Quark masses from regularized integrals of vector current spectral functions

We give estimates of quark masses from a comparison of two methods of regularizing the coefficient of the Schwinger term. The masses of the first radial excited states of ?, ω, and ? would have to be slightly higher than indicated by the new Orsay data for this method to yield real solutions for the masses of theu, d, ands quarks.     

Functionalized poly(oxanorbornene)‐block‐copolymers: Preparation via ROMP/click‐methodology

Block copolymers on basis of poly(oxanorbornenes) bearing functional moieties in their side‐chains are prepared via a combination of ROMP‐methods and 1,3‐dipolar‐“click”‐reactions. Starting from N‐substituted‐ω‐bromoalkyl‐oxanorbornenes and alkyl‐/perfluoroalkyl‐oxanorbornenes, block copolymers with molecular weights up to 25,000 g mol^?1 were generated. Subsequent nucleophilic exchange‐reactions yielded the block‐copolymers functionalized with ω‐azidoalkyl‐moieties in one block. The 1,3‐azide/alkine‐“click” reactions with a variety of terminal alkynes in the presence of a catalyst system consisting of tetrakis(acetonitrile)hexafluorophosphate copper(I) and tris(1‐benzyl‐5‐methyl‐1H‐ [1,2,3]triazol‐4‐ylmethyl)‐amine furnished the substituted block copolymers in high yields, as proven by NMR‐spectroscopy. The resulting polymers were investigated via temperature‐dependent SAXS‐methods, revealing their microphase separated structure as well as their temperature‐dependent behavior. The presented method offers the generation of a large set of different block‐copolymers from only a small set of starting materials because of the high versatility of the “click” reaction, thus enabling a simple and complete functionalization after the initial polymerization reaction. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 485–499, 2007     

Luminescent copolymers for applications in multicolor‐light‐emitting devices

Light‐emitting diodes based on organic materials [organic light‐emitting diodes (OLEDs)] have attracted much interest over the past decade. Several different attempts have been made to realize multicolor OLEDs. This article describes a new approach based on energy transfer in a donor/acceptor system. A copolymer containing both donor and acceptor compounds as comonomer units is prepared. The polymer consists of a derivative of a luminescent dye [4‐dicyanmethylene‐2‐methyl‐6‐4H‐pyran (DCM); acceptor compound], which is copolymerized with fluorene (donor compound) to combine the properties of an electroactive polymer with a highly luminescent dye. Photochemical processing is achieved by UV irradiation of this copolymer in the presence of gaseous trialkylsilanes. This reagent selectively saturates the C?C bonds in the DCM comonomer units while leaving the fluorene units essentially unaffected. As a result of the photochemical process, the red electroluminescence of the acceptor compound vanishes, and the blue‐green electroluminescence from the polyfluorene units is recovered. Compared with previous approaches based on polymer blends, this copolymer approach avoids problems associated with phase‐separation phenomena in the active layer of OLEDs. © 2006Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4317–4327, 2006     

Radiation conditions and uniqueness for stationary oscillations in elastic plates

Sommerfeld-type radiation conditions are indicated for the solutions of the system governing the small stationary oscillations in plates with transverse shear deformation, and a uniqueness theorem is proved in the case of the corresponding exterior Dirichlet and Neumann problems.

     

A trajectory-following method for unconstrained optimization

A trajectory-following method with interesting properties is considered for solving unconstrained nonlinear programming problems. The trajectory is defined by a special system of ordinary differential equations. This system uses only the gradient of the objective function. Numerical examples are given.The work of the second author was supported by the DFG Schwerpunkt Anwendungs-bezogene Optimierung and Steuerung.     

Statistical mechanics of probabilistic cellular automata

We investigate the behavior of discrete-time probabilistic cellular automata (PCA), which are Markov processes on spin configurations on ad-dimensional lattice, from a rigorous statistical mechanics point of view. In particular, we exploit, whenever possible, the correspondence between stationary measures on the space-time histories of PCAs on ^d and translation-invariant Gibbs states for a related Hamiltonian on ( ^d+1). This leads to a simple large-deviation formula for the space-time histories of the PCA and a proof that in a high-temperature regime the stationary states of the PCA are Gibbsian. We also obtain results about entropy, fluctuations, and correlation inequalities, and demonstrate uniqueness of the invariant state and exponential decay of correlations in a high-noise regime. We discuss phase transitions in the low-noise (or low-temperature) regime and review Toom's proof of nonergodicity of a certain class of PCAs.