Energy as a Fifth Dimension

A recent analysis of the experimental data on some physical phenomena ruled by the four fundamental interactions (electromagnetic, weak, strong and gravitational) seems to show the possibility of describing such interactions in terms of a deformation of the usual Minkowski spacetime, with a metric whose coefficients do depend on the energy of the process considered. In this paper, we show that such results can be accounted for in terms of a Kaluza-Klein-like scheme, based on a five-dimensional Riemannian space in which energy plays the role of the fifth dimension. The corresponding five-dimensional Einstein equations in vacuum are solved in some cases of physical relevance and it is shown that all the phenomenological metrics describing the four fundamental forces are recovered as special cases of the classes of solutions found. Possible developments of the formalism are also briefly outlined.     

Poisson randomization in occupancy problems

In occupancy problems we randomize the number of balls with a Poisson process of intensity α. Thus some classical formulas are very easily demonstrated and generalized with the aid of inclusion-exclusion principle. Then we give a general theorem to calculate the distributions and moments of particular random variables or waiting times when infinite balls are considered. This theorem can be applied to the well-known birthday and coupon collectors problems.     

First-principles studies of vanadia-titania catalysts: beyond the monolayer

Periodic density functional calculations have been used to investigate the structure and stability of epitaxial vanadium oxide films grown on the TiO(2)(001) anatase surface. The formation energy of films of V(2)O(5) stoichiometry, initially low, is found to rapidly increase with the film thickness, at variance to what is obtained for reduced pseudomorphic VO(2) films. This is in tune with results of oxygen-assisted molecular beam epitaxy. The oxidation of thick, viz. >2 monolayers (ML), VO(2) films yields a c(2 x 2) reconstructed surface, in agreement with low energy electron diffraction. These films are composed by partially reduced inner V atoms in a distorted-octahedral environment, and by isolated surface dioxovanadium centers exhibiting a distorted trigonal-bipyramidal coordination. Single scattering simulations of X-ray photoelectron diffraction patterns have also been performed, taking both 2- and 3-ML surface surface-oxidized films as models. Results are in fair agreement with experiments referring to films grown in oxidizing conditions, which suggests that coherent vanadia ultrathin films could be formed in vanadia-titania catalysts. The electronic structure of the films has been finally studied, finding that the terminal oxygens carried by the surface dioxovanadium species have a strong nucleophilic character, which makes them potential active centers for selective oxidation catalysis.     

Iridoid glucosides from Viburnum sargenti

The phytochemical study of aerial parts of Viburnum sargenti Koehne, a species spontaneous in Mongolia and Northern China, led to the isolation of three iridoid glucosides of Valeriana-type: the novel 7,10,2'-triacetylsuspensolide F, 1, and the known viburtinoside IV and V. In addition, (+)-epicatechin was also isolated.     

Flavonoids and iridoids from Stachys corsica

Two flavonoid glycosides containing acetylated allose, and two iridoid glucosides were obtained from a EtOH extract of Stachys corsica, an endemic plant of Sardinia and Corsica. All the compounds have previously been isolated from other species of Stachys.     

A macrocyclic ligand able to bind gallium(III) by preorganized pendant arms; coordination and kinetic studies

The equilibria and kinetics of the binding of gallium(III) to 4-(N),10-(N)-bis[2-(3-hydroxo-2-oxo-2-H-pyridine-1-y1)acetamido]-1,7-dimethyl-1,4,7,10-tetraazacyclododecane (L) were investigated in acidic medium at ionic strength 1 M (NaClO4). Spectrophotometric titrations in the UV region revealed that L is able to bind Ga3+ also at high H+ concentration. The kinetic (stopped-flow) experiments are interpreted on the basis of three parallel reaction paths (i) M3+ + H2L2+ = M(H2L)5+ where M(H2L)5+ is in a steady state, (ii) M(OH)2+ + H2L2+ = M(HL)4+ + H2O and (iii) M(OH)2+ + HL+ = ML3+ + H2O. The first-order rate constants for conversion of the outer-sphere into the inner-sphere complexes are similar to those of the Ga(III)/tropolone system which is known to react according to the dissociative Id mechanism and to the relevant rate constants for water exchange at the metal ion. The effects of pH on the UV-Vis absorption, fluorescence emission properties and NMR spectral features on the Ga(III)/L system were also investigated. Spectrophotometric titrations in the UV region reveal that, in acid medium the prevailing species is M(HL)4+ whereas the chelate ML3+ prevails for [H+] < 0.01 M. The results indicate metal coordination at the oxygen atoms of the 3-hydroxo-2-oxopyridine residues.     

Synthesis of alpha,beta-unsaturated 4,5-disubstituted gamma-lactones via ring-closing metathesis catalyzed by the first-generation Grubbs' catalyst

[reaction: see text] 4-Methyl-5-alkyl-2(5H)-furanones have been prepared by ruthenium-catalyzed ring-closing metathesis of the suitable methallyl acrylates. Despite the electron deficiency of the conjugated double bond and of the gem-disubstitution of the allylic alkene moiety in the starting acrylates, the first-generation Grubbs' catalyst I proved to be an effective promoter for the ring closure, affording the expected butenolides in good to high yields.     

Strong oscillations in molecular valence photoemission intensities

Photoemission from the two outermost ionizations [highest occupied molecular orbitals (HOMO and HOMO-1)] of Mg(eta(5)-C(5)H(5))(2) has been studied with synchrotron radiation in the gas phase. Strong oscillations in the HOMO-1/HOMO ratio, qualitatively similar to those well-known for fullerenes, are found. Excellent agreement with the experimental ratio is provided by accurate cross section calculations both at the density-functional theory and time-dependent density-functional theory level, indicating that a many electron response has a minor role for this effect. A comparison with the calculated values for other metal sandwich compounds indicate that the presence of oscillations is a widespread phenomenon, and a potential source of interesting information on the structural and electronic properties of the target molecule.     

New asymptotic behavior of the surface-atom force out of thermal equilibrium

The Casimir-Polder-Lifshitz force felt by an atom near the surface of a substrate is calculated out of thermal equilibrium in terms of the dielectric function of the material and of the atomic polarizability. The new force decays like 1/z3 at large distances (i.e., slower than at equilibrium), exhibits a sizable temperature dependence, and is attractive or repulsive depending on whether the temperature of the substrate is higher or smaller than the one of the environment. Our predictions can be relevant for experiments with ultracold atomic gases. Both dielectric and metal substrates are considered.