Interior regularity results for zeroth order operators approaching the fractional Laplacian

In this article we are interested in interior regularity results for the solution \({\mu _ \in } \in C(\bar \Omega )\) of the Dirichlet problem

$$\{ _{\mu = 0in{\Omega ^c},}^{{I_ \in }(\mu ) = {f_ \in }in\Omega }$$

where Ω is a bounded, open set and \({f_ \in } \in C(\bar \Omega )\) for all ? ∈ (0, 1). For some σ ∈ (0, 2) fixed, the operator \(\mathcal{I}_{\in}\) is explicitly given by

$${I_ \in }(\mu ,x) = \int_{{R^N}} {\frac{{[\mu (x + z) - \mu (x)]dz}}{{{ \in ^{N + \sigma }} + |z{|^{N + \sigma }}}}} ,$$

which is an approximation of the well-known fractional Laplacian of order σ, as ? tends to zero. The purpose of this article is to understand how the interior regularity of u? evolves as ? approaches zero. We establish that u_? has a modulus of continuity which depends on the modulus of f_?, which becomes the expected Hölder profile for fractional problems, as ? → 0. This analysis includes the case when f? deteriorates its modulus of continuity as ? → 0.

     

Accurate determination of the limiting anisotropy of rhodamine 101. Implications for its use as a fluorescence polarization standard

The S1-S0 limiting anisotropy of a widely used fluorophore, rhodamine 101, is determined with unprecedented accuracy. From time-resolved and steady-state fluorescence measurements in several solvents, it is shown that the limiting anisotropy of rhodamine 101 is for all practical purposes equal to the theoretical one-photon fundamental anisotropy value of 2/5, both in rigid and in fluid media. This fact, along with the favorable chemical and photophysical properties of rhodamine 101, point to its use as a standard for fluorescence polarization measurements. It is also shown that if the excitation pulse can be considered a delta impulse with respect to the time scale of the anisotropy decay (but not necessarily to the time scale of the intensity decay), then no deconvolution procedure is needed for anisotropy decay analysis.     

Analysis of metallic nanoparticles embedded in thin film semiconductors for optoelectronic applications

This paper reports about a study of the local plasmonic resonance (LSPR) produced by metal nanoparticles embedded in a dielectric or semiconductor matrix. It is presented an analysis of the LSPR for different nanoparticle metals, shapes, and embedding media composition. Metals of interest for nanoparticle composition are Aluminum and Gold. Shapes of interest are nanospheres and nanotriangles. We study in this work the optical properties of metal nanoparticles diluted in water or embedded in amorphous silicon, ITO and ZnO as a function of size, aspect-ratio and metal type. Following the analysis based on the exact solution of the Mie theory and DDSCAT numerical simulations, it is presented a comparison with experimental measurements realized with arrays of metal nanospheres. Simulations are also compared with the LSPR produced by gold nanotriangles (Au NTs) that were chemically produced and characterized by microscope and optical measurements.     

Octahedral bipyridine and bipyrimidine dioxomolybdenum(VI) complexes: characterization,application in catalytic epoxidation,and density functional mechanistic study

Complexes of the general formula [MoO(2)X(2)L(2)] (X=Cl, Br, Me; L(2)=bipy, bpym) have been prepared and fully characterized, including X-ray crystallographic investigations of all six compounds. Additionally, the highly soluble complex [MoO(2)Cl(2)(4,4'-bis(hexyl)-2,2'-bipyridine)] has been synthesized. The reaction of the complexes with tert-butyl hydroperoxide (TBHP) is an equilibrium reaction, and leads to MoV(I) eta(1)-alkylperoxo complexes that selectively catalyze the epoxidation of olefins. Neither the Mo-X bonds nor the Mo-N bonds are cleaved during this reaction. These experimental results are supported by theoretical calculations, which show that the attack of TBHP at the Mo center through the X-O-N face is energetically favored and the TBHP hydrogen atom is transferred to a terminal oxygen of the Mo=O moiety. After the attack of the olefin on the Mo-bound peroxo oxygen atom, epoxide and tert-butyl alcohol are formed. The latter compound acts as a competitive inhibitor for the TBHP attack, and leads to a significant reduction in the catalytic activity with increasing reaction time.     

Correlations between the viscoelastic behavior of pyrene-labeled associative polymers and the associations of their fluorescent hydrophobes

The viscoelastic behavior of a series of three pyrene-labeled hydrophobically modified alkali swellable emulsion copolymers (Py-HASEs) was investigated. All Py-HASEs thickened the aqueous solutions with viscosities orders of magnitude larger than that of a HASE control which displayed no pyrene hydrophobe. This fact demonstrated that the pyrene molecule is a good hydrophobe for associative thickeners such as HASEs. The Py-HASE solutions exhibited shear thinning, whose magnitude was found to increase with increasing pyrene content. A large shear-thinning effect indicates that a large fraction of the elastically active cross-links has been severed. Fluorescence measurements on the Py-HASEs confirmed that the smaller the pyrene content of the Py-HASE, the more intermolecular associations it formed, in agreement with the results obtained by rheology. Above the overlap concentration of the polymers, the zero-shear viscosity of the Py-HASE solutions increased steeply with increasing polymer concentration. The onset concentration where viscosity increases matches the onset concentration where intermolecular associations are being formed, as probed by fluorescence. Oscillatory rheological measurements were carried out to determine the terminal relaxation time, Td, and the storage modulus at the infinite time limit, G0, of the Py-HASE network. G0 was found to increase with decreasing pyrene contents, indicating that Py-HASEs with lower pyrene contents exhibited a higher density of elastically active chains. This result is in agreement with the trends obtained by the fluorescence and steady-state rheology measurements. A model is suggested that accounts for the fluorescence and rheology results.     

A Novel β-Glucosidase from Humicola insolens with High Potential for Untreated Waste Paper Conversion to Sugars

Humicola insolens produced a new β-glucosidase (BglHi2) under solid-state fermentation. The purified enzyme showed apparent molecular masses of 116 kDa (sodium dodecyl sulfate–polyacrylamide gel electrophoresis) and 404 kDa (gel-filtration), suggesting that it is a homotetramer. Mass spectrometry analysis showed amino acid sequence similarity with a β-glucosidase from Chaetomium thermophilum. Optima of pH and temperature were 5.0 and 65 °C, respectively, and the enzyme was stable for 60 min at 50 °C, maintaining 71 % residual activity after 60 min at 55 °C. BglHi2 hydrolyzed p-nitrophenyl-β-d-glucopyranoside and cellobiose. Cellobiose hydrolysis occurred with high apparent affinity (K _M?=?0.24?±?0.01 mmol L^?1) and catalytic efficiency (k _cat/K _M?=?1,304.92?±?53.32 L mmol^?1 s^?1). The activity was insensitive to Fe⁺³, Cr⁺², Mn⁺², Co⁺², and Ni²⁺, and 50–60 % residual activities were retained in the presence of Pb²⁺, Hg²⁺, and Cu²⁺. Mixtures of pure BglHi2 or H. insolens crude extract (CE) with crude extracts from Trichoderma reesei fully hydrolyzed Whatman no. 1 paper. Mixtures of H. insolens CE with T. reesei CE or Celluclast 1.5 L fully hydrolyzed untreated printed office paper, napkin, and magazine papers after 24–48 h, and untreated cardboard was hydrolyzed by a H. insolens CE/T. reesei CE mixture with 100 % glucose yield. Data revealed the good potential of BglHi2 for the hydrolysis of waste papers, promising feedstocks for cellulosic ethanol production.     

Chemical synthesis and crystallization of the dipeptide AcPheIleNH(2) in TTAB/heptane/octanol reversed micelles

The chemical synthesis of the dipeptide acetyl phenyl iso-leucin-amide (AcPheIleNH(2)) in tetradecyl trimethyl ammonium bromide (TTAB)/ heptane/octanol/carbonate buffer reversed micelles is described. The co-existence of the surfactant bounded minute water pools within the bulk organic solvent enables the simultaneous solubilization of the polar (IleNH(2)) and apolar (AcPheOEt) substrates, thus enabling the synthesis to take place at the micellar interface. The synthesis was favored by increasing the micellar interface via an increase in water content and surfactant concentration. The best dipeptide yield (87%) was obtained at 32 degrees C, with the largest concentrations of TTAB (200 mM) and water (1100 mM) tested. The low solubility of the dipeptide in the micellar media further led to the formation and growth of needle-like crystals during synthesis, thus enabling the removal of product from solution.     

Ultraweak-absorption microscopy of a single semiconductor quantum dot in the midinfrared range

We show that we can measure the room temperature ultraweak absorption of a single buried semiconductor quantum dot. This is achieved by monitoring the deformation field induced by the absorption of midinfrared laser pulses and locally detected with an atomic force microscope tip. The absorption is spectrally and spatially resolved around lambda approximately 10 microm wavelength with 60 nm lateral resolution (lambda/150). The electronic S-D intersublevel absorption of a single quantum dot is identified around 120 meV and exhibits a homogeneous linewidth of approximately 10 meV at room temperature.