Quinone transfer radical polymerization (QTRP) of styrene: Catalysis by different metal complexes

Styrene has been polymerized by a Quinone Transfer Radical Polymerization (QTRP) based on the redox reaction of an ortho‐quinone and a metal catalyst. Several metal acetylacetonates have been tested in this work. The radical polymerization of styrene is largely controlled when phenanthrenequinone (PhQ) is used with catalytic amounts of Co(acac)₂, Ni(acac)₂, Mn(acac)_{2 or 3}, and Al(acac)₃. As a rule, in the presence of all these metallic complexes, the polystyrene molar mass increases with the monomer conversion, and polydispersity (M_w/M_n) is in the 1.3–1.6 range (at least until 40% monomer conversion). Styrene polymerization has also been resumed by polystyrene chains prepared by QTRP. In the specific case of manganese acetylacetonates, an amine or phosphine ligand has to be added for the control to be effective. Finally, two mechanistic hypotheses have been proposed, depending on whether the oxidation state of the metal can be easily changed or not. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 2723‐2733, 2005     

Classical Yang-Mills-Dirac equations: Qualitative analysis of some solutions with a noncompact symmetry group

We consider classical Yang-Mills and Yang-Mills-Dirac equations on Minkowski space, with gauge group SU(2), and look for solutions invariant (up to a gauge transformation) under SO(3)×SO₀(1, 1) and SO₀(2, 1)×SO(2), respectively. In each case, we analyze the qualitative features of the solutions, in particular the asymptotic behavior as the solution approaches its singularities. The method is based on standard theorems from the theory of nonlinear ordinary differential equations.     

Preliminary Communications Thermotropic liquid crystal behaviour of 5,5'-[(4-hexadecyloxyphenyl)ethynyl]-2,2'-bipyridine

5,5'-[(4-Hexadecyloxyphenyl)ethynyl]-2,2'-bipyridine was synthesized by a palladium(O) cross-coupling reaction. Its thermotropic liquid crystalline behaviour was analysed using differential scanning calorimetry, polarizing microscopy, and X-ray diffraction. Three enantiotropic tilted smectic phases were identified upon heating: S_F, S_I, and S_C.     

Use of the Domain Derivative to Prove Symmetry Results in Partial Differential Equations

In this paper we present a different method for proving symmetry results in partial differential equations. The principal idea is to use the classical tool of shape optimization, namely, the differentiation with respect to the domain. The aim is to derive, from an optimality condition, information on the boundary of the domain.     

A construction of commutative nilsemigroups

All commutative nilsemigroups are constructed from congruences on free commutative semigroups.     

Nonlinear vibrations of loudspeaker-like structures

During high amplitudes of vibration, nonlinearities affect the electroacoustical behavior of electrodynamic transducers and are responsible for audible distortions. We distinguish two types of nonlinearities: electrical and mechanical. In this study, attention is paid to the mechanical and geometrical properties of loudspeaker-like structures. The loudspeaker is viewed as a combination of an annular plate with a circular plate. Nonlinear vibrations of such a structure are investigated, using the dynamic analog of the Von-Kármán equations. Furthermore, the influence of both material properties and geometrical parameters is studied. It is shown that nonlinear effects can be substantially reduced by choosing appropriate material and geometrical parameters.     

Sparse geometric graphs with small dilation

Given a set S of n points in , and an integer k such that 0k<n, we show that a geometric graph with vertex set S, at most n−1+k edges, maximum degree five, and dilation O(n/(k+1)) can be computed in time O(nlogn). For any k, we also construct planar n-point sets for which any geometric graph with n−1+k edges has dilation Ω(n/(k+1)); a slightly weaker statement holds if the points of S are required to be in convex position.     

Partial inner product spaces. II. Operators

We study linear operators between nondegenerate partial inner product spaces and their relationships to selfadjoint operators in a “middle” Hilbert space.