices of elliptic elements within our algebra and discuss spectral boundary value problems for differential operators.}, language = {en} } @unpublished{Harutyunyan2001, author = {Harutyunyan, Anahit V.}, title = {Toeplitz operators and division theorems in anisotropic spaces of holomorphic functions in the polydisc}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26110}, year = {2001}, abstract = {This work is an introduction to anisotropic spaces, which have an ω-weight of analytic functions and are generalizations of Lipshitz classes in the polydisc. We prove that these classes form an algebra and are invariant with respect to monomial multiplication. These operators are bounded in these (Lipshitz and Djrbashian) spaces. As an application, we show a theorem about the division by good-inner functions in the mentioned classes is proved.}, language = {en} }