Convergence of distorted Brownian motions and singular Hamiltonians

We prove a convergence theorem for sequences of Diffusion Processes corresponding to Dirichlet Forms of the kind .We obtain convergence in total variation norm of the corresponding probability measures on the path space C(₊;^d) under hypotheses which, for example, are satisfied in the case of H _loc ¹ ( ^d )-convergence of the 's, but we can allow more singular situations as regards the approximating sequences. We use then these results to give a criterion of convergence for generalized Schrödinger operators in which the potential function should not necessarily exists as a measurable function. We obtain convergence not only in strong resolvent sense, but we also obtain convergence in the uniform operator topology up to sets of arbitrarily small Lebesgue measure. Applications to the problem of the approximation of ordinary Schrödinger operators by generalized ones corresponding to zero-range interactions are given.     

On the Landau-Teller approximation for energy exchanges with fast degrees of freedom

We revisit the Landau-Teller heuristic approach to adiabatic invariants and, following Rapp, use it to investigate the energy exchanges between the different degrees of freedom, in simple Hamiltonian systems describing the collision of fast rotating or vibrating molecules with a fixed wall. We critically compare the theoretical results with particularly accurate numerical computations (quite small energy exchanges, namely of one part over 10³⁰, are measured).     

Fractal relaxed Dirichlet problems

Given aself similar fractal K ? ? ⁿ of Hausdorff dimension α>n?2, andc ₁>0, we give an easy and explicit construction, using the self similarity properties ofK, of a sequence of closed sets? _h such that for every bounded open setΩ?? ⁿ and for everyf ∈ L²(Ω) the solutions to $$\left\{ \begin{gathered} - \Delta u_h = f in \Omega \backslash \varepsilon _h \hfill \\ u_h = 0 on \partial (\Omega \backslash \varepsilon _h ) \hfill \\ \end{gathered} \right.$$ converge to the solution of the relaxed Dirichlet boundary value problem $$\left\{ \begin{gathered} - \Delta u + uc_1 \mathcal{H}_{\left| K \right.}^\alpha = f in \Omega \hfill \\ u = 0 on \partial \Omega \hfill \\ \end{gathered} \right.$$ (H _∣ ^α denotes the restriction of the α-dimensional Hausdorff measure toK). The condition α>n?2 is strict.     

Recognition of guests bearing donor and acceptor hydrogen bonding groups by heteroditopic calix[4]arene receptors

The synthesis of new hosts specifically designed for the recognition of neutral guests bearing donor-acceptor hydrogen bonding groups is described. These hosts are characterized by the presence of two distinct binding region in close proximity: the rigid π-donor cavity and the H-bond donor N-methylene-N′-phenylureido group inserted onto the upper rim of the calix[4]arene skeleton. The binding abilities of these receptors were investigated toward a series of neutral ditopic organic molecules in CDCl₃ solution by ¹H NMR spectroscopy. The results obtained show that rigidity of the calix[4]arene apolar cavity is the control element in determining efficiency. In fact, compared with the more rigid 2, host 10, where the rigidity of the cone structure is maintained by hydrogen bonding of the OH of the lower rim, a decrease of efficiency of almost one order of magnitude was observed. The cooperative effect of the two binding region of host 2 was verified with different classes of ditopic guests. Good efficiency in the recognition of urea derivatives and dimethylsulfoxide was achieved.     

Synthesis of new tren-based tris-macrocycles. Anion cluster assembling inside the cavity generated by a bowl-shaped receptor

The synthesis of three new tris-macrocycles, containing three [12]aneN(4) (L1), [12]aneN(3)O (L2), or [14]aneN(4) (L3) moieties appended to a tren unit, is reported. The crystal structure of the [(Na(ClO(4))(6)) subset L1(2)H(13)]Na(6)Cl(2)(ClO(4))(12) compound shows the anionic cluster [Na(ClO(4))(6)](5)(-) assembled inside the cavity defined by two bowl-shaped polyammonium receptors, held by multiple charge-charge and hydrogen bond interactions.     

Photocleavage studies of fluorescent amino acid conjugates bearing different types of linkages

The synthesis and photochemistry of 3-oxo-3H-benzopyran derivatives linked through ester, anhydride, urethane and carbonate bonds to representative l-amino acids, at the amino and carboxylic acid groups at the main chain or the hydroxyl group at the side chain, were carried out. The stability to photolysis of the resulting conjugates was studied at different wavelengths of irradiation (254, 300 and 350 nm), the anhydride and ester linkages being the most sensitive in the studied conditions.     

Matrix-isolation FT-IR spectra and theoretical study of dimethyl sulfate

The preferred conformations of dimethyl sulfate and their vibrational spectra were studied by matrix-isolation FT-IR spectroscopy and theoretical methods (DFT and MP2, with basis sets of different sizes, including the quadruple-zeta, aug-cc-pVQZ basis). Conformer GG (of C2 symmetry and exhibiting OSOC dihedral angles of 74.3 degrees ) was found to be the most stable conformer in both the gaseous phase and isolated in argon. Upon annealing of the matrix, the less stable observed conformer (GT; with C1 symmetry) quickly converts to the GG conformer, with the resulting species being embedded in a matrix-cage which corresponds to the most stable matrix-site for GG form. The highest energy TT conformer, which was assumed to be the most stable conformer in previous studies, is predicted by the calculations to have a relative energy of ca. 10 kJ mol-1 and was not observed in the spectra of the matrix-isolated compound.     

Baeyer-Villiger oxidation with potassium peroxomonosulfate supported on acidic silica gel

[reaction: see text] Potassium peroxomonosulfate deposited onto silica SiO2 x KHSO5 efficiently reacts with ketones in dichloromethane at room temperature to give the corresponding esters or lactones in quantitative yields. This method avoids hydrolysis of the reaction products. The Baeyer-Villiger reaction is catalyzed by potassium hydrogensulfate present in the supported reagent.     

Conformational studies by dynamic NMR. 94.1 cogwheel pathway for the stereomutations of durene derivatives containing the mesityl ring

The low-temperature NMR spectra of 1,4-bis(mesitoyl)durene, 1, and of 1,4-bis(mesitylethenyl)durene, 2, reveal the presence of syn and anti rotamers at the equilibrium, their relative proportions depending on the dielectric constant of the solvent. In solution the more stable rotamer of 1 is the anti whereas, in the case of 2, the more stable is the syn. Depending on the crystallization solvent employed the more (anti) and the less stable (syn) rotamers were both observed (X-ray diffraction) in the solid state of 1. On the other hand, only the less stable rotamer (anti) was found to be present in the solid state of 2. As shown by MM calculations, the syn-to-anti interconversion occurs via a correlated process (cogwheel pathway) involving the mesityl-C and durene-C bond rotations: the dynamic NMR technique yields an experimental barrier of 8.2 kcal mol(-)(1) for 1 and 13.1 kcal mol(-)(1) for 2. In the case of derivative 2 a second barrier, due to a second type of correlated rotation process (torsion), was also determined (8.6 kcal mol(-)(1)). As a consequence of the restriction of this second torsional motion the anti rotamer of 2 displays two distinguishable NMR spectra at -133 degrees C, corresponding to a pair of conformers with different symmetry (anti C(i)() and anti C(2)).     

Multielemental analysis of food and agricultural matrixes by inductively coupled plasma-mass spectrometry

The suitability of quadrupole inductively coupled plasma-mass spectrometry (ICP-MS) for multielemental analysis of food following microwave closed vessel digestion of samples was evaluated in relation to analytical challenges presented by some major food and agricultural matrixes. Fifteen key analytes (Al, As, Cd, Co, Cr, Cu, Fe, Mn, Mo, Ni, Pb, Se, Sn, V, Zn) were determined in 9 reference materials representative of 3 major groups of staple foods (cereals, seafood, and meat). For all measurements, the method of external calibration was used and Rh was selected as internal standard. Matrix-induced interferences were evaluated for each material, and suitable methods to overcome them were applied. Spectral interferences caused by C, Cl, and Ca content of digestates were quantitated and corrected by entering a simple system of mathematical correction equations into the instrument software before each analytical run. Full mastering of interferences together with adoption of a series of measures to control the reliability of analytical measurements produced accurate results for all the analytes. A standard analytical protocol is outlined for the benefit of both research and routine high-throughput laboratories that perform ICP-MS analyses of food.