两点拉伸型不动点定理及其应用

在研究各种非线性方程解的存在性问题时,上下解方法是一个强有力的工具.设 E是 Banach 空间,P 是 E 中的锥,E 中的半序由 P 导出.设 A:E→E 是一个算子.如果x_0∈E 满足     

Profile empirical likelihood for parametric and semiparametric models

This paper introduces a profile empirical likelihood and a profile conditionally empirical likelihood to estimate the parameter of interest in the presence of nuisance parameters respectively for the parametric and semiparametric models. It is proven that these methods propose some efficient estimators of parameters of interest in the sense of least-favorable efficiency. Particularly, for the decomposable semiparametric models, an explicit representation for the estimator of parameter of interest is derived from the proposed nonparametric method. These new estimations are different from and more efficient than the existing estimations. Some examples and simulation studies are given to illustrate the theoretical results. The first author is supported by NNSF projects (10371059 and 10171051) of China. The second author is supported by a grant from The Research Grants Council of the Hong Kong Special Administrative Region, China (#HKU7060/04P). The third author is supported by the University Research Committee of the University of Hong Kong and a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKU7323/01M).     

Studies on self-pumped phase conjugation in Cu-doped (K0.5Na0.5)0.2(Sr0.61Ba0.39)0.9Nb2O6 crystals

The use of Cu-doped (K_0.5Na_0.5)_0.2(Sr_0.61Ba_0.39)_0.9Nb₂O₆ as self-pumped phase conjugators using internal reflection is reported. Reflectivities as high as 63% at 5145.5 nm and 60% at 632.8 nm were realized. It was found that the photorefractive response changes significantly at different doping concentration. The responses of the crystals to the laser wavelength, incident angle and dopant concentration are studied.     

Effects of barium on the nonlinear electrical characteristics and dielectric properties of SnO2-based varistors

The effects of barium on electrical and dielectric properties of the SnO_2·Co_2O_3·Ta_2O_5 varistor system sintered at 1250℃ for 60min were investigated. It is found that barium significantly improves the nonlinear properties. The breakdown electrical field increases from 378.0 to 2834.5V/mm, relative dielectric constant (at 1kHz) falls from 1206 to 161 and the resistivity (at 1kHz) rises from 60.3 to 1146.5kΩ·cm with an increase of BaCO_3 concentration from 0mol% to 1.00mol%. The sample with 1.00mol% barium has the best nonlinear electrical property and the highest nonlinear coefficient (α=29.2). A modified defect barrier model is introduced to illustrate the grain-boundary barrier formation of barium-doped SnO_{2}-based varistors.     

The optical near-field speckles and their first order statistics on the basis of the integral equations of electromagnetic field

Speckle fields are the random light wave distributions produced when the light fields are scattered from random surfaces or a random medium. They appear in many optical phenomena that are related to light propagations[1,2] and have found wide appli-cations in a variety of scientific and technical fields. The examples of the recent impor-tant applications of speckles include the analysis of the movement of the granules[3], the three-dimensional imaging for the microstructures of metal nanocryst…     

Preparation and characterization of carbon xerogel (CX) and CX–SiO composite as anode material for lithium-ion battery

Carbon xerogel (CX), a kind of novel carbon material with low-density and continuous nano-porous structure that can be controlled and tailored on nanometer scale, has been prepared through the sol–gel polycondensation of resorcinol (R) with formaldehyde (F) followed by drying at ambient pressure and carbonization in inert atmosphere, and CX–SiO composite has been synthesized by high energy mechanical ball-milling of the obtained CX and commercial SiO at room temperature and atmosphere. The characteristics of CX and CX–SiO as anode material for lithium-ion battery have been systematically investigated on basis of field emission scanning electron microscope (FESEM), X-ray diffraction (XRD), electrochemical and charge–discharge tests. The results showed that, CX–SiO is composed of active carbon, graphite, SiO and dispersed Si crystal while CX consists of active carbon and graphite, CX–SiO has smaller and much more uniform particles than CX. SiO can greatly improve discharge capacity of CX with an acceptable sacrifice of cycling stability, and the charge–discharge capacity of CX–SiO comes mainly from lithium insertion–extraction in Si–SiO in the sample.     

Strong limit-point classification of singular Hamiltonian expressions

Strong limit-point criteria for singular Hamiltonian differential expressions with complex coefficients are obtained. The main results are extensions of the previous results due to Everitt, Giertz, and Weidmann for scalar differential expressions.

     

Supramolecular self-assembly of polypseudorotaxanes in ionic liquid

The polypseudorotaxanes (PPRs) have been prepared by supramolecular self-assembly of β-cyclodextrins (β-CDs) threaded onto the triblock copolymers (Pluronic F127) in an ionic liquid [1-n-butyl-3-methylimidazolium hexafluorophosphate (bmimPF₆)] with two different manners. Structural characterizations of the assembled PPRs are carried out in detail respectively with XRD, ¹³C CP/MAS NMR, ¹H NMR and DSC techniques. The results obtained indicate a channel-type crystalline structure for such produced inclusion complexes (ICs). Which one will finally be included inside β-CD, F127 or bmimPF₆, is related to the ethanol amount around the initially β-CD/bmimPF₆ ICs. At higher ethanol concentration, F127 may squeeze bmimPF₆ molecules out from β-CD and thread themselves instead into the cavity of β-CD and finally precipitate with more CDs being stacked.     

Investigation of charge effects on poling and stability for corona-poled polymer films

The optimal corona-poling temperature of polymer films was accurately determined by measuring the temperature dependence of the in situ second-harmonic (SH) intensity profile under the applied poling electric field. The in situ SH intensity profile was first measured by probing both the surface voltages and the poling currents induced by surface/space charges for the corona-poled polymer films. Moreover, charge effects on the stability of the chromophore orientation were first studied by using the thermally stimulated discharge-current technique. PACS 72.20.Jv; 42.65.Ky; 73.61.Ph; 81.40.Tv     

一类非线性算子方程的多重正解及其应用

本文利用不动点指数理论对一类非线性算子方程建立了多重正解的存在性定理，并将所获结果应用到Ｈａｍｍｅｒｓｔｅｉｎ积分方程和Ｓｔｕｒｍ Ｌｉｏｕｖｉｌｅ两点边值问题，得到了新的结论，本质上改进和推广了［２，４，５，６，８－１２］的工作．