Asymptotic expansions for eigenvalues in the presence of small inhomogeneities

We provide a rigorous derivation of an asymptotic formula for perturbations in the eigenvalues caused by the presence of a finite number of inhomogeneities of small diameter with conductivity different from the background conductivity. Copyright © 2003 John Wiley & Sons, Ltd.     

A representation of the Belavkin equation via Feynman path integrals

 The Belavkin equation, describing the continuous measurement of the position of a quantum particle, is studied. A rigorous representation of its solution by means of an infinite dimensional oscillatory integral (Feynman path integral) defined on the complex Cameron-Martin space is given. Received: 7 January 2002 / Revised version: 20 June 2002 / Published online: 19 December 2002 Mathematics Subject Classification (2000): 81, 81S40, 60H15 Key words or phrases: Belavkin equation – Continuous measurement – Quantum theory – Oscillatory integrals – Feynman path integrals     

Structure and properties of the mesophase of syndiotactic polystyrene. II. Effect of stepwise extraction on the preparation of the mesophase

In this study, a novel stepwise extraction method has been examined. The guest molecules housed between the helices of the clathrate δ form of syndiotactic polystyrene can be removed completely with this method. A systematic study of the preparation of a solvent‐free mesophase (emptied clathrate) membrane, its helical and residual solvent contents, and its structural transformations has been performed. In this first attempt, an enhancement in the TTGG helical content has been observed in the extracted membrane, and a conceptual mechanism is proposed. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 269–273, 2003     

On the equivalence of linear equations under nonlocal transformation

Linear nth order (n?3) ordinary differential equations have been shown to possess n+1, n+2 or n+4 Lie point symmetries. Each class contains equations which are equivalent under point transformation. By taking the example of third order equations, we show that all linear equations are equivalent if the class of transformation is broadened to include nonlocal transformations and hence the representative of this class of equations is y⁽ⁿ⁾=0.     

Anionic iron(II) alkoxides as initiators for the controlled ring‐opening polymerization of lactide

Hetero‐bimetallic Fe(II) alkoxide/aryloxides were evaluated as initiators for the ring‐opening polymerization of rac‐lactide. [(THF)NaFe(O^tBu)₃]₂ ( 1 ) and [(THF)₄Na₂Fe(2,6‐diisopropylphenolate)₄] ( 2 ) (THF = tetrahydrofuran) both polymerized lactide efficiently at room temperature, with complex 1 affording better control over the molecular weight parameters of the resultant polymer. At conversions below 70%, a linear increase in molecular weight with conversion was observed, indicative of a well‐controlled polymerization process. Complex 2 is the first example of a dianionic Fe(II) alkoxide and has been structurally characterized to reveal a distorted square planar FeO₄ array in which both Na counterions bridge two aryloxide ligands and are further complexed by two THF ligands. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3798–3803, 2003     

Numerical approximation of generalized Newtonian fluids using Powell–Sabin–Heindl elements: I. theoretical estimates

In this paper we consider the numerical approximation of steady and unsteady generalized Newtonian fluid flows using divergence free finite elements generated by the Powell–Sabin–Heindl elements. We derive a priori and a posteriori finite element error estimates and prove convergence of the method of successive approximations for the steady flow case. A priori error estimates of unsteady flows are also considered. These results provide a theoretical foundation and supporting numerical studies are to be provided in Part II. Copyright © 2003 John Wiley & Sons, Ltd.     

Förster energy transfer from poly(arylene–ethynylene)s to an erbium–porphyrin complex

We study the infrared emission at 1.54 μm of an organolanthanide complex, Er(III)-tetraphenylporphyrin [Er(TPP)acac], both as a result of direct optical excitation and via energy transfer from host π-conjugate polymers of type poly(arylene–ethynylene) [PAE]. In the first case, the emission of the neat complex is characterized in inert transparent materials and a value of the quantum yield at 1.54 μm φ_IR=4×10⁻⁴ is measured. Then, fluorescence resonance transfer is investigated in blends of Er(TPP)acac with PAEs by monitoring the quenching of the polymer fluorescence along with the enhancement of both the visible emission of the ligand and the near-infrared band of Er³⁺. These different procedures allow a detailed analysis of the transfer efficiency within a specific implementation of the Förster model for polymeric donors. The experimental values of the critical radius R₀, ranging from 1.3 to 2.5 nm for the different blends, are in good agreement with theory for a wide interval of the physical and spectroscopic parameters. This suggests that other mechanisms for excitation transfer do not play a significant role in these materials.     

Sulfobetaine‐containing diblock and triblock copolymers via reversible addition‐fragmentation chain transfer polymerization in aqueous media

A novel bifunctional acrylamido‐based reversible addition–fragmentation chain transfer (RAFT) chain‐transfer agent (CTA), N,N′‐ethylenebis[2‐(thiobenzoylthio)propionamide] (CTA2), has been synthesized and used for the controlled free‐radical polymerization of N,N‐dimethylacrylamide (DMA). A comparative study of CTA2 and the monofunctional CTA N,N‐dimethyl‐s‐thiobenzoylthiopropionamide (CTA1) has been conducted. Polymerizations mediated by CTA1 result in poly(N,N‐dimethylacrylamide) (PDMA) homopolymers with unimodal molecular weight distributions, whereas CTA2 yields unimodal, bimodal, and trimodal distributions according to the extent of conversion. The multimodal nature of the PDMAs has been attributed to termination events and/or chains initiated by primary radicals. The RAFT polymerization of DMA with CTA2 also results in a prolonged induction period that may be attributed to the higher local concentration of dithioester functionalities early in the polymerization. A series of ω‐ and α,ω‐dithioester‐capped PDMAs have been prepared in organic media and subsequently employed as macro‐CTAs for the synthesis of diblock and triblock copolymers in aqueous media with the zwitterionic monomer 3‐[2‐(N‐methylacrylamido)‐ethyldimethylammonio] propane sulfonate (MAEDAPS). Additionally, an ω‐dithioester‐capped MAEDAPS homopolymer has been used as a macro‐CTA for the block polymerization of DMA. To our knowledge, this is the first example of a near‐monodisperse, sulfobetaine‐containing block copolymer prepared entirely in aqueous media. The diblock and triblock copolymers form aggregates in pure water that can be dissociated by the addition of salt, as determined by ¹H NMR spectroscopy and dynamic light scattering. In pure water, highly uniform, micellelike aggregates with hydrodynamic diameters of 71–93 nm are formed. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1262–1281, 2003