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)     

Nonlinear Multigrid Methods for Numerical Solution of the Variably Saturated Flow Equation in Two Space Dimensions

The need of accurate and efficient numerical schemes to solve Richards’ equation is well recognized. This study is carried out to examine the numerical performances of the nonlinear multigrid method for numerical solving of the two-dimensional Richards’ equation modeling water flow in variably saturated porous media. The numerical approach is based on an implicit, second-order accurate time discretization combined with a vertex centered finite volume method for spatial discretization. The test problems simulate infiltration of water in 2D saturated–unsaturated soils with hydraulic properties described by van Genuchten–Mualem models. The numerical results obtained are compared with those provided by the modified Picard–preconditioned conjugated gradient (Krylov subspace) approach.     

Supramolecular Structure - A Key Parameter for Cellulose Biodegradation

Summary: Three different cellulosic substrata, like microcrystalline cellulose, cotton cellulose and spruce dissolving pulp, were chosen for biodegradation. The kinetics of the enzymatic hydrolysis of these celluloses by Trichoderma reesei, has been investigated. The experiments proved the fact that both the morphological structure and the crystalline one are crucial to the process and the ratio of the reactions. In addition, in order to obtain the most accessible cellulose substratum it was studied the biodegradation of cellulose allomorphs of spruce dissolving pulp. The insoluble cellulose fraction remaining after enzymatic hydrolysis was examined by X-ray diffraction method and it was established the degree of crystallinity and the average crystallite size. The enzymatic degradation is also proved by the decrease in the degree of polymerization of hydrolyzed samples.     

Supramolecular Systems from Natural Polymers and Maleic Polyelectrolytes

Summary: The formation of polyelectrolyte complexes by interaction between chitosan and maleic acid copolymers as strong/weak dibasic polyanions was investigated. The interaction between the sodium salt of maleic acid copolymers with styrene or vinyl acetate and the chitosan hydrochloride in aqueous solution was followed by potentiometric, conductometric and turbidimetric titration. The effect of the added low molecular salt on the complex formation was also investigated. The precipitated complexes were analyzed by FTIR spectroscopy and TG analysis. Preliminary layer-by-layer deposition experiments were performed to obtain thin films.     

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.     

Interface effects on Gd induced disordering of Co films on Pt(111)

Amorphization of epitaxial Co thin films grown on top of a Pt(111) surface has been studied by surface X-ray diffraction after deposition of Gd overlayers. The results indicate strong differences of the disordering process depending on the thickness of the Co film. First basic difference is that thick Co films (15 atomic layers) are only partially amorphized by 4 atomic layers of Gd on top of them, whereas thinner Co films (5 atomic layers) are completely disordered by just 2 atomic layers of Gd. Moreover, amorphization by Gd overlayers induces different stress relaxation processes in both cases. For 15 atomic layers thick Co films a preferential amorphization of the more strained Co grains is observed, leading to an effective relaxation of about ? 0.5% of the in-plane lattice parameter during amorphization, approaching its relaxed value. On the contrary, for 5 atomic layers thick Co films, the initial steps of disordering are accompanied by a stronger increase of the in-plane lattice constant, by about 1.4%, typical of Co–Pt interface alloy formation, followed by a complete amorphization. Furthermore, the magnetic characterization, carried out by magneto-optical Kerr effect and resonant magnetic surface X-ray diffraction, strongly supports that the amorphization of thin Co films is changing the nature of the Co/Pt interface. In particular, as Gd overlayers are deposited, and the amorphization proceeds, the structural disordering of the Co/Pt interface flips its characteristic perpendicular magnetic anisotropy toward in-plane orientation before the complete magnetic depolarization of the interface Pt atoms is reached. All these results confirm a marked dependence of amorphization processes on film thickness, which can be related to the enhanced influence of the nearby film/substrate interface.     

Nuclear multilinear operators with respect to a partition

We introduce the notion of multilinear nuclear operator with respect to a partition and extend Grothendieck??s characterizations of nuclear linear operators into $l_{1},$ resp. $L_{1}( \mu ),$ in this new setting. We give the necessary and sufficient conditions for a natural operator to be nuclear with respect to a partition.     

XRD and EPR structural investigation of some zinc borate glasses doped with iron ions

Glasses in the system xFe₂O₃·(100?x) [45ZnO·55B₂O₃] (0≤x≤10 mol%) have been prepared by melting at 1200 °C and rapidly cooling at room temperature. The obtained samples were submitted to an additional thermal treatment at 570 °C for 12 h in order to relax the glass structure as well as to improve the local order. The as cast and heat treated samples were investigated using X-ray diffraction (XRD) and electron paramagnetic resonance (EPR) measurements. The XRD patterns of all the studied samples show their vitreous nature. Structural modifications occurring in the heat treated samples compared to the untreated ones have been pointed out. EPR spectra of untreated and heat treated samples revealed resonance absorptions centered at g≈2.0, g≈4.3 and g≈6.4. The compositional variation of the line intensity and linewidth of the absorptions from g≈4.3 and g≈2.0 have been interpreted in terms of the variation in the concentration of the Fe³⁺ ions and the interaction between the iron ions. The EPR spectra of the untreated samples containing 5 mol% Fe₂O₃ have been studied at different temperatures (110–290 K). The line intensity of the resonance signals decreases with increase in temperature whereas the linewidth is found to be independent of temperature. It was also found that the temperature variation of reciprocal line intensity obeys the Boltzmann law.