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.     

Synthesis of macrocyclic polystyrene-polydimethylsiloxane block copolymers

A series of macrocyclic polystyrene (PS)-polydimethylsiloxane (PDMS) block copolymers and similar block copolymers was synthesized by sequential polymerization of styrene and hexamethyl cyclotrisiloxane (D₃) initiated by a difunctional anionic initiator in THF at −78° followed by coupling with Cl₂SiMe₂ in very dilute (10⁻⁵ – 10⁻⁶ M) solutions. Total molecular weights ranged from about 2–85 × 10³. The formation of monodisperse macrocyclic block copolymers was indicated by the lower (15–30%) hydrodynamic volume of the rings compared to that of the linear block copolymers. Carbon-13 and ²⁹Si NMR likewise supported the absence of linear polymer in the macrocyclic block copolymer. The behavior of second virial coefficient A₂ of the rings and the linears versus temperature was examined by static light scattering in cyclohexane. Below 20° the A₂ for the linear polymer goes negative while that for the cycle remains positive. Dynamic light scattering (DLS) as a function of temperature also reflects that the cyclic polymers remain well solvated even down to 12°C. The DLS autocorrelation functions for the linear triblock however demonstrate the onset of aggregation and phase separation as the temperature is reduced below 20°C.     

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.     

Phosphorescence quenching by conjugated polymers

Energy transfer between phosphors and conjugated polymers was investigated using a fluorene trimer (F3) as a model conjugated material. The phosphors studied were bis-cyclometalated iridium complexes (FP, PPY, BT, PQ, and BTP), with triplet energies of 2.6, 2.4, 2.2, 2.1, and 2.0 eV, respectively (based on phosphorescence spectra). Stern-Volmer analysis of luminescent quenching shows that energy transfer from either FP or PPY to F3 is an exothermic process with Stern-Volmer quenching constants (kqSV) of near 109 M-1 s-1 while energy transfer from BT, PQ, and BTP is endothermic (kqSV = 107-106 M-1 s-1). On the the basis of above results, the triplet energy of F3 is estimated to be less than 2.3 eV (530 nm). This study suggests that conjugated polymers, which typically have lower T1 energies than F3, should also quench phosphorescent emission in thin films and organic light-emitting diodes (OLEDs) incorporating these and related phosphorescent dopants.     

Oligomerization of vinyl monomers. XXI. Characterization of model carbanions of living poly(2-vinylpyridine) in THF by 7Li-NMR and conductance: Evidence for the occurrence and nature of triple ion formation

The formation of triple anions is demonstrated by ⁷Li-NMR in THF solutions of 1-lithio-1-(2-pyridyl)ethane, 1-lithio-1(3-methyl-2-pyridyl)ethane, and 1-lithio-1,3-di(2-pyridyl) butane. Good agreement with conductance data was demonstrated in the case of 1 . Triple anion formation in the case of 2 was found to be about twice as high as in 1 possibly as a result of the greater charge density on the carbanion in the case of 2 .     

Excimer formation of fluoradene. Evidence for aggregation in alcohols

The absorption of fluorescence spectra of fluoradene in several solvents have been measured. In addition to the expected fluorescence band, a broad structureless band at 440 nm is observed in hexane which increases in intensity with increasing fluoradene concentration. In alcoholic solutions and in polycrystalline solid, only the broad, red-shifted band is observed. This broad band is attributed to excimer emission. It is shown that in alcoholic solutions that rate of excimer formation via diffusion is unacceptably large and it is suggested that fluoradene is aggregated in these solvents.