Compressed sensing with preconditioning for sparse recovery with subsampled matrices of Slepian prolate functions

Efficient recovery of smooth functions which are s-sparse with respect to the basis of so-called prolate spheroidal wave functions from a small number of random sampling points is considered. The main ingredient in the design of both the algorithms we propose here consists in establishing a uniform L ^∞ bound on the measurement ensembles which constitute the columns of the sensing matrix. Such a bound provides us with the restricted isometry property for this rectangular random matrix, which leads to either the exact recovery property or the “best s-term approximation” of the original signal by means of the ? ¹ minimization program. The first algorithm considers only a restricted number of columns for which the L ^∞ holds as a consequence of the fact that eigenvalues of the Bergman’s restriction operator are close to 1 whereas the second one allows for a wider system of PSWF by taking advantage of a preconditioning technique. Numerical examples are spread throughout the text to illustrate the results.     

Dysprosium Complexes and Their Micelles as Potential Bimodal Agents for Magnetic Resonance and Optical Imaging

Six diethylene triamine pentaacetic acid (DTPA) bisamide derivatives functionalized with p‐toluidine (DTPA‐BTolA), 6‐aminocoumarin (DTPA‐BCoumA), 1‐naphthalene methylamine (DTPA‐BNaphA), 4‐ethynylaniline (DTPA‐BEthA), p‐dodecylaniline (DTPA‐BC₁₂PheA) and p‐tetradecyl‐aniline (DTPA‐BC₁₄PheA) were coordinated to dysprosium(III) and the magnetic and optical properties of the complexes were examined in detail. The complexes consisting of amphiphilic ligands (DTPA‐BC₁₂PheA and DTPA‐BC₁₄PheA) were further assembled into mixed micelles. Upon excitation into the ligand levels, the complexes display characteristic Dy^III emission with quantum yields of 0.3–0.5 % despite the presence of one water molecule in the first coordination sphere. A deeper insight into the energy‐transfer processes has been obtained by studying the photophysical properties of the corresponding Gd^III complexes. Since the luminescence quenching effect is decreased by the intervention of non‐ionic surfactant, quantum yields up to 1 % are obtained for the micelles. The transverse relaxivity r₂ per Dy^III ion at 500 MHz and 310 K reaches a maximum value of 27.4 s^?1 mM ^?1 for Dy‐DTPA‐BEthA and 36.0 s^?1 mM ^?1 for the Dy‐DTPA‐BC₁₂PheA assemblies compared with a value of 0.8 s^?1 mM ^?1 for Dy‐DTPA. The efficient T₂ relaxation, especially at high magnetic field strengths, is sustained by the high magnetic moment of the dysprosium ion, the coordination of water molecules with slow water exchange kinetics and long rotational correlation times. These findings open the way to the further development of bimodal optical and magnetic resonance imaging probes starting from single lanthanide compounds.     

Wide‐angle X‐ray scattering study of the lamellar/fibrillar transition for a semi‐crystalline polymer deformed in tension in relation with the evolution of volume strain

This work is devoted to the study of the deformation mechanisms of a high‐density polyethylene deformed in tension. Specific treatments were applied to synchrotron wide‐angle X‐ray scattering patterns obtained in situ with the aim of quantifying: (i) the evolution of the apparent crystal sizes during the deformation process, (ii) the reorientation dynamics of the fragmented crystals while aligning their chains along the drawing axis during the establishment of the fibrillar morphology, and (iii) the reorientation dynamics of the amorphous chains. In addition, the volume strain evolution was measured using 3D digital image correlation. The cavitation phenomenon was found to mainly occur during the lamellae fragmentation phase. At the end of the deformation process, when the lamellar structure is destroyed, the fragmented crystals have new degrees of freedom and become free to rotate to align their chains along the drawing axis. Crystal fragmentation is then no longer needed to allow material deformation, and there is no further volume strain increase. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1470–1480     

Dislocation dynamics simulations with climb: kinetics of dislocation loop coarsening controlled by bulk diffusion

Dislocation climb mobilities, assuming vacancy bulk diffusion, are derived and implemented in dislocation dynamics simulations to study the coarsening of vacancy prismatic loops in fcc metals. When loops cannot glide, comparison of the simulations with a coarsening model based on the line tension approximation shows good agreement. Dislocation dynamics simulations with both glide and climb are then performed. Allowing for glide of the loops along their prismatic cylinders leads to faster coarsening kinetics, as direct coalescence of the loops is now possible.     

Design of a lattice-matched III–V–N/Si photovoltaic tandem cell monolithically integrated on silicon substrate

In this paper, we present a comprehensive study of high efficiencies tandem solar cells monolithically grown on a silicon substrate using GaAsPN absorber layer. InGaAs(N) quantum dots and GaAsPN quantum wells have been grown recently on GaP/Si susbstrate for applications related to light emission. For photovoltaic applications, we consider the GaAsPN diluted nitride alloy as the top junction material due to both its perfect lattice matching with Si and ideal bandgap energy for current generation in association with the Si bottom cell. Numerical simulation of the top cell is performed. The effect of layer thicknesses and doping on the cell efficiency are evidenced. In these structures a tunnel junction (TJ) is needed to interconnect both the top and bottom sub-cells. We compare the simulated performances of different TJ structures and show that the GaP(n+)/Si(p+) TJ is promising to improve performances of the current–voltage characteristic.     

Cerium‐Complex‐Catalyzed Oxidation of Arylmethanols under Atmospheric Pressure of Dioxygen and Its Mechanism through a Side‐On μ‐Peroxo Dicerium(IV) Complex

A new Ce^IV complex [Ce{NH(CH₂CH₂N=CHC₆H₂‐3,5‐(tBu)₂‐2‐O)₂}(NO₃)₂] ( 1 ), bearing a dianionic pentadentate ligand with an N₃O₂ donor set, has been prepared by treating (NH₄)₂Ce(NO₃)₆ with the sodium salt of ligand L1 . Complex 1 in the presence of TEMPO and 4 Å molecular sieves (MS4 A) has been found to serve as a catalyst for the oxidation of arylmethanols using dioxygen as an oxidant. We propose an oxidation mechanism based on the isolation and reactivity study of a trivalent cerium complex [Ce{NH(CH₂CH₂N=CHC₆H₂‐3,5‐(tBu)₂‐2‐O)₂}(NO₃)(THF)] ( 2 ), its side‐on μ‐O₂ adduct [Ce{NH(CH₂CH₂N=CHC₆H₂‐3,5‐(tBu)₂‐2‐O)₂}(NO₃)]₂(μ‐η²:η²‐O₂) ( 3 ), and the hydroxo‐bridged Ce^IV complex [Ce{NH(CH₂CH₂N=CHC₆H₂‐3,5‐(tBu)₂‐2‐O)₂}(NO₃)]₂(μ‐OH)₂ ( 4 ) as key intermediates during the catalytic cycle. Complex 2 was synthesized by reduction of 1 with 2,5‐dimethyl‐1,4‐bis(trimethylsilyl)‐1,4‐diazacyclohexadiene. Bubbling O₂ into a solution of 2 resulted in formation of the peroxo complex 3 . This provides the first direct evidence for cerium‐catalyzed oxidation of alcohols under an O₂ atmosphere.     

Norbornene‐functionalized PEO‐b‐PCL: A versatile platform for mikto‐arm star,umbrella‐like,and comb‐like graft copolymers

Well‐defined in‐chain norbornene‐functionalized poly(ethylene oxide)‐b‐poly(?‐caprolactone) copolymers (NB‐PEO‐b‐PCL) were synthesized from a dual clickable containing both hydroxyl‐ and alkyne‐reactive groups, namely heterofunctional norbornene 3‐exo‐(2‐exo‐(hydroxymethyl)norborn‐5‐enyl)methyl hexynoate. A range of NB‐PEO‐b‐PCL copolymers were obtained using a combination of orthogonal organocatalyzed ring‐opening polymerization (ROP) and click copper‐catalyzed azide–alkyne cycloaddition (CuAAC). Ring‐opening metathesis polymerization (ROMP) of NB‐PEO‐b‐PCL macromonomers using ruthenium‐based Grubbs’ catalysts provides comb‐like and umbrella‐like graft copolymers bearing both PEO and PCL grafts on each monomer unit. Mikto‐arm star A₂B₂ copolymers were obtained through a new strategy based on thiol–norbornene photoinitiated click chemistry between 1,3‐propanedithiol and NB‐PEO‐b‐PCL. The results demonstrate that in‐chain NB‐PEO‐b‐PCL copolymers can be used as a platform to prepare mikto‐arm star, umbrella‐, and comb‐like graft copolymers. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55 , 4051–4061