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).     

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     

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.     

On values of the Riemann zeta function at positive integers

Lithuanian Mathematical Journal - We give new proofs of some known results on the values of the Riemann zeta function at positive integers and obtain some new theorems related to these values....     

Effect of contact stiffness modulation in contact-mode AFM under subharmonic excitation

We report on the effect of fast contact stiffness modulation on frequency response to 2:1 subharmonic resonance in contact-mode atomic force microscopy. The model of the contact-mode dynamic between the tip of the microbeam and the moving surface consists of a lumped single degree of freedom Hertzian contact oscillator. Perturbation methods are applied to obtain the frequency response of the slow dynamic of the system. We focus on the effect of the amplitude and the frequency of the modulation on the nonlinear characteristic of the contact stiffness, the jump phenomenon and the shift in the frequency response of the subharmonic. We also show the effect of the contact stiffness modulation on the interval of the unstable trivial solution which is directly correlated to the depth of the jump. The obtained results can directly influence the material properties and the loss of contact between the tip and the sample.     

Iodonium‐polyoxometalate and thianthrenium‐polyoxometalate as new one‐component UV photoinitiators for radical and cationic polymerization

Four novel onium salts (onium‐polyoxometalate) have been synthesized and characterized. They contain a diphenyliodonium or a thianthrenium (TH) moiety and a polyoxomolybdate or a polyoxotungstate as new counter anions. Outstandingly, these counter anions are photochemically active and can sensitize the decomposition of the iodonium or TH moiety through an intramolecular electron transfer. The phenyl radicals generated upon UV light irradiation (Xe–Hg lamp) are very efficient to initiate the radical polymerization of acrylates. Cations are also generated for the cationic polymerization of epoxides. Remarkably, these novel iodonium and TH salts are characterized by a higher reactivity compared with that of the diphenyliodonium hexafluorophosphate and the commercial TH salt, respectively. Interpenetrating polymer networks can also be obtained under air through a concomitant cationic/radical photopolymerization of an epoxy/acrylate blend (monomer conversions > 65%). The photochemical mechanisms are studied by steady‐state photolysis, cyclic voltammetry, and electron spin resonance techniques. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 981–989     

Infinite independent sets in distributive lattices

We show that a poset P contains a subset isomorphic to if and only if the poset J(P) consisting of ideals of P contains a subset isomorphic to the power set of κ. If P is a join-semilattice this amounts to the fact that P contains an independent set of size κ. We show that if κ := ω and P is a distributive lattice, then this amounts to the fact that P contains either or as sublattices, where Γ and Δ are two special meet-semilattices already considered by J. D. Lawson, M. Mislove and H. A. Priestley.Dedicated to the memory of Ivan RivalReceived April 22, 2003; accepted in final form July 11, 2004.This revised version was published online in August 2005 with a corrected cover date.     

Wavelet-type Transform and Bessel Potentials Associated with the Generalized Translation

Wavelet–type transform associated with singular Laplace–Bessel differential operator is introduced and the relevant Calderón–type reproducing formula is established. Representations of the generalized Bessel potentials 0)$ " align="middle" border="0"> and their inverses via the wavelet–type transform are obtained.