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.     

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].     

Contact hypersurfaces of Kaehler manifolds

Contact hypersurfaces of a Kaehler manifold have been characterized and classified, assuming the second fundamental form to be Codazzi (in particular, parallel). We have also discussed the special cases when the ambient space is a (i) Calabi-Yau manifold and (ii) a complex space-form.     

A note on minimization problems and multistep methods

Summary. We use the qualitative properties of the solution flow of the gradient equation to compute a local minimum of a real-valued function . Under the regularity assumption of all equilibria we show a convergence result for bounded trajectories of a consistent, strictly stable linear multistep method applied to the gradient equation. Moreover, we compare the asymptotic features of the numerical and the exact solutions as done by Humphries, Stuart (1994) and Schropp (1995) for one-step methods. In the case of -stable formulae this leads to an efficient solver for stiff minimization problems. Received July 10, 1995 / Revised version received June 27, 1996