Bi-Parametric Potentials, Relevant Function Spaces and Wavelet-Like Transforms

We introduce new potential type operators J^a_b = (E+(-D)^b/2)^-a/bJ^{\alpha}_{\beta} = (E+(-\Delta)^{\beta/2})^{-\alpha/\beta}, (α > 0, β > 0), and bi-parametric scale of function spaces H^a_{b, p}(\mathbbRⁿ)H^{\alpha}_{\beta , p}({\mathbb{R}}^n) associated with J^α_β. These potentials generalize the classical Bessel potentials (for β = 2), and Flett potentials (for β = 1). A characterization of the spaces H^a_{b, p}(\mathbbRⁿ)H^{\alpha}_{\beta, p}({\mathbb{R}}^n) is given with the aid of a special wavelet–like transform associated with a β-semigroup, which generalizes the well-known Gauss-Weierstrass semigroup (for β = 2) and the Poisson one (for β = 1).     

Influence of the operation pressure on slug length in near horizontal gas–liquid pipe flow

Slug flow is commonly observed in gas production offshore fields. At high operation pressure only short hydrodynamic slugs are observed. However, as the offshore fields become older, the operation pressure becomes lower and long slugs may form. At near atmospheric pressures the long slugs may reach a size of 500 pipe diameters or more. Such slugs can cause serious operational failures due to the strong fluctuating pressure. Identifying the operation pressure conditions at which the long slugs appear, may reduce or prevent these negative effects.     

Reactivity of phosphiranes toward nucleophiles: Theoretical and experimental investigations

The thermodynamic and kinetic parameters for the reaction of 1‐methylphosphirane with dimethylphosphide (PMe), proceeding via attack at the ring phosphorus atom to give Me₂P–PMe⁻ plus ethylene, were calculated at the G3(MP2)‐RAD(+) level. The rate constant for this mechanism (k = 1.1 × 10¹³ L mol⁻¹ s⁻¹ at 25°C) is seven orders of magnitude greater than that for the previously studied mechanism involving attack at carbon. Experimental investigations with 1‐phenylphosphirane gave consistent results: Treatment with LiPMePh yielded no detectable polymer, and quenching with MeI gave the known diphosphine (R*, R*)‐(±)/(R*, S*)‐MePhP‐‐PMePh. © 2008 Wiley Periodicals, Inc. Heteroatom Chem 19:178–181, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20405     

Bimorpholine-mediated enantioselective intramolecular and intermolecular aldol condensation

Monosalts of N-substituted bimorpholine derivatives are efficient organocatalysts in intramolecular and intermolecular aldol reactions. The properties of the catalysts can be tuned either by the selection of an appropriate acid for the salt formation or by the change of a substituent at the nitrogen atom. In aldol condensation, i-Pr-substituted bimorpholine is the most stereoselective catalyst affording products in high yield with enantioselectivities up to 95% ee.     

Inversion of Bessel Potentials with the Aid of Weighted Wavelet Transforms

A special type of weighted wavelet transforms is introduced and the relevant Calderón reproducing formula for functions f ∈ L^p(ℝⁿ ) is proved. By making use of these wavelet‐type transforms a new inversion formula of the classical Bessel potentials is obtained.     

Robust Variable-Step Perturb-and-Observe Sliding Mode Controller for Grid-Connected Wind-Energy-Conversion Systems

In order to extract efficient power generation, a wind turbine (WT) system requires an accurate maximum power point tracking (MPPT) technique. Therefore, a novel robust variable-step perturb-and-observe (RVS-P&O) algorithm was developed for the machine-side converter (MSC). The control strategy was applied on a WT based permanent-magnet synchronous generator (PMSG) to overcome the downsides of the currently published P&O MPPT methods. Particularly, two main points were involved. Firstly, a systematic step-size selection on the basis of power and speed measurement normalization was proposed; secondly, to obtain acceptable robustness for high and long wind-speed variations, a new correction to calculate the power variation was carried out. The grid-side converter (GSC) was controlled using a second-order sliding mode controller (SOSMC) with an adaptive-gain super-twisting algorithm (STA) to realize the high-quality seamless setting of power injected into the grid, a satisfactory power factor correction, a high harmonic performance of the AC source, and removal of the chatter effect compared to the traditional first-order sliding mode controller (FOSMC). Simulation results showed the superiority of the suggested RVS-P&O over the competing based P&O techniques. The RVS-P&O offered the WT an efficiency of 99.35%, which was an increase of 3.82% over the variable-step P&O algorithm. Indeed, the settling time was remarkably enhanced; it was 0.00794 s, which was better than for LS-P&O (0.0841 s), SS-P&O (0.1617 s), and VS-P&O (0.2224 s). Therefore, in terms of energy efficiency, as well as transient and steady-state response performances under various operating conditions, the RVS-P&O algorithm could be an accurate candidate for MPP online operation tracking.     

Multimeric Presentation of RGD Peptidomimetics Enhances Integrin Binding and Tumor Cell Uptake

The use of multimeric ligands is considered as a promising strategy to improve tumor targeting for diagnosis and therapy. Herein, tetrameric RGD (Arg-Gly-Asp) peptidomimetics were designed to target α_vβ₃ integrin-expressing tumor cells. These compounds were prepared by an oxime chemoselective assembly of cyclo(DKP-RGD) ligands and a cyclodecapeptide scaffold, which allows a tetrameric presentation. The resulting tetrameric RGD peptidomimetics were shown to improve α_vβ₃ integrin binding compared with the monomeric form. Interestingly, these compounds were also able to enhance tumor cell endocytosis in the same way as tetrameric RGD peptides. Altogether, the results show the potential of the tetrameric cyclo(DKP-RGD) ligands for in vivo imaging and drug delivery.