Synthesis and characterization of sulfonated copolyethersulfones

The present article deals with the synthesis and characterization of some sulfonated copolyethersulfones. The synthetic approach differs from the post sulfonation approach traditionally reported in the literature. The synthetic procedure is based on the use of sulfonated monomers which are then reacted with previously synthesized telechelic hydoxy‐ended poly (ether sulpnone)s. Combining the MALDI‐TOF MS and ¹H NMR analyses, with SEC‐Viscometry and TGA measurements, we demonstrate a powerful tool for characterizing the chemical composition, end chains, degree of sulfonation (DS) and molecular mass distribution (MMD) of disulfonated poly(arylene ether‐sulfone) copolymers. The characterization techniques allowed to determine the exact nature of the copolymers synthesized and to reveal some interesting features about the reaction. DMA data show that the glass transition temperature of sulfonated copolymers with similar DS increase as raise their MMD. Copolymers with a DS of 10–11 mol % reach a T_g of 244–246 °C. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 3010–3023, 2010     

A boundary element method to price time-dependent double barrier options

In this paper we propose a new method for pricing double-barrier options with moving barriers under the Black-Scholes and the CEV models. First of all, by applying a variational technique typical of the boundary element method, we derive an integral representation of the double-barrier option price in which two of the integrand functions are not given explicitly but must be obtained solving a system of Volterra integral equations of the first kind. Second, we develop an ad hoc numerical method to regularize and solve the system of integral equations obtained. Several numerical experiments are carried out showing that the overall algorithm is extraordinarily fast and accurate, even if the barriers are not differentiable functions. Moreover the numerical method presented in this paper performs significantly better than the finite difference approach.     

Photochemical behavior of some substituted benzophenoxazinones

Irradiation of some substituted benzophenoxazinones in methanol solution by visible light yields dimerization and substitution products. A possible radical mechanism is proposed and validated by quantum mechanical computations.