Optimal bounds for ratios of eigenvalues of one-dimensional Schrödinger operators with Dirichlet boundary conditions and positive potentials

Consider the Schrödinger equation –u+V(x)u=u on the intervalI, whereV(x)0 forxI and where Dirichlet boundary conditions are imposed at the endpoints ofI. We prove the optimal bound

Silica‐Coating of Hematite Nanoparticles Using Reactive Water‐Soluble Polyalkoxysiloxanes

In this article, we report on a new one‐step synthetic route to obtain multi‐functional silica‐coated hematite particles using a water‐based surfactant‐free technology. The synthesis and properties of uniform silica‐coated hematite particles with adjustable size, morphology, and silica shell thickness are discussed in detail. The developed method allows simultaneous formation of the silica shell around hematite core and incorporation of reactive groups on the surface of core–shell nanoparticles. Vinyl groups are introduced to the silica surface at once by pre‐functionalization of a water‐soluble hyperbranched polyalkoxysiloxanes with active double bonds. The reactivity of these surface‐immobilized vinyl groups is demonstrated by covalent attachment of rhodamine B using a thiol‐en click reaction.     

Effects of mobile phone exposure on time frequency fine structure of transiently evoked otoacoustic emissions

Mobile phones have become very commonly used worldwide within a short period of time. To date there is only limited knowledge about interaction between electromagnetic fields (EMFs) emitted by mobile phones and the auditory function. Moreover, there is widespread concern that there may be potential for harm. The aim of this study was to assess potential subtle changes in cochlear function by measuring the temporal and spectral fine structure of transiently evoked otoacoustic emissions (TEOAE) in normal hearing subjects after exposure to EMFs emitted by Global System for Mobile Communication (GSM) mobile phones. TEOAEs were recorded in 27 healthy young adults before and after 10 min of real or sham exposure in a double-blind design. TEOAE data were analyzed both globally (broadband analysis) and using the Wavelet Transform (analysis of the time-frequency fine structure). The broadband analysis revealed no significant effect on TEOAEs related to exposure, confirming results of previous studies; in addition, no significant change was detected in the analysis of the elementary wavelet components, suggesting that the temporal and spectral fine structure of TEOAEs is not affected by 10 min exposure to low-intensity EMFs emitted by GSM mobile phones.     

A Functional Analytic Approach to Perturbations of the Lorentz Gas

We present a functional analytic framework based on the spectrum of the transfer operator to study billiard maps associated with perturbations of the periodic Lorentz gas. We show that recently constructed Banach spaces for the billiard map of the classical Lorentz gas are flexible enough to admit a wide variety of perturbations, including: movements and deformations of scatterers; billiards subject to external forces; nonelastic reflections with kicks and slips at the boundaries of the scatterers; and random perturbations comprised of these and possibly other classes of maps. The spectra and spectral projections of the transfer operators are shown to vary continuously with such perturbations so that the spectral gap enjoyed by the classical billiard persists and important limit theorems follow.     

Quantitative Detection of Superoxide Ions in Whole Blood of the American Alligator (Alligator mississippiensis)

WST-1 and nitroblue tetrazolium (NBT) were used to quantify production of superoxide ions by leukocytes of the American alligator in whole blood. Because of the difficulty of isolating healthy leukocytes in alligators, these compounds were employed in whole blood instead of leukocyte preparations commonly used in other studies. The detection of superoxide was concentration- and time-dependent and linear with serial dilutions of whole blood. WST-1 reduction was inhibited by superoxide dismutase, indicating that the reduction was due to the presence of superoxide. Light microscopy revealed that superoxide production occurred in leukocytes, with no detectable contributions from other blood components.     

Quantitative assessment of motion correction for high angular resolution diffusion imaging

Several methods have been proposed for motion correction of high angular resolution diffusion imaging (HARDI) data. There have been few comparisons of these methods, partly due to a lack of quantitative metrics of performance. We compare two motion correction strategies using two figures of merit: displacement introduced by the motion correction and the 95% confidence interval of the cone of uncertainty of voxels with prolate tensors. What follows is a general approach for assessing motion correction of HARDI data that may have broad application for quality assurance and optimization of postprocessing protocols. Our analysis demonstrates two important issues related to motion correction of HARDI data: (1) although neither method we tested was dramatically superior in performance, both were dramatically better than performing no motion correction, and (2) iteration of motion correction can improve the final results. Based on the results demonstrated here, iterative motion correction is strongly recommended for HARDI acquisitions.     

Quantum Dots Microstructural Metrology: From Time-Resolved Spectroscopy to Spatially Resolved Electron Microscopy

Colloidal quantum dots (QDs) have unique optical and electrical properties with promising applications in next-generation semiconductor technologies, including displays, lighting, solar cells, photodetectors, and image sensors. Advanced analytical tools to probe the optical, morphological, structural, compositional, and electrical properties of QDs and their ensemble solid films are of paramount importance for the understanding of their device performance. In this review, comprehensive studies on the state-of-the-art metrology approaches used in QD research are introduced, with particular focus on time-resolved (TR) and spatially resolved (SR) spectroscopy and microscopy. Through discussing these analysis techniques in different QD system, such as various compositions, sizes, and shell structures, the critical roles of these TR-spectroscopic and SR-microscopic techniques are highlighted, which provide the structural, morphological, compositional, optical, and electrical information to precisely design QDs and QD solid films. The employment of TR and SR analysis in integrated QD device systems is also discussed, which can offer detailed microstructural information for achieving high performance in specific applications. In the end, the current limitations of these analytical tools are discussed, and the future development of the possibility of interdisciplinary research in both QD fundamental and applied fields is prospected.