Weyl laws on open manifolds

Under suitable invertibility hypothesis, the spectrum of the Dirac operator on certain open spin Riemannian manifolds is purely discrete, and obeys a growth law depending qualitatively on the (in)finiteness of the volume. The author has been partially supported by the Research and Training Network HPRN-CT-1999-00118 “Geometric Analysis” funded by the European Commission.     

Spectroscopic Characterization of a Lead–Lead Dioxide Automobile Battery

Here we combine small angle neutron scattering measurements (SANS) with X-ray diffraction analysis (XRD) and infrared spectroscopy (IR) measurements to obtain information about nanoparticles formed in a series of lead-lead dioxide samples mixed with various CuO concentrations. New vitreous systems with the xCuO???(100?x)[4PbO₂???Pb] composition where x?=?0, 30, and 70?mol% CuO were prepared by the melt-quenching method using CuO mixed in suitable proportion with the active electrodes of a disassembled car battery as the starting materials. The X-ray diffraction patterns permit the identification of the metallic Pb phase and the presence of oxidic nanoparticles of the lead and copper ions. By doping with higher CuO contents, the SANS curves have a concave shape indicating inhomogeneities and tendency of phase separation due to formation of nanoparticles of the lead and copper ions in recycled host matrix. The studied samples can be considered as polydispersed systems. The matrix is the solvent and the soluble phase is formed from the oxidic lead and/or copper particles with sizes smaller than 69?Å dispersed either inside the host matrix grains or between the host matrix grains. The formation of the nanoparticles in the host matrix and the knowledge of the type of nanoparticles have a decisive role in applications for the construction of essential components of the automobile batteries.     

Magnetic anisotropy of [Mo(CN)7]4- anions and fragments of cyano-bridged magnetic networks

Quantum chemistry calculations of CASSCF/CASPT2 level together with ligand field analysis are used for the investigation of magnetic anisotropy of [Mo(CN)7]4- complexes. We have considered three types of heptacyano environments: two ideal geometries, a pentagonal bipyramid and a capped trigonal prism, and the heptacyanomolybdate fragment of the cyano-bridged magnetic network K2[Mn(H2O)2]3[Mo(CN)7]2.6H2O. At all geometries the first excited Kramers doublet is found remarkably close to the ground one due to a small orbital energy gap in the ligand field spectrum, which ranges between a maximal value in the capped trigonal prism (800 cm(-1)) and zero in the pentagonal bipyramid. The small value of this gap explains (i) the axial form of the g tensor and (ii) the strong magnetic anisotropy even in strongly distorted complexes. Comparison with available experimental data for the g tensor of the mononuclear precursors reveals good agreement with the present calculations for the capped trigonal prismatic complex and a significant discrepancy for the pentagonal bipyramidal one. The calculations for the heptacyanomolybdate fragment of K2[Mn(H2O)2]3[Mo(CN)7]2.6H2O give g(perpendicular)/g(parallel) approximately 0.5 and the orientation of the local anisotropy axis close to the symmetry axis of an idealized pentagonal bipyramid. These findings are expected to be important for the understanding of the magnetism of anisotropic Mo(III)-Mn(II) cyano-bridged networks based on the [Mo(CN)7]4- building block.     

Spectroscopy and electronic structure of electron deficient zinc phthalocyanines

The effect of introduction of perfluoro alkyl groups into phthalocyanines, as evidenced by the spectroscopic properties of 1,4,8,11,15,18,22,25-octa-fluoro-2,3,9,10,16,17,23,24-octa-perfluoro isopropyl zinc phthalocyanine, ZnF(64)Pc(-2) and its ring-reduced radical anion species, [ZnF(64)Pc(-3)](-), are reported. A combination of UV-visible absorption and magnetic circular dichroism (MCD) spectroscopy, ESI and MALDI-TOF mass spectrometry, cyclic and differential pulse voltammetry, and complete theoretical calculations using INDO/S and DFT techniques reveals that the substitution of all sixteen hydrogen atoms in protio ZnPc(-2) by eight F and eight i-C(3)F(7) groups red shifts the Q and pi --> pi transitions and narrows the HOMO-LUMO gap while simultaneously preventing ring photooxidation and stabilizing the radical anion. The [ZnF(64)Pc(-3)](-) species, which is in equilibrium in solution with the neutral complex when a reducing agent is present, is unusually stable. The above effects are attributed to the strong electron withdrawing properties of the peripheral substituents, which render ZnF(64)Pc extremely electron deficient.     

Reactions of potent antitumor complex trans-[Ru(III)Cl4(indazole)2]- with a DNA-relevant nucleobase and thioethers: insight into biological action

Reactions of the complex trans-[RuCl(4)(Hind)(2)](-) (Hind = indazole), which is of clinical relevance today, with both the DNA model nucleobase 9-methyladenine (made) and the thioethers R(2)S (R = Me, Et), as models of the methionine residue in biological molecules possibly acting as nitrogen-competing sulfur-donor ligands for ruthenium atom, have been investigated to get insight into details of mechanism leading to antitumor activity. Three novel ruthenium complexes, viz., [Ru(III)Cl(3)(Hind)(2)(made)], 1, [Ru(II)Cl(2)(Hind)(2)(Me(2)S)(2)], 2, and [Ru(II)Cl(2)(Hind)(2)(Et(2)S)(2)], 3, have been isolated as solids. Oxidation of 2 and 3 with hydrogen peroxide in the presence of 12 M HCl in chloroform afforded the monothioether adducts, viz., [Ru(III)Cl(3)(Hind)(2)(Me(2)S)], 4, and [Ru(III)Cl(3)(Hind)(2)(Et(2)S)], 5. By dissolution of 2 or 3 in DMSO, replacement of both R(2)S ligands by DMSO molecules occurred with isolation of trans,trans,trans-[Ru(II)Cl(2)(Hind)(2)(DMSO)(2)], 6. The products were characterized by elemental analysis, IR, UV-vis, electrospray mass spectrometry, cyclic voltammetry, and X-ray crystallography (1.CH(2)Cl(2).CH(3)OH and 1.1.1H(2)O.0.9CH(3)OH, 2, and 5). The first crystallographic evidence for the monofunctional coordination of the 9-methyladenine ligand to ruthenium via N7 and the self-pairing of the complex molecules via H-bonding, using the usual Watson-Crick pairing donor and acceptor sites of two adjacent 9-methyladenine ligands, is reported. The electrochemical behavior of 1-5 has been studied in DMF and DMSO by cyclic voltammetry. The redox potential values have been interpreted on the basis of the Lever's parametrization method. The E(L) parameter was estimated for 9-methyladenine at 0.18 V, showing that this ligand behaves as a weaker net electron donor than imidazole (E(L) = 0.12 V). The kinetics of the reductively induced stepwise replacement of chlorides by DMF in 4 and 5 were studied by digital simulation of the cyclic voltammograms. The rate constant k(1) has been determined as 0.9 +/- 0.1 s(-)(1), which obeys the first-order rate law, while k(2) is concentration dependent (0.2 +/- 0.1 M(1)(-)(n)().s(-)(1) with n > 1 for 4 mM solutions of 4 and 5), indicating higher-order reactions mechanism.     

Monitoring Methylmalonic Aciduria by NMR Urinomics

The paper reports on monitoring methylmalonic aciduria (MMA)-specific and non-specific metabolites via NMR urinomics. Five patients have been monitored over periods of time; things involved were diet, medication and occasional episodes of failing to comply with prescribed diets. An extended dataset of targeted metabolites is presented, and correlations with the type of MMA are underlined. A survey of previous NMR studies on MMA is also presented.     

Forced symmetric oscillations of evolution equations

We show the existence of periodic forced symmetric solutions to certain classes of evolution equations in Hilbert spaces.