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Thu, 06 Feb 2014 11:01:33 +0200Thu, 06 Feb 2014 11:01:33 +0200A well-balanced solver for the Saint Venant Equations with variable cross-section
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3810
In this paper we construct a numerical solver for the Saint Venant equations. Special attention
is given to the balancing of the source terms, including the bottom slope and variable cross-
sectional profiles. Therefore a special discretization of the pressure law is used, in order to
transfer analytical properties to the numerical method. Based on this approximation a well-
balanced solver is developed, assuring the C-property and depth positivity. The performance
of this method is studied in several test cases focusing on accurate capturing of steady states.Raul Borschearticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3810Mon, 02 Jun 2014 11:01:33 +0200Homogeneous Penalizers and Constraints in Convex Image Restoration
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3347
Recently convex optimization models were successfully applied
for solving various problems in image analysis and restoration.
In this paper, we are interested in relations between
convex constrained optimization problems
of the form
\({\rm argmin} \{ \Phi(x)\) subject to \(\Psi(x) \le \tau \}\)
and their penalized counterparts
\({\rm argmin} \{\Phi(x) + \lambda \Psi(x)\}\).
We recall general results on the topic by the help of an epigraphical projection.
Then we deal with the special setting \(\Psi := \| L \cdot\|\) with \(L \in \mathbb{R}^{m,n}\)
and \(\Phi := \varphi(H \cdot)\),
where \(H \in \mathbb{R}^{n,n}\) and \(\varphi: \mathbb R^n \rightarrow \mathbb{R} \cup \{+\infty\} \)
meet certain requirements which are often fulfilled in image processing models.
In this case we prove by incorporating the dual problems
that there exists a bijective function
such that
the solutions of the constrained problem coincide with those of the
penalized problem if and only if \(\tau\) and \(\lambda\) are in the graph
of this function.
We illustrate the relation between \(\tau\) and \(\lambda\) for various problems
arising in image processing.
In particular, we point out the relation to the Pareto frontier for joint sparsity problems.
We demonstrate the performance of the
constrained model in restoration tasks of images corrupted by Poisson noise
with the \(I\)-divergence as data fitting term \(\varphi\)
and in inpainting models with the constrained nuclear norm.
Such models can be useful if we have a priori knowledge on the image rather than on the noise level.René Ciak; Behrang Shafei; Gabriele Steidlarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3347Thu, 15 Nov 2012 09:15:14 +0100The Generalized Assignment Problem with Minimum Quantities
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3290
We consider a variant of the generalized assignment problem (GAP) where the amount of space used in each bin is restricted to be either zero (if the bin is not opened) or above a given lower bound (a minimum quantity). We provide several complexity results for different versions of the problem and give polynomial time exact algorithms and approximation algorithms for restricted cases.
For the most general version of the problem, we show that it does not admit a polynomial time approximation algorithm (unless P=NP), even for the case of a single bin. This motivates to study dual approximation algorithms that compute solutions violating the bin capacities and minimum quantities by a constant factor. When the number of bins is fixed and the minimum quantity of each bin is at least a factor \(\delta>1\) larger than the largest size of an item in the bin, we show how to obtain a polynomial time dual approximation algorithm that computes a solution violating the minimum quantities and bin capacities by at most a factor \(1-\frac{1}{\delta}\) and \(1+\frac{1}{\delta}\), respectively, and whose profit is at least as large as the profit of the best solution that satisfies the minimum quantities and bin capacities strictly.
In particular, for \(\delta=2\), we obtain a polynomial time (1,2)-approximation algorithm.Sven Krumke; Clemens Thielenarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3290Mon, 08 Oct 2012 15:25:13 +0200Complexity and Approximability of the Maximum Flow Problem with Minimum Quantities
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3181
We consider the maximum flow problem with minimum quantities (MFPMQ), which is a variant of the maximum flow problem where
the flow on each arc in the network is restricted to be either zero or above a given lower bound (a minimum quantity), which
may depend on the arc. This problem has recently been shown to be weakly NP-complete even on series-parallel graphs.
In this paper, we provide further complexity and approximability results for MFPMQ and several special cases.
We first show that it is strongly NP-hard to approximate MFPMQ on general graphs (and even bipartite graphs) within any positive factor.
On series-parallel graphs, however, we present a pseudo-polynomial time dynamic programming algorithm for the problem.
We then study the case that the minimum quantity is the same for each arc in the network and show that, under this restriction, the problem is still
weakly NP-complete on general graphs, but can be solved in strongly polynomial time on series-parallel graphs.
On general graphs, we present a \((2 - 1/\lambda) \)-approximation algorithm for this case, where \(\lambda\) denotes the common minimum quantity of all arcs.Clemens Thielen; Stephan Westphalarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3181Fri, 06 Jul 2012 10:39:47 +0200Eine transfinite Zahl als Grenzwert
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2185
Wir zeigen, dass Aleph-Null diejenige transfinite Kardinalzahl ist, gegen die alle Zahlenfolgen streben, die (nach gängiger Definition) gegen (positiv) unendlich streben, und beleuchten dessen Konsequenzen. Diese beinhalten u.a., dass die Exponentialfunktion im Unendlichen unstetig ist.Thomas Limbergarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2185Thu, 15 Apr 2010 07:58:43 +0200A Mathematical Model for Diffusion and Exchange Phenomena in Ultra Napkins
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/709
The performance of napkins is nowadays improved substantially by embedding granules of a superabsorbent into the cellulose matrix. In this paper a continuous model for the liquid transport in such an Ultra Napkin is proposed. Its mean feature is a nonlinear diffusion equation strongly coupled with an ODE describing a reversible absorbtion process. An efficient numerical method based on a symmetrical time splitting and a finite difference scheme of ADI-predictor-corrector type has been developed to solve these equations in a three dimensional setting. Numerical results are presented that can be used to optimize the granule distribution.Joachim Weickertarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/709Tue, 17 Oct 2000 00:00:00 +0200A Model for the Cloudiness of Fabrics
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/562
Cloudy inhomogenities in artificial fabrics are graded by a fast method which is based on a Laplacian pyramid decomposition of the fabric image. This band-pass representation takes into account the scale character of the cloudiness. A quality measure of the entire cloudiness is obtained as a weighted mean over the variances of all scales.Joachim Weickertarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/562Wed, 07 Jun 2000 00:00:00 +0200Wirkungsnetze dynamischer Systeme
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1051
Aufgrund der vernetzten Strukturen und Wirkungszusammenhänge dynamischer Systeme werden die zugrundeliegenden mathematischen Modelle meist sehr komplex und erfordern ein hohes mathematisches Verständnis und Geschick. Bei Verwendung von spezieller Software können jedoch auch ohne tiefgehende mathematische oder informatorische Fachkenntnisse komplexe Wirkungsnetze dynamischer Systeme interaktiv erstellt werden. Als Beispiel wollen wir schrittweise das Modell einer Miniwelt entwerfen und Aussagen bezüglich ihrer Bevölkerungsentwicklung treffen.Wolfgang Eiden; Markus Heidenreicharticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1051Fri, 26 May 2000 00:00:00 +0200Wavelet Smoothing of Evolutionary Spectra by Non-Linear Thresholding
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/534
We consider wavelet estimation of the time-dependent (evolutionary) power spectrum of a locally stationary time series. Allowing for departures from stationary proves useful for modelling, e.g., transient phenomena, quasi-oscillating behaviour or spectrum modulation. In our work wavelets are used to provide an adaptive local smoothing of a short-time periodogram in the time-freqeuncy plane. For this, in contrast to classical nonparametric (linear) approaches we use nonlinear thresholding of the empirical wavelet coefficients of the evolutionary spectrum. We show how these techniques allow for both adaptively reconstructing the local structure in the time-frequency plane and for denoising the resulting estimates. To this end a threshold choice is derived which is motivated by minimax properties w.r.t. the integrated mean squared error. Our approach is based on a 2-d orthogonal wavelet transform modified by using a cardinal Lagrange interpolation function on the finest scale. As an example, we apply our procedure to a time-varying spectrum motivated from mobile radio propagation.Rainer von Sachs; Kai Schneiderarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/534Mon, 03 Apr 2000 00:00:00 +0200Wavelet Thresholding in Anisotropic Function Classes and Application to Adaptive Estimation of Evolutionary Spectra
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/563
We derive minimax rates for estimation in anisotropic smoothness classes. This rate is attained by a coordinatewise thresholded wavelet estimator based on a tensor product basis with separate scale parameter for every dimension. It is shown that this basis is superior to its one-scale multiresolution analog, if different degrees of smoothness in different directions are present.; As an important application we introduce a new adaptive wavelet estimator of the time-dependent spectrum of a locally stationary time series. Using this model which was resently developed by Dahlhaus, we show that the resulting estimator attains nearly the rate, which is optimal in Gaussian white noise, simultaneously over a wide range of smoothness classes. Moreover, by our new approach we overcome the difficulty of how to choose the right amount of smoothing, i.e. how to adapt to the appropriate resolution, for reconstructing the local structure of the evolutionary spectrum in the time-frequency plane.Michael H. Neumann; Rainer von Sachsarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/563Mon, 03 Apr 2000 00:00:00 +0200Wavelet Thresholding: Beyond the Gaussian I.I.D. Situation
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/564
With this article we first like to give a brief review on wavelet thresholding methods in non-Gaussian and non-i.i.d. situations, respectively. Many of these applications are based on Gaussian approximations of the empirical coefficients. For regression and density estimation with independent observations, we establish joint asymptotic normality of the empirical coefficients by means of strong approximations. Then we describe how one can prove asymptotic normality under mixing conditions on the observations by cumulant techniques.; In the second part, we apply these non-linear adaptive shrinking schemes to spectral estimation problems for both a stationary and a non-stationary time series setup. For the latter one, in a model of Dahlhaus on the evolutionary spectrum of a locally stationary time series, we present two different approaches. Moreover, we show that in classes of anisotropic function spaces an appropriately chosen wavelet basis automatically adapts to possibly different degrees of regularity for the different directions. The resulting fully-adaptive spectral estimator attains the rate that is optimal in the idealized Gaussian white noise model up to a logarithmic factor.Michael H. Neumann; Rainer von Sachsarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/564Mon, 03 Apr 2000 00:00:00 +0200Stochastic Reconstruction of Loading Histories from a Rainflow Matrix
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/565
This paper is devoted to the mathematica l description of the solution of the so-called rainflow reconstruction problem, i.e. the problem of constructing a time series with an a priori given rainflow m atrix. The algorithm we present is mathematically exact in the sense that no app roximations or heuristics are involved. Furthermore it generates a uniform distr ibution of all possible reconstructions and thus an optimal randomization of the reconstructed series. The algorithm is a genuine on-line scheme. It is easy adj ustable to all variants of rainflow such as sysmmetric and asymmetric versions a nd different residue techniques.Klaus Dreßler; Michael Hack; Wilhelm Krügerarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/565Mon, 03 Apr 2000 00:00:00 +0200Fatigue Lifetime Estimation Based on Rainflow Counted Data Using the Local Strain Approach
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/566
In the automotive industry both the loca l strain approach and rainflow counting are well known and approved tools in the numerical estimation of the lifetime of a new developed part especially in the automotive industry. This paper is devoted to the combination of both tools and a new algorithm is given that takes advantage of the inner structure of the most used damage parameters.Klaus Dreßler; Michael Hackarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/566Mon, 03 Apr 2000 00:00:00 +0200Multiscale Texture Enhancement
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/570
The ideas of texture analysis by means of the structure tensor are combined with the scale-space concept of anisotropic diffusion filtering. In contrast to many other nonlinear diffusion techniques, the proposed one uses a diffusion tensor instead of a scalar diffusivity. This allows true anisotropic behaviour. The preferred diffusion direction is determined according to the phase angle of the structure tensor. The diffusivity in this direction is increasing with the local coherence of the signal. This filter is constructed in such a way that it gives a mathematically well-funded scale-space representation of the original image. Experiments demonstrate its usefulness for the processing of interrupted one-dimensional structures such as fingerprint and fabric images.Joachim Weickertarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/570Mon, 03 Apr 2000 00:00:00 +0200Nonlinear Diffusion Scale-Spaces: From the Continuous to the Discrete Setting
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/589
A survey on continuous, semidiscrete and discrete well-posedness and scale-space results for a class of nonlinear diffusion filters is presented. This class does not require any monotony assumption (comparison principle) and, thus, allows image restoration as well. The theoretical results include existence, uniqueness, continuous dependence on the initial image, maximum-minimum principles, average grey level invariance, smoothing Lyapunov functionals, and convergence to a constant steady state.Joachim Weickertarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/589Mon, 03 Apr 2000 00:00:00 +0200Symmetric subgroups of rational groups of hermitian type
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/750
Bruce Huntarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/750Mon, 03 Apr 2000 00:00:00 +0200Modular subvarieties of arithmetic quotients of bounded symmetric domains
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/751
Bruce Huntarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/751Mon, 03 Apr 2000 00:00:00 +0200Heterotic Gauge Structure of Type II K3 Fibrations
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/752
Bruce Hunt; Rolf Schimmrigkarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/752Mon, 03 Apr 2000 00:00:00 +0200On the algebraic dimension of twistor spaces over the connected sum of four complex projective planes
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/753
Bernd Kreußlerarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/753Mon, 03 Apr 2000 00:00:00 +0200Plane curves of minimal degree with prescribed singularities
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/757
We prove that there exists a positive \(\alpha\) such thatfor any integer \(\mbox{$d\ge 3$}\) and any topological types \(\mbox{$S_1,\dots,S_n$}\) of plane curve singularities, satisfying \(\mbox{$\mu(S_1)+\dots+\mu(S_n)\le\alpha d^2$}\), there exists a reduced irreducible plane curve of degree \(d\) with exactly \(n\) singular points of types \(\mbox{$S_1,\dots,S_n$}\), respectively. This estimate is optimal with respect to theexponent of \(d\). In particular, we prove that for any topological type \(S\) there exists an irreducible polynomial of degree \(\mbox{$d\le 14\sqrt{\mu(S)}$}\) having a singular point of type \(S\).Gert-Martin Greuel; Christoph Lossen; Eugenii Shustinarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/757Mon, 03 Apr 2000 00:00:00 +0200A short note on functions of bounded semivariation and countably additive vector measures
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/759
In the scalar case one knows that a complex normalized function of boundedvariation \(\phi\) on \([0,1]\) defines a unique complex regular Borel measure\(\mu\) on \([0,1]\). In this note we show that this is no longer true in generalin the vector valued case, even if \(\phi\) is assumed to be continuous. Moreover, the functions \(\phi\) which determine a countably additive vectormeasure \(\mu\) are characterized.Peter Vietenarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/759Mon, 03 Apr 2000 00:00:00 +0200Two equivalent norms for vector-valued holomorphic functions
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/769
The following two norms for holomorphic functions \(F\), defined on the right complex half-plane \(\{z \in C:\Re(z)\gt 0\}\) with values in a Banach space \(X\), are equivalent:
\[\begin{eqnarray*} \lVert F \rVert _{H_p(C_+)} &=& \sup_{a\gt0}\left( \int_{-\infty}^\infty \lVert F(a+ib) \rVert ^p \ db \right)^{1/p}
\mbox{, and} \\ \lVert F \rVert_{H_p(\Sigma_{\pi/2})} &=& \sup_{\lvert \theta \lvert \lt \pi/2}\left( \int_0^\infty \left \lVert F(re^{i \theta}) \right \rVert ^p\ dr \right)^{1/p}.\end{eqnarray*}\] As a consequence, we derive a description of boundary values ofsectorial holomorphic functions, and a theorem of Paley-Wiener typefor sectorial holomorphic functions.Peter Vietenarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/769Mon, 03 Apr 2000 00:00:00 +0200Characterization of operators of positive scalar type
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/787
Let \(X\) be a Banach lattice. Necessary and sufficient conditions for a linear operator \(A:D(A) \to X\), \(D(A)\subseteq X\), to be of positive \(C^0\)-scalar type are given. In addition, the question is discussed which conditions on the Banach lattice imply that every operator of positive \(C^0\)-scalar type is necessarily of positive scalar type.Peter Vietenarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/787Mon, 03 Apr 2000 00:00:00 +0200Hyperbolic planes
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/790
Bruce Huntarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/790Mon, 03 Apr 2000 00:00:00 +0200Moduli spaces for torsion free modules on curve singularities I
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/804
Gert-Martin Greuel; Gerhard Pfisterarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/804Mon, 03 Apr 2000 00:00:00 +0200