Algorithms for range restricted iterative methods for linear discrete ill-posed problems

Range restricted iterative methods based on the Arnoldi process are attractive for the solution of large nonsymmetric linear discrete ill-posed problems with error-contaminated data (right-hand side). Several derivations of this type of iterative methods are compared in Neuman et al. (Linear Algebra Appl. in press). We describe MATLAB codes for the best of these implementations. MATLAB codes for range restricted iterative methods for symmetric linear discrete ill-posed problems are also presented.     

Synthesis of vinylcyclopentanes via samarium(II) mediated tandem reactions

In the presence of either visible light or HMPA, SmI₂ reacts with some carbohydrate derived ω-iodoallylic alcohols, and their acetylated derivatives, to give vinylcyclopentanediol and vinylcyclopentanetriol derivatives.     

Protein matrix elasticity determined by fluorescence anisotropy of its tryptophan residues

Rotational motions of Trp residues embedded within human hemoglobin matrix have been measured by using their steady-state fluorescence anisotropy. The mean square angular displacement theta2 of Trp residues, depending on the temperature, can be expressed by W = 1/2Ctheta2 where W is the thermal energy acting on the Trp residues and C the resilient torque constant of the protein matrix. To study the external medium influencing the protein dynamics, comparative experiments were made with protein in aqueous buffer and in the presence of 32% glycerol. The data show that between 5 degrees C and 25 degrees C, external medium acts on the protein matrix elasticity.     

LU implementation of the modified minimal polynomial extrapolation method for solving linear and nonlinear systems

We give an efficient implementation of the modified minimalpolynomial extrapolation (MMPE) method for solving linear andnonlinear systems. We will show how to choose the auxiliaryvectors in the MMPE method such that the resulting approximationsare always defined. This new implementation, which is basedon an LU factorization with a pivoting strategy, is inexpensiveboth in time and storage as compared with other extrapolationmethods.     

Reactivity of ionic liquids with kaolinite: melt intersalation of ethyl pyridinium chloride in an urea-kaolinite pre-intercalate

This paper reports a new route for the intercalation of an ionic liquid, namely 1-ethyl pyridinium chloride, into the interlamellar spaces of kaolinite. The intercalation was achieved using a kaolinite-urea intercalate as a starting material. The results of the XRD, FTIR, and TGA analyses confirmed the intercalation of ethyl pyridinium in the interlamellar spaces of kaolinite. 13C CP/MAS spectra indicated the complete displacement of urea by ethyl pyridinium. 29Si and 27Al NMR spectra of the starting materials and the products are also discussed as well as the results of the elemental analysis of the produced nanohybrid material.     

Divisor spaces on punctured Riemann surfaces

In this paper, we study the topology of spaces of -tuples of positive divisors on (punctured) Riemann surfaces which have no points in common (the divisor spaces). These spaces arise in connection with spaces of based holomorphic maps from Riemann surfaces to complex projective spaces. We find that there are Eilenberg-Moore type spectral sequences converging to their homology. These spectral sequences collapse at the term, and we essentially obtain complete homology calculations. We recover for instance results of F. Cohen, R. Cohen, B. Mann and J. Milgram, The topology of rational functions and divisors of surfaces, Acta Math. 166 (1991), 163-221. We also study the homotopy type of certain mapping spaces obtained as a suitable direct limit of the divisor spaces. These mapping spaces, first considered by G. Segal, were studied in a special case by F. Cohen, R. Cohen, B. Mann and J. Milgram, who conjectured that they split. In this paper, we show that the splitting does occur provided we invert the prime two.

     

A new implementation of the CMRH method for solving dense linear systems

The CMRH method [H. Sadok, Méthodes de projections pour les systèmes linéaires et non linéaires, Habilitation thesis, University of Lille1, Lille, France, 1994; H. Sadok, CMRH: A new method for solving nonsymmetric linear systems based on the Hessenberg reduction algorithm, Numer. Algorithms 20 (1999) 303–321] is an algorithm for solving nonsymmetric linear systems in which the Arnoldi component of GMRES is replaced by the Hessenberg process, which generates Krylov basis vectors which are orthogonal to standard unit basis vectors rather than mutually orthogonal. The iterate is formed from these vectors by solving a small least squares problem involving a Hessenberg matrix. Like GMRES, this method requires one matrix–vector product per iteration. However, it can be implemented to require half as much arithmetic work and less storage. Moreover, numerical experiments show that this method performs accurately and reduces the residual about as fast as GMRES. With this new implementation, we show that the CMRH method is the only method with long-term recurrence which requires not storing at the same time the entire Krylov vectors basis and the original matrix as in the GMRES algorithm. A comparison with Gaussian elimination is provided.     

Synthesis of well‐defined poly(dimethylsiloxane) telechelics having nitrobenzoxadiazole fluorescent chain‐ends via thiol‐ene coupling

Well‐defined PDMS telechelics having nitrobenzoxadiazole (NBD) fluorescent probes covalently attached at both chain‐ends were prepared in two steps and a series of fractionation procedures starting from commercially available divinyl‐terminated PDMS having a broad molar mass dispersity. First, thiol‐ene coupling between 6‐mercapto‐1‐hexanol and vinyl chain‐ends allowed the formation of dihydroxy‐terminated PDMS telechelics through the formation of a thioether linkage. The resulting material was then sequentially fractionated using dichloromethane/methanol mixtures to afford several well‐defined dihydroxy‐terminated PDMS fractions having sharp distributions of molar masses (M_n = 99.5–158 kDa and ? < 1.2). The NBD fluorescent probes were then attached at both chain‐ends by N,N′‐dicyclohexylcarbodiimide/4‐(dimethylamino)pyridine esterification coupling between the hydroxyl groups and 6‐(7‐nitrobenzofurazan‐4‐ylamino)hexanoic acid. The resulting fluorescent PDMS telechelics were characterized by SEC, ¹H NMR, UV–visible, and fluorescence spectroscopies. These materials are suitable probes to investigate the dynamics of polymer chains in bulk or at interfaces by the fringe pattern fluorescent recovery after photobleaching technique. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012