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.     

Determination of metal impurities in electrolytic iron by GF-AAS using electric dispersion in liquid medium

A laboratory-built electrospark system, operated in liquid medium, is used as dispersion method for metallic samples. The metallic colloidal solutions formed upon electrocorrosion behave as typical lyophobic colloidal systems, which are highly stable. The parameters influencing the formation of the colloidal solutions are optimized so that the electrospark system can be used in combination with graphite furnace-atomic absorption spectrometry for trace metal determinations. Dispersion rates for electrolytic iron range from 50 to 125 g min^–1, depending on the power. The colloidal solutions show the same atomization behaviour as true solutions, which makes calibration with aqueous standards feasible. The method has been used to determine manganese, chromium und copper in the NIST SRM 665 electrolytic iron.     

Quantum field theory in curved space-time as thermo field dynamics

The strong analogy between states defined in the context of quantum field theory in curved space-time (QFT-CST) and the ones defined in the thermo field dynamics (TFD) of Takahashi and Umezawa [1] is shown. This analogy is useful in order to introduce the entropy operator in CST in the same way as in TFD. When the extremum condition in the thermodynamical potential is imposed, a family of Bogoliubov transformations that give us a planckian spectrum is found, even in pathological cases such as the minimally coupled scalar field.     

Energy of the Photosubstitutionally Reactive Excited State of Pentaammine(pyridine)ruthenium(II)

The photosensitized aquation of pentaammine(pyridine)ruthenium(II) by several dyes has been studied under conditions where only the sensitizers absorb light. The ratio of the quantum yields for ammine and pyridine substitution was the same as that for direct photoaquation. Sensitization was effective with singlet sensitizers Rhodamine-B (17 452 cm(-)(1)) and Safranine-T (17 690 cm(-)(1)), as well as the triplet sensitizer biacetyl (19 000 cm(-)(1)), but no reaction was observed with Neutral-Red (16 900 cm(-)(1)). The results indicate that the excited state precursor of the observed photosubstitution in the complex lies in the energy range between 17 000 and 17 700 cm(-)(1).     

Synthesis and Structural Studies of Platinum Complexes Containing Monodentate, Bridging, and Chelating Formamidine Ligands

The reactions of K(2)PtCl(4) with N,N'-diphenylformamidine (HDPhF) and N,N'-di-p-tolylformamidine (HDTolF) produce the trans square-planar compounds PtCl(2)(HDPhF)(2), 1a, and PtCl(2)(HDTolF)(2), 1b. Compound 1a crystallizes as yellow parallelepipeds in the space group P2(1)/c with two independent molecules in the asymmetric unit and unit cell dimensions a = 23.427(7) ?, b = 16.677(6) ?, c = 12.980(4) ?, and beta = 96.10(2) degrees. These compounds are soluble in common organic solvents and have been used as starting materials for the preparation of diplatinum compounds. Treatment of 1a and 1b with NaOMe and the halide abstraction reagent TlPF(6) produces the compounds Pt(2)(&mgr;-DArF)(2)(eta(2)-DArF)(2), Ar = Ph (2a) and Tol (2b), respectively. Compound 2a crystallizes as yellow rods in the space group P&onemacr; with unit cell dimensions a = 12.296(3) ?, b = 12.310(4) ?, c = 15.374(4) ?, alpha = 90.75(2) degrees, beta = 91.02(2) degrees, and gamma = 110.20(2) degrees. Compound 2b crystallizes with a molecule of THF, as yellow rods in the space group P2(1)/c with a = 17.883(3) ?, b = 14.517(3) ?, c = 22.581(3) ?, and beta = 98.17(1) degrees. These compounds contain two cis bridging formamidinato ligands and two formamidinato ligands that are chelated to separate Pt centers. Upon heating, they further react to give the tetrabridged compounds Pt(2)(&mgr;-DArF)(4), Ar = Ph (3a), Tol (3b). Compound 3a crystallizes as orange cubes in the cubic space group I432 with a = 19.671(1) ?. On going from the bis-bridged, bis-chelate structure in 2a to the tetrabridged structure in 3a, the metal-metal separation decreases from 2.910(1) to 2.649(1) ?. Both 2band 3b have been oxidized to give the Pt(II)-Pt(III) compound Pt(2)(&mgr;-DTolF)(4)(PF(6)), 4. Compound 4 crystallizes as cubes in the tetragonal space group P4/ncc with a = 14.392(1) ? and c = 14.436(1) ?. The Pt-Pt distance in 4 is 2.5304(6) ?.     

Effects of Aqueous and Organic Solvents on the Conformational Properties of the Helix-Forming alpha-Methyl-beta-L-aspartamyl Residue

The conformational preferences of N-acetyl-N'-methyl-alpha-methyl-beta-L-aspartamide, which is the model compound for helical poly(beta-L-aspartate)s, have been determined by ab initio SCF-MO computations. Two driving patterns have been found for the existing 13 minimum energy conformations: (i) intramolecular hydrogen bonding interactions of both amide-amide and amide-ester type; and (ii) repulsive interactions between the four oxygen atoms contained in the molecule. Self-consistent reaction-field (SCRF) calculations based on the method proposed by Miertus, Scrocco, and Tomasi have been performed in order to evaluate the effect of the solvent on the conformational preferences of the compound subject of study. Water and carbon tetrachloride were the solvents chosen for this purpose, and results have been discussed and interpreted on the basis of their electronic structures. The conclusions drawn from this study are of assistance to understand some features of the conformational transitions experimentally found in poly(beta-L-aspartate)s.     

AlPO-Catalysed asymmetric Diels-Alder reactions of cyclopentadiene with chiral acrylates

Reactions of cyclopentadiene with several chiral acrylates are studied and compared with the same reactions catalysed by Zn(II)-exchanged K10 montmorillonite. In general, amorphous AlPO₄ is a more efficient catalyst than the clay. In particular, the reaction of cyclopentadiene with (−)-8-phenylmenthyl acrylate leads to 74% diastereomeric excess (d.e.) in methylene chloride at low temperatures. This result constitutes the highest asymmetric induction described to date for a solid-catalysed asymmetric Diels-Alder reaction. When the reactions are carried out in the absence of a solvent a noticeable decrease in selectivity is observed, probably due to an extensive competition of the non-catalysed reaction.     

A simple and very sensitive spectrophotometric method for the direct determination of copper ions

A sensitive spectrophotometric method for the direct determination of copper in aqueous samples without a preconcentration step has been developed. It is based on the formation of a yellow complex with the chromogenic reagent di-2-pyridyl ketone benzoylhydrazone (dPKBH) in an alkaline medium. The complex stoichiometry was 1:2 (Cu:dPKBH) and presents maximum absorbance at 370 nm. The influence of chemical variables affecting the behaviour of the system such as pH, concentration of dPKBH, buffer solution and ethanol, order of addition of the reagents and stability of the complex, were evaluated. The molar absorptivity (epsilon) was 3.92x10(4) L mol(-1) cm(-1), and Beer's law was obeyed up to 3 mg L(-1) of copper. The relative standard deviation was 0.46% (n=11) for a sample containing 1 mg L(-1) Cu(II). The limit of detection was 2.5 micro g L(-1) and was therefore more sensitive than the direct methods reported previously. Finally, the method was successfully validated by analysing several real samples with different matrices, such as tap water, natural water or copper alloys, with an average relative error of 2.46%.