Van Geemen's families of lines on special quintic threefolds

We study the families of lines on the quintic threefolds of the pencilx ₀ ⁵ +x ₁ ⁵ +x ₂ ⁵ +x ₃ ⁵ +x ₄ ⁵ -5tx ₀ x ₁ x ₂ x ₃ x ₄=0. We show that on the generic threefold of the pencil there exists a 1-dimensional family of lines that is not a cone. Partially supported by funds M.P.I.     

Study of recombination reactions of particles adsorbed on fractal and multifractal substrata

Recombination reactions of adsorbed particles on fractal and multifractal media are discussed within the framework of the random walk arguments. Theoretical results, which predict anomalous reaction orderX>2 in the low coverage regime, are checked by means of Monte Carlo simulations on two-dimensional structures and good agreement is found. Thermal desorption experiments on rough surfaces are simulated by studying temperature programmed reactions on fractal percolating clusters. For this case the simulations giveX≅2.5, i. e. the fractal reaction order is greater than the classical one (X=2). The influence of chemisorbed impurities (poison) on the recombination reaction is also studied and the reaction order is found to increase beyondX=2.5 when increasing the concentration of poison. Isothermal (recombination) desorption from energetically heterogeneous surfaces is simulated on two-dimensional substrata with multifractal distributions of activation energy of diffusion. For this caseX (withX>2) depends on the energetic heterogeneity of the substrata (X=2 for an homogeneous substratum). The obtained results point out that the fractal chemical kinetic behaviour is not only restricted to the low concentration regime, but it also covers the medium coverage regime, i.e. it holds for a monolayer surface coverageθ≦0.4 in fractal percolating clusters. Financially supported by the Consejo Nacional de Investigaciones Cientificas y Técnicas (CONICET) de la República Argentina     

A percolation model with disaggregation and aggregation

An alloy TiC_xN_1–x has been studied for compositionx=0.4, 0.6 by the KKR CPA method. The local density of states (DOS) andL-emission spectra of Ti were calculated and compared to experiment. The comparison with the TB CPA calculation was also made.     

Monte Carlo simulation of a bimolecular reaction of the type A+(1/2)B 2 → AB — The influence of A-desorption on kinetic phase transitions

The model recently proposed by Ziff et al. [1] for reactions of the type A+(1/2)B ₂ AB is extended in order to study the effect of A-desorption on irreversible (kinetic) phase transitions (IPT). The IPT from a stationary state with AB-production to a B-poisoned state is not influenced by A-desorption. On the other hand, desorption of A-species prevents the existence of a truly A-poinsoned state. Therefore the IPT from the stationary regime to an A-poisoned state does not occur but an apparent phase transition is observed for small values of the desorption probability (P _D). The rate of AB-production (R _AB ) crosses over from a regime where it becomes dominated by the rate of A-adsorption, when the coverage with A-species is negligible to another regime where R _AB is dominated by the rate of B ₂-adsorption, when the coverage with B-species is negligible. Within the former regime, R _AB decays exponentially with the mole fraction of A-molecules in the gas phase and exhibits a power law dependence with P _D (exponent =2).     

Stereochemistry of the insertion of disubstituted alkynes into the metal aminocarbyne bond in diiron complexes

Terminal alkynes (HCCR^′) (R^′=COOMe, CH₂OH) insert into the metal-carbyne bond of the diiron complexes [Fe₂{μ-CN(Me)(R)}(μ-CO)(CO)(NCMe)(Cp)₂][SO₃CF₃] (R=Xyl, 1a; CH₂Ph, 1b; Me, 1c; Xyl=2,6-Me₂C₆H₃), affording the corresponding μ-vinyliminium complexes [Fe₂{μ-σ:η³-C(R^′)CHCN(Me)(R)}(μ-CO)(CO)(Cp)₂][SO₃CF₃] (R=Xyl, R^′=COOMe, 2; R=CH₂Ph, R^′=COOMe, 3; R=Me, R^′=COOMe, 4; R=Xyl, R^′=CH₂OH, 5; R=Me, R^′=CH₂OH, 6). The insertion is regiospecific and C-C bond formation selectively occurs between the carbyne carbon and the CH moiety of the alkyne. Disubstituted alkynes (R^′CCR^′) also insert into the metal-carbyne bond leading to the formation of [Fe₂{μ-σ:η³-C(R^′)C(R^′)CN(Me)(R)}(μ-CO)(CO)(Cp)₂][SO₃CF₃] (R^′=Me, R=Xyl, 8; R^′=Et, R=Xyl, 9; R^′=COOMe, R=Xyl, 10; R^′=COOMe, R=CH₂Ph, 11; R^′=COOMe, R=Me, 12). Complexes 2, 3, 5, 8, 9 and 11, in which the iminium nitrogen is unsymmetrically substituted, give rise to E and/or Z isomers. When iminium substituents are Me and Xyl, the NMR and structural investigations (X-ray structure analysis of 2 and 8) indicate that complexes obtained from terminal alkynes preferentially adopt the E configuration, whereas those derived from internal alkynes are exclusively Z. In complexes 8 and 9, trans and cis isomers have been observed, by NMR spectroscopy, and the structures of trans-8 and cis-8 have been determined by X-ray diffraction studies. Trans to cis isomerization occurs upon heating in THF at reflux temperature. In contrast to the case of HCCR^′, the insertion of 2-hexyne is not regiospecific: both [Fe₂{μ-σ:η³-C(CH₂CH₂CH₃)C(Me)CN(Me)(R)}(μ-CO)(CO)(Cp)₂][SO₃CF₃] (R=Xyl, 13; R=Me, 15) and [Fe₂{μ-σ:η³-C(Me)C(CH₂CH₂CH₃)CN(Me)(R)}(μ-CO)(CO)(Cp)₂][SO₃CF₃] (R=Xyl, 14, R=Me, 16) are obtained and these compounds are present in solution as a mixture of cis and trans isomers, with predominance of the former.     

One-pot synthesis of the new dianionic ligand [Na]2[C5H4CO2(CH2)2NTs]; preparation and structures of two rhodium derivatives

The new dianionic ligand [Na]₂[C₅H₄CO₂(CH₂)₂NTs] (1) having an alkoxycarbonyl and an amide group in the same side chain has been prepared by a single step, high yield procedure. The synthesis of the related rhodium complexes [Rh{η⁵-C₅H₄CO₂(CH₂)₂N(H)Ts}(NBD)] (3) and [Rh{η⁵-C₅H₄CO₂ (CH₂)₂N(Me)Ts}(NBD)] (4) is reported as well as their X-ray molecular structures.     

Regularity results for the minimum time function with Hörmander vector fields

In a bounded domain of ${\mathbb{R}}^n$ with boundary given by a smooth $(n?1)$-dimensional manifold, we consider the homogeneous Dirichlet problem for the eikonal equation associated with a family of smooth vector fields $\{X_1,\dots ,X_N\}$ subject to Hörmander's bracket generating condition. We investigate the regularity of the viscosity solution T of such problem. Due to the presence of characteristic boundary points, singular trajectories may occur. First, we characterize these trajectories as the closed set of all points at which the solution loses point-wise Lipschitz continuity. Then, we prove that the local Lipschitz continuity of T, the local semiconcavity of T, and the absence of singular trajectories are equivalent properties. Finally, we show that the last condition is satisfied whenever the characteristic set of $\{X_1,\dots ,X_N\}$ is a symplectic manifold. We apply our results to several examples.     

Study of the gamma irradiation effects on the PMMA/HA and PMMA/SW

The behavior of the poly(methyl methacrylate) (PMMA) under the action of gamma radiation has been sufficiently studied. In this work, we present results from melt flow index (MFI), thermogravimetric analysis (TGA), differential scanning calorimetry (DSC) and electron paramagnetic resonance (EPR) of PMMA composites with hydroxyapatite (HA) and seaweed residues (SW) irradiated with gamma rays at 1.08 kGy/h. Composites of PMMA/HA and PMMA/SW with 10%, 20% and 30% of the filler were prepared. The results show an increase in the MFI values with the integral dose of radiation, being consistent with chain-scission reactions. No EPR signal was observed in pure PMMA, while in the composites, the typical EPR signal of the PMMA radicals was observed, which increased with the amount of HA or SW. When comparing the relative intensities of the EPR signals for both types of composites, a slight increase in the concentration of free radicals generated in the sample with SW respect to that of PMMA/HA composite was obtained. A decay of the total free radical concentration was observed as time elapsed.     

Synthesis and structural characterization of acetatobis(triphenylphosphine)dicarbonylrhenium(I). new car☐ylato derivatives of rhenium(I)

Acetatobis(triphenylphosphine)dicarbonylrhenium (I), (PPh₃)₂(CO)₂Re(O₂CCH₃), has been prepared in a novel way by treating (PPh₃)₂(CO)₂Re(NHCOR) (R = C₆H₅, p-MeC₆H₄) with triethylamine and water in the presence of air. Oxidation of the ethyl group of the tertiary amine is presumably involved in the formation of the acetate ligand. Three-dimensional single-crystal X-ray diffraction analysis shows that the complex is octahedral with the phosphines in trans positions and the acetate ion acting as a chelating ligand. The complex crystallizes in theP2₁/c space group with cell dimensions a = 17.63(2), b = 9.72(1), c = 20.95(2)Å, β = 104°38'(6'), Z = 4. The mean values of bond lengths observed are Re-P 2.415, Re-O 2.21 and Re-(CO) 1.85Å. The same acetate derivative and a series of car?ylato complexes (PPh₃)₂(CO)₂Re(O₂CR') have been obtained from reactions of Re(CO)₂(PPh₃)₃H with car?ylic acids R'COOH (R' = H, CH₃, CH₂Cl, CH₂CH₃, C₆H₅). When trifluoroacetic acid is used, a product of formula (PPh₃)₂(CO)₃Re(OC(O)CF₃) is isolated. The action of neutral ligands L on some of these products gave rise to derivatives of formula (PPh₃)₂(CO)₂(L)Re(OC(O)R') (L = CO, R' = H, CH₃, C₆H₅; L = pMeC₆H₄NC, R' = CH₃), having monodentate car?ylato moieties.