Novel dialkyl vinyl ether phosphonate monomers: Their synthesis and alternated radical copolymerizations with electron‐accepting monomers

Three new vinyl ether monomers containing phosphonate moieties were synthesized from transetherification reaction. We showed that the yield was dependent on the spacer length between the vinyl oxy group and the phosphonate moieties: when the spacer is a single methylene side reaction may occur, leading to the formation of acetal compounds. Free‐radical copolymerizations of phosphonate‐containing vinyl ether monomers with maleic anhydride were carried out, leading to alternated copolymers of rather low molecular weights (from 1000 to 7000 g/mol). Both gel permeation chromatography and ³¹P NMR analyses enhanced possible intramolecular transfer reactions occurring from the phosphonate moieties. Kinetic investigation showed that the electron‐withdrawing character of the phosphonate moieties tends to decrease the rate of copolymerization. Nevertheless, almost complete monomers conversion was reached after 30 min of reaction with dimethyl vinyloxyethylphosphonate (VEC₂PMe). Then, radical copolymerization of VEC₂PMe with a series of electron‐accepting monomers, that is, dibutyl maleate, dibutylitaconate, itaconic anhydride, butyl maleimide, and methyl maleimide, led to a series of alternated copolymers. From kinetic investigation, we showed that the higher the electron‐accepting effect, the faster the vinyl ether consumption and the higher the molecular weights. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

罗尔定理应用中的辅助函数构造法

给出在利用罗尔定理证明等式时所需辅助函数的一种构造方法，并借助实例加以说明．     

The dependence of polymer conductivity on the work function of metallic electrodes

It is shown that the occurrence of metallic conductivity in polymers is due to their electrification. In particular, the current density depends on the electron work function of metallic electrodes which are in contact with the polymer.     

The convolution and multiplication of one‐dimensional associated homogeneous distributions

The set of associated homogeneous distributions (AHDs) with support in R is an important subset of the tempered distributions because it contains the majority of the (one‐dimensional) distributions typically encountered in physics applications (including the δ distribution). In a previous work of the author, a convolution and multiplication product for AHDs on R was defined and fully investigated. The aim of this paper is to give an easy introduction to these new distributional products. The constructed algebras are internal to Schwartz’ theory of distributions and, when one restricts to AHDs, provide a simple alternative for any of the larger generalized function algebras, currently used in non‐linear models. Our approach belongs to the same class as certain methods of renormalization, used in quantum field theory, and are known in the distributional literature as multi‐valued methods. Products of AHDs on R, based on this definition, are generally multi‐valued only at critical degrees of homogeneity. Unlike other definitions proposed in this class, the multi‐valuedness of our products is canonical in the sense that it involves at most one arbitrary constant. A selection of results of (one‐dimensional) distributional convolution and multiplication products are given, with some of them justifying certain distributional products used in quantum field theory. Copyright © 2012 John Wiley & Sons, Ltd.     

Doppler effects of an oscillating line source in shear flow with a free surface

The linearised water-wave radiation problem for the oscillating 2D submerged source in an inviscid shear flow with a free surface is investigated analytically. There is a nonzero surface velocity. The depth is infinite and the vorticity is uniform. The amplitudes radiated from the source are calculated analytically. Due to Doppler effects, there may be up to four different emitted waves, and there is resonance with zero group velocity and infinite amplitude.     

Multiplicative processes and power laws in human reaction times derived from hyperbolic functions

In sensory psychophysics reaction time is a measure of the stochastic latency elapsed from stimulus presentation until a sensory response occurs as soon as possible. A random multiplicative model of reaction time variability is investigated for generating the reaction time probability density functions. The model describes a generic class of hyperbolic functions by Piéron?s law. The results demonstrate that reaction time distributions are the combination of log-normal with power law density functions. A transition from log-normal to power law behavior is found and depends on the transfer of information in neurons. The conditions to obtain Zipf?s law are analyzed.     

Taylor Expansions of Distributions

Classical Taylor expansions of holomorphic functions in the complex plane are extended to distributions in Rⁿand in domains     

Generating functions for volume-preserving transformations

A general implicit solution for determining volume-preserving transformations in the n-dimensional Euclidean space is obtained in terms of a set of 2n generating functions in mixed coordinates. For n=2, the proposed representation corresponds to the classical definition of a potential stream function in a canonical transformation. For n=3, the given solution defines a more general class of isochoric transformations, when compared to existing methods based on multiple potentials. Illustrative examples are discussed both in rectangular and in cylindrical coordinates for applications in mechanical problems of incompressible continua. Solving exactly the incompressibility constraint, the proposed representation method is suitable for determining three-dimensional isochoric perturbations to be used in bifurcation theory. Applications in non-linear elasticity are envisaged for determining the occurrence of complex instability patterns for soft elastic materials.     

A stochastic model for microtubule length dynamics

In this paper, we use random walk theory to describe the length dynamics of microtubules, one of the principal components of the cytoskeleton. We present a simple two-state model (growing and shrinking) of microtubule length evolution that incorporates a variable rate of switching between the states. Using the generating function technique, we calculate the mean length of microtubule, its variance and diffusion coefficient. We also report analytical and computer simulation results for the mean number of positive monomers in microtubule, and find good qualitative agreement with experimental data.