Hypergeometric approach to Weideman’s conjecture

By applying the derivative operator to Dixon’s formula, we prove several harmonic number identities including one of the hardest challenge identities conjectured by Weideman (2003). Received: 28 October 2005     

The cluster-galaxy cross-correlation and the average infall velocity around cluster in the modified CDM models

The cluster-galaxy cross-correlation and the average infall velocity around cluster for the tilted CDM models, the hot-cold mixed dark matter models (MDM) and theA CDM models are calculated. And it is found that the prediction of the cluster-galaxy cross-correlation of theA CDM models with Ω_A=0.9, Ω_C=0.1,h=1,b = 1 or 2 is much higher than that of observation for the radius larger than 10 h⁻¹ Mpc (H₀ = 100 h.kms⁻¹Mpc⁻¹), and the other models are compatible with the observation on the scale of (3–20) h⁻ Mpc. The results can be used to compare with new observations to restrict the nature of the dark matter and the biasing factor. Project supported by the National Natural Science Foundation of China (Grant No. 19733001).     

两类团体保险保单的定价问题

本文试图利用金融经济学中的不确定权益方法讨论两类团体保险保单的定价问题 ,即利用偏微分方程方法和推广的精算贴现 (GEDV)方法求得定价模型的解析解     

Field Trial of 40 Gbit/s ETDM Prototype System over 219 km of Installed Single Mode Fiber

Transmission of 40Gbit/s NRZ signal was successfully demonstrated over 219km of installed SMF in KT's Daejeon area network. After transmission, the measured power penalty was 0.5dB for all the tributary channels.     

Newton's method for sections on Riemannian manifolds: Generalized covariant -theory

One kind of the L-average Lipschitz condition is introduced to covariant derivatives of sections on Riemannian manifolds. A convergence criterion of Newton's method and the radii of the uniqueness balls of the singular points for sections on Riemannian manifolds, which is independent of the curvatures, are established under the assumption that the covariant derivatives of the sections satisfy this kind of the L-average Lipschitz condition. Some applications to special cases including Kantorovich's condition and the γ-condition as well as Smale's α-theory are provided. In particular, the result due to Ferreira and Svaiter [Kantorovich's Theorem on Newton's method in Riemannian manifolds, J. Complexity 18 (2002) 304–329] is extended while the results due to Dedieu Priouret, Malajovich [Newton's method on Riemannian manifolds: covariant alpha theory, IMA J. Numer. Anal. 23 (2003) 395–419] are improved significantly. Moreover, the corresponding results due to Alvarez, Bolter, Munier [A unifying local convergence result for Newton's method in Riemannian manifolds, Found. Comput. Math. to appear] for vector fields and mappings on Riemannian manifolds are also extended.     

Thermogelling behaviors of poly(caprolactone‐b‐ethylene glycol‐b‐caprolactone) triblock copolymer in the presence of hyaluronic acid

In this article, we studied the effect of hyaluronic acid (HA) on thermogelation of poly(caprolactone‐b‐ethylene glycol‐b‐caprolactone) (PCL‐PEG‐PCL) aqueous solution designed as an injectable system for prevention of postsurgical tissue adhesion. The PCL‐PEG‐PCL triblock copolymers were simply synthesized by ring‐opening polymerization of ε‐caprolactone (CL) in the presence of PEG as a polymeric initiator. The synthesized copolymers were confirmed by proton nuclear magnetic resonance (¹H‐NMR) spectroscopy. Possible interactions between HA and PCL‐PEG‐PCL triblock copolymers in the blend were evaluated by Fourier‐transform infrared spectroscopy (FTIR). The effect of HA on the micellization of PCL‐PEG‐PCL aqueous solution was investigated by dye solubilization method and electrophoretic lighting scattering (ELS) spectrophotometer. Also, the thermogelling behaviors of the PCL‐PEG‐PCL triblock copolymers in the presence of HA and their mechanism were investigated by test tube inverting method, ¹³C‐NMR, ¹H‐NMR, Advanced Rheometic Expansion System (ARES), and differential scanning calorimetry (DSC). The PCL‐PEG‐PCL/HA blend aqueous solutions undergo the sol‐gel‐sol transition in response to an increase in temperature (10–60 °C) and the gelation of the PCL‐PEG‐PCL was rather accelerated by HA. Presumably, this accelerated gelation seems to arise from the attractive interactions between them and the effect of chain confinement in the micelle corona region. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 3629–3637, 2008     

Organic solvent dispersion of poly(3,4‐ethylenedioxythiophene) with the use of polymeric ionic liquid

A nonaqueous dispersion of poly(3,4‐ethylenedioxythiophene) (PEDOT) was prepared with the use of polymeric ionic liquid (PIL) as a polymerization template and phase transfer medium. A detailed investigation was performed to understand the role of PIL in the course of polymerization and phase transfer reaction. On the basis of our findings from X‐ray photoelectric spectroscopy (XPS), we propose a mechanism by which the PIL leads to the nanostructured PEDOT colloids in various organic solvents and thus facilitating smoother surface morphologies of the PEDOT‐PIL films. In addition, the enhancement of charge transport was observed for PEDOT‐PIL complex when compared with PEDOT without PIL. Raman spectroscopy indicates that there is a reduced interaction between the charge carriers on the PEDOT and the counter ions bound to PIL, thus promoting charge carrier hopping rates. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 6872–6879, 2008     

Preparation of Enamines Catalyzed by Lewis Acids in the Presence of Solid Supports

A simple and effective preparation of enamines from bulky ketones and secondary amines has been achieved with the aid of Lewis acid on various solid supports. The optimized yields were higher than those obtained without the solid support. Factors affecting the yield and regioselectivity of these reactions were also studied. Evidence showed that the reaction proceeded simultaneously in solution and on the solid support.