Greedy wavelet projections are bounded on BV

Let be the space of functions of bounded variation on with . Let , , be a wavelet system of compactly supported functions normalized in , i.e., , . Each has a unique wavelet expansion with convergence in . If is the set of indicies for which are largest (with ties handled in an arbitrary way), then is called a greedy approximation to . It is shown that with a constant independent of . This answers in the affirmative a conjecture of Meyer (2001).

     

The continuous grey pattern problem

A new location problem is formulated and solved. It is the continuous version of the grey pattern problem which is a special case of the Quadratic Assignment Problem. The problem is a minimization of a convex function subject to non-convex constraints and has infinitely many optimal solutions. We propose several mathematical programming formulations that are suitable for a multi-start heuristic algorithm. In addition to solving these formulations by the Solver in Excel and Mathematica, a special Nelder–Mead algorithm is proposed. This special algorithm provided the best results. One suggested modification may improve the performance of the Nelder–Mead algorithm for other optimization problems as well.     

On upper bounds for high order Neumann eigenvalues of convex domains in Euclidean space

We derive sharp upper bounds for eigenvalues of the Laplacian under Neumann boundary conditions on convex domains with given diameter in Euclidean space. We use the Brunn-Minkowski theorem in order to reduce the problem to a question about eigenvalues of certain classes of Sturm-Liouville problems.

     

Generalized steiner problem in outerplanar networks

The generalized Steiner problem (GSP) is concerned with the determination of a minimum cost subnetwork of a given network where some (not necessarily all) vertices satisfy certain pairwise (vertex or edge) connectivity requirements.The GSP has applications to the design of water and electricity supply networks, communication networks and other large-scale systems where connectivity requirements ensure the communication between the selected vertices when some vertices and/or edges can become inoperational due to scheduled maintenance, error, or overload.The GSP is known to beNP-complete. In this paper we show that if the subnetwork is required to be biconnected or respectively edge-biconnected, and the underlying network is outerplanar, the GSP can be solved in linear time.     

Graph algorithms for DNA sequencing – origins,current models and the future

With the ubiquitous presence of next-generation sequencing in modern biological, genetic, pharmaceutical and medical research, not everyone pays attention to the underlying computational methods. Even fewer researchers know what were the origins of the current models for DNA assembly. We present original graph models used in DNA sequencing by hybridization, discuss their properties and connections between them. We also explain how these graph models evolved to adapt to the characteristics of next-generation sequencing. Moreover, we present a practical comparison of state-of-the-art DNA de novo assembly tools representing these transformed models, i.e. overlap and decomposition-based graphs. Even though the competition is tough, some assemblers perform better and certainly large differences may be observed in hardware resources utilization. Finally, we outline the most important trends in the sequencing field, and try to predict their impact on the computational models in the future.     

The sensitivity analysis of the drawpiece response on the finite element shape parameter

On this paper the numerical analysis of the drawing process is presented. The sensitivity analysis of the drawpiece response on the finite element shape parameter is realized. The sensitivity of stresses field on the edge and the round edge of drawpiece on the change sizes of the finite elements is defined. Precisely proportion between height and length of the finite element is examined. The analysis with the explicit method in the ANSYS LS–Dyna system is passed. The die and the stamp as not deformable bodies are accepted and with the shell finite elements are discretized. The drawpiece with the solid finite elements are discretized. Examples results of computer simulations are presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comparison of moments for tangent sequences of random variables

Summary It is shown that for all tangent sequences (d _n) and (e _n) of nonnegative or conditionally symmetric random variables and for every function satisfying the growth condition (2x)(x) the following inequality holds: . This generalizes results of J. Zinn and proves a conjecture of S. Kwapie and W.A. Woyczyski.