Characterization of the solutions set of inconsistent least-squares problems by an extended Kaczmarz algorithm

We give a new characterization of the solutions set of the general (inconsistent) linear least-squares problem using the set of limit-points of an extended version of the classical Kaczmarz’s projections method. We also obtain a “ step error reduction formula” which, in some cases, can give us apriori information about the convergence properties of the algorithm. Some numerical experiments with our algorithm and comparisons between it and others existent in the literature, are made in the last section of the paper.     

Influence of PbO and Ta2O5 on Some Physical Properties of MgCuZn Ferrites

Two series of MgCuZn ferrites are prepared by addition of Ta⁵⁺ and Pb²⁺ ions, separately. The variations of the sintered density, initial permeability, saturation magnetization, Curie temperature and electrical resistivity with the dopant concentration have been studied. The sintered density was found to increase when PbO content is 0.6 wt% or larger. Samples doped with PbO exhibit an appreciable higher resistivity compared to Ta‐doped and undoped samples as a result of the insulating layers on the grain boundaries. The temperature dependence of the electrical resistivity shows a change in slope in the neighbourhood of Curie temperature for all samples and this has been attributed to the influence of the magnetic ordering on the conduction mechanism. Also PbO addition improves the temperature dependence of the initial permeability. The origin of the beneficial effect of PbO compared to Ta₂O₅ is believed to be attributed to the melting of PbO and formation of liquid phase at grain boundaries.     

Crystal and molecular structures of 11-hydroxy-7-oxodrim-8(9)-ene

The crystal structure of 11-hydroxy-7-oxodrim-8(9)-ene is determined. The crystals are monoclinic. The unit cell parameters are a = 16.716(4) Å, b = 11.052(3) Å, c = 7.542(3) Å, γ = 76.11°, Z = 4, μ = 1.476 cm⁻¹, ρ_calcd = 1.147 g/cm³, and space group P2₁. The structure is solved by the direct method and refined by the least-squares procedure to R = 0.045. There are two molecules of 11-hydroxy-7-oxodrim-8(9)-ene in the asymmetric unit. Both molecules have the same conformation of the skeleton and can be described as rotomers differing in orientation of the OH groups with respect to the skeleton. In both molecules, the cyclohexane rings have a usual chair conformation. In the crystal, two independent molecules are linked by a hydrogen bond. The molecular pairs related by the twofold screw axes are linked by hydrogen bonds into helices running along the z-axis of the crystal. The helices are bound through van der Waals interactions. __________ Translated from Kristallografiya, Vol. 45, No. 2, 2000, pp. 275–278. Original Russian Text Copyright ? 2000 by Chumakov, Simonov, Mazus, Popa, Vlad. Deceased.     

On a stopping rule for iterative orthogonalization of symmetric matrices

In this paper we consider three versions of Kovarik's iterative orthogonalization algorithms, for approximating the minimal norm solution of symmetric least squares problems. Although the convergence of these algorithms is linear, in practical applications we observed that a too big number of iterations can dramatically deteriorate the already obtained approximation. In this respect we analyse the above mentioned Kovarik–like methods according to the modifications they make on the “machine zero” eigenvalues of the problem (symmetric) matrix. We establish a theoretical almost optimal formula for the number of iterations necessary to obtain an enough accurate approximation, as well as to avoid the above mentioned troubles. Experiments on collocation discretization of a Fredholm first kind integral equation ilustrate the efficiency of our considerations. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Poly(alkylene-H-phosphonate)s obtained by direct esterification and oxidation of hypophosphorous acid with ethylene glycol

This paper presents for the first time the synthesis of poly(alkylene-H-phosphonate)s by one-pot tandem reaction of hypophosphorous acid and ethylene glycol. Zirconium oxychloride was used as esterification catalyst, Nickel vinylphosphonate, Nickel sulfate, Nickel chloride hexahydrate were used as transfer hydrogenation catalyst. Nickel vinylphosphonate was synthesized in our laboratory and used for the first time as catalyst in this process. The compounds were characterized by ¹H-NMR, ¹³C-NMR and ³¹P-NMR spectroscopy. Molar masses were determined by SEC-MALLS technique and depend on the catalyst used. The obtained poly(alkylene-H-phosphonate)s have molar masses between 1.50 and 11.85 kDa, higher than those obtained by other methods mentioned in the literature.     

Biotinylated chitosan-based SPIONs with potential in blood-contacting applications

Haemocompatible biotinylated superparamagnetic nanoparticles (size range 300–700 nm) have been obtained by coating magnetite through ionic gelation with a mixture of chitosan and sodium tripolyphosphate, followed by subsequent functionalisation with biotin. The evaluations of their magnetic properties together with haemocompatibility tests have shown that these nanoparticles exhibit the prerequisite behaviour for use in magnetic field–assisted separations within biological systems.     

Colloid‐Electrospinning: Fabrication of Multicompartment Nanofibers by the Electrospinning of Organic or/and Inorganic Dispersions and Emulsions

Solution‐, melt‐, and co‐axial electrospinning are well‐known methods for producing nano‐ and microfibers. The electrospinning of colloids (or colloid‐electrospinning) is a new field that offers the possibility to elaborate multicompartment nanomaterials. However, the presence of colloids in the electrospinning feed further complicates theoretical predictions in a system that is dependent on chemical, physical, and process parameters. Herein, we give a summary of recent important results and discuss the perspectives of electrospinning of colloids for the synthesis and characterization of multicompartment fibers.     

The Vapor-Liquid Polycondensation of Cyclohexylphosphoric Dichloride with Hydroquinone

The vapor-liquid polycondensation of cyclohexylphosphoric dichloride with hydroquinone was investigated. The influence of the temperature, reaction time, base concentration, and molar ratio of reagents on the yield, inherent viscosity, and molecular weight of the obtained polymer was studied. Second order, central, composite, rotatable experimental design was used in order to carry out this work and to mark limits of the experimental field for optimal yields and high inherent viscosities.