Collocation Methods for Weakly Singular Second-kind Volterra Integral Equations with Non-smooth Solution

Collocation type methods are studied for the numerical solutionof the weakly singular Volterra integral equation of the secondkind: where the solution (t) is assumedto have the form f(t) = x(t)+r^?(t), x and being sufficientlysmooth. The solution is approximated near zero by a linear combinationof powers of t?, and away from zero by the usual polynomialrepresentation. Convergence is proved and many numerical experimentsare carried out with examples from the literature. A comparisonis made with a method of Brunner & Norsett (1981), originallydeveloped for (1) with a smooth solution. Special attentionis paid to the numerical approximation of the so-called momentintegrals which emerge in the collocation scheme.     

无机酸洗脱对胜利褐煤微晶结构及其自燃倾向性的影响

利用XRD、Raman、XPS和FT-IR表征技术,研究无机酸洗脱(HCl、H2SO4、HCl-HF)处理的胜利褐煤微晶结构的变化,采用自行设计的表面吸附仪-GC联用装置,对样品进行不同温度的低温脉冲氧化实验,考察了煤样在不同温度下氧吸附量的变化规律,通过低温脉冲氧吸附规律与TG/DTG和固定床燃烧实验关联,考察了煤样的自燃倾向。结果表明,无机酸洗脱对矿物质的脱除使得煤结构的有序度增加,石墨化程度提高,无机酸洗脱煤样与原煤相比吸氧量明显下降。随着吸附温度的升高,各煤样吸氧量明显增加,且随着脱除矿物质程度的增加,吸氧量呈减小的趋势,导致自燃倾向降低。     

An approximate treatment of scattering based on the delta boundary operator

The development of a scheme to treat two-dimensional electromagneticscattering by electrically large, perfectly conducting bodiesis described. It incorporates the effects of surface curvatureand non-local phenomena and has the potential to provide thebasis for a general technique yielding more accurate predictionsthan the widely used physical optics method.     

Fabrication of ordered catalytically active nanoparticles derived from block copolymer micelle templates for controllable synthesis of single-walled carbon nanotubes

We report the use of the block copolymer micelle approach to produce various transition metal nanoparticles such as iron, cobalt, and nickel with precisely controlled size and spacing. These uniformly sized catalyst nanoparticles derived from the block copolymer micelle approach have enabled the synthesis of carbon nanotubes (CNTs) with narrow size distribution. Because of the excellent film forming ability of the polymeric material, metal-bearing surface micelles produced from the solution micelles can be distributed uniformly on a surface, resulting in evenly dispersed catalyst nanoparticles. As a result, high quality and uniformly distributed CNTs have been synthesized. Spatially selective growth of CNTs from a lithographically patterned metal-bearing micelle film has been achieved. The polymer template approach can potentially be extended to synthesize single-metallic and bimetallic catalytically active nanoparticles with uniform size and spacing and is fully compatible with conventional lithographic process. Additionally, catalyst nanoparticles produced from this method do not coalesce at high growth temperature. All these attributes make this approach a promising fabrication pathway for controllable synthesis of CNTs.     

Generating suspended single-walled carbon nanotubes across a large surface area via patterning self-assembled catalyst-containing block copolymer thin films

Using self-assembled block copolymers as templates, catalytically active nanostructures with controlled size and space have been produced. A self-assembled polystyrene-b-polyferrocenylsilane thin film and monolayer of surface micelles of cobalt-complexed polystyrene-b-poly(2-vinylpyridine) are fully compatible with novolac-based conventional photoresists. Combining bottom-up self-assembly of catalyst-containing block copolymers with top-down microfabrication processing, plateaus covered with arrays of catalytically active nanostructures have been generated. Spatially selective growth of suspended single-walled carbon nanotubes over a large surface area has been achieved. Greatly enhanced Raman signals have been detected from the suspended tubes. This facile method of creating highly ordered catalyst nanostructures on top of posts enables the rational synthesis of suspended carbon nanotubes, thus facilitating the study of CNT properties by optical methods and enabling the fabrication of devices based on suspended CNTs.     

The electron energy loss spectrum of LiF in the band gap region

The eels of LiF has been measured in the range 0–18 eV with primary beam energies 50 eV and 1.5 keV. Four peaks are clearly resolved in the band gap region at room temperature. The amplitude of the three lower energy loss peaks was found to depend on beam exposure and temperature. It is concluded that the lowest energy peak arises at a beam induced defect, that the next two peaks arise in lithium metal liberated by the electron beam and that the peak nearest to the band edge is due to an intrinsic surface excitation.