TY - INPR A1 - Gosson, Maurice A. de T1 - Extended Weyl calculus and application to the phase-space Schrödinger equation N2 - We show that the Schr¨odinger equation in phase space proposed by Torres-Vega and Frederick is canonical in the sense that it is a natural consequence of the extendedWeyl calculus obtained by letting the Heisenberg group act on functions (or half-densities) defined on phase space. This allows us, in passing, to solve rigorously the TF equation for all quadratic Hamiltonians. T3 - Preprint - (2005) 11 Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29879 ER - TY - INPR A1 - Galstian, Anahit A1 - Yagdjian, Karen T1 - Exponential function of pseudo-differential operators N2 - The paper is devoted to the construction of the exponential function of a matrix pseudo-differential operator which do not satisfy any of the known theorems (see, Sec.8 Ch.VIII and Sec.2 Ch.XI of [17]). The applications to the construction of the fundamental solution for the Cauchy problem for the hyperbolic operators with the characteristics of variable multiplicity are given, too. T3 - Preprint - (1997) 13 KW - pseudodifferential operators KW - exponential function KW - Gevrey classes KW - hyperbolic operators KW - multiple characteristics Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-24982 ER - TY - JOUR A1 - Frede, Christiane A1 - Knobelsdorf, Maria T1 - Explorative Datenanalyse der Studierendenperformance in der Theoretischen Informatik JF - Commentarii informaticae didacticae N2 - In diesem Artikel werden die Ergebnisse einer explorativen Datenanalyse über die Studierendenperformance in Klausur- und Hausaufgaben eines Einführungskurses der Theoretischen Informatik vorgestellt. Da bisher empirisch wenig untersucht ist, welche Probleme Studierenden in den Einführungskursen haben und die Durchfallquoten in diesen Kursen sehr hoch sind, soll auf diesem Weg ein Überblick gegeben werden. Die Ergebnisse zeigen, dass alle Studierenden unabhängig von ihrer Klausurnote die niedrigste Performance in den Klausur- und Hausaufgaben aufweisen, in denen formale Beweise gefordert sind. Dieses Ergebnis stärkt die Vermutung, dass didaktische Ansätze und Maßnahmen sich insbesondere auf das Erlernen formaler Beweismethoden fokussieren sollten, um Informatik-Studierende nachhaltiger dabei zu unterstützen, in Theoretischer Informatik erfolgreich zu sein. KW - Theoretische Informatik KW - Explorative Datenanalyse KW - Formale Sprachen und Automaten KW - Studierendenperformance KW - Beweisaufgaben Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-416378 IS - 10 SP - 135 EP - 149 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Böckmann, Christine A1 - Niebsch, Jenny T1 - Examination of the nonlinear LIDAR-operator : the influence of inhomogeneous absorbing spheres on the operator N2 - The determination of the atmospheric aerosol size distribution is an inverse illposed problem. The shape and the material composition of the air-carried particles are two substantial model parameters. Present evaluation algorithms only used an approximation with spherical homogeneous particles. In this paper we propose a new numerically efficient recursive algorithm for inhomogeneous multilayered coated and absorbing particles. Numerical results of real existing particles show that the influence of the two parameters on the model is very important and therefore cannot be ignored. T3 - NLD Preprints - 47 KW - multiwavelength lidar KW - aerosol size distribution KW - inverse ill-posed problem KW - multilayered coated and absorbing aerosol KW - new recursive algorithm Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14725 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - Euler solutions of pseudodifferential equations N2 - We consider a homogeneous pseudodifferential equation on a cylinder C = IR x X over a smooth compact closed manifold X whose symbol extends to a meromorphic function on the complex plane with values in the algebra of pseudodifferential operators over X. When assuming the symbol to be independent on the variable t element IR, we show an explicit formula for solutions of the equation. Namely, to each non-bijectivity point of the symbol in the complex plane there corresponds a finite-dimensional space of solutions, every solution being the residue of a meromorphic form manufactured from the inverse symbol. In particular, for differential equations we recover Euler's theorem on the exponential solutions. Our setting is model for the analysis on manifolds with conical points since C can be thought of as a 'stretched' manifold with conical points at t = -infinite and t = infinite. T3 - Preprint - (1998) 09 KW - pseudodifferential operator KW - meromorphic family KW - residue Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25211 ER - TY - INPR A1 - Tarkhanov, Nikolai Nikolaevich T1 - Euler characteristic of Fredholm quasicomplexes N2 - By quasicomplexes are usually meant perturbations of complexes small in some sense. Of interest are not only perturbations within the category of complexes but also those going beyond this category. A sequence perturbed in this way is no longer a complex, and so it bears no cohomology. We show how to introduce Euler characteristic for small perturbations of Fredholm complexes. The paper is to appear in Funct. Anal. and its Appl., 2006. T3 - Preprint - (2006) 11 Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30117 ER - TY - INPR A1 - Savin, Anton A1 - Sternin, Boris T1 - Eta-invariant and Pontrjagin duality in K-theory N2 - The topological significance of the spectral Atiyah-Patodi-Singer η-invariant is investigated. We show that twice the fractional part of the invariant is computed by the linking pairing in K-theory with the orientation bundle of the manifold. The Pontrjagin duality implies the nondegeneracy of the linking form. An example of a nontrivial fractional part for an even-order operator is presented. T3 - Preprint - (2000) 08 KW - eta-invariant KW - K-theory KW - Pontrjagin duality KW - linking coefficients KW - Atiyah-Patodi-Singer theory KW - modulo n index Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25747 ER - TY - INPR A1 - Savin, Anton A1 - Sternin, Boris T1 - Eta invariant and parity conditions N2 - We give a formula for the η-invariant of odd order operators on even-dimensional manifolds, and for even order operators on odd-dimensional manifolds. Geometric second order operators are found with nontrivial η-invariants. This solves a problem posed by P. Gilkey. T3 - Preprint - (2000) 21 KW - eta invariant KW - parity conditions KW - K-theory KW - linking coefficients KW - Dirac operators KW - spectral flow KW - elliptic operators Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25869 ER - TY - INPR A1 - Pénisson, Sophie T1 - Estimation of the infection parameter in the different phases of an epidemic modeled by a branching process N2 - The aim of this paper is to build and compare estimators of the infection parameter in the different phases of an epidemic (growth and extinction phases). The epidemic is modeled by a Markovian process of order d > 1 (allowing non-Markovian life spans), and can be written as a multitype branching process. We propose three estimators suitable for the different classes of criticality of the process, in particular for the subcritical case corresponding to the extinction phase. We prove their consistency and asymptotic normality for two asymptotics, when the number of ancestors (resp. number of generations) tends to infinity. We illustrate the asymptotic properties with simulated examples, and finally use our estimators to study the infection intensity in the extinction phase of the BSE epidemic in Great-Britain. T3 - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2010, 04 Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49607 ER - TY - INPR A1 - Läuter, Henning T1 - Estimation in partly parametric additive Cox models N2 - The dependence between survival times and covariates is described e.g. by proportional hazard models. We consider partly parametric Cox models and discuss here the estimation of interesting parameters. We represent the ma- ximum likelihood approach and extend the results of Huang (1999) from linear to nonlinear parameters. Then we investigate the least squares esti- mation and formulate conditions for the a.s. boundedness and consistency of these estimators. T3 - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2003, 16 KW - Survival models with covariates KW - estimation of regression KW - maximum likelihood estimator KW - least squares estimator KW - boun- dedness KW - consistency Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-51509 ER -