The external multiplication for the Conley index

We construct an additional operation of the external multiplication on the cohomological Conley index defined by Mrozek for discrete semidynamical systems. The construction is based on the notion of the Conley index over a phase space introduced by Szybowski. We show how to apply the external multiplication to solve the problem of continuation of two isolated invariant sets and illustrate it by an example.     

Electrochemical and FTIR studies of -phenylalanine adsorption at the Au(111) electrode

The adsorption of -phenylalanine (Phe) at the Au(111) electrode surface has been studied using electrochemical techniques and subtractively normalized interfacial Fourier transform infrared (SNIFTIR) techniques. The electrochemical measurements of cyclic voltammetry, differential capacity and chronocoulometry were used to determine Gibbs energies of adsorption and the reference (E₁) and sample (E₂) potentials to be used in the spectroscopic measurements. The vibrational spectra have been used to determine: (i) the orientation of the molecule at the surface as a function of potential; (ii) the dependence of the band intensity on the surface coverage; (iii) the character of surface coordination, and (iv) the oxidation of adsorbed Phe molecules at positive potentials. The adsorption of Phe is characterized by ΔG values ranging from −18 to −37 kJ mol⁻¹ that are characteristic for a weak chemisorption of small aromatic molecules. The electrochemical and SNIFTIR measurements indicated that adsorbed Phe molecules change orientation as a function of applied potential. At the negatively charged surface Phe is predominantly adsorbed in the neutral form of the amino acid. At potentials positive to the pzc, adsorption occurs predominantly in the zwitterionic form with the ---COO⁻ group directed towards the surface and the ammonium group towards the solution. At more positive potentials electrocatalytic oxidation of Phe occurs and is marked by the appearance of the CO₂ asymmetric stretch band in the FTIR spectrum. Thus, relative to pzc, Phe is weakly chemisorbed at negative potentials, changes orientation at potentials close to the pzc and is oxidized at positive potentials.     

Synthesis and reactivity of bis(cycloamidinium-2-yl)alkane bromide tribromides,brominating agents and tectons for molecular engineering

Bis(cycloamidine-2-yl)alkanes easily form bromide tribromide salts in the reduction-oxidation processes with bromine. Bis(tetrahydroimidazolium-2-yl)ethane and bis(hexahydropyrimidinium-2-yl)-ethane bromide tribromides are such new convenient brominating agents for aromatic amides in chemo- and regioselective electrophilic substitutions and α-bromination reactions. Correspondence: Katarzyna Ostrowska, Department of Organic Chemistry, Jagiellonian University, R. Ingardena 3, PL-30060 Kraków, Poland.     

Influence of production progress on the heavy metal content in flax fibers

The aim of this work was to determine the content of selected heavy metals in flax materials depending on the stage of fiber manufacturing. Non-treated natural fiber composition was compared with that of fibers processed. Changes in the composition of yarn before and after the following scutching, hackling, washing, and bleaching were also investigated. Analysis of heavy metals was performed applying inductively coupled plasma mass spectrometry. Flax material was mineralized in closed Teflon vials with a mixture of concentrated nitric acid which were then placed in a microwave oven system. Analytical quality of the obtained results was checked by the determination of elements in the Certificate Reference Materials of IAEA-V-10. The acquired results proved that the content of metals in flax clearly varies depending on the treatment process applied (bleaching, washing, coloration). Significant differences were also connected with the dye used. Presented at the 35th International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 26–30 May 2008.     

Amino acid-functionalized cyclopentadienyl molybdenum tricarbonyl complex and its use in catalytic olefin epoxidation

The complex [(N-benzyloxycarbonylprolyl)cyclopentadienyl]-Mo(CO)₃Me was prepared by the reaction of the amino acid-functionalized cyclopentadienyl-lithium reagent with Mo(CO)₆, and subsequent methylation with CH₃I. The complex was characterized by FTIR, ¹H and ¹³C NMR, and elemental analysis. A single-crystal X-ray diffraction study showed that the complex is chiral, crystallizing in the orthorhombic P2₁2₁2₁ space group with the Flack parameter refining to –0.007(16), which unequivocally confirms the presence of an enantiomerically pure compound. The complex was examined as a catalyst precursor in the liquid-phase epoxidation of trans-β-methylstyrene at 280–330 K, using either tert-butylhydroperoxide (tert-BuOOH), cumylhydroperoxide or urea-hydrogen peroxide adduct as oxidant, and, optionally, a co-solvent. With chloroform and tert-BuOOH, the catalytic activity surpasses that previously reported for chiral complexes of the type CpMo(CO)₃X, giving the epoxide isomers ((R,R)-(+) and (S,S)-(?)-1-phenylpropylene oxide) in excellent selectivity, albeit with negligible enantiomeric excess. FTIR spectroscopy showed that the oxidative decarbonylation of the tricarbonyl complex with tert-BuOOH is fast under the reaction conditions used, and that the structural integrity of the amino acid-functionalized cyclopentadienyl group is retained during this process. The use of the ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate as a solvent for the catalyst generates a biphasic liquid–liquid reaction system that enables, at the end of a catalytic cycle, the separation and reutilization of the catalyst.     

A property of light-cones in Einstein's gravity

We prove that the area of cross-sections of future light-cones in a space–time of arbitrary dimension, solution of the Einstein equations with sources satisfying suitable energy conditions, is smaller than the area of corresponding cross-sections for Minkowskian cones, equal only in space–times which are Minkowskian to the future of the light-cone. To cite this article: Y. Choquet-Bruhat et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

The Symmetry Axioms in Laguerre Planes

We introduce two axioms in Laguerre geometry and prove that they provide a characterization of miquelian planes over fields of the characteristic different from 2. They allow to describe an involutory automorphism that sheds some new light on a Laguerre inversion as well as on a symmetry with respect to a pair of generators.     

Densitometric high performance thin-layer chromatography identification and quantitative analysis of psychotropic drugs

A thin-layer chromatography (TLC)-densitometry method has been developed to identify and quantify haloperidol, amitriptyline, sulpiride, promazine, fluphenazine, doxepin, diazepam, trifluoperazine, clonazepam, and chlorpromazine in selected psychotropic drugs. Separation was performed on precoated silica gel 60 F254 TLC plates. Chromatograms were developed in various mobile phases, and 8 of 30 tested phases were selected based on spot location and developing time. The identification and quantification were carried out based on ultraviolet densitometric measurements at chosen wavelengths. In addition to retention coefficients, the absorption spectra recorded directly from chromatograms were also used in qualitative analysis. Under established experimental conditions, high sensitivity of the method was achieved. The limit of detection ranged from 0.009 to 0.260 microg, depending on the wavelength selected for measuring. A satisfactory recovery, ranging from 92.99 to 104.70%, was achieved for individual constituents.     

Concurrence of mixed bipartite quantum states in arbitrary dimensions

We derive a lower bound for the concurrence of mixed bipartite quantum states, valid in arbitrary dimensions. As a corollary, a weaker, purely algebraic estimate is found, which detects mixed entangled states with a positive partial transpose.     

Composition and elastic stresses in multilayer structures with Si<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Ge<Subscript>x</Subscript> nanoislands

The composition and mechanical stresses in Si_1?xGe_x nanoislands involved in multilayer and single-layer structures grown under the same conditions are determined using Raman spectroscopy. It is demonstrated that an increase in the content of silicon in the nanoislands contained in a multilayer structure does not enhance their relaxation (as compared to that in a single layer) due to the absence of a free surface. The experimental scattering spectrum of folded acoustic phonons contains bands with sufficiently small half-widths, which indicates high quality of the grown superlattices with nanoislands.