TY - JOUR A1 - Dai Pra, Paolo A1 - Louis, Pierre-Yves A1 - Minelli, Ida T1 - Monotonicity and complete monotonicity for continuous-time Markov chains N2 - We analyze the notions of monotonicity and complete monotonicity for Markov Chains in continuous-time, taking values in a finite partially ordered set. Similarly to what happens in discrete-time, the two notions are not equivalent. However, we show that there are partially ordered sets for which monotonicity and complete monotonicity coincide in continuous time but not in discrete-time Y1 - 2006 UR - http://www.elsevier.com/locate/issn/1631073X U6 - https://doi.org/10.1016/j.crma.2006.04.007 SN - 1631-073X 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 - JOUR A1 - Böckmann, Christine A1 - Kirsche, Andreas T1 - Iterative regularization method for lidar remote sensing N2 - In this paper we present an inversion algorithm for ill-posed problems arising in atmospheric remote sensing. The proposed method is an iterative Runge-Kutta type regularization method. Those methods are better well known for solving differential equations. We adapted them for solving inverse ill-posed problems. The numerical performances of the algorithm are studied by means of simulations concerning the retrieval of aerosol particle size distributions from lidar observations. Y1 - 2006 UR - http://www.sciencedirect.com/science/journal/00104655 U6 - https://doi.org/10.1016/j.cpc.2005.12.019 SN - 0010-4655 ER - TY - JOUR A1 - Meyerhöfer, Wolfram T1 - Testen, Lernen und Gesellschaft : zwischen Autonomie und Heteronomie Y1 - 2006 SN - 978-388120-428-6 ER - TY - BOOK A1 - Janke, Thomas A1 - Wuttke, Hans A1 - Dietsch, Volker A1 - Janßen, Martin A1 - König, Gerhard A1 - Mentzendorff, Arne A1 - Simanowsky, Ursula A1 - Wuttke, Joachim T1 - Mathematik : Stochastik ; Orientierungswissen Analytische Geometrie ; Gymnasiale Oberstufe, NRW [Schülerbuch] Y1 - 2005 SN - 3-464-57213-7 PB - Cornelsen CY - Berlin ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Einsteins Arbeiten in Bezug auf die moderne Kosmologie : de Sitters Lösung der Einsteinschen Feldgleichung mit positivem kosmologischen Glied als Geometrie des inflationaeren Weltmodells N2 - Die Arbeit von Albert Einstein von 1918 zu Willem De Sitters Loesung der Einsteinschen Feldgleichung wird unter heutigem Gesichtspunkt kommentiert. Dazu wird zunaechst die Geometrie der De Sitterschen Raum-Zeit beschrieben, sowie ihre Bedeutung fuer das inflationaere Weltmodell erlaeutert. Y1 - 2005 UR - http://arXiv.org/abs/gr-qc/0506121 ER - TY - BOOK A1 - Janke, Thomas A1 - Wuttke, Hans A1 - Dietsch, Volker A1 - Janßen, Martin A1 - Koenig, Gerhard A1 - Mentzendorff, Arne A1 - Simanowsky, Ursula A1 - Wuttke, Joachim ED - Jahnke, Thomas T1 - Mathematik : Stochastik ; Gymnasiale Oberstufe, [Schülerbuch] Y1 - 2005 SN - 3-464-57218-8 PB - Cornelsen CY - Berlin ER - TY - JOUR A1 - Pfäffle, Frank T1 - Eigenvalues of Dirac Operators for Hyperbolic Degenerations N2 - We study the behaviour of the spectrum of the Dirac operator for sequences of compact hyperbolic manifolds whose limit is non-compact. If the spectrum of the limit manifold is descrete we show that the spectrum is approximated by the spectra of compact manifolds. Y1 - 2005 UR - http://www.springerlink.com/app/home/ contribution.asp?wasp=74877684beab42c4a04190542f838968&referrer=parent&backto=issue,1,6;journal,6,89;searchpublicationsre sults,1,2; ER - TY - BOOK A1 - Janke, Thomas A1 - Wuttke, Hans A1 - Dietsch, Volker A1 - Janßen, Martin A1 - König, Gerhard A1 - Mentzendorff, Arne A1 - Simanowsky, Ursula A1 - Wuttke, Joachim T1 - Mathematik : Stochastik ; Handreichungen für den Unterricht ; Gymnasiale Oberstufe [Schülerbuch] Y1 - 2005 SN - 3-464-57288-9 PB - Cornelsen CY - Berlin ER - TY - BOOK A1 - Tarkhanov, Nikolai Nikolaevich T1 - Unitary solutions of paratial differential equations T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2005 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Liu, Weian T1 - Monotone method for nonlocal systems of first order T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2005 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Zähle, Henryk T1 - Space-time regularity of catalytic super-Brownian motion N2 - The paper studies catalytic super-Brownian motion on the real line, where the branching rate is controlled by a catalyst. D. A. Dawson, K. Fleischmann and S. Roelly showed, for a broad class of catalysts, that, as for constant branching, the processes are absolutely continuous measures. This paper considers a class of catalysts, called moderate, which must satisfy a uniform boundedness condition and a condition controlling the degree of singularity---essentially that the mass of catalyst in small balls should (uniformly) be of order r^a, where a>0. The main result of this paper shows that for this class of catalysts there is a continuous density field for the process. Moreover the density is the unique solution (in law) of an appropriate SPDE. Y1 - 2005 UR - http://www.interscience.wiley.com/jpages/0025-584X/ ER - TY - THES A1 - Rätsch, Thoralf T1 - On the Equi-Constistency of the failure of the GAP-1 transfer property and an inaccessible cardinal Y1 - 2005 CY - Potsdam ER - TY - BOOK ED - Brückner, Axel T1 - Mathematik : Lehrbuch für die Klasse 10 ; Gymnasium Brandenburg Y1 - 2005 SN - 3-89818-142-1 PB - Paetec CY - Berlin ER - TY - BOOK A1 - Paneah, Boris T1 - On the general theory of the cauchy type functional equations with applications in analysis T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2005 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Böckmann, Christine A1 - Mironova, I. A1 - Muller, D. T1 - Microphysical aerosol parameters from multiwavelength lidar N2 - The hybrid regularization technique developed at the Institute of Mathematics of Potsdam University (IMP) is used to derive microphysical properties such as effective radius, surface-area concentration, and volume concentration, as well as the single-scattering albedo and a mean complex refractive index, from multiwavelength lidar measurements. We present the continuation of investigations of the IMP method. Theoretical studies of the degree of ill-posedness of the underlying model, simulation results with respect to the analysis of the retrieval error of microphysical particle properties from multiwavelength lidar data, and a comparison of results for different numbers of backscatter and extinction coefficients are presented. Our analysis shows that the backscatter operator has a smaller degree of ill- posedness than the operator for extinction. This fact underlines the importance of backscatter data. Moreover, the degree of ill-posedness increases with increasing particle absorption, i.e., depends on the imaginary part of the refractive index and does not depend significantly on the real part. Furthermore, an extensive simulation study was carried out for logarithmic-normal size distributions with different median radii, mode widths, and real and imaginary parts of refractive indices. The errors of the retrieved particle properties obtained from the inversion of three backscatter (355, 532, and 1064 nm) and two extinction (355 and 532 nm) coefficients were compared with the uncertainties for the case of six backscatter (400. 710, 800 nm. additionally) and the same two extinction coefficients. For known complex refractive index and up to 20% normally distributed noise, we found that the retrieval errors for effective radius, surface-area concentration, and volume concentration stay below approximately 15% in both cases. Simulations were also made with unknown complex refractive index. In that case the integrated parameters stay below approximately 30%, and the imaginary part of the refractive index stays below 35% for input noise up to 10% in both cases. In general, the quality of the retrieved aerosol parameters depends strongly on the imaginary part owing to the degree of ill-posedness. It is shown that under certain constraints a minimum data set of three backscatter coefficients and two extinction coefficients is sufficient for a successful inversion. The IMP algorithm was finally tested for a measurement case. (C) 2005 Optical Society of America Y1 - 2005 SN - 1084-7529 ER - TY - JOUR A1 - Bovier, Anton A1 - Gayrard, Veronique A1 - Klein, Markus T1 - Metastability in reversible diffusion processes : II. Precise asymptotics for small eigenvalues N2 - We continue the analysis of the problem of metastability for reversible diffusion processes, initiated in [BEGK3], with a precise analysis of the low-lying spectrum of the generator. Recall that we are considering processes with generators of the form -epsilonDelta + delF(.) del on R-d or subsets of Rd, where F is a smooth function with finitely many local minima. Here we consider only the generic situation where the depths of all local minima are different. We show that in general the exponentially small part of the spectrum is given, up to multiplicative errors tending to one, by the eigenvalues of the classical capacity matrix of the array of capacitors made of balls of radius epsilon centered at the positions of the local minima of F. We also get very precise uniform control on the corresponding eigenfunctions. Moreover, these eigenvalues can be identified with the same precision with the inverse mean metastable exit times from each minimum. In [BEGK3] it was proven that these mean times are given, again up to multiplicative errors that tend to one, by the classical Eyring- Kramers formula Y1 - 2005 SN - 1435-9855 ER - TY - JOUR A1 - Rasch, T. A1 - Schindler, R. T1 - A new condensation principle N2 - We generalize del(A), which was introduced in [Schinfinity], to larger cardinals. For a regular cardinal kappa>N-0 we denote by del(kappa)(A) the statement that Asubset of or equal tokappa and for all regular theta>kappa(o), {X is an element of[L-theta[A]](<) : X &AND; &ISIN; &AND; otp (X &AND; Ord) &ISIN; Card (L[A&AND;X&AND;])} is stationary in [L-[A]](<). It was shown in [Sch&INFIN;] that &DEL;(N1) (A) can hold in a set-generic extension of L. We here prove that &DEL;(N2) (A) can hold in a set-generic extension of L as well. In both cases we in fact get equiconsistency theorems. This strengthens results of [Ra00] and [Ran01]. &DEL;(N3) () is equivalent with the existence of 0# Y1 - 2005 SN - 1432-0665 ER - TY - JOUR A1 - Gosson, Maurice A. de T1 - Extended Weyl calculus and application to the phase-space Schrodinger equation N2 - We show that the Schrodinger equation in phase space proposed by Torres-Vega and Frederick is canonical in the sense that it is a natural consequence of the extended Weyl 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 Y1 - 2005 ER - TY - JOUR A1 - Baumgaertel, Hellmut A1 - Grundling, H. T1 - Superselection in the presence of constraints N2 - Superselection and constraints occur together in many gauge theories, and here we begin a study of such systems. Our main focus will be to analyze compatibility questions between constraining and superselection, and we will develop an example modelled on QED in which our framework is realized. We proceed from a generalization of Doplicher- Roberts superselection theory to the case of the nontrivial center, and a set of Dirac quantum constraints and find conditions under which the superselection structures will survive constraining in some form. This involves an analysis of the restriction and factorization of superselection structures. (c) 2005 American Institute of Physics Y1 - 2005 SN - 0022-2488 ER - TY - JOUR A1 - Baake, Ellen A1 - Baake, Michael A1 - Bovier, Anton A1 - Klein, Markus T1 - An asymptotic maximum principle for essentially linear evolution models N2 - Recent work on mutation-selection models has revealed that, under specific assumptions on the fitness function and the mutation rates, asymptotic estimates for the leading eigenvalue of the mutation-reproduction matrix may be obtained through a low-dimensional maximum principle in the limit N --> infinity (where N, or N-d with d greater than or equal to 1, is proportional to the number of types). In order to extend this variational principle to a larger class of models, we consider here a family of reversible matrices of asymptotic dimension N-d and identify conditions under which the high-dimensional Rayleigh-Ritz variational problem may be reduced to a low-dimensional one that yields the leading eigenvalue up to an error term of order 1/N. For a large class of mutation-selection models, this implies estimates for the mean fitness, as well as a concentration result for the ancestral distribution of types Y1 - 2005 SN - 0303-6812 ER - TY - JOUR A1 - Klein, Markus A1 - Korotyaev, Evgeni A1 - Pokrovski, A. T1 - Spectral asymptotics of the harmonic oscillator perturbed by bounded potentials N2 - Consider the operator T = -d(2)/dx(2) + x(2) + q(x) in L-2 (R), where q is a real function with q' and integral(0)(x) q(s) ds bounded. The spectrum of T is purely discrete and consists of simple eigenvalues. We determine their asymptotics mu(n) = (2n + 1) + (2 pi)(-1) integral(-pi)(pi) q(root 2n+1 sin theta)d theta + O(n(-1/3)) and we extend these results for complex q. Y1 - 2005 SN - 1424-0637 ER - TY - JOUR A1 - Gunther, U. A1 - Zhuk, Alexandre A1 - Bezerra, Valdir B. A1 - Romero, C. T1 - AdS and stabilized extra dimensions in multi-dimensional gravitational models with nonlinear scalar curvature terms R-1 and R-4 N2 - We study multi-dimensional gravitational models with scalar curvature nonlinearities of types R-1 and R-4. It is assumed that the corresponding higher dimensional spacetime manifolds undergo a spontaneous compactification to manifolds with a warped product structure. Special attention has been paid to the stability of the extra-dimensional factor spaces. It is shown that for certain parameter regions the systems allow for a freezing stabilization of these spaces. In particular, we find for the R-1 model that configurations with stabilized extra dimensions do not provide a late-time Acceleration (they are AdS), whereas the solution branch which allows. for accelerated expansion (the dS branch) is incompatible with stabilized factor spaces. In the case of the R-4 model, we obtain that the stability region in parameter space depends on the total dimension D = dim(M) of the higher dimensional spacetime M. Tor D > 8 the stability region consists of a single (absolutely stable) sector which is shielded from a conformal singularity (and an antigravity sector beyond it) by a potential barrier of infinite height and width. This sector is smoothly connected with the stability region of a curvature-linear model. For D < 8 an additional (metastable) sector exists Which is separated from the conformal singularity by a potential barrier of finite height and width so that systems in this sector are prone to collapse into the conformal singularity. This second sector is not smoothly connected with the first (absolutely stable) one. Several limiting cases and the possibility of inflation are discussed for the R-4 model Y1 - 2005 SN - 0264-9381 ER - TY - JOUR A1 - Holschneider, Matthias A1 - Diallo, Mamadou Sanou A1 - Kulesh, Michail A1 - Ohrnberger, Matthias A1 - Luck, E. A1 - Scherbaum, Frank T1 - Characterization of dispersive surface waves using continuous wavelet transforms N2 - In this paper, we propose a method of surface waves characterization based on the deformation of the wavelet transform of the analysed signal. An estimate of the phase velocity (the group velocity) and the attenuation coefficient is carried out using a model-based approach to determine the propagation operator in the wavelet domain, which depends nonlinearly on a set of unknown parameters. These parameters explicitly define the phase velocity, the group velocity and the attenuation. Under the assumption that the difference between waveforms observed at a couple of stations is solely due to the dispersion characteristics and the intrinsic attenuation of the medium, we then seek to find the set of unknown parameters of this model. Finding the model parameters turns out to be that of an optimization problem, which is solved through the minimization of an appropriately defined cost function. We show that, unlike time-frequency methods that exploit only the square modulus of the transform, we can achieve a complete characterization of surface waves in a dispersive and attenuating medium. Using both synthetic examples and experimental data, we also show that it is in principle possible to separate different modes in both the time domain and the frequency domain Y1 - 2005 SN - 0956-540X ER - TY - JOUR A1 - Savin, Anton A1 - Sternin, Boris T1 - Boundary value problems on manifolds with fibered boundary N2 - We define a class of boundary value problems on manifolds with fibered boundary. This class is in a certain sense a deformation between the classical boundary value problems and the Atiyah-Patodi-Singer problems in subspaces (it contains both as special cases). The boundary conditions in this theory are taken as elements of the C*-algebra generated by pseudodifferential operators and families of pseudodifferential operators in the fibers. We prove the Fredholm. property for elliptic boundary value problems and compute a topological obstruction (similar to Atiyah-Bott obstruction) to the existence of elliptic boundary conditions for a given elliptic operator. Geometric operators with trivial and nontrivial obstruction are given. (c) 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Y1 - 2005 SN - 0025-584X ER - TY - JOUR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - Mixed problems with parameter N2 - Let X be a smooth n-dimensional manifold and D be an open connected set in X with smooth boundary OD. Perturbing the Cauchy problem for an elliptic system Au = f in D with data on a closed set Gamma subset of partial derivativeD, we obtain a family of mixed problems depending on a small parameter epsilon > 0. Although the mixed problems are subjected to a noncoercive boundary condition on partial derivativeDF in general, each of them is uniquely solvable in an appropriate Hilbert space D-T and the corresponding family {u(epsilon)} of solutions approximates the solution of the Cauchy problem in D-T whenever the solution exists. We also prove that the existence of a solution to the Cauchy problem in D-T is equivalent to the boundedness of the family {u(epsilon)}. We thus derive a solvability condition for the Cauchy problem and an effective method of constructing the solution. Examples for Dirac operators in the Euclidean space R-n are treated. In this case, we obtain a family of mixed boundary problems for the Helmholtz equation Y1 - 2005 SN - 1061-9208 ER - TY - JOUR A1 - Savin, Anton T1 - Elliptic operators on manifolds with singularities and K-homology N2 - Elliptic operators on smooth compact manifolds are classified by K-homology. We prove that a similar classification is valid also for manifolds with simplest singularities: isolated conical points and edges. The main ingredients of the proof of these results are: Atiyah-Singer difference construction in the noncommutative case and Poincare isomorphism in K- theory for ( our) singular manifolds. As an application we give a formula in topological terms for the obstruction to Fredholm problems on manifolds with edges Y1 - 2005 SN - 0920-3036 ER - TY - BOOK A1 - Berman, Gennady A1 - Tarkhanov, Nikolai Nikolaevich T1 - The dynamics of four wave interactions T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2004 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - Mixed problems with a parameter T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2004 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Popivanov, P. R. T1 - Lorenz transformations and creation of logarithmic singularities to the solutions of some nonstrictly hyperbolic semilinear systems with two space variables T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2004 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - THES A1 - Romanovskiy, Nikolai T1 - Systems of elasticity theory Y1 - 2004 ER - TY - JOUR A1 - Junek, Heinz A1 - Menghini, Marta T1 - Processi di crescita e decadimento N2 - Dynamical processes with particular reference to opposite phenomena as growth and decay, may be translated into the mathematical language of difference equations or recursive equations. Such equations can be treated in the discrete case(where the principal mathematical instrument is furnished by geometrical progressions) or in the continuous case (where the mathematical instrument is particularly represented by exponential functions and logarithms). The variety of problems and of resolution methods renders the proposed material apt to be used in a significant way in the high school. Y1 - 2004 ER - TY - JOUR A1 - Braunß, Hans-Andreas A1 - Junek, Heinz T1 - Factorization of injective ideals by interpolation N2 - We construct a factorization of certain multilinear mappings through linear operators belonging to closed, injective operator ideals using interpolation technique. An extension of the duality theorem for interpolation spaces is also obtained. Y1 - 2004 SN - 0022-247x ER - TY - JOUR A1 - Witt, Ingo T1 - Local asymptotic types N2 - 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 Y1 - 2004 SN - 0025-2611 ER - TY - JOUR A1 - Bär, Christian A1 - Dahl, Matthias T1 - The first dirac eigenvalue on manifolds with positive scalar curvature N2 - We show that on every compact spin manifold admitting a Riemannian metric of positive scalar curvature Friedrich's eigenvalue estimate for the Dirac operator can be made sharp up to an arbitrarily small given error by choosing the metric suitably. Y1 - 2004 UR - http://xxx.uni-augsburg.de/abs/math.DG/0305277 ER - TY - JOUR A1 - Devchand, Chandrashekar A1 - Fairlie, David A1 - Nuyts, Jean A1 - Weingart, Gregor T1 - Ternutator identities N2 - The ternary commutator or ternutator, defined as the alternating sum of the product of three operators, has recently drawn much attention as an interesting structure generalizing the commutator. The ternutator satisfies cubic identities analogous to the quadratic Jacobi identity for the commutator. We present various forms of these identities and discuss the possibility of using them to define ternary algebras. Y1 - 2009 UR - http://iopscience.iop.org/1751-8121/ U6 - https://doi.org/10.1088/1751-8113/42/47/475209 SN - 1751-8113 ER - TY - JOUR A1 - Shin, Seoleun A1 - Sommer, Matthias A1 - Reich, Sebastian A1 - Névir, Peter T1 - Evaluation of three spatial discretization schemes with the Galewsky et al. test N2 - We evaluate the Hamiltonian particle methods (HPM) and the Nambu discretization applied to shallow-water equations on the sphere using the test suggested by Galewsky et al. (2004). Both simulations show excellent conservation of energy and are stable in long-term simulation. We repeat the test also using the ICOSWP scheme to compare with the two conservative spatial discretization schemes. The HPM simulation captures the main features of the reference solution, but wave 5 pattern is dominant in the simulations applied on the ICON grid with relatively low spatial resolutions. Nevertheless, agreement in statistics between the three schemes indicates their qualitatively similar behaviors in the long-term integration. Y1 - 2010 UR - http://www3.interscience.wiley.com/cgi-bin/jhome/106562719 U6 - https://doi.org/10.1002/Asl.279 SN - 1530-261X ER - TY - THES A1 - Hohberger, Horst T1 - Semiclassical asymptotics for the scattering amplitude in the presence of focal points at infinity Y1 - 2006 CY - Potsdam ER - TY - THES A1 - Martin, Calin-Iulian T1 - Operator Algebras and Complexes of Operators Manifolds with Corners Y1 - 2006 CY - Potsdam ER - TY - JOUR A1 - de Azevedo Botelho, Geraldo Mßrcio A1 - Braunss, H. A. A1 - Junek, Heinz A1 - Pellegrino, Daniel Marinho T1 - Inclusions and coincidences for multiple summing multilinear mappings N2 - Using complex interpolation we prove new inclusion and coincidence theorems for multiple (fully) summing multilinear and holomorphic mappings. Among several other results we show that continuous n- linear forms on cotype 2 spaces are multiple (2; q(k),..., q(k))-summing, where 2(k-1) < n <= 2(k), q(0) = 2 and q(k+1) = 2q(k)/1+q(k) for k >= 0. Y1 - 2009 UR - http://www.ams.org/publications/journals/journalsframework/proc SN - 0002-9939 ER - TY - BOOK ED - Jahnke, Thomas ED - Meyerhöfer, Wolfram T1 - Pisa und Co : Kritik eines Programm Y1 - 2006 SN - 3-88120-428-8 PB - Franzbecker CY - Hildesheim ER - TY - JOUR A1 - Jahnke, Thomas T1 - Zur Ideologie von PISA und Co Y1 - 2006 SN - 978-388120-428-6 ER - TY - THES A1 - Dines, Nicoleta T1 - Elliptic operators on corner manifolds Y1 - 2006 ER - TY - THES A1 - Li, Xianhua T1 - Arithmetic properties and the characterization of finite groups Y1 - 2006 CY - Potsdam ER - TY - BOOK A1 - Krupchyk, K. A1 - Tarkhanov, Nikolai Nikolaevich A1 - Tuomela, J. T1 - Generalised elliptic boundary problems T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2005 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Tarkhanov, Nikolai Nikolaevich A1 - Vasilevski, Nikolai T1 - Microlocal analysis of the Bochner-Martinelli Integral T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2005 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK ED - Gil, Juan ED - Grieser, Daniel ED - Lesch, Matthias T1 - Approaches to singular analysis : a volume of advances in partial differential equations T3 - Operator theory : advances and applications Y1 - 2001 SN - 3-7643-6518-8 U6 - https://doi.org/10.1007/978-3-0348-8253-8 VL - 125 PB - Birkhäuser Basel CY - Basel ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Schwarzschild and Synge once again N2 - We complete the historical overview about the geometry of a Schwarzschild black hole at its horizon by emphasizing the contribution made by Synge in [6] to its clarification Y1 - 2005 UR - http://arXiv.org/abs/gr-qc/0408017 SN - 0001-7701 ER - TY - THES A1 - Pibaljommee, Bundit T1 - M-solid Pseudovarieties Y1 - 2005 CY - Potsdam ER - TY - JOUR A1 - Bär, Christian A1 - Gouduchon, Paul A1 - Moroianu, Andrei T1 - Generalized Cylinders in Semi-Riemannian and Spin Geometry N2 - We use a construction which we call generalized cylinders to give a new proof of the fundamental theorem of hypersurface theory. It has the advantage of being very simple and the result directly extends to semi-Riemannian manifolds and to embeddings into spaces of constant curvature. We also give a new way to identify spinors for different metrics and to derive the variation formula for the Dirac operator. Moreover, we show that generalized Killing spinors for Codazzi tensors are restrictions of parallel spinors. Finally, we study the space of Lorentzian metrics and give a criterion when two Lorentzian metrics on a manifold can be joined in a natural manner by a 1-parameter family of such metrics. Y1 - 2005 UR - http://xxx.uni-augsburg.de/abs/math.DG/0303095 ER - TY - BOOK A1 - Gosson, Maurice A. de T1 - On the weyl representation of metapletic operators T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2005 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Tarkhanov, Nikolai Nikolaevich T1 - Operator algebras related to the Bochner-Matinelli integral T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2005 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Gosson, Maurice A. de T1 - Extended weyl calculus and application to the phase-space scrödinger equation T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2005 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Janke, Thomas A1 - Wuttke, Hans A1 - Dietsch, Volker A1 - Janßen, Martin A1 - König, Gerhard A1 - Mentzendorff, Arne A1 - Simanowsky, Ursula A1 - Wuttke, Joachim T1 - Mathematik : Stochastik ; Orientierungswissen Analytische Geometrie ; Handreichungen für den Unterricht ; Gymnasiale Oberstufe NRW [Schülerbuch] Y1 - 2005 SN - 3-464-57283-8 PB - Cornelsen CY - Berlin ER - TY - BOOK A1 - Janke, Thomas A1 - Wuttke, Hans A1 - Alpers, Karsten A1 - Jahnke, Thomas A1 - Janßen, Martin A1 - Siekmann, Angelika A1 - Simanowsky, Ursula ED - Janke, Thomas ED - Wuttke, Hans T1 - Fokus Mathematik ; Analytische Geometrie Lineare Algebra ; Gymnasiale Oberstufe ; Baden-Württemberg Y1 - 2005 SN - 3-464-57340-0 PB - Cornelsen CY - Berlin ER - TY - BOOK A1 - Meyerhöfer, Wolfram T1 - Tests im Test: das Beispiel PISA Y1 - 2005 SN - 3-938094-12-5 PB - Budrich CY - Opladen ER - TY - BOOK A1 - Tarkhanov, Nikolai Nikolaevich T1 - Root functions of elliptic boundary problems in domains with conic points on the boundary T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2005 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Wenyi, Chen A1 - Tianbo, Wang T1 - The hypoellipticity of differential forms on closed manifolds T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2005 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Krainer, Thomas T1 - Resolvents of elliptic boundary problems on conic manifolds T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2005 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Fang, Daoyuan A1 - Xu, Jiang T1 - Asymptotic behavior of solutions to multidimensional nonisentropic hydrodynamic model for semiconductors T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2005 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Krainer, Thomas T1 - Elliptic boundary problems on manifolds with polycylindrical ends T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2005 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Aizenberg, Lev A. A1 - Tarkhanov, Nikolai Nikolaevich T1 - Stable expansions in homogeneous polynomials T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2005 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Savin, Anton A1 - Sternin, Boris T1 - Pseudodifferential subspaces and their applications in elliptic theory T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2005 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Makhmudov, O. I. A1 - Niyozov, I. E. T1 - The cauchy problem for the lame system in infinite domains in Rm T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2005 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Glebov, S. G. A1 - Kiselev, O. M. T1 - The forced KdV equation and passage throught the resonance T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2005 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Makhmudov, O. I. A1 - Niyozov, I. E. T1 - Regularization of the cauchy problem for the system of elasticity theory in Rm T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2005 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Louis, Pierre-Yves T1 - Increasing coupling for probabilistic cellular automata N2 - We give a necessary and sufficient condition for the existence of an increasing coupling of N (N greater as 2) synchronous dynamics on S^Zd (PCA). Increasing means the coupling preserves stochastic ordering. We first present our main construction theorem in the case where S is totally ordered; applications to attractive PCAs are given. When S is only partially ordered, we show on two examples that a coupling of more than two synchronous dynamics may not exist. We also prove an extension of our main result for a particular class of partially ordered spaces. Y1 - 2005 UR - http://www.sciencedirect.com/ science?_ob=JournalURL&_cdi=5672&_auth=y&_acct=C000053886&_version=1&_urlVersion=0&_userid=1584062&md5=a190494148436adc6a 89f14409e6e76e ER - TY - BOOK A1 - Kneis, Gert T1 - Mathematik für Wirtschaftswissenschaftler T3 - Internationale Standardlehrbücher der Wirtschafts- und Sozialwissenschaften Y1 - 2005 SN - 3-486-57665-8 U6 - https://doi.org/10.1515/9783486836707 PB - De Gruyter Oldenbourg CY - München ER - TY - JOUR A1 - Dreher, M A1 - Witt, Ingo T1 - Energy estimates for weakly hyperbolic systems of the first order N2 - For a class of first-order weakly hyperbolic pseudo-differential systems with finite time degeneracy, well- posedness of the Cauchy problem is proved in an adapted scale of Sobolev spaces. These Sobolev spaces are constructed in correspondence to the hyperbolic operator under consideration, making use of ideas from the theory of elliptic boundary value problems on manifolds with singularities. In addition, an upper bound for the loss of regularity that occurs when passing from the Cauchy data to the solutions is established. In many examples, this upper bound turns out to be sharp Y1 - 2005 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Untitled Y1 - 2005 ER - TY - JOUR A1 - Kawanabe, Motoaki A1 - Müller, Klaus-Robert T1 - Estimating functions for blind separation when sources have variance dependencies N2 - A blind separation problem where the sources are not independent, but have variance dependencies is discussed. For this scenario Hyvarinen and Hurri (2004) proposed an algorithm which requires no assumption on distributions of sources and no parametric model of dependencies between components. In this paper, we extend the semiparametric approach of Amari and Cardoso (1997) to variance dependencies and study estimating functions for blind separation of such dependent sources. In particular, we show that many ICA algorithms are applicable to the variance-dependent model as well under mild conditions, although they should in principle not. Our results indicate that separation can be done based only on normalized sources which are adjusted to have stationary variances and is not affected by the dependent activity levels. We also study the asymptotic distribution of the quasi maximum likelihood method and the stability of the natural gradient learning in detail. Simulation results of artificial and realistic examples match well with our theoretical findings Y1 - 2005 ER - TY - JOUR A1 - Kirsche, Andreas A1 - Böckmann, Christine T1 - Rational approximations for ill-conditioned equation systems N2 - In this study we present iterative methods using rational approximations, e.g... Pade approximants, which work very well for strongly ill-conditioned systems. In principle all methods of the family are convergent. One type of those methods has the advantage that their convergence behavior is very fast without additional a-priori information on the optimal relaxation parameter. (c) 2005 Elsevier Inc. All rights reserved Y1 - 2005 ER - TY - JOUR A1 - Dzhunushaliev, Vladimir T1 - Colored flux tube in Euclidean spacetime N2 - The flux tube solution in the Euclidean spacetime with the color longitudinal electric field in the SU(2) Yang- Mills-Higgs theory with broken gauge symmetry is found. Some arguments are given that this flux tube is a pure quantum object in the SU(3) quantum theory reduced to the SU(2) Yang-Mills-Higgs theory Y1 - 2005 SN - 0894-9875 ER - TY - JOUR A1 - Gosson, Maurice A. de T1 - On the Weyl representation of metaplectic operators N2 - We study the Weyl representation of metaplectic operators associated to a symplectic matrix having no non- trivial fixed point, and justify a formula suggested in earlier work of Mehlig and Wilkinson. We give precise calculations of the associated Maslov-type indices; these indices intervene in a crucial way in Gutzwiller's formula of semiclassical mechanics, and are simply related to an index defined by Conley and Zehnder Y1 - 2005 ER - TY - JOUR A1 - Gosson, Maurice A. de T1 - Symplectically covariant Schrodinger equation in phase space N2 - A classical theorem of Stone and von Neumann states that the Schrodinger representation is, up to unitary equivalences, the only irreducible representation of the Heisenberg group on the Hilbert space of square-integrable functions on configuration space. Using the Wigner-Moyal transform, we construct an irreducible representation of the Heisenberg group on a certain Hilbert space of square-integrable functions defined on phase space. This allows us to extend the usual Weyl calculus into a phase-space calculus and leads us to a quantum mechanics in phase space, equivalent to standard quantum mechanics. We also briefly discuss the extension of metaplectic operators to phase space and the probabilistic interpretation of the solutions of the phase-space Schrodinger equation Y1 - 2005 ER - TY - BOOK A1 - Gauthier, P. M. A1 - Tarkhanov, Nikolai Nikolaevich T1 - A covering proberty of the Riemann zeta-funktion T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2004 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Ma, Li A1 - Chen, Dezhong T1 - Curve Shotening in a Riemannian Manifold T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2004 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK ED - Gil, Juan ED - Krainer, Thomas ED - Witt, Ingo T1 - Aspects of Boundary Problems in Analysis and Geometry : advances in partial differential equations T3 - Operator Theory : Advances and Applications Y1 - 2004 SN - 3-7643-7069-6 VL - 151 PB - Birkhäuser CY - Basel ER - TY - BOOK A1 - Calin, Ovidium A1 - Chang, Der-Chen T1 - The Geometry on a Step 3 Grushin Model T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2004 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - THES A1 - Changphas, Thawhat T1 - Monoids of Hypersubstitutions Y1 - 2004 CY - Potsdam ER - TY - JOUR A1 - Ginoux, Nicolas T1 - Dirac operators on Lagrangian submanifolds N2 - We study a natural Dirac operator on a Lagrangian submanifold of a Kähler manifold. We first show that its square coincides with the Hodge-de Rham Laplacian provided the complex structure identifies the Spin structures of the tangent and normal bundles of the submanifold. We then give extrinsic estimates for the eigenvalues of that operator and discuss some examples. Y1 - 2004 UR - http://users.math.uni-potsdam.de/~ginoux/SousvLagr_v4.pdf ER - TY - BOOK ED - Brückner, Axel T1 - Mathematik : Lehrbuch für die Klasse 9 ; Brandenburg ; Gymnasium Y1 - 2004 SN - 3-89818-138-3 PB - Paetec CY - Berlin ER - TY - BOOK ED - Brückner, Axel T1 - Mathematik : Lehrbuch für die Klasse 8 ; Gymnasium Brandenburg Y1 - 2004 SN - 3-89818-130-8 PB - Paetec CY - Berlin ER - TY - BOOK A1 - Alpers, Karsten A1 - Dietzsch, Volker A1 - Epp, Thomas A1 - Jahnke, Thomas A1 - Janßen, Martin A1 - Siekmann, Angelika A1 - Simanowsky, Ursula A1 - Wuttke, Hans T1 - Mathematik : Analytische Geometrie lineare Algebra ; Orientierungswissen Stochastik ; Handreichungen für den Unterricht ; Gymnasiale Oberstufe ; NRW T3 - Orientierungswissen Stoachstik Y1 - 2004 SN - 3-464-57282-x PB - Cornelsen CY - Berlin ER - TY - JOUR A1 - Louis, Pierre-Yves T1 - Ergodicity of PCA: equivalence between spatial and temporal mixing conditions N2 - For a general attractive Probabilistic Cellular Automata on SZd, we prove that the (time-) convergence towards equilibrium of this Markovian parallel dynamics exponentially fast in the uniform norm is equivalent to a condition (A). This condition means the exponential decay of the influence from the boundary for the invariant measures of the system restricted to finite boxes. For a class of reversible PCA dynamics on {;1, +1}Zd, with a naturally associated Gibbsian potential ;, we prove that a (spatial-) weak mixing condition (WM) for ; implies the validity of the assumption (A); thus exponential (time-) ergodicity of these dynamics towards the unique Gibbs measure associated to ; holds. On some particular examples we state that exponential ergodicity holds as soon as there is no phase transition. Y1 - 2004 UR - http://www.math.washington.edu/%7Eejpecp/ECP/viewarticle.php?id=1704&layout=abstract ER - TY - JOUR A1 - Zähle, Henryk T1 - Heat equation with strongly inhomogeneous noise N2 - The author considers the heat equation in dimension one with singular drift and inhomogeneous space-time white noise. In particular, the quadratic variation measure of the white noise is not required to be absolutely continuous w.r.t. the Lebesgue measure, neither in space nor in time. Under some assumptions the author gives statements on strong and weak existence as well as strong and weak uniqueness of continuous solutions. Y1 - 2004 UR - http://www.sciencedirect.com/science/journal/03044149 ER - TY - JOUR A1 - Baumgärtel, Hellmut A1 - Lledo, Fernando T1 - Duality of compact groups and Hilbert C*-systems for C*-algebras with a nontrivial center N2 - In this paper we present duality theory for compact groups in the case when the C*-algebra A, the fixed point algebra of the corresponding Hilbert C*-system (F, 9), has a nontrivial center Z superset of C1 and the relative commutant satisfies the minimality condition A' boolean AND F = Z, as well as a technical condition called regularity. The abstract characterization of the mentioned Hilbert C*-system is expressed by means of an inclusion of C*- categories T-c < T, where T-c is a suitable DR-category and T a full subcategory of the category of endomorphisms of A. Both categories have the same objects and the arrows of T can be generated from the arrows of T-c and the center Z. A crucial new element that appears in the present analysis is an abelian group C(G), which we call the chain group of G, and that can be constructed from certain equivalence relation defined on (G) over cap, the dual object of G. The chain group, which is isomorphic to the character group of the center of g, determines the action of irreducible endomorphisms of A when restricted to Z. Moreover, C(g) encodes the possibility of defining a symmetry epsilon also for the larger category T of the previous inclusion Y1 - 2004 SN - 0129-167X ER - TY - JOUR A1 - Chelkak, D. A1 - Kargaev, P. A1 - Korotyaev, Evgeni T1 - Inverse problem for harmonic oscillator perturbed by potential, characterization N2 - Consider the perturbed harmonic oscillator Ty=-y''+x(2)y+q(x)y in L-2(R), where the real potential q belongs to the Hilbert space H={q', xq is an element of L-2(R)}. The spectrum of T is an increasing sequence of simple eigenvalues lambda(n)(q)=1+2n+mu(n), ngreater than or equal to0, such that mu(n)-->0 as n-->infinity. Let psi(n)(x,q) be the corresponding eigenfunctions. Define the norming constants nu(n)(q)=lim(xup arrowinfinity)log |psi(n) (x,q)/psi(n) (-x,q)|. We show that {mu(n)}(0)(infinity) is an element of H {nu(n)}(0)(infinity) is an element of H-0 for some real Hilbert space and some subspace H-0 subset of H. Furthermore, the mapping Psi:q-- >Psi(q)=({lambda(n)(q)}(0)(infinity), {nu(n)(q)}(0)(infinity)) is a real analytic isomorphism between H and S x H-0, where S is the set of all strictly increasing sequences s={s(n)}(0)(infinity) such that s(n)=1+2n+h(n), {h(n)}(0)(infinity) is an element of H. The proof is based on nonlinear functional analysis combined with sharp asymptotics of spectral data in the high energy limit for complex potentials. We use ideas from the analysis of the inverse problem for the operator -y"py, p is an element of L-2(0,1), with Dirichlet boundary conditions on the unit interval. There is no literature about the spaces H,H-0. We obtain their basic properties, using their representation as spaces of analytic functions in the disk Y1 - 2004 SN - 0010-3616 ER - TY - JOUR A1 - Ziehe, Andreas A1 - Laskov, Pavel A1 - Nolte, G A1 - Müller, Klaus-Robert T1 - A fast algorithm for joint diagonalization with non-orthogonal transformations and its application to blind source separation N2 - A new efficient algorithm is presented for joint diagonalization of several matrices. The algorithm is based on the Frobenius-norm formulation of the joint diagonalization problem, and addresses diagonalization with a general, non- orthogonal transformation. The iterative scheme of the algorithm is based on a multiplicative update which ensures the invertibility of the diagonalizer. The algorithm's efficiency stems from the special approximation of the cost function resulting in a sparse, block-diagonal Hessian to be used in the computation of the quasi-Newton update step. Extensive numerical simulations illustrate the performance of the algorithm and provide a comparison to other leading diagonalization methods. The results of such comparison demonstrate that the proposed algorithm is a viable alternative to existing state-of-the-art joint diagonalization algorithms. The practical use of our algorithm is shown for blind source separation problems Y1 - 2004 ER - TY - JOUR A1 - Laub, Julian A1 - Müller, Klaus-Robert T1 - Feature discovery in non-metric pairwise data N2 - Pairwise proximity data, given as similarity or dissimilarity matrix, can violate metricity. This occurs either due to noise, fallible estimates, or due to intrinsic non-metric features such as they arise from human judgments. So far the problem of non-metric pairwise data has been tackled by essentially omitting the negative eigenvalues or shifting the spectrum of the associated (pseudo) covariance matrix for a subsequent embedding. However, little attention has been paid to the negative part of the spectrum itself. In particular no answer was given to whether the directions associated to the negative eigenvalues would at all code variance other than noise related. We show by a simple, exploratory analysis that the negative eigenvalues can code for relevant structure in the data, thus leading to the discovery of new features, which were lost by conventional data analysis techniques. The information hidden in the negative eigenvalue part of the spectrum is illustrated and discussed for three data sets, namely USPS handwritten digits, text-mining and data from cognitive psychology Y1 - 2004 ER - TY - JOUR A1 - Böckmann, Christine A1 - Wandinger, Ulla A1 - Ansmann, Albert A1 - Bösenberg, Jens A1 - Amiridis, Vassilis A1 - Boselli, Antonella A1 - Delaval, Arnaud A1 - De Tomasi, Ferdinando de A1 - Frioud, Max A1 - Grigorov, Ivan Videnov A1 - Hagard, Arne A1 - Horvat, Matej A1 - Iarlori, Marco A1 - Komguem, Leonce A1 - Kreipl, Stephan A1 - Larchevque, Gilles A1 - Matthias, Volker A1 - Papayannis, Alexandros A1 - Pappalardo, GGelsomina A1 - Rocadenbosch, Francesc A1 - Rodrigues, Jose António A1 - Schneider, Johannes A1 - Shcherbakov, Valery A1 - Wiegner, Matthias T1 - Aerosol lidar intercomparison in the framework of the EARLINET project : 2. Aerosol backscatter algorithms N2 - An intercomparison of aerosol backscatter lidar algorithms was performed in 2001 within the framework of the European Aerosol Research Lidar Network to Establish an Aerosol Climatology (EARLINET). The objective of this research was to test the correctness of the algorithms and the influence of the lidar ratio used by the various lidar teams involved in the EARLINET for calculation of backscatter-coefficient profiles from the lidar signals. The exercise consisted of processing synthetic lidar signals of various degrees of difficulty. One of these profiles contained height- dependent lidar ratios to test the vertical influence of those profiles on the various retrieval algorithms. Furthermore, a realistic incomplete overlap of laser beam and receiver field of view was introduced to remind the teams to take great care in the nearest range to the lidar. The intercomparison was performed in three stages with increasing knowledge on the input parameters. First, only the lidar signals were distributed; this is the most realistic stage. Afterward the lidar ratio profiles and the reference values at calibration height were provided. The unknown height- dependent lidar ratio had the largest influence on the retrieval, whereas the unknown reference value was of minor importance. These results show the necessity of making additional independent measurements, which can provide us with a suitable approximation of the lidar ratio. The final stage proves in general, that the data evaluation schemes of the different groups of lidar systems work well. (C) 2004 Optical Society of America Y1 - 2004 SN - 0003-6935 ER - TY - JOUR A1 - Bovier, Anton A1 - Eckhoff, Michael A1 - Gayrard, Veronique A1 - Klein, Markus T1 - Metastability in reversible diffusion processes : I. Sharp asymptotics for capacities and exit times N2 - We develop a potential theoretic approach to the problem of metastability for reversible diffusion processes with generators of the form -epsilonDelta+ delF(.) del on R-d or subsets of R-d, where F is a smooth function with finitely many local minima. In analogy to previous work on discrete Markov chains, we show that metastable exit times from the attractive domains of the minima of F can be related, up to multiplicative errors that tend to one as epsilon down arrow 0, to the capacities of suitably constructed sets. We show that these capacities can be computed, again up to multiplicative errors that tend to one, in terms of local characteristics of F at the starting minimum and the relevant saddle points. As a result, we are able to give the first rigorous proof of the classical Eyring - Kramers formula in dimension larger than 1. The estimates on capacities make use of their variational representation and monotonicity properties of Dirichlet forms. The methods developed here are extensions of our earlier work on discrete Markov chains to continuous diffusion processes Y1 - 2004 SN - 1435-9855 ER - TY - JOUR A1 - Gräter, Joachim A1 - Weese, Martin T1 - On the norm equation over function fields N2 - If K is an algebraic function field of one variable over an algebraically closed field k and F is a finite extension of K, then any element a of K can be written as a norm of some b in F by Tsen's theorem. All zeros and poles of a lead to zeros and poles of b, but in general additional zeros and poles occur. The paper shows how this number of additional zeros and poles of b can be restricted in terms of the genus of K, respectively F. If k is the field of all complex numbers, then we use Abel's theorem concerning the existence of meromorphic functions on a compact Riemarm surface. From this, the general case of characteristic 0 can be derived by means of principles from model theory, since the theory of algebraically closed fields is model-complete. Some of these results also carry over to the case of characteristic p > 0 using standard arguments from valuation theory Y1 - 2004 SN - 0024-6107 ER - TY - JOUR A1 - Guenther, Ulrich A1 - Starobinsky, A. A. A1 - Zhuk, Alexandre T1 - Multidimensional cosmological models : Cosmological and astrophysical implications and constraints N2 - We investigate four-dimensional effective theories which are obtained by dimensional reduction of multidimensional cosmological models with factorizable geometry and we consider the interaction between conformal excitations of the internal space (geometrical moduli excitations) and Abelian gauge fields. It is assumed that the internal space background can be stabilized by minima of an effective potential. The conformal excitations over such a background have the form of massive scalar fields (gravitational excitons) propagating in the external spacetime. We discuss cosmological and astrophysical implications of the interaction between gravexcitons and four-dimensional photons as well as constraints arising on multidimensional models of the type considered in our paper. In particular, we show that due to the experimental bounds on the variation of the fine-structure constant, gravexcitons should decay before nucleosynthesis starts. For a successful nucleosynthesis, the masses of the decaying gravexcitons should be mgreater than or similar to10(4) GeV. Furthermore, we discuss the possible contribution of gravexcitons to ultrahigh-energy cosmic rays. It is shown that, at energies Esimilar to10(20) eV, the decay length of gravexcitons with masses mgreater than or similar to10(4) GeV is very small, but that for mless than or similar to10(2) GeV it becomes much larger than the Greisen-Zatsepin-Kuzmin cutoff distance. Finally, we investigate the possibility for gravexciton-photon oscillations in strong magnetic fields of astrophysical objects. The corresponding estimates indicate that even the high-magnetic- field strengths B of magnetars (special types of pulsars with B>B(critical)similar to4.4x10(13) G) are not sufficient for an efficient and copious production of gravexcitons Y1 - 2004 SN - 0556-2821 ER - TY - JOUR A1 - Hanke, Timo T1 - An explicit example of a noncrossed product division algebra N2 - The paper presents an explicit example of a noncrossed product division algebra of index and exponent 8 over the field Q(s) (t). It is an iterated twisted function field in two variables D (x, sigma) (y, tau) over a quaternion division algebra D which is defined over the number field Q(root3, root-7). The automorphisms sigma and tau are computed by solving relative norm equations in extensions of number fields. The example is explicit in the sense that its structure constants are known. Moreover, it is pointed out that the same arguments also yield another example, this time over the field Q((s)) ((t)), given by an iterated twisted Laurent series ring D((x, sigma)) ((y, tau)) over the same quaternion division algebra D. (C) 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Y1 - 2004 SN - 0025-584X ER - TY - JOUR A1 - Kytmanov, Alexander M. A1 - Myslivets, Simona A1 - Tarkhanov, Nikolai Nikolaevich T1 - Holomorphic Lefschetz formula for manifolds with boundary N2 - The classical Lefschetz fixed point formula expresses the number of fixed points of a continuous map f : M-->M in terms of the transformation induced by f on the cohomology of M. In 1966 Atiyah and Bott extended this formula to elliptic complexes over a compact closed manifold. In particular, they presented a holomorphic Lefschetz formula for compact complex manifolds without boundary, a result, in the framework of algebraic geometry due to Eichler (1957) for holomorphic curves. On compact complex manifolds with boundary the Dolbeault complex is not elliptic, hence the Atiyah- Bott theory is no longer applicable. To get rid of the difficulties related to the boundary behaviour of the Dolbeault cohomology, Donelli and Fefferman (1986) derived a fixed point formula for the Bergman metric. The purpose of this paper is to present a holomorphic Lefschetz formula on a strictly convex domain in C-n, n>1 Y1 - 2004 SN - 0025-5874 ER - TY - JOUR A1 - Kytmanov, Alexander M. A1 - Myslivets, S. G. A1 - Tarkhanov, Nikolai Nikolaevich T1 - On a holomorphic Lefschetz formula in strictly pseudoconvex subdomains of complex manifolds N2 - The classical Lefschetz formula expresses the number of fixed points of a continuous map f: M -> M in terms of the transformation induced by f on the cohomology of M. In 1966, Atiyah and Bott extended this formula to elliptic complexes over a compact closed manifold. In particular, they obtained a holomorphic Lefschetz formula on compact complex manifolds without boundary. Brenner and Shubin (1981, 1991) extended the Atiyah-Bott theory to compact manifolds with boundary. On compact complex manifolds with boundary the Dolbeault complex is not elliptic, therefore the Atiyah- Bott theory is not applicable. Bypassing difficulties related to the boundary behaviour of Dolbeault cohomology, Donnelly and Fefferman (1986) obtained a formula for the number of fixed points in terms of the Bergman metric. The aim of this paper is to obtain a Lefschetz formula on relatively compact strictly pseudoconvex subdomains of complex manifolds X with smooth boundary, that is, to find the total Lefschetz number for a holomorphic endomorphism f(*) of the Dolbeault complex and to express it in terms of local invariants of the fixed points of f. Y1 - 2004 SN - 1064-5616 ER - TY - JOUR A1 - Liu, Xiaochun A1 - Witt, Ingo T1 - Pseudodifferential calculi on the half-line respecting prescribed asymptotic types N2 - Given asymptotics types P, Q, pseudodifferential operators A is an element of L-cl(mu) (R+) are constructed in such a way that if u(t) possesses conormal asymptotics of type P as t --> +0, then Au(t) possesses conormal asymptotics of type Q as t --> +0. This is achieved by choosing the operators A in Schulze's cone algebra on the half-line R+, controlling their complete Mellin symbols {sigma(M)(u-j) (A); j is an element of N}, and prescribing the mapping properties of the residual Green operators. The constructions lead to a coordinate invariant calculus, including trace and potential operators at t = 0, in which a parametrix construction for the elliptic elements is possible. Boutet de Monvel's calculus for pseudodifferential boundary problems occurs as a special case when P = Q is the type resulting from Taylor expansion at t = 0. Y1 - 2004 SN - 0378-620X ER - TY - JOUR A1 - Yin, H. C. A1 - Witt, Ingo T1 - Global singularity structure of weak solutions to 3-D semilinear dispersive wave equations with discontinuous initial data N2 - We study the global singularity structure of solutions to 3-D semilinear wave equations with discontinuous initial data. More precisely, using Strichartz' inequality we show that the solutions stay conormal after nonlinear interaction if the Cauchy data are conormal along a circle. (C) 2003 Elsevier Inc. All rights reserved Y1 - 2004 SN - 0022-0396 ER - TY - JOUR A1 - Zhuk, Alexandre A1 - Gunther, U. T1 - Massive scalar fields in the early universe N2 - We discuss the role of gravitational excitons/radions in different cosmological scenarios. Gravitational excitons are massive moduli fields which describe conformal excitations of the internal spaces and which, due to their Planck-scale suppressed coupling to matter fields, are WIMPs. It is demonstrated that, depending on the concrete scenario, observational cosmological data set strong restrictions on the allowed masses and initial oscillation amplitudes of these particles Y1 - 2004 SN - 0218-2718 ER -