A unification of unitary similarity transforms to compressed representations

In this paper a new framework for transforming arbitrary matrices to compressed representations is presented. The framework provides a generic way of transforming a matrix via unitary similarity transformations to, e.g., Hessenberg, Hessenberg-like form and combinations of both. The new algorithms are deduced, based on the QR-factorization of the original matrix. Relying on manipulations with rotations, all the algorithms consist of eliminating the correct set of rotations, resulting in a matrix obeying the desired structural constraints. Based on this new reduction procedure we investigate further correspondences such as irreducibility, uniqueness of the reduction procedure and the link with (rational) Krylov methods. The unitary similarity transform to Hessenberg-like form as presented here, differs significantly from the one presented in earlier work. Not only does it use less rotations to obtain the desired structure, also the convergence to rational Ritz-values is not observed in the conventional approach.     

Preparation of high-resolution 238U α-sources by electrodeposition: a comprehensive study

In this paper the source preparation procedures for high-resolution ²³⁸U sources are described and compared. This work was done within collaboration between CIEMAT and IRMM in the frame of MetroFission, a project of the European Metrology Research Programme, in order to determine the alpha-emission probabilities of ²³⁸U. ²³⁸U was deposited from organic (iso-propanol) and inorganic-H₂SO₄/(NH₄)₂SO₄, saturated NH₄NO₃-electrolyte solutions on metal backings. The parameters affecting electrodeposition were studied and optimized. The activity distribution of uranium was checked by autoradiography. Results show that the ²³⁸U source quality is significantly better using the saturated NH₄NO₃ than the two other electrolytes. By this method, sources of 18.6–22 mm diameter, 26 μg cm^?2 surface density, ~15–18 keV resolution and a peak to valley ratio higher than 50 could be made. This reconciles the inherently opposing requirements of high resolution and sufficient count rate needed to determine the alpha–emission probabilities accurately.     

Triblock copolymer synthesis via controlled radical polymerization in solution using S‐tert‐alkyl‐N,N‐alkoxycarbonylalkyldithiocarbamate RAFT agents

This paper presents the solution homopolymerization, random and block copolymerization of acrylic monomers, mediated using an S‐(1,4‐phenylenebis(propane‐2,2‐diyl)) bis(N,N‐butoxycarbonylmethyldithiocarbamate) RAFT agent. Fair to good control was obtained over the solution homopolymerization of various acrylic monomers. Although inhibition periods were observed, nearly no retardation was found to occur. Satisfactory control was also obtained over the solution copolymerization of n‐butyl acrylate with methacrylic acid, mediated using this RAFT agent. Finally, triblock copolymer synthesis, starting from the macromolecular intermediates produced in the homo‐ and copolymerization experiments, was studied, and was shown to be successful. The observed relatively broad molar mass distributions could be explained by a partial decomposition of the dithiocarbamate‐based RAFT agent during synthesis and/or polymerization, for which strong indications were obtained by performing a careful MALDI‐ToF MS analysis. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6419–6434, 2006     

Improved lower bounds for the capacitated lot sizing problem with setup times

We present new lower bounds for the capacitated lot sizing problem, applying decomposition to the network reformulation. The demand constraints are the linking constraints and the problem decomposes into subproblems per period containing the capacity and setup constraints. Computational results and a comparison to other lower bounds are presented.     

When is a matrix unitary or Hermitian plus low rank?

Hermitian and unitary matrices are two representatives of the class of normal matrices whose full eigenvalue decomposition can be stably computed in quadratic computing complexity once the matrix has been reduced, for instance, to tridiagonal or Hessenberg form. Recently, fast and reliable eigensolvers dealing with low‐rank perturbations of unitary and Hermitian matrices have been proposed. These structured eigenvalue problems appear naturally when computing roots, via confederate linearizations, of polynomials expressed in, for example, the monomial or Chebyshev basis. Often, however, it is not known beforehand whether or not a matrix can be written as the sum of a Hermitian or unitary matrix plus a low‐rank perturbation. In this paper, we give necessary and sufficient conditions characterizing the class of Hermitian or unitary plus low‐rank matrices. The number of singular values deviating from 1 determines the rank of a perturbation to bring a matrix to unitary form. A similar condition holds for Hermitian matrices; the eigenvalues of the skew‐Hermitian part differing from 0 dictate the rank of the perturbation. We prove that these relations are linked via the Cayley transform. Then, based on these conditions, we identify the closest Hermitian or unitary plus rank k matrix to a given matrix A, in Frobenius and spectral norm, and give a formula for their distance from A. Finally, we present a practical iteration to detect the low‐rank perturbation. Numerical tests prove that this straightforward algorithm is effective.     

Synthesis of α-Alkylidene-β-Ethoxycarbonyl Cyclopentanones and -γ-Butyrolactones

Synthesis of (E,Z)-α-Alkylidene-β-ethoxycarbonyl cyclopentanones 5 and (E,Z)-α-alkylidene-γ-butyrolactones 7 by condensing phosphonates 3 or 6 with a variety of aldehydes in the presence of aqueous potassium carbonate (6-10M) as base is reported.     

A Levinson-like algorithm for symmetric strongly nonsingular higher order semiseparable plus band matrices

In this paper, we will derive a solver for a symmetric strongly nonsingular higher order generator representable semiseparable plus band matrix. The solver we will derive is based on the Levinson algorithm, which is used for solving strongly nonsingular Toeplitz systems.     

A numerical example showing that deflations based on rotation leads to higher relative accuracy in QR algorithm

We present a numerical example illustrating that the deflation procedure in Francis's implicitly shifted QR algorithm can be improved by a deflation criteria based on the QR decomposition of the upper Hessenberg matrix. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spatially adaptive PIV interrogation based on data ensemble

This paper proposes a specific application of the approach recently proposed by the authors to achieve an autonomous and robust adaptive interrogation method for PIV data sets with the focus on the determination of mean velocity fields. Under circumstances such as suboptimal flow seeding distribution and large variations in the velocity field properties, neither multigrid techniques nor adaptive interrogation with criteria based on instantaneous conditions offer enough robustness for the flow field analysis. A method based on the data ensemble to select the adaptive interrogation parameters, namely, the window size, aspect ratio, orientation, and overlap factor is followed in this study. Interrogation windows are sized, shaped and spatially distributed on the basis of the average seeding density and the gradient of the velocity vector field. Compared to the instantaneous approach, the ensemble-based criterion adapts the windows in a more robust way especially for the implementation of non-isotropic windows (stretching and orientation), which yields a higher spatial resolution. If the procedure is applied recursively, the number of correlation samples can be optimized to satisfy a prescribed level of window overlap ratio. The relevance and applicability of the method are illustrated by an application to a shock-wave-boundary layer interaction problem. Furthermore, the application to a transonic airfoil wake verifies by means of a dual-resolution experiment that the spatial resolution in the wake can be increased by using non-isotropic interrogation windows.