A generalization of the maximal-spacings in several dimensions and a convexity test.

The notion of maximal-spacing in several dimensions was introduced and studied by Deheuvels (Probab. Theory Related Fields 64(4), 411–424, 1983), for data uniformly distributed on the unit cube. Later on, Janson (Ann. Prob. 15, 274–280, 1987) extended the results to data uniformly distributed on any bounded set, and obtained a very fine result, namely, he derived the asymptotic distribution of different maximal-spacings notions. These results have been very useful in many statistical applications. We extend Janson’s results to the case where the data are generated from a Hölder continuous density that is bounded from below and whose support is bounded. As an application, we develop a convexity test for the support of a distribution.     

Growth and structure of nematic spherulites under shallow thermal quenches

The growth kinetics, shape, interfacial and internal orientation texture of a submicron nematic spherulite arising during the isotropic-to-nematic liquid crystal phase transformation under shallow thermal quenches is analyzed using theory, scaling, and numerical simulations based on the Landau – de Gennes model (The Physics of Liquid Crystals, 2nd edn. Clarendon, Oxford). The numerical computations from this model yield interfacial cusp formation that relaxes through the nucleation of two disclination lines of topological charge +1/2 and subsequently leads to intra-droplet texturing and a net topological charge within the spherulite of +1. The timing of these events suggests that cusp formation at the interface is intimately associated with the interfacial defect shedding mechanism (J. Chem. Phys. 124:244902, 2006) for shallow quenches. These results are different than predictions for deep quenches (J. Chem. Phys. 124:244902, 2006) where interfacial defect shedding leads to four defects and a net topological charge of +2. A liquid crystal dynamic shape equation is derived from the Landau – de Gennes model to account for the interface shape changes in terms of surface viscosity, the driving forces due to the uniaxial nematic-isotropic free energy difference, capillary forces, and friction forces, and used to semi-quantitatively show that during cusp formation and defect shedding, gradient elasticity, capillary forces and friction play significant roles in decelerating and accelerating the surface. An interfacial eigenvalue analysis shows that during the shallow quench, disclination lines nucleate within the interface itself and then texturize the nematic droplet as they migrate from within the interface to the bulk of the growing nematic droplet. After defect shedding, the spherulite is nearly circular and grows with constant velocity, in agreement with experiments. The results shed new light on intra-spherulite texturing mechanisms in phase ordering under weak driving forces.      

Antioxidant and Anti-Proliferative Activity of Essential Oil and Main Components from Leaves of Aloysia polystachya Harvested in Central Chile

The aim of this study was to determine, first, the chemical composition of Aloysia polystachya (Griseb) Moldenke essential oil, from leaves harvested in central Chile; and second, its antioxidant and cytotoxic activity. Eight compounds were identified via gas chromatography–mass spectrometry (GC–MS) analyses, with the most representative being R-carvone (91.03%), R-limonene (4.10%), and dihydrocarvone (1.07%). For Aloysia polystachya essential oil, antioxidant assays (2,2-diphenyl-1-picrylhydrazyl (DPPH), H₂O₂, ferric reducing antioxidant power (FRAP), and total reactive antioxidant potential (TRAP)) showed good antioxidant activity compared to commercial antioxidant controls; and anti-proliferative assays against three human cancer cell lines (colon, HT-29; prostate, PC-3; and breast, MCF-7) determined an IC₅₀ of 5.85, 6.74, and 9.53 µg/mL, and selectivity indices of 4.75, 4.12, and 2.92 for HT-29, PC-3, and MCF-7, respectively. We also report on assays with CCD 841 CoN (colon epithelial). Overall, results from this study may represent, in the near future, developments for natural-based cancer treatments.     

Radical Silyl- and Germylzincation of Propargylic Alcohols

The silyl- and germylzincation of terminal or internal propargylic alcohols by reaction with (Me₃Si)₃SiH/Et₂Zn, [(Me₃Si)₃Si]₂Zn/Et₂Zn or Ph₃GeH/Et₂Zn is examined. These reactions proceed through the addition of silicon- or germanium-centered radicals across the carbon≡carbon triple bond followed by the trapping by diethylzinc of the produced vinyl radical through homolytic substitution at the zinc atom. The influence of the hydroxy unit on the regio- and stereoselectivity of these reactions is discussed and compared to its role played in radical hydrosilylation and hydrogermylation reactions. Protocols developed to achieve the β-regioselective silylzincation of propargyl alcohol and the α-regioselective germylzincation of internal propargylic alcohols are particularly important, as they occur with trans stereoselectivity. For both procedures the C(sp²)−Zn bond remains available for subsequent in-situ electrophilic substitution leading overall to net alkyne trans difunctionalization.     

Synthesis and Modeling of Ezetimibe Analogues

Ezetimibe is a well-known drug that lowers blood cholesterol levels by reducing its absorption in the small intestine when joining to Niemann-Pick C1-like protein (NPC1L1). A ligand-based study on ezetimibe analogues is reported, together with one-hit synthesis, highlighted in the study. A convenient asymmetric synthesis of (2S,3S)-N-α-(R)-methylbenzyl-3-methoxycarbonylethyl-4-methoxyphenyl β-lactam is described starting from Baylis–Hillman adducts. The route involves a domino process: allylic acetate rearrangement, stereoselective Ireland–Claisen rearrangement and asymmetric Michael addition, which provides a δ-amino acid derivative with full stereochemical control. A subsequent inversion of ester and acid functionality paves the way to the lactam core after monodebenzylation and lactam formation. It also shows interesting results when it comes to a pharmacophore study based on ezetimibe as the main ligand in lowering blood cholesterol levels, revealing which substituents on the azetidine-2-one ring are more similar to the ezetimibe skeleton and will more likely bind to NPC1L1 than ezetimibe.     

Exceptionally Inert Lanthanide(III) PARACEST MRI Contrast Agents Based on an 18‐Membered Macrocyclic Platform

We report a macrocyclic ligand based on a 3,6,10,13‐tetraaza‐1,8(2,6)‐dipyridinacyclotetradecaphane platform containing four hydroxyethyl pendant arms (L¹) that forms extraordinary inert complexes with Ln³⁺ ions. The [EuL¹]³⁺ complex does not undergo dissociation in 1 M HCl over a period of months at room temperature. Furthermore, high concentrations of phosphate and Zn²⁺ ions at room temperature do not provoke metal‐complex dissociation. The X‐ray crystal structures of six Ln³⁺ complexes reveal ten coordination of the ligand to the metal ions through the six nitrogen atoms of the macrocycle and the four oxygen atoms of the hydroxyethyl pendant arms. The analysis of the Yb³⁺‐ and Pr³⁺‐induced paramagnetic ¹H NMR shifts show that the solid‐state structures are retained in aqueous solution. The intensity of the ¹H NMR signal of bulk water can be modulated by saturation of the signals of the hydroxy protons of Pr³⁺, Eu³⁺, and Yb³⁺ complexes following chemical‐exchange saturation transfer (CEST). The ability of these complexes to provide large CEST effects at 25 and 37 °C and pH 7.4 was confirmed by using CEST magnetic resonance imaging experiments.     

Field‐Induced Slow Magnetic Relaxation in a Mononuclear Manganese(III)–Porphyrin Complex

We report on a novel manganese(III)–porphyrin complex with the formula [Mn^III(TPP)(3,5‐Me₂pyNO)₂]ClO₄?CH₃CN ( 2 ; 3,5‐Me₂pyNO=3,5‐dimethylpyridine N‐oxide, H₂TPP=5,10,15,20‐tetraphenylporphyrin), in which the Mn^III ion is six‐coordinate with two monodentate 3,5‐Me₂pyNO molecules and a tetradentate TPP ligand to build a tetragonally elongated octahedral geometry. The environment in 2 is responsible for the large and negative axial zero‐field splitting (D=?3.8 cm^?1), low rhombicity (E/|D|=0.04) of the high‐spin Mn^III ion, and, ultimately, for the observation of slow magnetic‐relaxation effects (E_a=15.5 cm^?1 at H=1000 G) in this rare example of a manganese‐based single‐ion magnet (SIM). Structural, magnetic, and electronic characterizations were carried out by means of single‐crystal diffraction studies, variable‐temperature direct‐ and alternating‐current measurements and high‐frequency and ‐field EPR spectroscopic analysis followed by quantum‐chemical calculations. Slow magnetic‐relaxation effects were also observed in the already known analogous compound [Mn^III(TPP)Cl] ( 1 ; E_a=10.5 cm^?1 at H=1000 G). The results obtained for 1 and 2 are compared and discussed herein.     

Identification of olive pollen allergens using a fluorescence‐based 2D multiplex method

Olive (Olea europaea L.) pollen is a major health concern in the Mediterranean countries and some olive growing regions in America and Australia. The molecular variability of pollen allergens constitutes a handicap for commercial extract standardization, which is the base of current diagnosis and vaccination procedures. In this paper, we report a time‐saving and plant material saving multiplex detection method for the rapid and simultaneous analysis of Ole e 1, Ole e 2, and Ole e 5 allergen polymorphism on a single blot. This method combines high‐resolution 2DE techniques with high‐sensitive fluorescence‐based detection methods. Using this strategy, we were capable to identify a higher number of allergen forms compared with classical 1D approach. The use of fluorescent probes and the increased resolution of 2D blots avoided overlapping effects, and allow estimating the amount of individual allergen forms. In addition, the pattern and identity of the IgE‐reactive proteins of either a population or individual patients allergic to olive pollen was also effortlessly determined in a single additional step. This flexible method might be extended to a higher number of olive allergens and cultivars, and is also applicable to other allergogenic plant species and sources.     

Scope of partial least‐squares regression applied to the enantiomeric composition determination of ketoprofen from strongly overlapped chromatographic profiles

Valuable quantitative information could be obtained from strongly overlapped chromatographic profiles of two enantiomers by using proper chemometric methods. Complete separation profiles where the peaks are fully resolved are difficult to achieve in chiral separation methods, and this becomes a particularly severe problem in case that the analyst needs to measure the chiral purity, i.e., when one of the enantiomers is present in the sample in very low concentrations. In this report, we explore the scope of a multivariate chemometric technique based on unfolded partial least‐squares regression, as a mathematical tool to solve this quite frequent difficulty. This technique was applied to obtain quantitative results from partially overlapped chromatographic profiles of R‐ and S‐ketoprofen, with different values of enantioresolution factors (from 0.81 down to less than 0.2 resolution units), and also at several different S:R enantiomeric ratios. Enantiomeric purity below 1% was determined with excellent precision even from almost completely overlapped signals. All these assays were tested on the most demanding condition, i.e., when the minor peak elutes immediately after the main peak. The results were validated using univariate calibration of completely resolved profiles and the method applied to the determination of enantiomeric purity of commercial pharmaceuticals.