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.     

Reduced word manipulation: patterns and enumeration

We develop the technique of reduced word manipulation to give a range of results concerning reduced words and permutations more generally. We prove a broad connection between pattern containment and reduced words, which specializes to our previous work for vexillary permutations. We also analyze general tilings of Elnitsky’s polygon and demonstrate that these are closely related to the patterns in a permutation. Building on previous work for commutation classes, we show that reduced word enumeration is monotonically increasing with respect to pattern containment. Finally, we give several applications of this work. We show that a permutation and a pattern have equally many reduced words if and only if they have the same length (equivalently, the same number of 21-patterns) and that they have equally many commutation classes if and only if they have the same number of 321-patterns. We also apply our techniques to enumeration problems of pattern avoidance and give a bijection between 132-avoiding permutations of a given length and partitions of that same size, as well as refinements of these data and a connection to the Catalan numbers.     

Spotlight Tiling

This article introduces spotlight tiling, a type of covering which is similar to tiling. The distinguishing aspects of spotlight tiling are that the “tiles” have elastic size, and that the order of placement is significant. Spotlight tilings are decompositions, or coverings, and can be considered dynamic as compared to typical static tiling methods. A thorough examination of spotlight tilings of rectangles is presented, including the distribution of such tilings according to size, and how the directions of the spotlights themselves are distributed. The spotlight tilings of several other regions are studied, and suggest that further analysis of spotlight tilings will continue to yield elegant results and enumerations.     

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。     

Bose-Einstein correlations in neutrino and antineutrino interactions in deuterium

Bose-Einstein correlations between pions of equal charge have been observed in Charged Current and Neutral Current (anti)neutrino-deuterium interactions in the BEBC bubble chamber exposed to the SPS wide band beam. The pion emission region is found to be essentially spherical with a mean radius of (0.48±0.07) fm; the chaoticity parameter is 0.36±0.04.     

Untersuchung von Fette

Ohne Zusammenfassung     

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.