Nowhere zero 4‐flow in regular matroids

Jensen and Toft 8 conjectured that every 2‐edge‐connected graph without a K₅‐minor has a nowhere zero 4‐flow. Walton and Welsh 19 proved that if a coloopless regular matroid M does not have a minor in {M(K_3,3), M*(K₅)}, then M admits a nowhere zero 4‐flow. In this note, we prove that if a coloopless regular matroid M does not have a minor in {M(K₅), M*(K₅)}, then M admits a nowhere zero 4‐flow. Our result implies the Jensen and Toft conjecture. © 2005 Wiley Periodicals, Inc. J Graph Theory     

Synthesis of 2,7‐Carbazolenevinylene‐Based Copolymers and Characterization of Their Photovoltaic Properties

New electroactive and photoactive conjugated copolymers consisting of alternating 2,7‐carbazole and oligothiophene moieties linked by vinylene groups have been developed. Different oligothiophene units have been introduced to study the relationship between the polymer structure and the electronic properties. The resulting copolymers are characterized by UV‐vis spectroscopy, size‐exclusion chromatography, and thermal and electrochemical analyses. Bulk heterojunction photovoltaic cells from different copolymers and a soluble fullerene derivative, [6,6]‐phenyl‐C₆₁ butyric acid methyl ester, have been fabricated, and promising preliminary results are obtained. For instance, non‐optimized devices using poly(N‐(4‐octyloxyphenyl)‐2,7‐carbazolenevinylene‐alt‐3″,4″‐dihexyl‐2,2′;5′,2″;5″,2″′;5″′,2″″‐quinquethiophenevinylene 1″,1″‐dioxide) as an absorbing and hole‐carrier semiconductor exhibit power conversion efficiency up to 0.8 % under air mass (AM) 1.5 illumination. These features make 2,7‐carbazolenevinylene‐based and related polymers attractive candidates for solar‐cell applications.     

Water‐Stable,Magnetic Silica–Cobalt/Cobalt Oxide–Silica Multishell Submicrometer Spheres

A method to produce monodisperse magnetic composite spheres with diameters from less than 100 nm to more than 1 μm in water solution is reported. The spheres consist of a dielectric silica core and a cobalt/cobalt oxide shell which can be protected from further oxidation with an outer shell of silica or, alternatively, they can be covered with the polymer polyvinylpyrrolidone as a stabilizer. The formation of a uniform magnetic shell proceeds with the adsorption of metallic cobalt seeds, produced by the reduction of cobalt chloride with sodium borohydride, on a self‐assembled layer of polyelectrolytes on the silica core. In the second step, an outer silica shell can be formed by the hydrolysis and condensation of (3‐aminopropyl)trimethoxysilane and tetraethoxysilane. The double‐shell composite spheres show excellent sphericity, monodispersity, and a magnetic hysteresis loop at room temperature.     

Use and Disuse of Contextual Primes in Dynamic News Environments

This study reexamines the news priming effects of the 1991 Persian Gulf War. Suggesting an alternative approach to those used in previous studies, this study assesses individuals' use and disuse of a contextual prime (i.e., the air war) in dynamic news environments. With a short-term, quasi-experimental approach considering the air war as a prime stimulus, a path analysis suggests robust evidence of the short-term accessibility effects of priming. More importantly, as suggested in Martin's (1986) set/reset model, this study extends priming effects beyond the simple hydraulic patterns of accessibility effects. It reveals that both attitudes toward military action and attitudes toward a diplomatic solution were used in subsequent judgments of the president's job performance and handling of the war. The associations between attitudes toward a diplomatic solution and subsequent judgments were even stronger than those between attitudes toward military action and the same subsequent judgments, despite the clear prowar primes of news discourse in the air-war context. This pattern was more greatly intensified among those in the high news attention group than those in the low news attention group     

Efficient synthesis of an aldehyde‐capped polythiophene containing fluorinated electron‐withdrawing groups

To incorporate an acceptor type polythiophene segment onto a supramolecular block copolymer for potential light harvesting applications, effective synthetic routes for the end‐functionalized and acceptor‐substituted polythiophenes are critical. The Ullmann coupling reaction can be utilized to obtain electron‐deficient polythiophenes and to attach terminal thiophene units that carry functional groups. In this article, the reactions involving a 2,5‐dibromothiophene monomer containing an electron‐withdrawing fluorinated ester and 5‐bromo‐2‐thiophenecarboxaldehyde (the end‐capper) were studied in detail. It was found that the Ullmann coupling reaction of the dibromide is very fast (completed in a few minutes) and the terminal bromine group does not survive long under the reaction condition. These findings lead to the development of an effective procedure for aldehyde end‐capping of electron‐deficient polythiophenes. Polymers with molecular weights around 4000 Da are routinely obtained. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 41–47, 2007     

Normalization and Fermi–Coulomb and Coulomb hole sum rules for approximate wave functions

For approximate wave functions, we prove the theorem that there is a one‐to‐one correspondence between the constraints of normalization and of the Fermi–Coulomb and Coulomb hole charge sum rules at each electron position. This correspondence is surprising in light of the fact that normalization depends on the probability of finding an electron at some position. In contrast, the Fermi–Coulomb hole sum rule depends on the probability of two electrons staying apart because of correlations due to the Pauli exclusion principle and Coulomb repulsion, while the Coulomb hole sum rule depends on Coulomb repulsion. We demonstrate the theorem for the ground state of the He atom by the use of two different approximate wave functions that are functionals rather than functions. The first of these wave function functionals is constructed to satisfy the constraint of normalization, and the second that of the Coulomb hole sum rule for each electron position. Each is then shown to satisfy the other corresponding sum rule. The significance of the theorem for the construction of approximate “exchange‐correlation” and “correlation” energy functionals of density functional theory is also discussed. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007