On universal central extensions of precrossed and crossed modules

We study the connection between universal central extensions in the categories of precrossed and crossed modules. They are compared with several kinds of universal central extensions in the categories of groups, epimorphisms of groups, groups with operators and modules over a group. We study the relationship between the homologies defined in these categories. Applications to relative algebraic K-theory are also obtained.     

Limit Regimes of Braking of Disc-Type Composite Flywheels Made by Filament Winding

A set of invariants describing the limit regimes of braking disk-type wound composite flywheels is suggested. The limit regime is determined by using a linear failure criterion. It is shown that, for generating short-time impulses of very high power, a set of small identical flywheels is more effective than one large flywheel with an equivalent mass. Particular examples illustrating the theory considered are discussed.     

A generalized mean-value theorem

We give another proof of Seymour and Zaslavsky's theorem: For every familyf ₁,f ₂,...,f _n of continous functions defined on [0, 1], there exists a finite setF[0, 1] such that the average sum off _k overF coincides with the integral off _k for everyk=1, 2,...,n.     

Defect concentration in Ti-substituted YIG from TG curves

The article discusses theory and experiment about the measurement of defect concentration in Ti-substituted yttrium iron garnet by means of thermogravimetry techniques. The two possible cases arising from oxygen interchange with atmosphere, oxygen vacancies and interstitial cations, may be analyzed quantitatively from the derived expressions. The possibility of another type of defects being present in the samples, not associated to oxygen evolution, is not excluded. Measurements were carried out in air and CO₂ for different Ti contents. The substitution tends to increase slightly the defect parameter θ in YIG, while a CO₂ reducing atmosphere is much more effective than the Ti substitution for increasing θ. Calculations for a given single-phased sample sintered in air show two possibilities: a deficit of one oxygen atom for every 2.5 unit cells of 96 atoms, or one excess cation for every 3.5 cells. Other samples show very similar results. The accuracy involved in the measurements is about 2–3%.     

Correction: Direct synthesis of the organic and Ge free Al containing BOG zeolite (ITQ-47) and its application for transformation of biomass derived molecules

Aluminosilicate boggsite (Si/Al-BOG) has been hydrothermally synthesized without adding organic structure-directing agents (OSDAs) in the synthesis gel using the borosilicogermanium ITQ-47 (Si/B-ITQ-47) zeolite as seeds. The introduction of the costly and environmentally less benign phosphazene organic structure-directing agent is not required to grow the zeolite. Physicochemical characterization experiments show that Si/Al-BOG has good crystallinity, high surface area, tetrahedral Al³⁺ species, and acid sites. In order to test the catalytic performance of the zeolite, the synthesis of l,l-lactide from l-lactic acid was performed. Si/Al-BOG exhibits 88.2% conversion of l-lactic acid and 83.8% l,l-lactide selectivity, which are better than those of other zeolites studied up to now.

Aluminosilicate boggsite (Si/Al-BOG) has been hydrothermally synthesized without adding organic structure-directing agents (OSDAs) in the synthesis gel using the borosilicogermanium ITQ-47 (Si/B-ITQ-47) zeolite as seeds.     

Selective crystallization of calcium salts by poly(acrylate)-grafted chitosan

The biopolymer chitosan was chemically modified by grafting polyacrylamide or polyacrylic acid in a homogeneous aqueous phase using potassium persulfate (KPS) as redox initiator system in the presence of N,N-methylene-bis-acrylamide as a crosslinking agent. The influence of the grafted chitosan on calcium salts crystallization in vitro was studied using the sitting-drop method. By using polyacrylamide grafted chitosan as substrate, rosette-like CaSO4 crystals were observed. This was originated by the presence of sulfate coming from the initiator KPS. By comparing crystallization on pure chitosan and on grafted chitosan, a dramatic influence of the grafted polymer on the crystalline habit of both salts was observed. Substrates prepared by combining sulfate with chitosan or sulfate with polyacrylamide did not produce similar CaSO4 morphologies. Moreover, small spheres or donut-shaped CaCO3 crystals on polyacrylic acid grafted chitosan were generated. The particular morphology of CaCO3 crystals depends also on other synthetic parameters such as the molecular weight of the chitosan sample and the KPS concentration.     

Factorization and reflexivity on Fock spaces

The framework of the paper is that of the full Fock space and the Banach algebraF which can be viewed as non-commutative analogues of the Hardy spacesH ² andH respectively.An inner-outer factorization for any element in as well as characterization of invertible elements inF are obtained. We also give a complete characterization of invariant subspaces for the left creation operatorsS ₁ ,..., S _n of . This enables us to show that every weakly (strongly) closed unital subalgebra of {(S ₁ ,..., S _n ) F } is reflexive, extending in this way the classical result of Sarason [S]. Some properties of inner and outer functions and many examples are also considered.The first author was supported in part by NSF DMS 93-21369 1991Mathematics Subject Classification. Primary 47D25, Secondary 32A35, 47A67.     

The dilution of silica in a NiZnCo spinel ferrite matrix

Silica may dissolve up to about 0.05 wt% in an iron excess NiZnCo spinel matrix, affecting noticeably the magnetic properties at low and high values of the applied field. The initial permeability is reduced by about 50% with the addition of only 0.1 % SiO₂, while the coercivity almost triples, without noticeable changes in porosity or grain distribution. The vacancy and Fe²⁺ content of the sintered material also show a considerable change. The energy associated to the transformation Fe³⁺ Fe²⁺ for the samples without SiO₂ was found to be 0.41–0.42 eV, while for the samples with SiO₂ additions it decreased to 0.26 eV. The changes in magnetic properties are thought to be caused, more than because of the mentioned changes in ion distribution, by the stresses and defects created in the lattice due to the very small size of the Si⁴⁺ ion, which substitutes Fe³⁺ ions in tetrahedral sites. The transition Fe³⁺ Fe²⁺ seems to take place exclusively in the octahedral sites.     

Synthesis, 1H, 13C-NMR and mass spectral study of aryloxyquinuclidinium salts

A series of 3 -aryl -3 -hydroxy-N -(4 ′-aryloxobutyl)quinuclidinium salts have been synthesized. The ¹H nmr, ¹³C nmr and mass spectra of these compounds are described and discussed.