TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Wismath, Shelly T1 - A characterization of k-normal varieties N2 - Let v be a valuation of terms of type tau, assigning to each term t of type tau a value v(t) greater than or equal to 0. Let k greater than or equal to 1 be a natural number. An identity s approximate to t of type tau is called k- normal if either s = t or both s and t have value greater than or equal to k, and otherwise is called non-k-normal. A variety V of type tau is said to be k-normal if all its identities are k-normal, and non-k-normal otherwise. In the latter case, there is a unique smallest k-normal variety N-k(A) (V) to contain V , called the k-normalization of V. Inthe case k = 1, for the usual depth valuation of terms, these notions coincide with the well-known concepts of normal identity, normal variety, and normalization of a variety. I. Chajda has characterized the normalization of a variety by means of choice algebras. In this paper we generalize his results to a characterization of the k-normalization of a variety, using k-choice algebras. We also introduce the concept of a k-inflation algebra, and for the case that v is the usual depth valuation of terms, we prove that a variety V is k-normal iff it is closed under the formation of k- inflations, and that the k-normalization of V consists precisely of all homomorphic images of k-inflations of algebras in V Y1 - 2004 SN - 0002-5240 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 - 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 - 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 - GEN A1 - Roelly, Sylvie A1 - Dai Pra, Paolo T1 - An existence result for infinite-dimensional Brownian diffusions with non- regular and non Markovian drift N2 - We prove in this paper an existence result for infinite-dimensional stationary interactive Brownian diffusions. The interaction is supposed to be small in the norm ||.||∞ but otherwise is very general, being possibly non-regular and non-Markovian. Our method consists in using the characterization of such diffusions as space-time Gibbs fields so that we construct them by space-time cluster expansions in the small coupling parameter. KW - infinite-dimensional Brownian diffusion KW - space-time Gibbs field KW - cluster expansion Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6684 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 - 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 - JOUR A1 - Schulze, Bert-Wolfgang A1 - Seiler, Jörg T1 - Boundary value problems with global projection conditions N2 - Parametrices of elliptic boundary value problems for differential operators belong to an algebra of pseudodifferential operators with the transmission property at the boundary. However, generically, smooth symbols on a manifold with boundary do not have this property, and several interesting applications require a corresponding more general calculus. We introduce here a new algebra of boundary value problems that contains Shapiro-Lopatinskij elliptic as well as global projection conditions; the latter ones are necessary, if an analogue of the Atiyah-Bott obstruction does not vanish. We show that every elliptic operator admits (up to a stabilisation) elliptic conditions of that kind. Corresponding boundary value problems are then Fredholm in adequate scales of spaces. Moreover, we construct parametrices in the calculus. (C) 2003 Elsevier Inc. All rights reserved Y1 - 2004 SN - 0022-1236 ER - TY - BOOK A1 - Kapanadze, David A1 - Schulze, Bert-Wolfgang T1 - Boundary-contact Problems for Domains with Conical Singularities 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 - 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 - 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 - BOOK A1 - Liu, Xiaochun A1 - Schulze, Bert-Wolfgang T1 - Ellipticity on Manifolds with edges and boundary T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2004 SN - 1437-739X PB - Univ. CY - Potsdam 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 - 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 - 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 - Tarkhanov, Nikolai Nikolaevich T1 - Fixed point formula for holomorphic functions N2 - We show a Lefschetz fixed point formula for holomorphic functions in a bounded domain D with smooth boundary in the complex plane. To introduce the Lefschetz number for a holomorphic map of D, we make use of the Bergman kernel of this domain. The Lefschetz number is proved to be the sum of the usual contributions of fixed points of the map in D and contributions of boundary fixed points, these latter being different for attracting and repulsing fixed points Y1 - 2004 SN - 0002-9939 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 - BOOK A1 - Schulze, Bert-Wolfgang A1 - Volpato, A. T1 - Green operators in the edge calculus T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2004 SN - 1437-739X PB - Univ. CY - Potsdam 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 -