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.     

Docking validation resources: protein family and ligand flexibility experiments

A database consisting of 780 ligand-receptor complexes, termed SB2010, has been derived from the Protein Databank to evaluate the accuracy of docking protocols for regenerating bound ligand conformations. The goal is to provide easily accessible community resources for development of improved procedures to aid virtual screening for ligands with a wide range of flexibilities. Three core experiments using the program DOCK, which employ rigid (RGD), fixed anchor (FAD), and flexible (FLX) protocols, were used to gauge performance by several different metrics: (1) global results, (2) ligand flexibility, (3) protein family, and (4) cross-docking. Global spectrum plots of successes and failures vs rmsd reveal well-defined inflection regions, which suggest the commonly used 2 ? criteria is a reasonable choice for defining success. Across all 780 systems, success tracks with the relative difficulty of the calculations: RGD (82.3%) > FAD (78.1%) > FLX (63.8%). In general, failures due to scoring strongly outweigh those due to sampling. Subsets of SB2010 grouped by ligand flexibility (7-or-less, 8-to-15, and 15-plus rotatable bonds) reveal that success degrades linearly for FAD and FLX protocols, in contrast to RGD, which remains constant. Despite the challenges associated with FLX anchor orientation and on-the-fly flexible growth, success rates for the 7-or-less (74.5%) and, in particular, the 8-to-15 (55.2%) subset are encouraging. Poorer results for the very flexible 15-plus set (39.3%) indicate substantial room for improvement. Family-based success appears largely independent of ligand flexibility, suggesting a strong dependence on the binding site environment. For example, zinc-containing proteins are generally problematic, despite moderately flexible ligands. Finally, representative cross-docking examples, for carbonic anhydrase, thermolysin, and neuraminidase families, show the utility of family-based analysis for rapid identification of particularly good or bad docking trends, and the type of failures involved (scoring/sampling), which will likely be of interest to researchers making specific receptor choices for virtual screening. SB2010 is available for download at http://rizzolab.org .     

Evaluation of DOCK 6 as a pose generation and database enrichment tool

In conjunction with the recent American Chemical Society symposium titled "Docking and Scoring: A Review of Docking Programs" the performance of the DOCK6 program was evaluated through (1) pose reproduction and (2) database enrichment calculations on a common set of organizer-specified systems and datasets (ASTEX, DUD, WOMBAT). Representative baseline grid score results averaged over five docking runs yield a relatively high pose identification success rate of 72.5?% (symmetry corrected rmsd) and sampling rate of 91.9?% for the multi site ASTEX set (N?=?147) using organizer-supplied structures. Numerous additional docking experiments showed that ligand starting conditions, symmetry, multiple binding sites, clustering, and receptor preparation protocols all affect success. Encouragingly, in some cases, use of more sophisticated scoring and sampling methods yielded results which were comparable (Amber score ligand movable protocol) or exceeded (LMOD score) analogous baseline grid-score results. The analysis highlights the potential benefit and challenges associated with including receptor flexibility and indicates that different scoring functions have system dependent strengths and weaknesses. Enrichment studies with the DUD database prepared using the SB2010 preparation protocol and native ligand pairings yielded individual area under the curve (AUC) values derived from receiver operating characteristic curve analysis ranging from 0.29 (bad enrichment) to 0.96 (good enrichment) with an average value of 0.60 (27/38 have AUC?≥?0.5). Strong early enrichment was also observed in the critically important 1.0-2.0?% region. Somewhat surprisingly, an alternative receptor preparation protocol yielded comparable results. As expected, semi-random pairings yielded poorer enrichments, in particular, for unrelated receptors. Overall, the breadth and number of experiments performed provide a useful snapshot of current capabilities of DOCK6 as well as starting points to guide future development efforts to further improve sampling and scoring.     

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.