Multidimensional weighted Opial inequalities

In this article we produce Opial-type weighted multidimensional inequalities over balls and arbitrary smooth bounded domains. The inequalities are sharp. The functions under consideration vanish on the boundary.     

Randomlyn-cyclic digraphs

A digraphD is randomlyn-cyclic (n≥3) if for each vertexv ofD, every (directed) path with initial vertexv and having length at mostn−1 can be extended to av−v (directed) cycle of lengthn. Several results related to and examples of randomlyn-cyclic digraphs are presented. Also, all randomlyn-cyclic digraphs forn=3, 4, and 5 are determined. Research supported by a Western Michigan University faculty research fellowship. Research supported in part by a College of Arts and Sciences and Graduate College research assistantship from Western Michigan University.     

Maghemite/poly(<Emphasis Type="SmallCaps">d,l</Emphasis>-lactide-<Emphasis Type="Italic">co</Emphasis>-glycolyde) composite nanoplatform for therapeutic applications

A reproducible methodology is described for the synthesis, by following the double emulsion/solvent evaporation technique, of magnetic nanocomposites (average diameter ≈ 135 nm) consisting of maghemite nuclei and a biodegradable poly(d,l-lactide-co-glycolide) matrix. The heterogeneous structure of the nanoparticles can confer them the responsiveness to magnetic gradients, giving both the possibility of their use as a drug delivery system and adequate heating characteristics for a hyperthermia effect. The physical chemistry of the nanocomposites was extensively characterized, this establishing that their surface properties were similar to that of pure poly(d,l-lactide-co-glycolide). From an electrokinetic point of view, zeta potential determinations (as a function of the ionic strength, and pH) pointed out that the nanocomposites were almost indistinguishable from the copolymer. The surface thermodynamic analysis agreed with the electrophoretic one in suggesting that the coverage of the magnetic nuclei was complete, since the hydrophilic nature of maghemite was modified and the nanoparticles turned into hydrophobic, just like the copolymer, when they were embedded into poly(d,l-lactide-co-glycolide). The magnetic behaviours of the composite nanoparticles were also checked. Their heating properties were studied in vitro in a high-frequency alternating gradient of magnetic field: a stable maximum temperature of 47 °C was satisfactorily achieved within 45 min. Blood compatibility of the nanocomposites was also defined in vitro. To our knowledge, this is the first time that such kind of magnetic-sensitive nanoformulation with very promising characteristics (e.g. blood compatibility, magnetic drug targeting capabilities, and hyperthermia) has been developed for therapeutic purposes.     

Optical fiber refractometers based on indium tin oxide coatings fabricated by sputtering

This Letter presents the fabrication of optical fiber refractometers based on indium tin oxide (ITO) coatings deposited by sputtering with response in the visible region. ITO thin films have been sputtered by means of a rotating mechanism that enables the fabrication of smooth and homogeneous coatings onto the optical fiber core. The ITO coating acts as a resonance supporting layer. This permits us to couple light from the waveguide to the ITO-coating/external medium region at specific wavelength ranges. The device is sensitive to external medium refractive index, which allows its utilization as a refractometer. The sensitivity is dependent on the coating thickness, ranging from 523.21 to 1221 nm/refractive index unit in the explored sensors. The sensor development process is time effective compared to other techniques such as dip coating or layer-by-layer self-assembly, which is interesting in terms of mass production.     

Irradiation effects in CaF2 probed by Raman scattering

The formation conditions and dynamics of Ca colloids and point defects that appear in irradiated single crystals of CaF₂ were investigated by Raman spectroscopy. The intensity changes in the Raman spectra because of the presence of different concentrations of point defects and Ca colloids that emerged in CaF₂ after irradiation with 2.2 GeV Au ions were used to study their distribution and stability under illumination with three laser wavelengths (473, 532 and 633 nm) at different output powers (2 to 200 mW). A damage saturation at a fluence of 6 × 10¹¹ ion cm⁻² was observed. The dependence of the spectral changes on the ion fluence can be described by a core/halo damage cross‐section model. A radius of 13–18 nm was obtained for the outer (halo) cylinder, in agreement with previous swelling studies. Illuminations of irradiated samples with blue (473 nm) and green (532 nm) lasers were found to be extremely efficient in bleaching the samples, while illumination with a red (633 nm) laser did not lead to a sample recovery. This indicates that the bleaching process is governed by recombination of point defects that have to overcome an energy barrier. Typical time constants for the processes involved are presented. Copyright © 2016 John Wiley & Sons, Ltd.     

Limits of the paraxial approximation in laser beams

The validity of the paraxial approximation for laser beams in free space is studied via an integral criterion based on the propagation invariants of Helmholtz and paraxial wave equations. This approach allows one to determine the paraxial limit for beams with nondefined spot size and for beams described by more parameters in addition to typical longitudinal wavelength and transverse waist. As examples, the paraxiality of higher-order Hermite, Laguerre, and Bessel-Gaussian beams was completely determined. This method could be extended to nonlinear optics and Bose condensates.     

Characterization based on conditional expectations of adjacent order statistics: A unified approach

In this paper, we show a unified approach to the problem of characterizing general distribution functions based on the conditional expectation between adjacent order statistics, or , where is a real, continuous and strictly monotonic function. We have the explicit expression of the distribution function from the above order mean function, and , and we give necessary and sufficient conditions so that any real function can be an order mean function. Our results generalize the results given for the discrete, absolutely continuous and continuous cases. Further, we show stability theorems for these characterizations.

     

A new concept in lightning parameters measurement

Nowadays the electrical activity measured in tall objects has been widely characterized, but the collected data of lightning rods installed in buildings do not amount to enough to obtain reliable statistics. The measures stored at relatively few points are not representative of the different types of installations. Furthermore, the protection model applied for lightning air terminal installations is based on theoretical models. This paper describes the design of a micro-station to measure some lightning parameters in real lightning air terminal installations correlated to the nature of emplacement instead of triggering lightning or choosing points with a high number of lightning impacts.     

Exchange coupling in halo-bridged dinuclear Cu(II) compounds: a density functional study

A density functional study of exchange coupling in halo-bridged dinuclear copper(II) compounds has been carried out. Coupling constants calculated for full unmodeled structures, as determined by X-ray diffraction, are in excellent agreement with experimental data, confirming the ability of the computational strategy used in this work to predict the magnetic behavior of such compounds. Model calculations have been used to examine the influence of several factors on the coupling constant: the nature of the bridging and terminal ligands, the coordination environment around copper atoms, and some structural distortions frequently found in this family of complexes. A ferromagnetic coupling is predicted when N-donor terminal ligands are present, especially for bromo-bridged systems, an interesting synthetic target.