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.     

Long-Range proton-proton coupling constants. I. Propanic coupling involving a methyl group 4JMeH

An equation is formulated on the basis of theoretical INDO/FPT calculations which describes the angular dependence of the propanic long-range coupling constant ⁴J_MeH in substituted HCCCH₃ fragments. This equation is a truncated Fourier series in the torsion angle ?, HCCMe, which takes into account the dependence of the Fourier coefficients on the bond angle θ, CCMe. The substituent effects are assumed to be additive. Some parameters in the equation may be obtained from the ⁴J_MeH couplings in propane and neopentane derivatives. The calculated effect upon ⁴J_MeH of changes in the bond angle θ is significant and it seems to be in part the cause of some effects which have been attributed to conformational dependence.     

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%.     

Effects of processing on the structure of zein/oleic Acid films investigated by x-ray diffraction

Zein films plasticized with oleic acid were formed by solution casting, by the stretching of moldable resins, and by blown film extrusion. The effects of the forming process on film structure were investigated by X-ray diffraction. Wide-angle X-ray scattering (WAXS) patterns showed d-spacings at 4.5 and 10 A, which were attributed to the zein alpha-helix backbone and inter-helix packing, respectively. The 4.5 A d-spacing remained stable under processing while the 10 A d-spacing varied with processing treatment. Small-angle X-ray scattering (SAXS) detected a long-range periodicity for the formed films but not for unprocessed zein, which suggests that the forming process-promoted film structure development is possibly aided by oleic acid. The SAXS d-spacing varied among the samples (130-238 A) according to zein origin and film-forming method. X-ray scattering data suggest that the zein molecular structure resists processing but the zein supramolecular arrangements in the formed films are dependent on processing methods. Structural model for a zein molecular aggregate (based on Matsushima et al.10). Rectangular prisms of individual zein molecules are hexagonally aligned parallel to each other.     

Asymmetric hetero Diels-Alder as an access to carbacephams.

A short and efficient asymmetric synthesis of the (6R,7S)-7-tert-butoxycarbonylamino-2-ketocarbacepham is described. The key step involves the hetero Diels-Alder reaction of the benzylimine derived from the enantiomer of Garner's aldehyde with Danishefsky's diene.     

Unusual monodentate binding mode of 2,2'-dipyridylamine (L) in isomeric trans-(acac)2RuII(L)2, trans-[(acac)2RuIII(L)2]ClO4, and cis-(acac)2RuII(L)2 (acac = acetylacetonate). synthesis, structures, and spectroscopic, electrochemical, and magnetic aspects

The reaction of cis-Ru(acac)2(CH3CN)2 (acac = acetylacetonate) with 2,2'-dipyridylamine (L) in ethanolic medium resulted in facile one-pot synthesis of stable [(acac)2RuIII(L)]ClO4 ([1]ClO4), trans-[(acac)2RuII(L)2] (2), trans-[(acac)2RuIII)L)2]ClO4 ([2]ClO4), and cis-[(acac)2RuII(L)2] (3). The bivalent congener 1 was generated via electrochemical reduction of [1]ClO4. Although in [1]+ the dipyridylamine ligand (L) is bonded to the metal ion in usual bidentate fashion, in 2/[2]+ and 3, the unusual monodentate binding mode of L has been preferentially stabilized. Moreover, in 2/[2]+ and 3, two such monodentate L's have been oriented in the trans- and cis-configurations, respectively. The binding mode of L and the isomeric geometries of the complexes were established by their single-crystal X-ray structures. The redox stability of the Ru(II) state follows the order 1 < 2 < 3. In contrast to the magnetic moment obtained for [1]ClO4, mu = 1.84 muB at 298 K, typical for low-spin Ru(III) species, the compound [2]ClO4 exhibited an anomalous magnetic moment of 2.71 muB at 300 K in the solid state. The variable-temperature magnetic measurements showed a pronounced decrease of the magnetic moment with the temperature, and that dropped to 1.59 muB at 3 K. The experimental data can be fitted satisfactorily using eq 2 that considered nonquenched spin-orbit coupling and Weiss constant in addition to the temperature-independent paramagnetism. [1]ClO4 and [2]ClO4 displayed rhombic and axial EPR spectra, respectively, in both the solid and the solution states at 77 K.     

Organonickel(II) Complexes with Anionic N-Donor Ligands. Hydration of coordinated nitriles at a nickel(II) site

The hydroxo complex (Bu₄N)₂[Ni₂(C₆F₅)₄(μ-OH)₂]reacts with 2,3,4,5,6-pentafluoro benzenamine (C₆F₅-NH₂), 1,3-diaryltriaz-1-enes (ArNH? N=N? Ar, Ar = Ph, 4-MeC₆H₄, 4-MeOC₆H₄), 7-aza-1H-indole (= 1H-pyrrolo[2.3-b]pyridine; Hazind), N-phenylpyridin-2-amine(pyNHPh), and N-phenylpyridine-2-carboxamide (py-CONHPh) at room temperature in acetone to give the binuclear complexes (Bu₄N)₂[Ni₂(C₆F₅)₄(μ-C₆F₅NH)₂] ( 1 ) and (Bu₄N)₂[{Ni(C₆F₅)₂} 2(μ-OH)(μ-azind)] ( 2 ) and the mononuclear complexes Bu₄N[Ni(C₆F₅)2(ArN₃Ar)] ( 3 – 5 ), Bu₄N[Ni(C₆F₅)₂(pyNPh)] ( 6 ), and Bu₄N[Ni(C₆F₅)₂(pyCONPh)] ( 7 ). The hydroxo.complex (Bu₄N)₂[{Ni(C₆F₅)2-(μ-OH)}₂] promotes the nucleophilic addition of water to pyridine-2-carbonitrile, 2-aminoacetonitrile, and 2-(dimethylamino)acetonitrile, and complexes 8 – 10 containing pyridine-2-carboxamidato, 2-aminoacetamidato and 2-(dimethylamino)acetamidato ligands are formed. Analytical (C, H, N) and spectroscopic (IR, ¹H and ¹⁹F-NMR, and FAB-MS) data were used for structural assignments. A single-crystal X-ray diffraction study of (Bu₄N)₂[{Ni(C₆F₅)₂}₂(μ-OH)(μ-azind)] ( 2 ) established the binuclear nature of the anion; the two Ni-atoms are bridged by an OH group and a 7-aza-7H-indol-7-yl group, but the central Ni? O? Ni? N? C? N ring is not planar, the dihedral angle between the Ni? O? Ni and Ni? N? C? N? Ni planes being 84.4°.     

Fluorimetric determination of the fungicide benomyl after solvolysis

A simple spectrofluorimetric method for the determination of the fungicide benomyl in grapes is described. Benomyl is rapidly solvolysed in organic solvents to give the highly fluorescent metabolite carbendazim. Solvent effects on the spectral shape and their influence on analytical performance are studied. DMF was found to be the best solvent. The method is sensitive to 12 ng/ml benomyl, and has an RSD at the 0.5 g/ml level of 2.2%. The method is suitable for determining benomyl in spiked grapes, with recoveries in the range 97 to 104%.     

Enzymatic desaturation of fatty acids: delta11 desaturase activity on cyclopropane acid probes

The formation of methylenecyclopropanes by enzymatic desaturation of 11-cyclopropylundecanoic acid (1) and its disubstituted derivatives cis- and trans-3-5 has been investigated using the Delta(11) desaturase of Spodoptera littoralis as model enzyme. Gas chromatography coupled to mass spectrometry analyses of methanolyzed lipidic extracts from tissues incubated with each probe revealed that all the cyclopropyl fatty acids were transformed into the corresponding 11-cyclopropylidene acids, except for compound trans-5 (5b), which was not desaturated at C11. The formation of methylenecyclopropane 9 as the only reaction product from 1 indicates that a potential radical intermediate is too short-lived to allow rearrangement reactions. Information on the Delta(11) desaturase substrate binding domain is provided considering the cyclopropyl probes 3-5 as conformationally restricted analogues of the straight-chain substrates.