On the chromatic polynomial of a graph

Let P(G,λ) be the chromatic polynomial of a graph G with n vertices, independence number α and clique number ω. We show that for every λ≥n, ()^α≤≤ () ^{n −ω}. We characterize the graphs that yield the lower bound or the upper bound.?These results give new bounds on the mean colour number μ(G) of G: n− (n−ω)() ^{n −ω}≤μ(G)≤n−α() ^α. Received: December 12, 2000 / Accepted: October 18, 2001?Published online February 14, 2002     

Enantioselective reduction and deracemisation using the non-conventional yeast Pichia glucozyma in water/organic solvent biphasic systems: preparation of (S)-1,2-diaryl-2-hydroxyethanones (benzoins)

Water/organic solvent two-liquid-phase systems have been successfully applied in the synthesis of enantiomerically pure (S)-benzoin through two different methodologies catalysed by whole cells from the non-conventional yeast Pichia glucozyma: the stereoselective monoreduction of benzil and the deracemisation of benzoin. The presence of the organic solvent influences the redox systems implied in the reactions, avoiding the formation of the corresponding diols, increasing the enantioselectivity and allowing the easy isolation of the products in high yields and excellent enantiomeric excesses. The use of both strategies has been extended to the preparation of different chiral benzoin derivatives.     

Parallel organization of contralateral and ipsilateral prefrontal cortical projections in the rhesus monkey

Background  

The neocortical commissures have a fundamental role in functional integration across the cerebral hemispheres. We investigated whether commissural projections in prefrontal cortices are organized according to the same or different rules as those within the same hemisphere, by quantitatively comparing density, topography, and laminar origin of contralateral and ipsilateral projections, labeled after unilateral injection of retrograde tracers in prefrontal areas.     

Organization of nanoscale objects via polymer demixing

We present an extremely versatile method for the lateral organization of nano-scale objects (NOs) based on the phenomenon of polymer demixing. NOs are suspended in a solution of two immiscible polymers, which is used to form a thin polymer film by spin coating. During spin coating the two polymers separate to give a microphase structure, whose length scale depends on the experimental conditions. The NOs spontaneously partition into one or other of the polymer phases resulting in their lateral organization. In this work, the organization of CdSe nanoparticles and fluorescent organic dyes was studied by fluorescence microscopy. The NOs were organized in the polymer film in stochastic patterns or in ordered designs on substrates pre-patterned by soft-lithography techniques. Single-particle measurements, using confocal microscopy, showed that at low concentrations there was little aggregation of the particles.     

Stereoselective synthesis of beta-(chloro)vinylsilanes using a regio- and (E)-stereoselective bis-stannylation of unsymmetrically substituted butadiynes: application to the synthesis of a masked triyne

[reaction: see text] A highly regio- and stereoselective bis-stannylation of unsymmetrically substituted butadiyne 3 provides bis-stannane 4. Selective lithiation of the internal tin residue effects a 1,4-retro-Brook rearrangement to afford vinylsilane 5. This was elaborated into the novel diethynylethene 1, which also functions as a masked triyne.     

Reaction diastereoselectivity of chiral aminoalcohols/[Co(II)NO3]+ complexes in evaporating ESI nanodroplets: new insights from a joint experimental and computational investigation

The nature of the ionic species, formed by electrospray ionization (ESI) of Co(NO₃)₂/CH₃OH solutions with a pair of aminoalcohols W and Y, has been investigated by mass spectrometric and computational methods. Collision induced dissociation (CID) of ions, formally corresponding to the [WYCoNO₃]⁺ structures, yields fragmentation patterns which reflect not only the expected [WYCoNO₃]⁺ connectivity but also that of other isomeric structures. Formation of these latter species is observed only in the presence of a tertiary aminoalcohol, like N‐methylpseudoephedrine. The CID patterns are found to be strongly dependent on the chemical form (whether the free aminoalcohol or its hydrochloride), the configuration, and the relative concentration of the W and Y aminoalcohols. This variability parallels the results of classical MD (molecular dynamics) simulations of the [WYCoNO₃]⁺ adducts which show a drastic alteration of the mechanical–dynamical features of the adducts by simply changing the charge state of W and/or Y, their absolute configuration, or by removing the solvent. The present experimental and computational study confirms the observation of fast stereoselective reactions in ESI nanodroplets before their evaporation and warns against any automatic correlation between the ESI spectrum of an analyte and its structure in solution. Copyright © 2009 John Wiley & Sons, Ltd.     

The Influence of Ripeness on the Phenolic Content,Antioxidant and Antimicrobial Activities of Pumpkins (Cucurbita moschata Duchesne)

Cucurbita moschata Duchesne (Cucurbitaceae) is a plant food highly appreciated for the content of nutrients and bioactive compounds, including polyphenols and carotenoids, which contribute to its antioxidant and antimicrobial capacities. The purpose of this study was to identify phenolic acids and flavonoids of Cucurbita moschata Duchesne using high-performance liquid chromatography–diode array detection–electrospray ionization tandem mass spectrometry (HPLC–DAD–ESI-MS) at different ripening stages (young, mature, ripened) and determine its antioxidant and antimicrobial activities. According to the results, phenolic acids and flavonoids were dependent on the maturity stage. The mature fruits contain the highest total phenolic and flavonoids contents (97.4 mg GAE. 100 g⁻¹ and 28.6 mg QE. 100 g⁻¹).A total of 33 compounds were identified. Syringic acid was the most abundant compound (37%), followed by cinnamic acid (12%) and protocatechuic acid (11%). Polyphenol extract of the mature fruits showed the highest antioxidant activity when measured by DPPH (0.065 μmol TE/g) and ABTS (0.074 μmol TE/g) assays. In the antimicrobial assay, the second stage of ripening had the highest antibacterial activity. Staphylococcus aureus was the most sensitive strain with an inhibition zone of 12 mm and a MIC of 0.75 mg L⁻¹. The lowest inhibition zone was obtained with Salmonella typhimurium (5 mm), and the MIC value was 10 mg L⁻¹.     

Optimization of high-order harmonic generation by adaptive control of a sub-10-fs pulse wave front

We present a method for the optimization of high-order harmonic generation based on wave-front correction of the driving laser beam. The technique exploits wave-front adaptive control by means of a deformable mirror, governed by an optimization procedure.