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161.
Say that two compositions of n into k parts are related if they differ only by a cyclic shift. This defines an equivalence relation on the set of such compositions. Let ${\left\langle \begin{array}{c}n \\ k\end{array} \right\rangle}$ denote the number of distinct corresponding equivalence classes, that is, the number of cyclic compositions of n into k parts. We show that the sequence ${\left\langle\begin{array}{c}n \\ k\end{array}\right\rangle}$ is log-concave and prove some results concerning ${\left\langle \begin{array}{c}n \\ k \end{array} \right\rangle}$ modulo two. 相似文献
162.
Frank Lenzen Florian Becker Jan Lellmann Stefania Petra Christoph Schnörr 《Computational Optimization and Applications》2013,54(2):371-398
We introduce a class of adaptive non-smooth convex variational problems for image denoising in terms of a common data fitting term and a support functional as regularizer. Adaptivity is modeled by a set-valued mapping with closed, compact and convex values, that defines and steers the regularizer depending on the variational solution. This extension gives rise to a class of quasi-variational inequalities. We provide sufficient conditions for the existence of fixed points as solutions, and an algorithm based on solving a sequence of variational problems. Denoising experiments with spatial and spatio-temporal image data and an adaptive total variation regularizer illustrate our approach. 相似文献
163.
Wave propagation and evoked side effects, such as material failure, are important parts of analysis of dynamically exposed structures like buildings or machinery. One of the numerical analysis tools for wave propagation is the well-known Finite Element Method (FEM) with its impressive performance but also with the drawback of not being able to model easily material failure, discontinuities and contacts. In contrast, the Discrete Element Method (DEM) is capable to describe these effects on a meso-scale more easily. The here selected concept is based on a DEM particle which is considered as deformable, and can establish and remove lasting bonds with other particles. The simulation example used is a thin rod that has been an extensive numerical and experimental research subject since the last century. A longitudinal wave is excited within the thin rod by simulating an impact on one end of the rod in a free-free configuration. It is found, that the simulation data, the velocity profile and the resulting displacement at the end of the rod, are in good agreement with experimental obtained data. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
164.
An inequality is established involving colengths of the tightclosure of ideals of systems of parameters in local rings withsome mild conditions. As an application, a proof is given ofa result due to Goto and Nakamura (first conjectured by Watanabeand Yoshida), which states that the HilbertSamuel multiplicityof a parameter ideal is greater than or equal to the colengthof the tight closure of the ideal. The result is also furtherrefined. 2000 Mathematics Subject Classification 13D40, 13A35,13H15. 相似文献
165.
An interior point method for monotone linear complementarity problems acting in a wide neighborhood of the central path is
presented. The method has
-iteration complexity and is superlinearly convergent even when the problem does not possess a strictly complementary solution.
Mathematics Subject Classification (2000): 49M15, 65K05, 90C33
Work supported by the National Science Foundation under Grant No. 0139701.
An erratum to this article is available at. 相似文献
166.
167.
A QMR-based interior-point algorithm for solving linear programs 总被引:5,自引:0,他引:5
A new approach for the implementation of interior-point methods for solving linear programs is proposed. Its main feature
is the iterative solution of the symmetric, but highly indefinite 2×2-block systems of linear equations that arise within
the interior-point algorithm. These linear systems are solved by a symmetric variant of the quasi-minimal residual (QMR) algorithm,
which is an iterative solver for general linear systems. The symmetric QMR algorithm can be combined with indefinite preconditioners,
which is crucial for the efficient solution of highly indefinite linear systems, yet it still fully exploits the symmetry
of the linear systems to be solved. To support the use of the symmetric QMR iteration, a novel stable reduction of the original
unsymmetric 3×3-block systems to symmetric 2×2-block systems is introduced, and a measure for a low relative accuracy for
the solution of these linear systems within the interior-point algorithm is proposed. Some indefinite preconditioners are
discussed. Finally, we report results of a few preliminary numerical experiments to illustrate the features of the new approach. 相似文献
168.
Ludwig Lausser Florian Schmid Lyn-Rouven Schirra Adalbert F. X. Wilhelm Hans A. Kestler 《Advances in Data Analysis and Classification》2018,12(4):917-936
Predicting phenotypes on the basis of gene expression profiles is a classification task that is becoming increasingly important in the field of precision medicine. Although these expression signals are real-valued, it is questionable if they can be analyzed on an interval scale. As with many biological signals their influence on e.g. protein levels is usually non-linear and thus can be misinterpreted. In this article we study gene expression profiles with up to 54,000 dimensions. We analyze these measurements on an ordinal scale by replacing the real-valued profiles by their ranks. This type of rank transformation can be used for the construction of invariant classifiers that are not affected by noise induced by data transformations which can occur in the measurement setup. Our 10 \(\times \) 10 fold cross-validation experiments on 86 different data sets and 19 different classification models indicate that classifiers largely benefit from this transformation. Especially random forests and support vector machines achieve improved classification results on a significant majority of datasets. 相似文献
169.
Benedict Vasco Normenyo Florian Luca Alain Togbé 《Periodica Mathematica Hungarica》2018,77(2):318-328
In this paper, all base 10 repdigits expressible as sums of three Pell numbers are found. 相似文献
170.
A weighting of the edges of a hypergraph is called vertex‐coloring if the weighted degrees of the vertices yield a proper coloring of the graph, i.e. every edge contains at least two vertices with different weighted degrees. In this article, we show that such a weighting is possible from the weight set for all hypergraphs with maximum edge size and not containing edges solely consisting of identical vertices. The number is best possible for this statement. 相似文献