Characterizing equivalent discrete Morse functions

We get a characterization theorem for equivalent discrete Morse functions defined on simplicial complexes in terms of their gradient vector field. As a consequence, we also characterize them in the 1-dimensional case by using critical elements. The authors are partially supported by the P.A.I. project (Junta de Andalucia, SPAIN, 2009/FQM-189 and 327) and by the MEC-FEDER grants MTM2007-61284 and MTM2007-65726 (MEC, SPAIN, 2007).     

Irregular scattering of particles confined to ring-bounded cavities

The classical motion of a free particle that scatters elastically from ring-bounded cavities is analyzed numerically. When the ring is a smooth circle the scattering follows a regular and periodic pattern. However, for rings composed ofN scatterers the flow is irregular, of Lyapunov type. The Lyapunov exponent is found to depend logarithmically withN, which is consistent with the theoretical derivation of Chernov for polygon-shaped billiard systems. The escape time from cavities bounded by a ring ofN separated scatterers is demonstrated to follow a geometric distribution as a function of the aperture size. An empirical scaling is proposed between the Lyapunov exponent, the escape time, andN.     

Photoionization cross section and asymmetry parameter of LiH: a mixed GTO/STOCOS L basis set calculation

The outer-shell photoionization cross section and the asymmetry parameter are computed ab initio for LiH up to a photon energy of 50 eV. The calculations employ an L² K-matrix technique at the Static-Exchange Approximation (SEA) and at the Random Phase Approximation (RPA) levels, using mixed GTO/STOCOS bases. The results shows a fairly good internal coherence and are in good agreement with those obtained previously with pure Polynomial Spherical GTO (PSGTO) bases.     

α-Radical Phosphines: Synthesis,Structure, and Reactivity

A series of phosphines featuring a persistent radical were synthesized in two steps by condensation of dialkyl-/diarylchlorophosphines with stable cyclic (alkyl)(amino)carbenes (cAACs) followed by one-electron reduction of the corresponding cationic intermediates. Structural, spectroscopic, and computational data indicate that the spin density in these phosphines is mainly localized on the original carbene carbon from the cAAC fragment; thus, it remains in the α-position with respect to the central phosphorus atom. The potential of these α-radical phosphines to serve as spin-labeled ligands is demonstrated through the preparation of several Au^I derivatives, which were also structurally characterized by single-crystal X-ray diffraction.     

Simultaneous Spectrophotometric Determination of Silicate and Phosphate by Flow Injection Analysis

Abstract

A method is reported for the simultaneous determination of phosphate and silicate by flow injection analysis based on the different rate of formation of the heteromolybdic acids of the two anions. Measurements are based on the colour of the ion-pairs formed between the said molybdic acids and Rhodamine B. The method allows the determination of the two anions at a rate of 20 samples/h over the ranges 0.05–2.5 ppm (phosphate) and 0.8–15 ppm (silicate), which allows application to a variety of waters.     

Potentiometric stripping analysis automation

A semi-automatic system for potentiometric stripping analysis (PSA) based on the use of a potentiostat, a pH-meter with RS232C interface, and a personal computer is described. The appropriate software developed allows automatic control of the pre-electrolysis time, data acquisition and manual or automatic data treatment. Several elements can be determined at ng/ml level.