@article{DaiPraLouisMinelli2006, author = {Dai Pra, Paolo and Louis, Pierre-Yves and Minelli, Ida}, title = {Monotonicity and complete monotonicity for continuous-time Markov chains}, issn = {1631-073X}, doi = {10.1016/j.crma.2006.04.007}, year = {2006}, abstract = {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which monotonicity and complete monotonicity coincide in continuous time but not in discrete-time}, language = {en} } @unpublished{VasilievTarkhanov2016, author = {Vasiliev, Serguei and Tarkhanov, Nikolai Nikolaevich}, title = {Construction of series of perfect lattices by layer superposition}, volume = {5}, number = {11}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-100591}, pages = {11}, year = {2016}, abstract = {We construct a new series of perfect lattices in n dimensions by the layer superposition method of Delaunay-Barnes.}, language = {en} } @article{BoeckmannKirsche2006, author = {B{\"o}ckmann, Christine and Kirsche, Andreas}, title = {Iterative regularization method for lidar remote sensing}, issn = {0010-4655}, doi = {10.1016/j.cpc.2005.12.019}, year = {2006}, abstract = {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.}, language = {en} } @article{Meyerhoefer2006, author = {Meyerh{\"o}fer, Wolfram}, title = {Testen, Lernen und Gesellschaft : zwischen Autonomie und Heteronomie}, isbn = {978-388120-428-6}, year = {2006}, language = {de} } @book{JankeWuttkeDietschetal.2005, author = {Janke, Thomas and Wuttke, Hans and Dietsch, Volker and Janßen, Martin and K{\"o}nig, Gerhard and Mentzendorff, Arne and Simanowsky, Ursula and Wuttke, Joachim}, title = {Mathematik : Stochastik ; Orientierungswissen Analytische Geometrie ; Gymnasiale Oberstufe, NRW [Sch{\"u}lerbuch]}, publisher = {Cornelsen}, address = {Berlin}, isbn = {3-464-57213-7}, pages = {352 S.}, year = {2005}, language = {de} } @article{Schmidt2005, author = {Schmidt, Hans-J{\"u}rgen}, title = {Einsteins Arbeiten in Bezug auf die moderne Kosmologie : de Sitters L{\"o}sung der Einsteinschen Feldgleichung mit positivem kosmologischen Glied als Geometrie des inflationaeren Weltmodells}, year = {2005}, abstract = {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.}, language = {de} } @book{JankeWuttkeDietschetal.2005, author = {Janke, Thomas and Wuttke, Hans and Dietsch, Volker and Janßen, Martin and Koenig, Gerhard and Mentzendorff, Arne and Simanowsky, Ursula and Wuttke, Joachim}, title = {Mathematik : Stochastik ; Gymnasiale Oberstufe, [Sch{\"u}lerbuch]}, editor = {Jahnke, Thomas}, publisher = {Cornelsen}, address = {Berlin}, isbn = {3-464-57218-8}, pages = {351 S.}, year = {2005}, language = {de} } @article{Pfaeffle2005, author = {Pf{\"a}ffle, Frank}, title = {Eigenvalues of Dirac Operators for Hyperbolic Degenerations}, year = {2005}, abstract = {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.}, language = {en} } @book{JankeWuttkeDietschetal.2005, author = {Janke, Thomas and Wuttke, Hans and Dietsch, Volker and Janßen, Martin and K{\"o}nig, Gerhard and Mentzendorff, Arne and Simanowsky, Ursula and Wuttke, Joachim}, title = {Mathematik : Stochastik ; Handreichungen f{\"u}r den Unterricht ; Gymnasiale Oberstufe [Sch{\"u}lerbuch]}, publisher = {Cornelsen}, address = {Berlin}, isbn = {3-464-57288-9}, pages = {312 S.}, year = {2005}, language = {de} } @book{Tarkhanov2005, author = {Tarkhanov, Nikolai Nikolaevich}, title = {Unitary solutions of paratial differential equations}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {35 S.}, year = {2005}, language = {en} } @book{Liu2005, author = {Liu, Weian}, title = {Monotone method for nonlocal systems of first order}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {16 S.}, year = {2005}, language = {en} } @article{Zaehle2005, author = {Z{\"a}hle, Henryk}, title = {Space-time regularity of catalytic super-Brownian motion}, year = {2005}, abstract = {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.}, language = {en} } @phdthesis{Raetsch2005, author = {R{\"a}tsch, Thoralf}, title = {On the Equi-Constistency of the failure of the GAP-1 transfer property and an inaccessible cardinal}, address = {Potsdam}, pages = {99 S.}, year = {2005}, language = {en} } @book{OPUS4-13368, title = {Mathematik : Lehrbuch f{\"u}r die Klasse 10 ; Gymnasium Brandenburg}, editor = {Br{\"u}ckner, Axel}, publisher = {Paetec}, address = {Berlin}, isbn = {3-89818-142-1}, pages = {248 S.}, year = {2005}, language = {de} } @book{Paneah2005, author = {Paneah, Boris}, title = {On the general theory of the cauchy type functional equations with applications in analysis}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {34 S.}, year = {2005}, language = {en} } @article{BoeckmannMironovaMuller2005, author = {B{\"o}ckmann, Christine and Mironova, I. and Muller, D.}, title = {Microphysical aerosol parameters from multiwavelength lidar}, issn = {1084-7529}, year = {2005}, abstract = {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}, language = {en} } @article{BovierGayrardKlein2005, author = {Bovier, Anton and Gayrard, Veronique and Klein, Markus}, title = {Metastability in reversible diffusion processes : II. Precise asymptotics for small eigenvalues}, issn = {1435-9855}, year = {2005}, abstract = {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}, language = {en} } @article{RaschSchindler2005, author = {Rasch, T. and Schindler, R.}, title = {A new condensation principle}, issn = {1432-0665}, year = {2005}, abstract = {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\#}, language = {en} } @article{Gosson2005, author = {Gosson, Maurice A. de}, title = {Extended Weyl calculus and application to the phase-space Schrodinger equation}, year = {2005}, abstract = {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}, language = {en} } @article{BaumgaertelGrundling2005, author = {Baumgaertel, Hellmut and Grundling, H.}, title = {Superselection in the presence of constraints}, issn = {0022-2488}, year = {2005}, abstract = {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}, language = {en} } @article{BaakeBaakeBovieretal.2005, author = {Baake, Ellen and Baake, Michael and Bovier, Anton and Klein, Markus}, title = {An asymptotic maximum principle for essentially linear evolution models}, issn = {0303-6812}, year = {2005}, abstract = {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}, language = {en} } @article{KleinKorotyaevPokrovski2005, author = {Klein, Markus and Korotyaev, Evgeni and Pokrovski, A.}, title = {Spectral asymptotics of the harmonic oscillator perturbed by bounded potentials}, issn = {1424-0637}, year = {2005}, abstract = {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.}, language = {en} } @article{GuntherZhukBezerraetal.2005, author = {Gunther, U. and Zhuk, Alexandre and Bezerra, Valdir B. and Romero, C.}, title = {AdS and stabilized extra dimensions in multi-dimensional gravitational models with nonlinear scalar curvature terms R-1 and R-4}, issn = {0264-9381}, year = {2005}, abstract = {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}, language = {en} } @article{HolschneiderDialloKuleshetal.2005, author = {Holschneider, Matthias and Diallo, Mamadou Sanou and Kulesh, Michail and Ohrnberger, Matthias and Luck, E. and Scherbaum, Frank}, title = {Characterization of dispersive surface waves using continuous wavelet transforms}, issn = {0956-540X}, year = {2005}, abstract = {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}, language = {en} } @article{SavinSternin2005, author = {Savin, Anton and Sternin, Boris}, title = {Boundary value problems on manifolds with fibered boundary}, issn = {0025-584X}, year = {2005}, abstract = {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}, language = {en} } @article{ShlapunovTarkhanov2005, author = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich}, title = {Mixed problems with parameter}, issn = {1061-9208}, year = {2005}, abstract = {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}, language = {en} } @article{Savin2005, author = {Savin, Anton}, title = {Elliptic operators on manifolds with singularities and K-homology}, issn = {0920-3036}, year = {2005}, abstract = {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}, language = {en} } @book{BermanTarkhanov2004, author = {Berman, Gennady and Tarkhanov, Nikolai Nikolaevich}, title = {The dynamics of four wave interactions}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {25 S.}, year = {2004}, language = {en} } @book{ShlapunovTarkhanov2004, author = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich}, title = {Mixed problems with a parameter}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {28 S.}, year = {2004}, language = {en} } @book{Popivanov2004, author = {Popivanov, P. R.}, title = {Lorenz transformations and creation of logarithmic singularities to the solutions of some nonstrictly hyperbolic semilinear systems with two space variables}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {17 S.}, year = {2004}, language = {en} } @phdthesis{Romanovskiy2004, author = {Romanovskiy, Nikolai}, title = {Systems of elasticity theory}, pages = {59 S.}, year = {2004}, language = {en} } @article{JunekMenghini2004, author = {Junek, Heinz and Menghini, Marta}, title = {Processi di crescita e decadimento}, year = {2004}, abstract = {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.}, language = {it} } @article{BraunssJunek2004, author = {Braunß, Hans-Andreas and Junek, Heinz}, title = {Factorization of injective ideals by interpolation}, issn = {0022-247x}, year = {2004}, abstract = {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.}, language = {en} } @article{Witt2004, author = {Witt, Ingo}, title = {Local asymptotic types}, issn = {0025-2611}, year = {2004}, 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} } @article{BaerDahl2004, author = {B{\"a}r, Christian and Dahl, Matthias}, title = {The first dirac eigenvalue on manifolds with positive scalar curvature}, year = {2004}, abstract = {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.}, language = {en} } @article{DevchandFairlieNuytsetal.2009, author = {Devchand, Chandrashekar and Fairlie, David and Nuyts, Jean and Weingart, Gregor}, title = {Ternutator identities}, issn = {1751-8113}, doi = {10.1088/1751-8113/42/47/475209}, year = {2009}, abstract = {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.}, language = {en} } @article{ShinSommerReichetal.2010, author = {Shin, Seoleun and Sommer, Matthias and Reich, Sebastian and N{\´e}vir, Peter}, title = {Evaluation of three spatial discretization schemes with the Galewsky et al. test}, issn = {1530-261X}, doi = {10.1002/Asl.279}, year = {2010}, abstract = {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.}, language = {en} } @phdthesis{Hohberger2006, author = {Hohberger, Horst}, title = {Semiclassical asymptotics for the scattering amplitude in the presence of focal points at infinity}, address = {Potsdam}, pages = {93 S. : graph. Darst.}, year = {2006}, language = {en} } @phdthesis{Martin2006, author = {Martin, Calin-Iulian}, title = {Operator Algebras and Complexes of Operators Manifolds with Corners}, address = {Potsdam}, pages = {138 S.}, year = {2006}, language = {en} } @article{deAzevedoBotelhoBraunssJuneketal.2009, author = {de Azevedo Botelho, Geraldo Mßrcio and Braunss, H. A. and Junek, Heinz and Pellegrino, Daniel Marinho}, title = {Inclusions and coincidences for multiple summing multilinear mappings}, issn = {0002-9939}, year = {2009}, abstract = {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.}, language = {en} } @book{OPUS4-12339, title = {Pisa und Co : Kritik eines Programm}, editor = {Jahnke, Thomas and Meyerh{\"o}fer, Wolfram}, publisher = {Franzbecker}, address = {Hildesheim}, isbn = {3-88120-428-8}, pages = {349 S.}, year = {2006}, language = {de} } @article{Jahnke2006, author = {Jahnke, Thomas}, title = {Zur Ideologie von PISA und Co}, isbn = {978-388120-428-6}, year = {2006}, language = {de} } @phdthesis{Dines2006, author = {Dines, Nicoleta}, title = {Elliptic operators on corner manifolds}, pages = {174 S. : graph. Darst.}, year = {2006}, language = {en} } @phdthesis{Li2006, author = {Li, Xianhua}, title = {Arithmetic properties and the characterization of finite groups}, address = {Potsdam}, pages = {X, 186 S. : graph. Darst.}, year = {2006}, language = {en} } @book{KrupchykTarkhanovTuomela2005, author = {Krupchyk, K. and Tarkhanov, Nikolai Nikolaevich and Tuomela, J.}, title = {Generalised elliptic boundary problems}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {27 S.}, year = {2005}, language = {en} } @book{TarkhanovVasilevski2005, author = {Tarkhanov, Nikolai Nikolaevich and Vasilevski, Nikolai}, title = {Microlocal analysis of the Bochner-Martinelli Integral}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {9 S.}, year = {2005}, language = {en} } @book{OPUS4-12576, title = {Approaches to singular analysis : a volume of advances in partial differential equations}, series = {Operator theory : advances and applications}, volume = {125}, journal = {Operator theory : advances and applications}, editor = {Gil, Juan and Grieser, Daniel and Lesch, Matthias}, publisher = {Birkh{\"a}user Basel}, address = {Basel}, isbn = {3-7643-6518-8}, doi = {10.1007/978-3-0348-8253-8}, pages = {256 S.}, year = {2001}, language = {en} } @article{Schmidt2005, author = {Schmidt, Hans-J{\"u}rgen}, title = {Schwarzschild and Synge once again}, issn = {0001-7701}, year = {2005}, abstract = {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}, language = {en} } @phdthesis{Pibaljommee2005, author = {Pibaljommee, Bundit}, title = {M-solid Pseudovarieties}, address = {Potsdam}, pages = {x, 95 S.}, year = {2005}, language = {en} } @article{BaerGouduchonMoroianu2005, author = {B{\"a}r, Christian and Gouduchon, Paul and Moroianu, Andrei}, title = {Generalized Cylinders in Semi-Riemannian and Spin Geometry}, year = {2005}, abstract = {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.}, language = {en} } @book{Gosson2005, author = {Gosson, Maurice A. de}, title = {On the weyl representation of metapletic operators}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {15 S.}, year = {2005}, language = {en} } @book{Tarkhanov2005, author = {Tarkhanov, Nikolai Nikolaevich}, title = {Operator algebras related to the Bochner-Matinelli integral}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {15 S.}, year = {2005}, language = {en} } @book{Gosson2005, author = {Gosson, Maurice A. de}, title = {Extended weyl calculus and application to the phase-space scr{\"o}dinger equation}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {7 S.}, year = {2005}, language = {en} } @book{JankeWuttkeDietschetal.2005, author = {Janke, Thomas and Wuttke, Hans and Dietsch, Volker and Janßen, Martin and K{\"o}nig, Gerhard and Mentzendorff, Arne and Simanowsky, Ursula and Wuttke, Joachim}, title = {Mathematik : Stochastik ; Orientierungswissen Analytische Geometrie ; Handreichungen f{\"u}r den Unterricht ; Gymnasiale Oberstufe NRW [Sch{\"u}lerbuch]}, publisher = {Cornelsen}, address = {Berlin}, isbn = {3-464-57283-8}, pages = {351 S.}, year = {2005}, language = {de} } @book{JankeWuttkeAlpersetal.2005, author = {Janke, Thomas and Wuttke, Hans and Alpers, Karsten and Jahnke, Thomas and Janßen, Martin and Siekmann, Angelika and Simanowsky, Ursula}, title = {Fokus Mathematik ; Analytische Geometrie Lineare Algebra ; Gymnasiale Oberstufe ; Baden-W{\"u}rttemberg}, editor = {Janke, Thomas and Wuttke, Hans}, publisher = {Cornelsen}, address = {Berlin}, isbn = {3-464-57340-0}, pages = {271 S.}, year = {2005}, language = {de} } @book{Meyerhoefer2005, author = {Meyerh{\"o}fer, Wolfram}, title = {Tests im Test: das Beispiel PISA}, publisher = {Budrich}, address = {Opladen}, isbn = {3-938094-12-5}, pages = {224 S.}, year = {2005}, language = {de} } @book{Tarkhanov2005, author = {Tarkhanov, Nikolai Nikolaevich}, title = {Root functions of elliptic boundary problems in domains with conic points on the boundary}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {20 S.}, year = {2005}, language = {en} } @book{WenyiTianbo2005, author = {Wenyi, Chen and Tianbo, Wang}, title = {The hypoellipticity of differential forms on closed manifolds}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {11 S.}, year = {2005}, language = {en} } @book{Krainer2005, author = {Krainer, Thomas}, title = {Resolvents of elliptic boundary problems on conic manifolds}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {52 S.}, year = {2005}, language = {en} } @book{FangXu2005, author = {Fang, Daoyuan and Xu, Jiang}, title = {Asymptotic behavior of solutions to multidimensional nonisentropic hydrodynamic model for semiconductors}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {29 S.}, year = {2005}, language = {en} } @book{Krainer2005, author = {Krainer, Thomas}, title = {Elliptic boundary problems on manifolds with polycylindrical ends}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {32 S.}, year = {2005}, language = {en} } @book{AizenbergTarkhanov2005, author = {Aizenberg, Lev A. and Tarkhanov, Nikolai Nikolaevich}, title = {Stable expansions in homogeneous polynomials}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {23 S.}, year = {2005}, language = {en} } @book{SavinSternin2005, author = {Savin, Anton and Sternin, Boris}, title = {Pseudodifferential subspaces and their applications in elliptic theory}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {46 S.}, year = {2005}, language = {en} } @book{MakhmudovNiyozov2005, author = {Makhmudov, O. I. and Niyozov, I. E.}, title = {The cauchy problem for the lame system in infinite domains in Rm}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {27 S.}, year = {2005}, language = {en} } @book{GlebovKiselev2005, author = {Glebov, S. G. and Kiselev, O. M.}, title = {The forced KdV equation and passage throught the resonance}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {18 S.}, year = {2005}, language = {en} } @book{MakhmudovNiyozov2005, author = {Makhmudov, O. I. and Niyozov, I. E.}, title = {Regularization of the cauchy problem for the system of elasticity theory in Rm}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {14 S.}, year = {2005}, language = {en} } @article{Louis2005, author = {Louis, Pierre-Yves}, title = {Increasing coupling for probabilistic cellular automata}, year = {2005}, abstract = {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.}, language = {en} } @book{Kneis2005, author = {Kneis, Gert}, title = {Mathematik f{\"u}r Wirtschaftswissenschaftler}, series = {Internationale Standardlehrb{\"u}cher der Wirtschafts- und Sozialwissenschaften}, journal = {Internationale Standardlehrb{\"u}cher der Wirtschafts- und Sozialwissenschaften}, publisher = {De Gruyter Oldenbourg}, address = {M{\"u}nchen}, isbn = {3-486-57665-8}, doi = {10.1515/9783486836707}, pages = {381 S.}, year = {2005}, language = {de} } @article{DreherWitt2005, author = {Dreher, M and Witt, Ingo}, title = {Energy estimates for weakly hyperbolic systems of the first order}, year = {2005}, abstract = {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}, language = {en} } @article{Schmidt2005, author = {Schmidt, Hans-J{\"u}rgen}, title = {Untitled}, year = {2005}, language = {de} } @article{KawanabeMueller2005, author = {Kawanabe, Motoaki and M{\"u}ller, Klaus-Robert}, title = {Estimating functions for blind separation when sources have variance dependencies}, year = {2005}, abstract = {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}, language = {en} } @article{KirscheBoeckmann2005, author = {Kirsche, Andreas and B{\"o}ckmann, Christine}, title = {Rational approximations for ill-conditioned equation systems}, year = {2005}, abstract = {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}, language = {en} } @article{Dzhunushaliev2005, author = {Dzhunushaliev, Vladimir}, title = {Colored flux tube in Euclidean spacetime}, issn = {0894-9875}, year = {2005}, abstract = {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}, language = {en} } @article{Gosson2005, author = {Gosson, Maurice A. de}, title = {On the Weyl representation of metaplectic operators}, year = {2005}, abstract = {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}, language = {en} } @article{Gosson2005, author = {Gosson, Maurice A. de}, title = {Symplectically covariant Schrodinger equation in phase space}, year = {2005}, abstract = {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}, language = {en} } @book{GauthierTarkhanov2004, author = {Gauthier, P. M. and Tarkhanov, Nikolai Nikolaevich}, title = {A covering proberty of the Riemann zeta-funktion}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {11 S.}, year = {2004}, language = {en} } @book{MaChen2004, author = {Ma, Li and Chen, Dezhong}, title = {Curve Shotening in a Riemannian Manifold}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {20 S.}, year = {2004}, language = {en} } @book{OPUS4-14127, title = {Aspects of Boundary Problems in Analysis and Geometry : advances in partial differential equations}, series = {Operator Theory : Advances and Applications}, volume = {151}, journal = {Operator Theory : Advances and Applications}, editor = {Gil, Juan and Krainer, Thomas and Witt, Ingo}, publisher = {Birkh{\"a}user}, address = {Basel}, isbn = {3-7643-7069-6}, pages = {XII, 560 S.}, year = {2004}, language = {en} } @book{CalinChang2004, author = {Calin, Ovidium and Chang, Der-Chen}, title = {The Geometry on a Step 3 Grushin Model}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {22 S.}, year = {2004}, language = {en} } @phdthesis{Changphas2004, author = {Changphas, Thawhat}, title = {Monoids of Hypersubstitutions}, address = {Potsdam}, pages = {vii, 88 S.}, year = {2004}, language = {en} } @article{Ginoux2004, author = {Ginoux, Nicolas}, title = {Dirac operators on Lagrangian submanifolds}, year = {2004}, abstract = {We study a natural Dirac operator on a Lagrangian submanifold of a K{\"a}hler 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.}, language = {en} } @book{OPUS4-14776, title = {Mathematik : Lehrbuch f{\"u}r die Klasse 9 ; Brandenburg ; Gymnasium}, editor = {Br{\"u}ckner, Axel}, publisher = {Paetec}, address = {Berlin}, isbn = {3-89818-138-3}, pages = {240 S.}, year = {2004}, language = {de} } @book{OPUS4-14781, title = {Mathematik : Lehrbuch f{\"u}r die Klasse 8 ; Gymnasium Brandenburg}, editor = {Br{\"u}ckner, Axel}, publisher = {Paetec}, address = {Berlin}, isbn = {3-89818-130-8}, pages = {240 S.}, year = {2004}, language = {de} } @book{AlpersDietzschEppetal.2004, author = {Alpers, Karsten and Dietzsch, Volker and Epp, Thomas and Jahnke, Thomas and Janßen, Martin and Siekmann, Angelika and Simanowsky, Ursula and Wuttke, Hans}, title = {Mathematik : Analytische Geometrie lineare Algebra ; Orientierungswissen Stochastik ; Handreichungen f{\"u}r den Unterricht ; Gymnasiale Oberstufe ; NRW}, series = {Orientierungswissen Stoachstik}, journal = {Orientierungswissen Stoachstik}, publisher = {Cornelsen}, address = {Berlin}, isbn = {3-464-57282-x}, pages = {456 S.}, year = {2004}, language = {de} } @article{Louis2004, author = {Louis, Pierre-Yves}, title = {Ergodicity of PCA: equivalence between spatial and temporal mixing conditions}, year = {2004}, abstract = {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.}, language = {en} } @article{Zaehle2004, author = {Z{\"a}hle, Henryk}, title = {Heat equation with strongly inhomogeneous noise}, year = {2004}, abstract = {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.}, language = {en} } @article{BaumgaertelLledo2004, author = {Baumg{\"a}rtel, Hellmut and Lledo, Fernando}, title = {Duality of compact groups and Hilbert C*-systems for C*-algebras with a nontrivial center}, issn = {0129-167X}, year = {2004}, abstract = {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}, language = {en} } @article{ChelkakKargaevKorotyaev2004, author = {Chelkak, D. and Kargaev, P. and Korotyaev, Evgeni}, title = {Inverse problem for harmonic oscillator perturbed by potential, characterization}, issn = {0010-3616}, year = {2004}, abstract = {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}, language = {en} } @article{ZieheLaskovNolteetal.2004, author = {Ziehe, Andreas and Laskov, Pavel and Nolte, G and M{\"u}ller, Klaus-Robert}, title = {A fast algorithm for joint diagonalization with non-orthogonal transformations and its application to blind source separation}, year = {2004}, abstract = {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}, language = {en} } @article{LaubMueller2004, author = {Laub, Julian and M{\"u}ller, Klaus-Robert}, title = {Feature discovery in non-metric pairwise data}, year = {2004}, abstract = {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}, language = {en} } @article{BoeckmannWandingerAnsmannetal.2004, author = {B{\"o}ckmann, Christine and Wandinger, Ulla and Ansmann, Albert and B{\"o}senberg, Jens and Amiridis, Vassilis and Boselli, Antonella and Delaval, Arnaud and De Tomasi, Ferdinando de and Frioud, Max and Grigorov, Ivan Videnov and Hagard, Arne and Horvat, Matej and Iarlori, Marco and Komguem, Leonce and Kreipl, Stephan and Larchevque, Gilles and Matthias, Volker and Papayannis, Alexandros and Pappalardo, GGelsomina and Rocadenbosch, Francesc and Rodrigues, Jose Ant{\´o}nio and Schneider, Johannes and Shcherbakov, Valery and Wiegner, Matthias}, title = {Aerosol lidar intercomparison in the framework of the EARLINET project : 2. Aerosol backscatter algorithms}, issn = {0003-6935}, year = {2004}, abstract = {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}, language = {en} } @article{BovierEckhoffGayrardetal.2004, author = {Bovier, Anton and Eckhoff, Michael and Gayrard, Veronique and Klein, Markus}, title = {Metastability in reversible diffusion processes : I. Sharp asymptotics for capacities and exit times}, issn = {1435-9855}, year = {2004}, abstract = {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}, language = {en} } @article{GraeterWeese2004, author = {Gr{\"a}ter, Joachim and Weese, Martin}, title = {On the norm equation over function fields}, issn = {0024-6107}, year = {2004}, abstract = {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}, language = {en} } @article{GuentherStarobinskyZhuk2004, author = {Guenther, Ulrich and Starobinsky, A. A. and Zhuk, Alexandre}, title = {Multidimensional cosmological models : Cosmological and astrophysical implications and constraints}, issn = {0556-2821}, year = {2004}, abstract = {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}, language = {en} } @article{Hanke2004, author = {Hanke, Timo}, title = {An explicit example of a noncrossed product division algebra}, issn = {0025-584X}, year = {2004}, abstract = {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}, language = {en} } @article{KytmanovMyslivetsTarkhanov2004, author = {Kytmanov, Alexander M. and Myslivets, Simona and Tarkhanov, Nikolai Nikolaevich}, title = {Holomorphic Lefschetz formula for manifolds with boundary}, issn = {0025-5874}, year = {2004}, abstract = {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}, language = {en} } @article{KytmanovMyslivetsTarkhanov2004, author = {Kytmanov, Alexander M. and Myslivets, S. G. and Tarkhanov, Nikolai Nikolaevich}, title = {On a holomorphic Lefschetz formula in strictly pseudoconvex subdomains of complex manifolds}, issn = {1064-5616}, year = {2004}, abstract = {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.}, language = {en} } @article{LiuWitt2004, author = {Liu, Xiaochun and Witt, Ingo}, title = {Pseudodifferential calculi on the half-line respecting prescribed asymptotic types}, issn = {0378-620X}, year = {2004}, abstract = {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.}, language = {en} } @article{YinWitt2004, author = {Yin, H. C. and Witt, Ingo}, title = {Global singularity structure of weak solutions to 3-D semilinear dispersive wave equations with discontinuous initial data}, issn = {0022-0396}, year = {2004}, abstract = {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}, language = {en} } @article{ZhukGunther2004, author = {Zhuk, Alexandre and Gunther, U.}, title = {Massive scalar fields in the early universe}, issn = {0218-2718}, year = {2004}, abstract = {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}, language = {en} }