Synthesis and properties of new poly(ether sulfone)amides

High molecular-weight aromatic polyamides were obtained from 1,5- and 2,6-bis-(4′-carboxy-4-phenylenoxy-sulfonyl)naphthalene by direct polycondensation reaction in N-methyl-2-pyrrolidone with various aromatic diamines, using triphenyl phosphite and pyridine as condensing agents. The polymers were characterized by elemental analysis, thermogravimetric analysis, differential scanning calorimetry, and infrared analysis. The polyamides, obtained in quantitative yield, possessed inherent viscosities in the range 0.42–1.70 dL/g, glass transition temperatures between 245–310°C, and 10% weight loss temperatures in nitrogen and air above 435 and 424°C, respectively. Most of the polymers were soluble in aprotic solvents. The effect of the structure on properties, such as solubility, T_g, and thermal behavior, were also studied. © 1996 John Wiley & Sons, Inc.     

Effect of ethanol on micellization and on decarboxylation of 6-nitrobenzisoxazole-3-carboxylate in aqueous cationic micelles

The effects of ethanol on the critical micellar concentration (cmc) and the rates of decarboxylation of 6-nitrobenzisoxazole-3-carboxylate (6-NBIC) have been investigated in aqueous cationic surfactants of the cetyltrialkylammonium family with bromide [CT(R)ABr], chloride [CT(R)ACl], and nitrate [CT(R)ANO3] counterions, and methyl (CTAX), n-propyl (CTPAX), and n-butyl (CTBAX) as the head group alkyl moieties. Effects upon cmc and reactivity are similar, featuring a break at the ethanol mole fraction, x(EtOH), of ca. 0.055; these effects have been related to changes in solvent structure, with formation of a clathrate at x(EtOH) = 0.055. Rate data in CTBABr were further investigated and fitting of raw kinetic data to the pseudophase model is possible up to x(EtOH) = 0.1, showing an unexpected decrease of rate constant values in the micellar pseudophase, kM', as ethanol content increases: a significant variation of micellar ionization degree could account for this kinetic effect.     

A partial differential equation connected to option pricing with stochastic volatility: Regularity results and discretization

This paper completes a previous work on a Black and Scholes equation with stochastic volatility. This is a degenerate parabolic equation, which gives the price of a European option as a function of the time, of the price of the underlying asset, and of the volatility, when the volatility is a function of a mean reverting Orstein-Uhlenbeck process, possibly correlated with the underlying asset. The analysis involves weighted Sobolev spaces. We give a characterization of the domain of the operator, which permits us to use results from the theory of semigroups. We then study a related model elliptic problem and propose a finite element method with a regular mesh with respect to the intrinsic metric associated with the degenerate operator. For the error estimate, we need to prove an approximation result.

     

Lignin Chemistry: Biosynthetic Study and Structural Characterisation of Coniferyl Alcohol Oligomers Formed In Vitro in a Micellar Environment

Model coniferyl alcohol lignin (the so‐called dehydrogenative polymerisate, DHP) was produced in water under homogeneous conditions guaranteed by the presence of a micellised cationic surfactant. A complete study of the activity of the enzymatic system peroxidase/H₂O₂ under our reaction conditions was reported and all the reaction products up to the pentamer were characterised by ¹H NMR spectroscopy and ESI mass spectrometry. Our system, and the molecules that have been generated in it, represent a closer mimicry of the natural microenvironment since an enzyme, under micellar conditions, reproduces the cell system better than in buffer alone. On the basis of the oligomers structures a new biosynthetic perspective was proposed that focused attention on a coniferyl alcohol dimeric quinone methide as the key intermediate of the reaction. A formal, strictly alternate sequence of a radical and an ionic step underlines the reaction, thus generating ordered oligolignols structures. Alternatively to other model lignins, our olignols present a lower degree of radical coupling between oligomeric units. This offers a closer biosynthetic situation to the observation of a low rate of radical generation in the cell wall.     

Comparison of Different Definitions of Traces for a Class of Ramified Domains with Self-Similar Fractal Boundaries

We consider a class of ramified bidimensional domains Ω with a self-similar fractal boundary Γ^?∞?, which is supplied with a probability measure μ called the self-similar measure. Emphasis is put on the case when the domain is not a ε???δ domain as defined by Jones and the fractal set is not totally disconnected. We compare two notions of trace on Γ^?∞? for functions in W ^1,q (Ω): the classical one, see for instance the book by Jonnson and Wallin, 1984, using the strict definition of a function at a point of $\overline{\Omega}$ , and another one proposed in 2007 and heavily relying on self-similarity. We prove that the two traces coincide μ-almost everywhere on Γ^?∞?. As a corollary, we characterize the critical number $\bar q$ for which for all $q<\bar q$ (resp. $q > \bar q$ ) there is a (resp. no) continuous extension operator from W ^1,q (Ω) to W ^1,q (?²).