Markov shifts and topological entropy of families of homoclinic tangles

The existence of a homoclinic orbit in dynamical systems implies chaotic behaviour with positive entropy. In this work, we determine explicitly the Markov shifts associated to certain Smale horseshoe homoclinic orbits which allow us to compute a lower bound for the topological entropy that such a system can have. It is done associating a heteroclinic orbit which belongs to the same isotopy class and then determining the Markov partition of the dynamical core of an end periodic mapping.     

Rapid Discrimination of Crystal Handedness by X-ray Natural Circular Dichroism (XNCD) Mapping

An original method for determining the handedness of individual non-centrosymmetric crystals in a mixture using a tightly-focused, circularly polarized X-ray beam is presented. The X-ray natural circular dichroism (XNCD) spectra recorded at the metal K-edge on selected crystals of [Δ-M(en)₃](NO₃)₂ and [Λ-M(en)₃](NO₃)₂ (M=Co^II, Ni^II) show extrema at the metal pre-edge (7712 eV for Co, 8335 eV for Ni). A mapping of a collection of some 220 crystals was performed at the respective energies by using left and right circular polarizations. The difference in absorption for the two polarizations, being either negative or positive, directly yielded the handedness of the crystal volume probed by the beam. By using this technique, it was found that the addition of l -ascorbic acid during the synthesis of [Co(en)₃](NO₃)₂ resulted in an enantiomeric enrichment of the Λ-isomer of 67±13 %, whereas the Ni analogue was similarly, but conversely, enriched in the Δ-isomer (65±22 %).     

Dynamic Kinetic Resolution of 2-(Quinolin-8-yl)Benzaldehydes: Atroposelective Iridium-Catalyzed Transfer Hydrogenative Allylation

An atroposelective Ir-catalyzed dynamic kinetic resolution (DKR) of 2-(quinolin-8-yl)benzaldehydes/1-naphthaldehydes by transfer hydrogenative coupling of allyl acetate is disclosed. The allylation reaction takes place with simultaneous installation of central and axial chirality, reaching high diastereoselectivities and excellent enantiomeric excesses when ortho-cyclometalated iridium-DM-BINAP is used as the catalyst. The racemization of the substrates occurs through a designed transient Lewis acid-base interaction between the quinoline nitrogen atom and the aldehyde carbonyl group.     

Parameterization of the in-water motions of falling cylinders using high-speed video

A methodology to observe the motions of large cylinders falling freely at large (~10⁶) Reynolds numbers using a stereometric, high-speed video technique is presented. Parameter variation in length, weight, center of mass, and nose shape combined with changes in release height and initial inclination angle were used to estimate the influence of net drag forces on six cylinder bodies. Cylinders with coincident centers of volume and mass typically assumed body orientations with the major axis aligned normal to the path of descent indicating that buoyancy forces and turbulent drag balanced the inertia of the body and displaced water. Displacement of the center of mass resulted in more vertical orientations and more complex motions. Abrupt changes in position, orientation, and velocity were also observed when air-dropped cylinders separated from a trapped cloud of bubbles signifying the onset of less predictable behaviors.     

Palladium‐Catalysed Direct Cross‐Coupling of Organolithium Reagents with Aryl and Vinyl Triflates

A palladium‐catalysed cross‐coupling of organolithium reagents with aryl and vinyl triflates is presented. The reaction proceeds at 50 or 70 °C with short reaction times, and the corresponding products are obtained with moderate to high yields, with a variety of alkyl and (hetero)aryl lithium reagents.     

First report of non‐coloured flavonoids in Echium plantagineum bee pollen: differentiation of isomers by liquid chromatography/ion trap mass spectrometry

Apicultural products have been widely used in diet complements as well as in phytotherapy. Bee pollen from Echium plantagineum was analysed by high‐performance liquid chromatography/photodiode‐array detection coupled to ion trap mass spectrometry (HPLC‐PAD‐MSⁿ) with an electrospray ionisation interface. The structures have been determined by the study of the ion mass fragmentation, which characterises the interglycosidic linkage in glycosylated flavonoids and differentiates positional isomers. Twelve non‐coloured flavonoids were characterised, being kaempferol‐3‐O‐neohesperidoside the major compound, besides others in trace amounts. These include quercetin, kaempferol and isorhamnetin glycosides, with several of them being isomers. Acetylated derivatives are also described. This is the first time that non‐coloured flavonoids are reported from this pollen, with MS fragmentation proving to be most useful in the elucidation of isomeric structures. Copyright © 2010 John Wiley & Sons, Ltd.