On the Cartan–Jacobson Theorem

The well-known Cartan–Jacobson theorem claims that the Lie algebra of derivations of a Cayley algebra is central simple if the characteristic is not 2 or 3. In this paper we have studied these two cases, with the following results: if the characteristic is 2, the theorem is also true, but, if the characteristic is 3, the derivation algebra is not simple. We have also proved that in this last case, there is a unique nonzero proper seven-dimensional ideal, which is a central simple Lie algebra of type A₂, and the quotient of the derivation algebra modulo this ideal turns out to be isomorphic, as a Lie algebra, to the ideal itself. The original motivation of this work was a series of computer-aided calculations which proved the simplicity of derivation algebras of Cayley algebras in the case of characteristic not 3. These computations also proved the existence of a unique nonzero proper ideal (which turns out to be seven-dimensional) in the algebra of derivations of split Cayley algebras in characteristic 3.     

Monitoring managerial efficiency in the performing arts: A regional theatres network perspective

Managerial efficiency within the performing arts programming can be understood as the technical efficiency of transforming the resources cultural managers have available into a determined cultural output. Through this explanation different conceptions on the finished performance product it leads us to select two different output variables (number of performances, and number of attendances). In this way, three different models are considered regarding those conceptual points of view. Data on the Circuït Teatral Valencià, a Spanish regional theatres network, is used to develop empirically the concept of Managerial Efficiency and set up a framework to allow us to monitor it.     

Indirect spectrophotometric determination of cyanide

A spectrophotometric method for cyanide based on its inhibition of the colour formation reaction between nickel(II) and 3-(4,5-dimethyl-2-thiazolylazo)-2,6-dihydroxybenzoic acid has been developed, and allows the determination of down to 0.1 g of cyanide. Most of the interferences can be avoided by displacement of the hydrogen cyanide using an arsine generator.     

Twistor holomorphic Lagrangian surfaces in the complex projective and hyperbolic planes

We completely classify all the twistor holomorphic Lagrangian immersions in the complex projective plane ², i.e. those Lagrangian immersions such that their twistor lifts to the twistor space over ² are holomorphic. This classification provides a one-parameter family of examples of Lagrangian spheres in ².Research partially supported by a DGICYT grant No. PB91-0731.     

Effect of acetate on ferrihydrite crystallization

Mössbauer spectroscopy was used to follow the aging of ferrihydrite with different amounts of acetate, to achieve more crystalline products. Mössbauer spectra of fresh samples did not show any magnetic components. After two years aging, the solids presented crystalline fractions. Hematite formation was inhibited as acetate content increased in solids. For an acetate/iron molar ratio equal to 0.63 goethite was formed instead of hematite. X-ray diffraction confirmed these results. This work shows that synthetic samples can be used for elucidating the anti-hematitic effect of organic matter already detected in soils.     

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.     

Cohomology of the complement of a free divisor

We prove that if is a ``strongly quasihomogeneous" free divisor in the Stein manifold , and is its complement, then the de Rham cohomology of can be computed as the cohomology of the complex of meromorphic differential forms on with logarithmic poles along , with exterior derivative. The class of strongly quasihomogeneous free divisors, introduced here, includes free hyperplane arrangements and the discriminants of stable mappings in Mather's nice dimensions (and in particular the discriminants of Coxeter groups).

     

Titanosilicates as Supports for an Enzymatic Alcoholysis Reaction

Novel [Cr^III(amp)(bipy)(Cl)] (1) (H₂amp = N-(hydroxyphenyl)salicyldimine; bipy = 2,2-bipyridyl) and [Cr^III(app)(bipy)(Cl)]⁺ (2) (H₂app = N-(hydroxyphenyl)pyridine-2-carboxaldimine; bipy = 2,2-bipyridyl) complexes have been synthesized and characterized by physico-chemical methods. Complexes 1 and 2 have been employed as catalysts in the oxidation of both saturated and unsaturated hydrocarbons using tert-butylhydroperoxide (t-BuOOH). The significance of the results with respect to oxo-functionalization of C-H bonds both in unsaturated and saturated hydrocarbons is noted.     

Assessing the non-specific hydroxyl radical scavenging properties of melanoidins in a Fenton-type reaction system

Soluble high molecular weight fraction (>10 kDa, named melanoidins) was isolated from Maillard reaction model systems, coffee, beer and sweet wine by ultrafiltration. Deoxyribose method was adjusted for measuring the hydroxyl radical scavenging properties of melanoidins. The presence of competitive melanoidins with deoxyribose for OH decrease the rate of deoxyribose degradation. Possible interferences to the deoxyribose method have been evaluated. Most of isolated melanoidins exhibited a variable and measurable non-site-specific hydroxyl scavenging activity in a Fenton-type reaction system. The iron reducing properties of melanoidins at the reaction conditions were evaluated with ferrozine. It has established a kinetic approach to assess the second rate constants of hydroxyl radical scavenging reactions of melanoidins. This approach may be a valuable tool for addressing the structure-activity relationships of melanoidins in a future. There is no correlation between browning (absorbance at 420 nm) and efficiency for scavenging hydroxyl radicals in solution.     

Global optimization of ionic Mg(n)F(2n) (n=1-30) clusters

The global optimization basin-hopping (BH) method has been used to locate the global minima (GM) of Mg(n)F(2n) (n=1-30) clusters using a Born-Mayer-type potential. Some of the GM were particularly difficult to find, requiring more than 1.5 x 10(4) BH steps. We have found that both the binding energy per MgF2 unit and the effective volume of the GM isomers increase almost linearly with n, and that cluster symmetry decreases with cluster size. The data derived from the BH runs reveal a growing density of local minima just above the GM as n increases. Despite this, the attraction basin around each GM is relatively large, since after all their atomic coordinates are randomly displaced by values as high as 2.0 bohrs, the perturbed structures, upon reoptimization, relax back to the GM in more than 50% of the cases (except for n=10 and 11). The relative stabilities derived from energy second differences suggest that n=8,10,13,15, and 20 are probably the magic numbers for these systems. Mass spectrum experiments would be very useful to clarify this issue.