Ince-Gaussian series representation of the two-dimensional fractional Fourier transform

We introduce the Ince-Gaussian series representation of the two-dimensional fractional Fourier transform in elliptical coordinates. A physical interpretation is provided in terms of field propagation in quadratic graded-index media whose eigenmodes in elliptical coordinates are derived for the first time to our knowledge. The kernel of the new series representation is expressed in terms of Ince-Gaussian functions. The equivalence among the Hermite-Gaussian, Laguerre-Gaussian, and Ince-Gaussian series representations is verified by establishing the relation among the three definitions.     

Extension and lifting of polynomials

We characterize the Banach spaces enjoying polynomial lifting properties, and the spaces that admit compact extensions of polynomials.Received: 20 June 2002     

Alternative formulation for invariant optical fields: Mathieu beams

Based on the separability of the Helmholtz equation into elliptical cylindrical coordinates, we present another class of invariant optical fields that may have a highly localized distribution along one of the transverse directions and a sharply peaked quasi-periodic structure along the other. These fields are described by the radial and angular Mathieu functions. We identify the corresponding function in the McCutchen sphere that produces this kind of beam and propose an experimental setup for the realization of an invariant optical field.     

Determination of amino acids in apple extracts by high performance liquid chromatography

Summary A rapid and sensitive method for the simultaneous determination of primary amino acids in apple is described. After sample preparation, amino acids were derivatized with o-phthaldialdehyde/2-mercaptoethanol and separated on a reversed phase column with a gradient of phosphate buffer-tetrahydrofuran-methanol as the mobile phase. Detection was carried out with a fluorescence detector at excitation and emission wavelengths of 340 nm and 425 nm respectively. Recovery studies showed good results for all substances (91–109%) (with coefficients of variation ranging, from 0.1 to 9.0%). This method was applied to the monitoring of amino acids during the ripening of apples.     

Solid surface mapping by inverse gas chromatography

Inverse gas chromatography (IGC) at infinite dilution, is a technique for characterising solid surfaces. Current practice is the injection of n-alkane homologous series to obtain the free energy of adsorption of the CH2 group, from which the London component of the solid surface free energy, gamma(d)s, is calculated. A value around 40 mJ/m2 is obtained for poly(ethylene), and 30 mJ/m2 for a clean glass fibre, while the potential surface interactivity of a glass fibre is far greater than that of poly(ethylene). A specific component of the surface, in mJ/m2, should be calculated in order to obtain significant parameters. As applied up to date, when calculating the specific component of the surface energy, the fact that W(sp)a energy values are in a totally different scale than AN or DN values is a major drawback. Consequently, Ka and Kb values obtained are in arbitrary energy units, different from those of the London component measured by injecting the n-alkane series. This paper proposes a method to obtain Ka and Kb values of the surface in the same energetic scale than the London component. The method enables us to correct the traditional London component of a solid, obtaining a new value, where the amount of WaCH2 accounting for Debye interactions with polar sites, is excluded. As a result, an approach to surface mapping is performed in several different substrate materials. We show results obtained on different solid surfaces: poly(ethylene), clean glass fibre, glass beads, chemically modified glass beads and carbon fibre.     

First intermolecular cyclopropanation of Fischer dialkylaminocarbene complexes. Synthesis of 1-aminocyclopropanecarboxylic acid derivatives

[reaction: see text] The first cyclopropanation reaction of olefins with Fischer dialkylaminocarbene complexes is presented. The reaction yields 1-aminocyclopropanecarboxylic acid derivatives in a single step, usually with high diastereoselectivity. An approach to the asymmetric version of this reaction is also presented. The synthetic utility of the procedure is exemplified by the synthesis of both cycles of metanoproline in a single step. In addition, the synthesis of the first Fischer carbene containing a halocarbonyl group is reported.     

The electrophilic reactions of pentacyanonitrosylferrate(II) with hydrazine and substituted derivatives. Catalytic reduction of nitrite and theoretical prediction of eta(1)-, eta(2)-N(2)O bound intermediates

The electrophilic reactivity of the pentacyanonitrosylferrate(II) ion, [Fe(CN)(5)NO](2)(-), toward hydrazine (Hz) and substituted hydrazines (MeHz, 1,1-Me(2)Hz, and 1,2-Me(2)Hz) has been studied by means of stoichiometric and kinetic experiments (pH 6-10). The reaction of Hz led to N(2)O and NH(3), with similar paths for MeHz and 1,1-Me(2)Hz, which form the corresponding amines. A parallel path has been found for MeHz, leading to N(2)O, N(2), and MeOH. The reaction of 1,2-Me(2)Hz follows a different route, characterized by azomethane formation (MeNNMe), full reduction of nitrosyl to NH(3), and intermediate detection of [Fe(CN)(5)NO](3)(-). In the above reactions, [Fe(CN)(5)H(2)O](3)(-) was always a product, allowing the system to proceed catalytically for nitrite reduction, an issue relevant in relation to the behavior of the nitrite and nitric oxide reductase enzymes. The mechanism comprises initial reversible adduct formation through the binding of the nucleophile to the N-atom of nitrosyl. The adducts decompose through OH(-) attack giving the final products, without intermediate detection. Rate constants for the adduct-formation steps (k = 0.43 M(-)(1) s(-)(1), 25 degrees C for Hz) decrease with methylation by about an order of magnitude. Among the different systems studied, one-, two-, and multielectron reductions of bound NO(+) are analyzed comparatively, with consideration of the role of NO, HNO (nitroxyl), and hydroxylamine as bound intermediates. A DFT study (B3LYP) of the reaction profile allows one to characterize intermediates in the potential hypersurface. These are the initial adducts, as well as their decomposition products, the eta(1)- and eta(2)-linkage isomers of N(2)O.     

On the liquid-crystalline properties of methacrylic polymers containing 4′-(4-alkyloxyphenyl)azobenzene mesogens

In this article, we report on the synthesis and thermotropic behaviour of methacrylic polymers containing 4′-(4-alkyloxyphenyl)azobenzene mesogens attached to the backbone through n-alkyloxy spacers of 6 or 10 methylene groups. Polymerisations were carried out via free radicals using azobisisobutyronitrile (AIBN) as initiator. Chemical structures of polymers and their precursors were characterised by ¹H NMR spectroscopy. Thermogravimetric analysis showed that azopolymers are thermally stable up to temperatures around 300°C. The thermotropic liquid-crystalline (LC) behaviour was studied by differential scanning calorimetry (DSC), polarized optical microscopy (POM) and X-ray diffraction (XRD). Results indicate that all synthesised mesogens, monomers and polymers developed two or more orthogonal LC phases in wide temperature ranges. Mesogens and monomers developed nematic and smectic phases, whereas polymers exhibited only smectic phase. In polymers, the arrangement of mesogens depends on the relative length of the spacer and the terminal flexible chain; two distinct structural models were proposed based on chemical interactions and steric constrains. The trans–cis photoisomerisation of monomers and polymers in solution was also studied. High cis-isomer contents (>80%) were reached in relative short irradiation times despite the steric constrains imposed by the polymer backbone.     

Micellar-stabilized room-temperature phosphorimetric determination of the fungicide thiabendazole in canned pineapple samples

A method for the determination of the fungicide thiabendazole (TBZ) by micellar-stabilized room-temperature phosphorescence is described. It does not require any separation step and allows the direct determination of the fungicide in canned pineapple samples. The effect of various experimental conditions is discussed in detail. The analytical curve of thiabendazole gives a linear dynamic range of 23.8–500.0 ng mL^–1 and a detection limit of 23.8 ng mL^–1. Recoveries of 103.9 and 89.2% for syrup and canned pineapple pulp, respectively, were obtained for 250 ng mL^–1 thiabendazole.