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- ItemAdaptive smoothing of digital images: The R package adimpro(Los Angeles, Calif. : UCLA, Dept. of Statistics, 2007) Polzehl, J.; Tabelow, K.Digital imaging has become omnipresent in the past years with a bulk of applications ranging from medical imaging to photography. When pushing the limits of resolution and sensitivity noise has ever been a major issue. However, commonly used non-adaptive filters can do noise reduction at the cost of a reduced effective spatial resolution only. Here we present a new package adimpro for R, which implements the propagationseparation approach by (Polzehl arid Spokoiriy 2006) for smoothing digital images. This method naturally adapts to different structures of different size in the image and thus avoids oversmoothing edges and fine structures. We extend the method for imaging data with spatial correlation. Furthermore we show how the estimation of the dependence between variance and mean value can be included. We illustrate the use of the package through some examples.
- ItemA propagation-separation approach to estimate the autocorrelation in a time-series(Göttingen : Copernicus, 2008) Divine, D.V.; Polzehl, J.; Godtliebsen, F.The paper presents an approach to estimate parameters of a local stationary AR(1) time series model by maximization of a local likelihood function. The method is based on a propagation-separation procedure that leads to data dependent weights defining the local model. Using free propagation of weights under homogeneity, the method is capable of separating the time series into intervals of approximate local stationarity. Parameters in different regions will be significantly different. Therefore the method also serves as a test for a stationary AR(1) model. The performance of the method is illustrated by applications to both synthetic data and real time-series of reconstructed NAO and ENSO indices and GRIP stable isotopes.
- ItemClassification and clustering: models, software and applications(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Mucha, Hans-Joachim; Ritter, GunterWe are pleased to present the report on the 30th Fall Meeting of the working group ``Data Analysis and Numerical Classification'' (AG-DANK) of the German Classification Society. The meeting took place at the Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin, from Friday Nov. 14 till Saturday Nov. 15, 2008. Already 12 years ago, WIAS had hosted a traditional Fall Meeting with special focus on classification and multivariate graphics (Mucha and Bock, 1996). This time, the special topics were stability of clustering and classification, mixture decomposition, visualization, and statistical software.
- ItemExperimental investigations on the suppression of Q-switching in monolithic 40 GHz mode-locked semiconductor lasers(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Hüttl, BerndInherent Q-switching as a source of intra-cavity pulse energy modulations, i.e. unwanted amplitude noise, is still a challenging task in order to fabricate monolithic mode-locked semiconductor lasers in view of different commercial applications. In this paper, the results of experimental investigations on the influence of the quantum well number on the occurrence and suppression of Q-switching in 40 GHz mode-locked multiple quantum well buried heterostructure lasers are presented. Improved mode-locked lasers emit short optical pulses (<=1.6 ps) with very low amplitude noise (1-2%) and timing jitter (50-100 fs).
- ItemMaximal parabolic regularity for divergence operators on distribution spaces(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Haller-Dintelmann, Robert; Rehberg, JoachimWe show that elliptic second order operators A of divergence type fulfill maximal parabolic regularity on distribution spaces, even if the underlying domain is highly non-smooth, the coefficients of A are discontinuous and A is complemented with mixed boundary conditions. Applications to quasilinear parabolic equations with non-smooth data are presented
- ItemMode transitions in distributed-feedback tapered master-oscillator power-amplifier(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Radziunas, Mindaugas; Tronciu, Vasile Z.; Bandelow, Uwe; Lichtner, Mark; Spreemann, Martin; Wenzel, HansTheoretical and experimental investigations have been carried out to study the spectral and spatial behavior of monolithically integrated distributed-feedback tapered master-oscillators power-amplifiers emitting around 973 nm. Introduction of self and cross heating effects and the analysis of longitudinal optical modes allows us to explain experimental results. The results show a good qualitative agreement between measured and calculated characteristics.
- ItemA model of an electrochemical flow cell with porous layer(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Ehrhardt, Matthias; Fuhrmann, Jürgen; Linke, AlexanderIn this paper we discuss three different mathematical models for fluid-porous interfaces in a simple channel geometry that appears e.g. in thin-layer channel flow cells. Here the difficulties arise from the possibly different orders of the corresponding differential operators in the different domains. A finite volume discretization of this model allows to calculate the limiting current of the H_2 oxidation in a porous electrode with platinum catalyst particles.
- ItemFeedback stabilization of magnetohydrodynamic equations(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Lefter, CǎtǎlinWe prove the local exponential stabilizability for the MHD system, with internally distributed feedback controllers. These controllers take values in a finite dimensional space which is the unstable manifold of the elliptic part of the linearized operator. The stabilization of the linear system is derived using a unique continuation property for systems of parabolic and elliptic equations, as well as the equivalence between controllability and feedback stabilizability in the case of finite dimensional systems. The feedback that stabilizes the linearized system is also stabilizing the nonlinear system in the domain of a fractional power of the elliptic operator.
- ItemFinite element error analysis for state-constrained optimal control of the Stokes equations(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Reyes, Juan Carlos de los; Meyer, Christian; Vexler, BorisAn optimal control problem for 2d and 3d Stokes equations is investigated with pointwise inequality constraints on the state and the control. The paper is concerened with the full discretization of the control problem allowing for different types of discretization of both the control and the state. For instance, piecewise linear and continuous approximations of the control are included in the present theory. Under certain assumptions on the $L^infty$-error of the finite element discretization of the state, error estimates for the control are derived which can be seen to be optimal since their order of convergence coincides with the one of the interpolation error. The assumptions of the $L^infty$-finite-element-error can be verified for different numerical settings. The theoretical results are confirmed by numerical examples.
- ItemThe heat treatment of steel - a mathematical control problem(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Hömberg, Dietmar; Kern, DanielaThe goal of this paper is to show how the heat treatment of steel can be modelled in terms of a mathematical optimal control problem. The approach is applied to laser surface hardening and the cooling of a steel slab including mechanical effects. Finally, it is shown how the results can be utilized in industrial practice by a coupling with machine-based control.