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.     

Carbohydrate molecular recognition: a spectroscopic investigation of carbohydrate-aromatic interactions

The physical basis of carbohydrate molecular recognition at aromatic protein binding sites is explored by creating molecular complexes between a series of selected monosaccharides and toluene (as a truncated model for phenylalanine). They are formed at low temperatures under molecular beam conditions, and detected and characterized through mass-selected, infrared ion depletion spectroscopy-a strategy which exploits the extraordinary sensitivity of their vibrational signatures to the local hydrogen-bonded environment of their OH groups. The trial set of carbohydrates, alpha- and beta-anomers of glucose, galactose and fucose, reflects ligand fragments in naturally occurring protein-carbohydrate complexes and also allows an investigation of the effect of systematic structural changes, including the shape and extent of 'apolar' patches on the pyranose ring, removal of the OH on the exocyclic hydroxymethyl group, and removal of the aglycon. Bound complexes invariably form, establishing the general existence of intrinsic intermolecular potential minima. In most of the cases explored, comparison between recorded and computed vibrational spectra of the bound and free carbohydrates in the absence of solvent water molecules reveal that dispersion forces involving CH-pi interactions, which promote little if any distortion of the bound carbohydrate, predominate although complexes bound through specific OH-pi hydrogen-bonded interactions have also been identified. Since the complexes form at low temperatures in the absence of water, entropic contributions associated with the reorganization of surrounding water molecules, the essence of the proposed 'hydrophobic interaction', cannot contribute and other modes of binding drive the recognition of sugars by aromatic residues. Excitingly, some of the proposed structures mirror those found in naturally occurring protein-carbohydrate binding sites.     

Strong cooperative enhancement of two-photon absorption in double-strand conjugated porphyrin ladder arrays

We present the two-photon absorption (2PA) spectra of a series of conjugated porphyrin oligomers containing N = 2, 4, 8, and ca. 13 monomer units, meso-meso connected with butadiyne linkers. We demonstrate that, in the coplanar double-strand arrays, self-assembled upon addition of 4,4'-bipyridyl, the conjugation length increases dramatically, leading to very strong cooperative enhancement of 2PA. We analyze the scaling of 2PA in both the double-strand and rotationally free single-strand arrays and show how the effective conjugation length in both cases is linked to the observed 2PA properties. By introducing a "conjugation signature" for the 2PA strength, we show that, in double-strand arrangement, the conjugation embraces the whole molecule up to the tetramer level, whereas in single-strand arrangement, it is always less than N, except for N = 2, but keeps increasing until N = 8. Our finding of extremely strong 2PA cross section, sigma2 approximately 105 GM, in double-strand oligomers peaking at 1.3 mum can find use for signal processing in fiber-optic devices.     

Quantification of casein phosphorylation with conformational interpretation using Raman spectroscopy

Raman spectroscopy is emerging as a powerful method for obtaining both quantitative and qualitative information from biological samples. One very interesting area of research, for which the technique has rarely been used, is the detection, quantification and structural analysis of post-translational modifications (PTMs) on proteins. Since Raman spectra can be used to address both of these questions simultaneously, we have developed near infrared Raman spectroscopy with appropriate chemometric approaches (partial least squares regression) to quantify low concentration (4 microM) mixtures of phosphorylated and dephosphorylated bovine alpha(s)-casein. In addition, we have used these data in conjunction with Raman optical activity (ROA) spectra and NMR to assess the structural changes that occur upon phosphorylation.     

Amplified optical nonlinearity in a self-assembled double-strand conjugated porphyrin polymer ladder

Addition of 4,4'-bipyridyl to a solution of a meso-meso butadiyne-linked conjugated zinc porphyrin polymer in chloroform results in self-assembly of a double-strand ladder complex. Excess ligand causes this duplex to dissociate into single strands. These binding processes were elucidated by near-IR and NMR titrations, as well as by gel permeation chromatography and small-angle neutron scattering. Ladder-making and -breaking are highly cooperative, with Hill coefficients of 3.0 and 3.7, respectively. Self-assembly of the ladder holds the pi-system in a planar conformation, enhancing the conjugation, resulting in a red-shift and intensification of the Q-band. Both the real and imaginary parts of the third-order susceptibility per macrocycle are amplified by ladder formation, as revealed by degenerate four-wave mixing measurements at 1064 nm. At this wavelength, the double-strand polymer complex has |chi(3)xyyx| = 6.0 x 10-17 m2 V-2 per macrocycle, compared with 6.6 x 10-18 m2 V-2 for the single-strand polymer under the same conditions.