Asymptotic stability at infinity of planar vector fields

Let >0 andX be aC ¹ vector field on the plane such that: (i) for allq², Det(DX(q))>0; and (ii) for allp², with p, Trace(D(X(p))<0. IfX has a singularity and ² Trace(DX)dxdy is less than 0 (resp. greater or equal than 0), then the point at infinity of the Riemann sphere ²{} is a repellor (resp. an attractor) ofX.     

Mercury determination by CV-AAS in wastewater and sewage sludge from a stabilization pond system

The mercury concentrations in wastewater and sewage sludge of a stabilization pond system have been evaluated. The system is built by three parallel facultative ponds followed by two systems of three maturation ponds in series. The samples of wastewater and sludge were digested using nitric acid and placed into a Parr-type bomb for 4 h at 110° C. Mercury was measured by Cold Vapour Atomic Absorption Spectrometry (CV-AAS) at 253.7 nm with sodium tetrahydroborate as reductant. The methodologies were checked with an USEPA quality control sample, a standard reference material from NIST and with another method of mineralization (cold mineralization) showing good results. Concentrations of mercury in wastewater between 1.47 ± 0.75 gl^–1 have been found at the entrance of the system and 0.74 ± 0.0 gl^–1 at the exit, while in sludge the results were between 0.29 ± 0.12 gkg^–1 in the facultative pond and 0.04 ± 0.02 gkg^–1 in the second maturation pond (exit).     

Modular stopped-flow/diode-array detection system for simultaneous kinetic analysis

The coupling of a stopped-flow module to a diode-array spectrophotometric detector has been exploited for the simultaneous kinetic resolution of mixtures. The analytical possibilities are shown with the resolution of a mixture of two analytes (hydrazine and phenylhydrazine), yielding products with different spectral features (after reaction with p-dimethylaminobenzaldehyde), so that only the simultaneous measurement of their respective initial rates at their corresponding maximum absorption wavelengths is possible. The method allows 0.02–30 μg ml^?1 hydrazine and 8–2200 μg ml^?1 phenylhydrazine to be determined simultaneously.     

Simultaneous determination of histamine and spermidine by second-derivative synchronous fluorescence spectrometry

The method is based on formation of the fluorescent condensation products with o-phthaldialdehyde; 0.5–2000 ng ml^?1 histamine and 3–700 ng ml^?1 spermidine can be quantified, with relative standard deviations of 2–3%. Histamine/spermidine ratios of 2.5:1–1:30 can be handled. A selectivity study is reported.     

The glass-to-gel transition in solvent-swollen polystyrene networks

Glass transition temperatures have been determined for polystyrenes crosslinked with 1–10% divinylbenzene and swollen with toluene, chloroform, N,N-dimethylformamide, and tetrahydrofuran to as high as 0.7 weight fraction solvent. The T_g′s depend approximately on the weight fractions and the T_g′s of the components according to the empirical equation 1nT_g = m₁ 1nT_g1 + m₂ 1nT_g2 of Pochan. The T_g′s of the networks swollen with toluene also fit approximately a quasithermodynamic equation of Karasz based on the T_g′s and the ΔC_p′s at T_g of the components.     

Spectrophotometric determination of tin(IV) by extraction of the ternary tin/iodide/5,7-dichloro-8-quinolinol complex

The characteristics of the ternary complexes formed by fluoride, bromide, iodide and thiocyanate with tin(IV) and 5,7-dichloro-8-quinolinol (HCQ) have been studied. A spectrophotometric method is proposed for the determination of tin(IV) (1–20 μg ml^?1), based on the extraction into chloroform of the tin/iodide/HCQ complex. Aluminium, bismuth and lead do not interfere, but antimony, copper, iron(III) and fluoride do. Copper and iron can be eliminated by preliminary extraction in the absence of iodide.     

Synthesis, solid-state structure, and bonding analysis of the beryllocenes [Be(C5Me4H)2], [Be(C5Me5)2], and [Be(C5Me5)(C5Me4H)

The beryllocenes [Be(C(5)Me(4)H)(2)] (1), [Be(C(5)Me(5))(2)] (2), and [Be(C(5)Me(5))(C(5)Me(4)H)] (3) have been prepared from BeCl(2) and the appropriate KCp' reagent in toluene/diethyl ether solvent mixtures. The synthesis of 1 is facile (20 degrees C, overnight), but generation of decamethylberyllocene 2 demands high temperatures (ca. 115 degrees C) and extended reaction times (3-4 days). The mixed-ring beryllocene 3 is obtained when the known [(eta(5)-C(5)Me(5))BeCl] is allowed to react with K[C(5)Me(4)H], once more under somewhat forcing conditions (115 degrees C, 36 h). The structures of the three metallocenes have been determined by low-temperature X-ray studies. Both 1 and 3 present eta5/eta1 geometries of the slip-sandwich type, whereas 2 exhibits an almost regular, ferrocene-like, sandwich structure. In the mixed-ring compound 3, C(5)Me(5) is centrally bound to beryllium and the eta(1)-C(5)Me(4)H ring bonds to the metal through the unique CH carbon atom. This is also the binding mode of the eta(1)-ring of 1. To analyze the nature of the bonding in these molecules, theoretical calculations at different levels of theory have been performed on compounds 2 and 3, and a comparison with the bonding in [Be(C(5)H(5))(2)] has been made. As for the latter molecule, energy differences between the eta5/eta5 and the eta5/eta1 structures of 2 are very small, being of the order of a few kcal mol(-1). Constrained space orbital variations (CSOV) calculations show that the covalent character in the bonding is larger for [Be(C(5)Me(5))(2)] than for [Be(C(5)H(5))(2)] due to larger charge delocalization and to increased polarizability of the C(5)Me(5) fragment.