Strichartz Estimates for Schrödinger Equations on Scattering Manifolds

The present article is concerned with Schrödinger equations on non-compact Riemannian manifolds with asymptotically conic ends. It is shown that, for any admissible pair (including the endpoint), local in time Strichartz estimates outside a large compact set are centered at origin hold. Moreover, we prove global in space Strichartz estimates under the nontrapping condition on the metric.     

Wavelength dispersive X-ray analysis and cathodoluminescence techniques for monitoring the chemical removal of AlInN on an N-face GaN surface

This paper shows the selective etching process of an AlInN sacrificial layer, lattice-matched to GaN, on N-face GaN by an aqueous solution of 1,2-diaminoethane. Using the wavelength dispersive X-ray (WDX) spectrometers on an electron probe micro-analyser, together with an optical spectrometer and silicon CCD array added to the light microscope, and sharing the same focus as the electron microscope, cathodoluminescence spectra are collected from exactly the same spot as sampled by the WDX spectrometers. This technique allows the compositional properties of the etched AlInN layer and the optical properties of the semiconductor layers underlying the sacrificial layer to be scrutinised, verifying the etching selectivity and the efficiency of the process.     

Carbon nanotubes as solid-phase extraction sorbents prior to atomic spectrometric determination of metal species: A review

New materials have significant impact on the development of new methods and instrumentation for chemical analysis. From the discovery of carbon nanotubes in 1991, single and multi-walled carbon nanotubes – due to their high adsorption and desorption capacities – have been employed as sorption substrates in solid-phase extraction for the preconcentration of metal species from diverse matrices. Looking for successive improvements in sensitivity and selectivity, in the past few years, carbon nanotubes have been utilized as sorbents for solid phase extraction in three different ways: like as-grown, oxidized and functionalized nanotubes. In the present paper, an overview of the recent trends in the use of carbon nanotubes for solid phase extraction of metal species in environmental, biological and food samples is presented. The determination procedures involved the adsorption of metals on the nanotube surface, their quantitative desorption and subsequent measurement by means of atomic spectrometric techniques such as flame atomic absorption spectrometry, electrothermal atomic absorption spectrometry or inductively coupled plasma atomic emission spectrometry/mass spectrometry, among others. Synthesis, purification and types of carbon nanotubes, as well as the diverse chemical and physical strategies for their functionalization are described. Based on 140 references, the performance and general properties of the applications of solid phase extraction based on carbon nanotubes for metal species atomic spectrometric determination are discussed.     

Ultrasound-assisted matrix solid-phase dispersive liquid extraction for the determination of intermediates in hair dyes with ion chromatography

A novel one-step sample preparation technique called ultrasound-assisted matrix solid-phase dispersive liquid extraction was developed. After sample matrices being dispersed, target analytes were extracted into acid solutions and fat and lipin were dissolved in n-hexane while the interfering components were retained by dispersing sorbent. The extraction process could be rapidly accomplished within 9 min with high sample throughput under the synergistic effects of vibration, ultrasound action and heating. The extraction efficiency of approach was demonstrated for the determination of intermediates in commercial hair dyes with ion chromatography. Linearity ranges of 0.2–100 mg L⁻¹ and detection limits varying from 0.019 to 0.048 mg L⁻¹ were achieved. The recoveries ranged from 85.7 to 107.0% with the relative standard deviations (RSDs) of 0.31–3.7%. These results showed that the method was simple, time-saving, reliable and suitable for the routine analysis of intermediates in large numbers of hair dyes.     

Ionic liquid-based ultrasound-assisted dispersive liquid–liquid microextraction followed high-performance liquid chromatography for the determination of ultraviolet filters in environmental water samples

In the present study, a rapid, highly efficient and environmentally friendly sample preparation method named ionic liquid-based ultrasound-assisted dispersive liquid–liquid microextraction (IL-USA-DLLME), followed by high performance liquid chromatography (HPLC) has been developed for the extraction and preconcentration of four benzophenone-type ultraviolet (UV) filters (viz. benzophenone (BP), 2-hydroxy-4-methoxybenzophenone (BP-3), ethylhexyl salicylate (EHS) and homosalate (HMS)) from three different water matrices. The procedure was based on a ternary solvent system containing tiny droplets of ionic liquid (IL) in the sample solution formed by dissolving an appropriate amount of the IL extraction solvent 1-hexyl-3-methylimidazolium tris(pentafluoroethyl)trifluorophosphate ([HMIM][FAP]) in a small amount of water-miscible dispersive solvent (methanol). An ultrasound-assisted process was applied to accelerate the formation of the fine cloudy solution, which markedly increased the extraction efficiency and reduced the equilibrium time. Various parameters that affected the extraction efficiency (such as type and volume of extraction and dispersive solvents, ionic strength, pH and extraction time) were evaluated. Under optimal conditions, the proposed method provided good enrichment factors in the range of 354–464, and good repeatability of the extractions (RSDs below 6.3%, n = 5). The limits of detection were in the range of 0.2–5.0 ng mL⁻¹, depending on the analytes. The linearities were between 1 and 500 ng mL⁻¹ for BP, 5 and 500 ng mL⁻¹ for BP-3 and HMS and 10 and 500 ng mL⁻¹ for EHS. Finally, the proposed method was successfully applied to the determination of UV filters in river, swimming pool and tap water samples and acceptable relative recoveries over the range of 71.0–118.0% were obtained.     

Separation Transformation and New Exact Solutions of the (N+1)-dimensional Dispersive Double sine-Gordon Equation

In this paper,the separation transformation approach is extended to the(N + 1)-dimensional dispersive double sine-Gordon equation arising in many physical systems such as the spin dynamics in the B phase of 3 He superfluid.This equation is first reduced to a set of partial differential equations and a nonlinear ordinary differential equation.Then the general solutions of the set of partial differential equations are obtained and the nonlinear ordinary differential equation is solved by F-expansion method.Finally,many new exact solutions of the(N + 1)-dimensional dispersive double sine-Gordon equation are constructed explicitly via the separation transformation.For the case of N 2,there is an arbitrary function in the exact solutions,which may reveal more novel nonlinear structures in the high-dimensional dispersive double sine-Gordon equation.     

目标宽带电磁散射特性的自适应分析

本文采用有理逼近中的误差分析方法, 对渐近波形估计的计算结果进行了误差分析, 从而提出了一种有效计算带宽的估计方法, 并构造了一种任意给定频段自适应扫频计算方法. 通过对不同几何形态的三维导体目标、色散介质目标的宽带电磁散射特性进行分析, 并将计算结果与解析解、矩量法逐点计算进行了比较, 验证了此算法的有效性.     

Microscopical Investigations of PEDOT:PSS Thin Films

Electron microscopy studies are used to explore the morphology of thin poly(3,4‐ethylenedioxythiophene) and polystyrene sulfonate acid (PEDOT:PSS) films. The figures show that the films are composed of grains with diameters in the range of about 50 nm. Energy dispersive X‐ray spectroscopy analysis reveals that individual grains have a PEDOT‐rich core and a PSS‐rich shell with a thickness of about 5–10 nm. Atomic force microscopy (AFM) is then used to analyze the topography of fracture surfaces of ruptured PEDOT:PSS tensile specimens. These AFM scans also show that the films are composed of grains dispersed in a matrix. The investigations presented herein yield a picture of PEDOT:PSS morphology with unprecedented clarity.     

Higher Order Dissipative-Dispersive System and Application

In this paper, a generalized nonlinear dissipative and dispersive equation with time and space-dependent coefficients is considered. We show that the control of the higher order term is possible by using an adequate weight function to define the energy. The existence and uniqueness of solutions are obtained via a Picard iterative method. As an application to this general Theorem, we prove the well-posedness of the Camassa-Holm type equation.