Cationic polymerization with boron halides. V. Synthesis of poly(isobutylene-b-styrene) and poly(styrene-b-isobutylene)

Block copolymers of isobutylene and styrene, PIB-b-PSt and PSt-b-PIB, have been prepared by a two-step synthesis involving (1) preparation of terminally chlorinated (telechelic) polyisobutylene or polystyrene “prepolymers” by using the H₂O/BCl₃ initiator system and (2) blocking from these telechelic prepolymers a second polymer segment by using an alkyaluminum, e.g., Et₂AlCl coinitiator. The telechelic polyisobutylene and polystyrene contain tertiary and benzylic chlorine termini, respectively. Block copolymer characterization included detailed selective solvent extraction procedures, coupled with GPC determinations, PMR, solubility, and intrinsic viscosity studies. The synthesis of PIB-b-PSt and PSt-b-PIB provides direct chemical evidence for the presence and position of active chlorine termini in BCl₃-coinitiated olefin polymerizations.     

Harnack Inequalities for Functional SDEs Driven by Subordinate Brownian Motions

Potential Analysis - Using coupling by change of measure and an approximation technique, Wang’s Harnack inequalities are established for a class of functional SDEs driven by subordinate...     

A theory of tensor products for module categories for a vertex operator algebra,I

This is the first part in a series of papers developing a tensor product theory for modules for a vertex operator algebra. The goal of this theory is to construct a vertex tensor category structure on the category of modules for a suitable vertex operator algebra. The notion of vertex tensor category is essentially a complex analogue of the notion of symmetric tensor category, and in fact a vertex tensor category produces a braided tensor category in a natural way. The theory applies in particular to many familiar rational vertex operator algebras, including those associated with WZNW models, minimal models and the moonshine module. In this paper (Part I), we introduce the notions ofP(z)- andQ(z)-tensor product, whereP(z) andQ(z) are two special elements of the moduli space of spheres with punctures and local coordinates, and we present the fundamental properties and constructions ofQ(z)-tensor products.     

The effects of media properties on the horseradish peroxidase-catalyzed fluorogenic reaction

The effects of media properties including buffers, acidity, solvents and surfactant on horseradish peroxidase-catalyzed fluorogenic reaction were investigated. The results showed that the so-called non-fluorescent hydrogen donors were in fact fluorescent. There existed an acid—base equilibrium in the fluorescent dimer product. For p -hydroxyphenylpropionic acid, a pK_a value of 8.0 for the product was obtained from its titration curve. The product fluorescence increased with higher pH, however, a longer time was needed to reach the reaction equilibrium due to the pH mismatch problem. Cationic micelles cetyltrimethylammonium bromide and cetyltrimethylammonium chloride could reduce the pH mismatch and offered a way to further increase the determination sensitivity. Finally, a micelle-enhanced flow-injection analysis of horseradish peroxidase is suggested.     

Exact solution of a vertex model ind dimensions

We consider a class of vertex models describing directed lines on a lattice in arbitraryd dimensions, and solve the model exactly for the Cartesian lattice and in the case that each loop of lines carries a fugacity - 1. Our analysis, which can be carried out for arbitrary lattices, is based on an equivalence of the vertex model with a dimer problem. The dimer problem is, in turn, solved using the method of Pfaffians. It is found that the system is frozen below a critical temperatureT _cwith the critical exponent = (3 –d)/2.