Symmetries and conservation laws of Navier-Stokes equations

All the symmetries and conservation laws of Navier-Stokes equations are calculated.     

Fluorinated,crosslinkable terpolymers based on vinylidene fluoride and bearing sulfonic acid side groups for fuel‐cell membranes

The radical terpolymerization of 8‐bromo‐1H,1H,2H‐perfluorooct‐1‐ene with vinylidene fluoride (VDF) and perfluoro(4‐methyl‐3,6‐dioxaoct‐7‐ene) sulfonyl fluoride is presented. Changing the feed compositions of these three fluorinated comonomers enabled us to obtain different random‐type poly[vinylidene fluoride‐ter‐perfluoro(4‐methyl‐3,6‐dioxaoct‐7‐ene) sulfonyl fluoride‐ter‐8‐bromo‐1H,1H,2H‐perfluorooct‐1‐ene] terpolymers containing various sulfonyl fluoride and brominated side groups. Yields higher than 70% were reached in all cases. The hydrolysis of the sulfonyl fluoride group into the ? SO₃Li function in the presence of lithium carbonate was quantitatively achieved without the content of VDF being affected, and so dehydrofluorination of the VDF base unit was avoided. These original terpolymers were then crosslinked via dangling bromine atoms in the presence of a peroxide/triallyl isocyanurate system, which produced films insoluble in organic solvents such as acetone and dimethylformamide (which totally dissolved uncured terpolymers). The acidification of ? SO₃Li into the ? SO₃H function enabled protonic membranes to be obtained. The thermal stabilities of the crosslinked materials were higher than those of the uncured terpolymers, and their electrochemical performances were investigated. According to the contents of the sulfonic acid side functions, the ion‐exchange capacities ranged from 0.6 to 1.5 mequiv of H⁺/g, whereas the water uptake and conductivities ranged from 5–26% (±11%) and from 0.5 to 6.0 mS/cm, respectively. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4566–4578, 2006     

Synthesis of poly(p‐phenylene sulfide) from bis(4‐bromophenyl) disulfide

Improved reaction conditions for the preparation of poly(p‐phenylene sulfide) (PPS) directly from bis(4‐bromophenyl) disulfide (BBD) have been established. Heating BBD with magnesium metal afforded only a low molecular weight polymer. PPS with a melting temperature around 280 °C was obtained from BBD in the presence of sodium carbonate or zinc metal. The best results were obtained with the addition of a catalytic amount of KI to the zinc–BBD mixture. Polymers prepared by the above methods are semicrystalline and dissolve in 1‐chloronaphthalene and have properties comparable to commercial PPS. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 900–904, 2006     

Synthesis of poly(ethylene oxide) with pending 2,2,6,6‐tetramethylpiperidine‐1‐oxyl groups and its further initiation of the grafting polymerization of styrene

A new stratagem for the synthesis of amphiphilic graft copolymers of hydrophilic poly(ethylene oxide) as the main chain and hydrophobic polystyrene as the side chains is suggested. A poly(ethylene oxide) with pending 2,2,6,6‐tetramethylpiperidine‐1‐oxyls [poly(4‐glycidyloxy‐2,2,6,6‐tetramethylpiperidine‐1‐oxyl‐co‐ethylene oxide)] was first prepared by the anionic ring‐opening copolymerization of ethylene oxide and 4‐glycidyloxy‐2,2,6,6‐tetramethylpiperidine‐1‐oxyl, and then the graft copolymerization of styrene was completed with benzoyl peroxide as the initiator in the presence of poly(4‐glycidyloxy‐2,2,6,6‐tetramethylpiperidine‐1‐oxyl‐co‐ethylene oxide). The polymerization of styrene was under control, and comblike, amphiphilic poly(ethylene oxide)‐g‐polystyrene was obtained. The copolymer and its intermediates were characterized with size exclusion chromatography, ¹H NMR, and electron spin resonance in detail. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3836–3842, 2006     

Bounds on the inverses of nonnegative triangular matrices with monotonicity properties

Some bounds on the entries and on the norm of the inverse of triangular matrices with nonnegative and monotone entries are found. All the results are obtained by exploiting the properties of the fundamental matrix of the recurrence relation which generates the sequence of the entries of the inverse matrix. One of the results generalizes a theorem contained in a recent article of one of the authors about Toeplitz matrices.     

Comparative kinetics of phospholipase A2 action on liposomes and monolayers of phosphatidylcholine spread at the air-water interface

A detailed kinetic model describing the surface transformation of spread liposomes along with their enzymatic hydrolysis was developed. The model was applied to the hydrolysis of the long-chain phosphatidylcholine generating reaction products which remain at the interface and to medium-chain substrates from which the products desorb rapidly into the bulk phase. The overall kinetic constants of the hydrolysis in liposomal systems were compared with those obtained with monolayers under barostatic conditions. The values of the interfacial Michaelis-Menten constant were estimated.     

On the geometries of the rational unfoldings of X k

With a view to applications to self-regulating dynamical processes in biology, we determine the geometric structure of what we call isotangent curves, i.e. curves parametrized by the slopes of their points. They come up naturally as bifurcation curves of rational unfoldings of X ^k, and we classify them according to degree and number of cusps. They, as well as their isotangent involute curves, turn up in simulations of these processes.     

Pair formation in age-structured populations

The modelling problems associated with pair formation in age-structured populations are discussed in this paper. The author also formulates a class of models for pair formation in human populations and derives some results on persistent distributions.