Generation of analytic semigroups in theL p topology by elliptic operators inR n

Strongly elliptic differential operators with (possibly) unbounded lower order coefficients are shown to generate analytic semigroups of linear operators onL ^p(R ⁿ ), 1≦p≦∞. An explicit characterization of the domain is given for 1<p<∞. An application to parabolic problems is also included. This work has been partially supported by the Research Funds of the Ministero della Pubblica Istruzione. The authors are members of GNAFA (Consiglio Nazionale delle Ricerche).     

Numerical simulation of free-surface thermally influenced flows for nonhomogeneous fluids

A finite-difference technique is presented to simulate the behavior of natural water bodies under the influence of pollutants and temperature differences. The mathematical model, which has been discretized, is the closed system obtained by combining the Navier-Stokes equations, the heat transfer equation, the diffusion equations, and an equation relating the fluid density to both the chemical concentration and the temperature. The numerical method is based on the marker-and-cell method, which has been extended to consider the volume expansion due to heat transfer and the density variations.     

The crystal and molecular structure of the tetraethylammonium salt of tetrahydridopentadecacarbonyltetrarhenate(2−) in two crystallographic forms

The structure of the title compound, (NEt₄)₂[H₄Re₄(CO)₁₅], is reported in two crystallographic modifications, I and II. Both forms axe monoclinic and the cell constants are as follows: I, a 11.355(2), b 21.204(4), c 17.416(3) Å, β 94.15(2)°, space group P2₁/c; II, a 21.831(4), b 17.584(3), c 11.446(2) Å, β 96.02(2)°, space group P2₁,/n. Two sets of 3042 (I) and 2870 (II) independent diffraction intensities, collected by counter methods, were used for the solution and refinement of the two structures. The final conventional R factors have values 5.5% (I) and 6.3% (II), respectively. The crystal packings are compared, showing different conformations of the (NEt₄)⁺ cations. The anions contain a tetrametal cluster formed by an isosceles triangle plus an apically bound metal atom; the carbonyl groups are all terminally bonded to the rhenium atoms. Some differences, present both in the metal atom clusters and in the carbonyl dispositions, are discussed and compared with a third, previously reported, crystallographic modification of the same compound.     

The state of 57Fe in pure and oxidized tin chalcogenides by Mössbauer spectroscopy

A Mössbauer spectroscopy study has been made of the stabilization states of ⁵⁷Fe in pure tin chalcogenides. The values of the isomer shifts and the quadrupole splittings lead to the conclusion that iron presents the electronic configuration 3d⁵4s^x at high spin in the interstitial position. This result is confirmed varying the ⁵⁷Fe neighbours by partial substitution of tellurium with oxygen. In this case, too, the values of Mössbauer parameters confirm the same results. The quadrupole moment present in pure SnTe doped ⁵⁷Co, and the shift of isomer shift towards less positive values for the oxidizated samples have been qualitatively justified as well.     

Carbon-13 NMR characterisation of carboxyl derivatives of 1-ureidopyrroles

1-Ureido-5-methyl-2,3-dicarbethoxypyrrole under acidic conditions afforded different partially hydrolyzed or decarboxylated products. It has been possible to characterize two isomeric monoethyl esters of dicarboxylic acids of 1-ureidopyrroles by proton gated decoupled carbon-13 nmr spectra on the basis of multiplicities of the carbonyl carbons resonances.     

Oxidation of tertiary polycycl1c amines by RuO4

The reactions of certain tertiary polycyclic amines such as N-benzyl-9-azabicy-clo- [3,3,1]-nonane, N-benzyl-5, 6-dihydro-11H-dibenz [b,e] azepine, and N-benzyl-1,2,3,4-tetrahydroisoquinoline with ruthenium tetroxide, taking place in both heterogeneous and homogeneous systems, have made it possible to establish the order of reactivity of the various methylene groups adjacent to the nitrogen with respect to this oxidizing agent.     

Diffusion-controlled solid-state reactions of spherical particles, a general model for multiphase binary systems

The formal treatment of the diffusion-controlled growth of n binary compounds with narrow homogeneity range during the reaction of a sphere of reactant A immersed in reactant B is presented and discussed. Both constituents are assumed to be mobile. The reaction products are assumed to grow simultaneously as uniform and compact concentric layers with ideal contact at the interfaces as well as at the external surface of the sphere. The kinetic equations follow from the coupling between chemical reactions and partitioning of the diffusion flux at phase boundaries. The results for the formation of two and three compounds are presented. The influence of the initial radius of the sphere, of the relative magnitude of the kinetic constants, and of the volume variation is discussed in detail.     

Synthesis of gold nanoparticles by laser ablation in toluene: quenching and recovery of the surface plasmon absorption

Gold nanoparticles are synthesized by laser ablation of a gold plate in toluene. The nanoparticles do not show their characteristic surface plasmon absorption (SPA) and are found to be included in a graphitic matrix. The absence of this absorption is found to derive from the presence of the matrix which prevents the growth of large nanoparticles and covers them, suppressing the SPA according to the Mie model for core@shell particles. It is possible to recover the nanoparticle SPA by oxidizing the carbon matrix, obtaining, therefore, some control on the activity of this absorption.