A remark on a maximal function over a Cantor set of directions

LetM _e ⁰ be the maximal operator over segments of length 1 with directions belonging to a Cantor set. It has been conjectured that this operator is bounded onL ². We consider a sequence of operators over finite sets of directions converging toM _e ⁰ . We improve the previous estimate for the (L ²,L ²)-norm of these particular operators. We also prove thatM _e ⁰ is bounded from some subsets ofL ² toL ². These subsets are composed of positive functions whose Fourier transforms have a very weak decay or are supported in a vertical strip. Partially supported by Spanish DGICYT grant no. PB90-0187.     

Directional operators and radial functions on the plane

LetEçS ¹ be a set with Minkowski dimensiond(E)1. We consider the Hardy-Littlewood maximal function, the Hilbert transform and the maximal Hilbert transform along the directions ofE. The main result of this paper shows that these operators are bounded onL _rad ^p (R²) forp>1+d(E) and unbounded whenp<1+d(E). We also give some end-point results.     

Lines of curvature near umbilical points on surfaces immersed in R4

LetM be a compact orientable surface,I:M R⁴ an immersion of classC ^r and a normal unitary smooth vector field. We prove that in the space of pairs (I, ) the family of pairs all whose umbilical points are Darbouxian is generic.     

Quantitative analysis of six pesticides in fruits by capillary electrophoresis-electrospray-mass spectrometry

A method to identify and quantify six pesticide residues - dinoseb, pirimicarb, procymidone, pyrifenox, pyrimethanil, and thiabendazole - in peaches and nectarines using capillary electrophoresis-electrospray ionization-quadrupole ion trap-tandem mass spectrometry (CE-ESI-MS/MS) is described. Separation was carried out using a buffer of 0.3 M ammonium acetate at pH 4 with 10% methanol. Pesticide residues present in peach and nectarine samples were preconcentrated by solid-phase extraction using C(18), eluted with CH(2)Cl(2), concentrated to dryness, and redissolved in buffer to obtain lower detection limits. The recoveries of the analytes ranged from 58 to 99% and the relative standard deviations were 9 to 19%. Under optimized CE-MS/MS conditions the minimum detectable levels for the six pesticides in spiked peach samples were between 0.01 mg/kg for pirimicarb and 0.05 mg/kg for procymidone with pressure injection of 50 mbar for 5 s (5 nL) at a signal-to-noise ratio of 3, which constitutes a severalfold increase in sensitivity compared to CE-MS, using a single quadrupole, and to conventional CE-UV. The potential of the method was demonstrated by analyzing different samples taken from regional agricultural cooperatives. The pesticides most often detected were thiabendazole and procymidone.     

Crosslinking of vinyl‐terminated biphenyl and naphthalene side‐chain liquid‐crystalline poly(epichlorohydrin) derivatives

We performed the crosslinking of vinyl‐terminated biphenyl and naphthalene side‐chain liquid‐crystalline polyethers using peroxide‐type initiators with and without the addition of tertiary amine promoters. The crosslinking temperatures were chosen in the range of mesophase stability to allow the mesophase order to be frozen. The biphenyl derivatives, with a high isotropization temperature, were crosslinked to a large extent. This led to anisotropic thermosets. To crosslink naphthalene derivatives, amine promoters were needed, but degrees of crosslinking were lower, and anisotropic elastomers were obtained. Crosslinking processes were studied by differential scanning calorimetry, polarized optical microscopy, and Fourier transform infrared spectroscopy. The nature of the frozen mesophase was confirmed by X‐ray diffraction studies on mechanically oriented samples. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2237–2244, 2002     

HRGC of wine free amino acids as a tool for elementary wine characterization

In this paper we show that wine free amino acids derivatized as isopropyl N-heptafluorobutyryl esters can be used as a tool for wine characterization. Elementary wines of eight Vitis vinifera varieties were studied during a seven year period. The characteristic wine amino acids for each variety were assessed by means of pattern recognition techniques. A “star symbol plot” was used for graphic representation.     

Synthesis of fluorinated drimanes. Preparation of 9αF-drimenin

A stereoselective approach to the 9α-fluorinated analogue of the natural drimane sesquiterpene drimenin starting from β-ionone is described. β-Ionone is transformed into a bicyclic β-cetoester from which 9αF-drimenin is prepared through stereoselective electrophilic fluorination at the C-9 with N-fluorobenzenesulfonimide followed by Wittig methylenation, allylic bromination, bromine-hydroxyl exchange and γ-lactonization.     

Electro-initiated cationic polymerizations-VI: Anodic electrochemical behaviour and direct electropolymerization of anethole in 1,2-dichloroethane

A study has been made of the cationic electropolymerization of trans-anethole initiated by a direct electron transfer mechanism at a Pt anode in 1,2-dichloroethane solution with tetrabutylammonium perchlorate as supporting electrolyte. The electrochemical behaviour of the system has been preliminarily investigated by voltammetry at rotating and stationary Pt electrode and also by chronoamperometry. The results are consistent with an ECE oxidation process of anethole with formation first of a radical cation and finally of a dication. Polymerization experiments by electrolysis at the oxidation potential of the monomer have been also carried out both under continuous electrolysis and with short initial pulses of current. The results have been analysed and some kinetic parameters of the system have been evaluated.     

Reactivity of 2-halo-2H-azirines. 1. Reactions with nucleophiles.

Nucleophilic substitution reactions of 2-halo-2H-azirines 1a, 1b, 1d, and 1e with potassium phthalimide and aniline allowed the preparation of new substituted 2H-azirines 2-5. The reactions of 2-bromo-2H-azirine 1a with methylamine led to the synthesis of alpha-diimines 7 and 8. 2-Halo-2H-azirines were also established as building blocks for the synthesis of a range of heterocyclic compounds, namely, quinoxalines 10a-10d, 3-oxazoline 14, and 2H-[1,4]oxazines 18 and 20. X-ray crystal structures of alpha-diimine 7, 3-oxazoline 14, and 2H-[1,4]oxazine 18 are reported.     

Spectrophotometric flow-injection determination of zinc in plant digests based on a spot test

A spot test was implemented in a flow-injection system for the spectrophotometric determination of zinc in digests of plant materials. It is based on the influence of Zn²⁺ on the oxidation rate of 1-naphthylethylenediamine (NED) by hexacyanoferrate(III) under acidic conditions. In order to control the precipitate formation and to maintain the resulting suspension, a micellar medium was established by adding Triton X-100. The proposed system handles about 65 samples per hour, meaning 72 μg NED and 9.0 mg K₃[Fe(CN)₆] per determination. Baseline drift is usually <0.01 absorbance per hour and the analytical signals for 0.5-2.5 mg l⁻¹ Zn range within ca. 0.07-0.45 absorbance. Linearity of the analytical curve is fair (r>0.999, n=6) and detection limit was estimated as 0.2 mg l⁻¹ Zn. Results are precise (R.S.D.<1%, n=10) and in agreement with flame atomic absorption spectrometry and with certified values of standard reference materials.