Orthogonal similarity transformation of a symmetric matrix into a diagonal-plus-semiseparable one with free choice of the diagonal

In this paper we describe an orthogonal similarity transformation for transforming arbitrary symmetric matrices into a diagonal-plus-semiseparable matrix, where we can freely choose the diagonal. Very recently an algorithm was proposed for transforming arbitrary symmetric matrices into similar semiseparable ones. This reduction is strongly connected to the reduction to tridiagonal form. The class of semiseparable matrices can be considered as a subclass of the diagonalplus- semiseparable matrices. Therefore we can interpret the proposed algorithm here as an extension of the reduction to semiseparable form. A numerical experiment is performed comparing thereby the accuracy of this reduction algorithm with respect to the accuracy of the traditional reduction to tridiagonal form, and the reduction to semiseparable form. The experiment indicates that all three reduction algorithms are equally accurate. Moreover it is shown in the experiments that asymptotically all the three approaches have the same complexity, i.e. that they have the same factor preceding the n³ term in the computational complexity. Finally we illustrate that special choices of the diagonal create a specific convergence behavior. The research was partially supported by the Research Council K.U.Leuven, project OT/05/40 (Large rank structured matrix computations), by the Fund for Scientific Research–Flanders (Belgium), projects G.0078.01 (SMA: Structured Matrices and their Applications), G.0176.02 (ANCILA: Asymptotic aNalysis of the Convergence behavior of Iterative methods in numerical Linear Algebra), G.0184.02 (CORFU: Constructive study of Orthogonal Functions) and G.0455.0 (RHPH: Riemann-Hilbert problems, random matrices and Padé-Hermite approximation), and by the Belgian Programme on Interuniversity Poles of Attraction, initiated by the Belgian State, Prime Minister's Office for Science, Technology and Culture, project IUAP V-22 (Dynamical Systems and Control: Computation, Identification & Modelling). The scientific responsibility rests with the authors.     

Meta-heuristics for dynamic lot sizing: A review and comparison of solution approaches

Proofs from complexity theory as well as computational experiments indicate that most lot sizing problems are hard to solve. Because these problems are so difficult, various solution techniques have been proposed to solve them. In the past decade, meta-heuristics such as tabu search, genetic algorithms and simulated annealing, have become popular and efficient tools for solving hard combinatorial optimization problems. We review the various meta-heuristics that have been specifically developed to solve lot sizing problems, discussing their main components such as representation, evaluation, neighborhood definition and genetic operators. Further, we briefly review other solution approaches, such as dynamic programming, cutting planes, Dantzig–Wolfe decomposition, Lagrange relaxation and dedicated heuristics. This allows us to compare these techniques. Understanding their respective advantages and disadvantages gives insight into how we can integrate elements from several solution approaches into more powerful hybrid algorithms. Finally, we discuss general guidelines for computational experiments and illustrate these with several examples.     

Dynamical renormalization of kinetic van der Waals spin models

An exact dynamical renormalization approach in differential form is proposed for kinetic van der Waals spin systems with general many-body interactions. The problem of restoring covariance in the evolution equation after renormalization of the model is solved by introducing a suitable renormalized time parameter, which depends also on the magnetization of the spin configuration. The study of the behavior of this renormalized time near criticality leads to a scaling relation for the linear relaxation time. This relation can be shown to imply the exact results for the dynamical critical behavior of the system.On leave of absence from Instituto di Fisica e Unità G.N.S.M. del C.N.R., Università di Padova, Padova, Italy.     

Fast liquid chromatography-tandem mass spectrometry methodology for the analysis of alkylphenols and their ethoxylates in wastewater samples from the tank truck cleaning industry

Analytical and Bioanalytical Chemistry - A fast methodology to quantify 4-tert-octylphenol (4-t-OP) and 4-nonylphenol (4-NP) and their mono- and di-ethoxylates was developed, validated, and applied...     

Integration of positive constructible functions against Euler characteristic and dimension

Following recent work of R. Cluckers and F. Loeser [Fonctions constructible et intégration motivic I, C. R. Math. Acad. Sci. Paris 339 (2004) 411-416] on motivic integration, we develop a direct image formalism for positive constructible functions in the globally subanalytic context. This formalism is generalized to arbitrary first-order logic models and is illustrated by several examples on the p-adics, on the Presburger structure and on o-minimal expansions of groups. Furthermore, within this formalism, we define the Radon transform and prove the corresponding inversion formula.     

Analysis of selected constituents in methanolic extracts of Hypericum perforatum collected in different localities by capillary ITP-CZE

The on-line combination of CZE with capillary ITP (ITP-CZE) was used for the separation and quantification of selected flavonoids and phenolic acids in Hypericum perforatum leaves and flowers collected in six different localities in Slovakia. The leading electrolyte in the ITP preseparation step was 10 mM HCl with Tris as counterion (pH* 7.2). The terminating electrolyte was 50 mM boric acid of pH* 8.2 (adjusted with barium hydroxide). The BGE in the electrophoretic step contained 25 mM beta-hydroxy-4-morpholinopropanesulfonic acid (MOPSO), 50 mM Tris, 65 mM boric acid, pH* 8.3. The content of methanol in all electrolytes was 20% v/v. The total time of the analysis (including the preseparation step) was approximately 35 min. The rectilinear calibration ranges were between 0.125 and 5.0 microg/mL with kaempferol as internal standard. The correlation coefficients ranged between 0.9912 (for quercitrin and chlorogenic acid) and 0.9988 (for isoquercitrin). The RSD values are between 0.86 and 7.78% (n = 6) when determining rutin and quercetin (4 microg/mL). The optimized method was employed for the assay of flavonoids in medicinal plant extract of different collections of Hypericum perforatum haulm. The variability of the content of the active components depending on the place of collection was confirmed.