On the b-Coloring of Cographs and <Emphasis Type="Italic">P</Emphasis><Subscript>4</Subscript>-Sparse Graphs

A b-coloring of a graph is a coloring such that every color class admits a vertex adjacent to at least one vertex receiving each of the colors not assigned to it. The b-chromatic number of a graph G, denoted by χ _b (G), is the maximum number t such that G admits a b-coloring with t colors. A graph G is b-continuous if it admits a b-coloring with t colors, for every . We define a graph G to be b-monotonic if χ _b (H ₁) ≥ χ _b (H ₂) for every induced subgraph H ₁ of G, and every induced subgraph H ₂ of H ₁. In this work, we prove that P ₄-sparse graphs (and, in particular, cographs) are b-continuous and b-monotonic. Besides, we describe a dynamic programming algorithm to compute the b-chromatic number in polynomial time within these graph classes. Flavia Bonomo: Partially supported by ANPCyT PICT-2007-00533 and PICT-2007-00518, and UBACyT Grants X069 and X606 (Argentina). Guillermo Durán: Partially supported by FONDECyT Grant 1080286 and Millennium Science Institute “Complex Engineering Systems” (Chile), and ANPCyT PICT-2007-00518 and UBACyT Grant X069 (Argentina). Javier Marenco: Partially supported by ANPCyT PICT-2007-00518 and UBACyT Grant X069 (Argentina).     

Biosynthetic studies on the botcinolide skeleton: new hydroxylated lactones from Botrytis cinerea

[reaction: see text] The biosynthetic origin of the botcinolide skeleton was investigated by means of feeding 13C- and 2H-labeled precursors to Botrytis cinerea. Three new compounds, two homobotcinolide derivatives, 3-O-acetylhomobotcinolide (5) and 8-methylhomobotcinolide (6), and a new 11-membered lactone (7), were isolated. Their structures were elucidated on the basis of spectroscopic data, including one-bond and long-range 1H-13C correlations. The relative stereochemistries were determined by combined analyses of NOE data and 1H-1H coupling constants. According to the results of feeding experiments with 13C- and 2H-labeled acetate and l-S-methylmethionine, 5 is an acetate-derived polyketide whose methyl groups originate from l-S-methylmethionine. This is a rare example of the incorporation of a methyl from methionine into a supposed C3 starter unit of the polyketide synthesis.     

Development of a non-aqueous capillary electrophoresis method with UV-visible and fluorescence detection for phenolics compounds in olive oil

Response surface methodology has been applied to the optimization of a simple and rapid non-aqueous capillary electrophoresis method for the separation and determination of several phenolic compounds belonging to the different families present in olive oil. A Box–Behnken design was employed and a total of 27 experiments were performed using olive oil samples spiked with the phenols and injected directly in the capillary after dilution 1:1 with 1-propanol. Finally, the background electrolyte (BGE) was constituted of 25 mM boric acid and 18 mM KOH in a mixture of 74:26 (v/v) 1-propanol/methanol. The hydrophobicity of the BGE allows its miscibility with the olive oil and, as a consequence, the possibility of characterizing and determining these kinds of compounds in this sample without any pretreatment. A hydrodynamic injection (6 s, −30 mbar) was applied and the separation was carried out using 35 °C and +20 kV of separation temperature and voltage, respectively. A capillary with two detection windows for serial online UV and fluorescence detection was satisfactorily employed. The validation of the method was carried out by setting the calibration curves, and the figures of merit were finally obtained. A lineal relationship between the corrected peak area and concentration and limits of detection in the order of micrograms per milliliter were found.     

Retinyl palmitate polymeric nanocapsules as carriers of bioactives

Nanocapsules containing poly(d,l-lactide) shell and retinyl palmitate core have been prepared by the pre-formed polymer interfacial deposition method. Dynamic light scattering measurements yielded an average hydrodynamic diameter of ～220nm and a polydispersity index of ～0.12. Small-angle neutron scattering experiments revealed the presence of two populations of nanocapsules of core diameters ～192 and 65nm. Freeze fracture transmission electron microscopy showed a polydisperse population of nanocapsules (NC), with a poly(d,l-lactide) shell thickness between 11 and 3nm. For comparison purposes, nanoemulsions (NE, no polymer) and nanospheres (NS, polymer matrix) were also prepared. Each type of nanoparticles exhibited a different morphology (when examined by electron microscopy), in particular NC showed deformability by capillary adhesion. All three types of nanoparticles successfully encapsulated the poorly water-soluble molecules baicalein and benzophenone-3. The thermal behavior of the various nanoparticles was different to a physical mixture of its individual components. Cytotoxicity and phototoxicity assays, performed in human keratinocytes (HaCaT) and murine fibroblasts (BALB/c 3T3), showed that the NC were only cytotoxic at high concentrations. In vitro release studies of benzophenone-3, by the dialysis bag method using NC and NS, showed a sustained release; however, permeation studies using plastic surgery human abdominal skin in Franz diffusion cells showed that a higher amount of benzophenone-3 from NC penetrated into the skin, most probably due to the deformable nature of these nanoparticles.     

Application of hydrophobic silica based aerogels and xerogels for removal of toxic organic compounds from aqueous solutions

This work is devoted to the application of hydrophobic silica based aerogels and xerogels for the removal of three toxic organic compounds from aqueous solutions. These materials were tested and characterized regarding their morphology, particle size distribution, surface area and porous structure. The equilibrium tests were carried out at different adsorbate concentrations and the experimental data were correlated by means of Langmuir and Freundlich isotherms. The equilibrium data were well described by Langmuir and Freundlich in most cases. The maximum adsorption capacity by Langmuir model was observed for the adsorption of benzene onto aerogel (192.31 mg/g), though the most promising results were obtained for toluene adsorption due to the greater adsorption energy involved. Comparing these results with other reported results, the hydrophobic silica based aerogels/xerogels were found to exhibit a remarkable performance for the removal of benzene and toluene. In addition, the regeneration of previously saturated aerogel/toluene was also investigated by using an ozonation process. The adsorption/regeneration tests with ozone oxidation showed that the aerogel might be regenerated, nevertheless the materials lost their hydrophobicity and thus different methods should be evaluated in forthcoming investigations.     

Wavelength dependence of the suppressed ionization of molecules in strong laser fields

We study ionization of molecules by an intense laser field over a broad wavelength regime, ranging from 0.8 to 1.5 μm experimentally and from 0.6 to 10 μm theoretically. A reaction microscope is combined with an optical parametric amplifier to achieve ionization yields in the near-infrared wavelength regime. Calculations are done using the strong-field S-matrix theory and agreement is found between experiment and theory, showing that ionization of many molecules is suppressed compared to the ionization of atoms with identical ionization potentials at near-infrared wavelengths at around 0.8 μm, but not at longest wavelengths (10 μm). This is due to interference effects in the electron emission that are effective at low photoelectron energies but tend to average out at higher energies. We observe the transition between suppression and nonsuppression of molecular ionization in the near-infrared wavelength regime (1-5 μm).     

Synthese D' α-hydroxy-aldehydes chiraux a partir du D-mannitol. Intermediaires pour la synthese de metabolites de l'acide arachidonique.

Enantiomerically pure α-hydroxy-aldehydes, key intermediates for the synthesis of arachidonic acid metabolites, are prepared from D-mannitol by nucleophilic opening of diastereoisomeric diepoxides.     

Molecular orbital theory and tunnelling currents

Summary The parameters appearing in an effective tight-binding Hamiltonian are shown to be simply related to the tunnelling currents and the overlap between the different orbitals of the constituent atoms. Different systems are considered and the results show that our approach applies both to molecular and condensed-matter systems.

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Riassunto Si mostra che i parametri presenti in una hamiltoniana efficace a legame forte sono correlati semplicemente alle correnti di tunnel e alla sovrapposizione tra i diversi orbitali degli atomi costituenti. Si considerano diversi sistemi e i risultati mostrano che il nostro approccio si applica sia a sistemi molecolari che di materia condensata.

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Резюме ПоказЫвается, что параметрЫ, появляющиеср в эффективном Гамильтониане в приближении силъной связи, связнЫ с туннелънЫми токами и перекрЫтием между разяичнЫми орбиталями составляюших атомов. Рассматриваются различнЫе системЫ. ПолученнЫе результатЫ показЫвают, что наш подход применим к молекулярнЫм системам и к конденсироваииому веществу.

     

The inf-sup condition and error estimates for the Arnold-Falk plate bending element

Summary We prove a discrete inf-sup condition for a mixed plate element introduced by Arnold and Falk.By using this condition, we obtain optimal error estimates for the shear strain which are valid uniformly in the plate thickness.This research was performed while the author was visiting the Center for Applied Mathematics, Purdue University, West Lafayette, IN 47907, USA