Expected Reflection Distance in G(r, 1, n) after a Fixed Number of Reflections

Extending to r > 1 a formula of the authors, we compute the expected reflection distance of a product of t random reflections in the complex reflection group G(r, 1, n). The result relies on an explicit decomposition of the reflection distance function into irreducible G(r, 1, n)-characters and on the eigenvalues of certain adjacency matrices.Received December 8, 2003     

Well-dispersed gold nanowire suspension for assembly application

A method for fabricating well-dispersed nanowire suspension has been demonstrated in the paper. Thin gold nanowires were prepared by template synthesis, and then functionalized with sulphonate group-terminated thiols before suspended in different solvents. The degree of aggregation of the obtained suspension was evaluated with transmission electron microscopy (TEM) and UV-vis spectroscopy. It was found that the degree of aggregation was predominated by the solvents, and the best degree of dispersion was obtained when isopropyl alcohol (IPA) was used as the solvent. The gold nanowires from the suspension can be selectively assembled onto chemically patterned substrates. This well-dispersed nanowire suspension is potentially useful for fabricating novel nanodevices.     

The role of As2O3 on the stability and some physical properties of PbO-Sb2O3 glasses

PbO-Sb₂O₃ glasses added with different concentrations of As₂O₃ (10-55 mol%) were prepared to understand their IR spectra, elastic properties (Young's modulus E, Shear modulus G, microhardness H), optical absorption and dielectric properties (constant ε, loss tan δ, ac conductivity σ_ac over a moderately wide range of frequency and temperature and breakdown strength in air medium at room temperature). Results have indicated that the structure of the PbO-Sb₂O₃-As₂O₃ glass is more rigid when the concentration of As₂O₃ is around 40 mol%.     

Exact controllability of infinite dimensional systems persists under small perturbations

This paper studies the concept of controllability for infinite-dimensional linear control systems in Banach spaces. First, we prove that the set of admissible control operators for the semigroup generator is unchanged if we perturb the generator by the Desch–Schappacher perturbations. Second we show that exact controllability is not changed by such perturbations.     

Sulfonated poly(aryl ether ketone)s containing naphthalene moieties obtained by direct copolymerization as novel polymers for proton exchange membranes

A series of sulfonated poly(aryl ether ketone)s (SPAEKs) were prepared by aromatic nucleophilic polycondensation of 2,6‐dihydroxynaphthalene with 5,5′‐carbonyl‐bis(2‐fluorobenzenesulfonate) and 4,4′‐difluorobenzophenone. The structure and degree of sulfonation (DS) of the SPAEKs were characterized using ¹H NMR spectroscopy. The experimentally observed DS values were close to the expected values derived from the starting material ratios. The thermal stabilities of the SPAEKs were characterized by thermogravimetric analysis, which showed that in acid and sodium salt forms they were thermally stable in air up to about 240 and 380 °C, respectively. Transparent membranes cast from the directly polymerized SPAEKs exhibited good mechanical properties in both dry and hydrated states. The dependence of water uptake and of membrane swelling on the DS at different temperatures was studied. SPAEK membranes with a DS from 0.72 to 1.60 maintained adequate mechanical properties after immersion in water at 80 °C for 24 h. The proton conductivity of SPAEK membranes with different degrees of sulfonation was measured as a function of temperature. The proton conductivity of the SPAEK films increased with increased DS, and the highest room temperature conductivity (4.2 × 10^?2 S/cm) was recorded for a SPAEK membrane with a DS of 1.60, which further increased to 1.1 × 10^?1 S/cm at 80 °C. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2866–2876, 2004     

New functionalized polyesters to achieve controlled architectures

Following our continued interest in the production of bioerodible and biodegradable functional polymers for biomedical applications, we synthesized and characterized new unsaturated polyesters. The presence of functional groups in the polymer backbone provided sites for chemical modification, and through a variation in the structure, the physical properties, such as the hydrophilicity and solubility, could be affected. With 1,1-di-n-butyl-stanna-2,7-dioxacyclo-4-heptene as the initiator in the ring-opening polymerization of polyesters, a new set of functionalized polyesters was created. The polymerization of ϵ-caprolactone resulted in poly(ϵ-caprolactone) with a double bond incorporated into the structure. The polymers were obtained in a controlled manner with low molecular dispersities. The double bond was previously incorporated into L -lactide polymers, and the two reactions were compared in this study. The conversion of ϵ-caprolactone, with a degree of polymerization of 50, was completed within 140 min, whereas for L -lactide, only a 45% conversion took place in the same period of time. The dispersities were somewhat higher with ϵ-caprolactone because of the higher reaction rate and, therefore, lower selectivity. The incorporated CC double bond in the polyesters provided a variety of opportunities for further modifications. In this case, the double bond of the L -lactide macromonomers was oxidized into epoxides. Epoxidation was carried out with m-chloroperoxybenzoic acid as a chemical reagent. The conversion of the double bonds into epoxides was completed, and the obtained yields were good (>95%). As a result of the mild reaction conditions, the epoxidation of the double bond was carried out quantitatively without any side reactions. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 444–452, 2004     

Functionalization of polyethylene/silane copolymers in posttreatment reactions

7‐Octenyldimethylphenylsilane was copolymerized with ethylene via Et(Ind)₂ZrCl₂ methylaluminoxane catalyst system without loss of catalyst activity or decrease in molar mass. The comonomer contents in the polymer samples were at a level of 0.15–1.0 mol % and the reactive phenylsilane groups were posttreated to different alcoxy‐ and halosilane groups, for example, Si? F, Si? Cl, Si? OCH₃, and Si? OCH₂CH₃. The posttreatment reactions had no major effect on the molar masses or on the thermal properties (measured with differential scanning calorimetry) of the copolymers. The reaction pathways were nearly independent of the comonomer contents and the reactions reached 70–100% conversions. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 1461–1467, 2004     

Yb:FAP和Yb:C_3S_2-FAP晶体光谱的温度特性和选择激发

报导了Yb :FAP和Yb :C3S2 _FAP晶体在不同温度下的吸收光谱和荧光光谱实验结果 ,研究发现由于电子_声子近共振耦合作用 ,Yb :FAP和Yb :C3S2 _FAP晶体均存在有明显的振动谱 ,Yb :FAP晶体的零声子线在低温下还劈裂为相差 10cm- 1 的两条线 .采用激光选择激发技术研究了Yb3 离子在FAP和C3S2 _FAP晶体中的格位特征 ,结果表明Yb3 离子在这两种基质中都只占据Ca(Ⅱ )格位 ,但由于CaF2 的挥发 ,导致了Ca(Ⅱ )格位的局部畸变 .     

On a Definitizable Analog of the Trigonometric Moment Problem Generating an Indefinite Toeplitz Form

We prove the existence of an integro-polynomial representation for a sequence of numbers such that there exists a difference operator mapping this sequence to a sequence that generates the solvable trigonometric moment problem. A similar result related to the power moment problem was given in [12].