对一道研究生入学试题的四种解答

分别利用洛必达法则,罗尔定理,拉格朗日中值定理等知识,对2007年黑龙江大学硕士研究生入学考试的一道试题给出四种解答,即证明了 f （x）是常函数,如果 f （x）是实数域上可微的周期函数且其导函数在无穷大处存在极限。     

Graphene-based passively Q-switched dual-wavelength erbium-doped fiber laser

We demonstrate a compact Q-switched dual-wavelength erbium-doped fiber (EDF) laser based on graphene as a saturable absorber (SA). By optically driven deposition of graphene on a fiber core, the SA is constructed and inserted into a diode-pumped EDF laser cavity. Also benefiting from the strong third-order optical nonlinearity of graphene to suppress the mode competition of EDF, a stable dual-wavelength Q-switching operation has been achieved using a two-reflection peak fiber Bragg grating as the external cavity mirror. The Q-switched EDF laser has a low pump threshold of 6.5 mW at 974 nm and a wide range of pulse-repetition rate from 3.3 to 65.9 kHz. The pulse duration and the pulse energy have been characterized. This is, to the best of our knowledge, the first demonstration of a graphene-based Q-switched laser.     

Synthesis and characterization of sulfonated poly(phthalazinone ether phosphine oxide)s by direct polycondensation for proton exchange membranes

A series of sulfonated poly(phthalazinone ether phosphine oxide)s (sPPEPO) were prepared via aromatic nucleophilic substitution polycondensation of 4‐(4‐hydroxyphenyl) phthalazinone (HPPZ) with sulfonated bis(4‐fluorophenyl)phenyl phosphine oxide (sBFPPO) and bis(4‐fluorophenyl)phenyl phosphine oxide (BFPPO) at various ratios. The properties such as molecular weight, ion exchange capacity (IEC), swelling, thermal stability, proton conductivity, and morphology were investigated. sPPEPO with high IEC exhibited high proton conductivity while they still showed low swelling. Typically, sPPEPO with IEC of 1.54 and 1.69 meq/g exhibited high conductivity of 0.091 and 0.19 S/cm, and low swelling ratios of 14.3% and 19.5% at 80 °C, respectively. The low swelling was attributed to the strong intermolecular interaction including the electrostatic force and hydrogen bond. sPPEPO would be promising candidates used as polyelectrolyte membranes for fuel cells. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 1758–1769, 2008     

Sulfonated poly(arylene thioether phosphine oxide)s copolymers for proton exchange membrane fuel cells

High molecular weight sulfonated poly(arylene thioether phosphine oxide)s (sPATPO) with various sulfonation degrees were prepared directly by aromatic nucleophilic polycondensation of 4,4′-thiobisbenzenethiol with sulfonated bis(4-fluorophenyl) phenyl phosphine oxide and bis(4-fluorophenyl) phenyl phosphine oxide. sPATPO in the acid form with sulfonation degrees of 60–100% exhibits a glass transition temperature higher than 230 °C and a 5% weight loss temperature above 400 °C, indicating high thermal stability. sPATPO with a high sulfonation degree shows high proton conductivity and good resistance to swelling as well. For instance, sPATPO-70 displays the conductivity of 0.0783 S/cm and a swelling ratio of 11.6% at 90 °C. TEM micrographs showed that sPATPO membranes with a high sulfonation degree could form continuous ion channels, which are favorable for improving the proton conductivity but harmful to remaining the mechanical property. The membranes are expected to show good performances in fuel cell applications.     

两性树脂与水处理

两性树脂可简单地分为两大类：一类是不能形成内盐的，其性能与阴和阳离子交换树脂的混合物相近。另一类则能形成内盐，并由此产生了一系列新的特性，这类树脂的选择性，膨胀性及吸附容量等在一定范围内都随溶液中电解质浓度提高而提高＾〔２〕，因此可适用于浓电解质溶液的分离提纯。本文重点论述了形成内盐的一些规律性，尤其是树脂的交联度和功能基性质以及环境条件如温度，浓度和ｐＨ等与形成内盐的关系。     

关于Hill方程稳定性准则的控制方法证明

Optimal estimates of the stability of Hill‘s equation are obtained. The discussion is based on Pontryagin‘s maximum principle.     

Confined crystallization of binary n-alkane mixtures: stabilization of a new rotator phase by enhanced surface freezing and weakened intermolecular interactions

The present work reports the confined crystallization behaviours of binary even-even normal alkane (n-alkane) mixtures of n-octadecane (n-C(18)H(38)) and n-eicosane (n-C(20)H(42)), which are microencapsulated in monodisperse microcapsules, using the combination of differential scanning calorimetry (DSC) and temperature-dependent X-ray diffraction (XRD). A new metastable rotator phase (RII) absent in the bulk state, has been detected for the n-alkane mixture in confined geometry under all the investigated compositions. Such a crossover is attributed to the lower interfacial energy due to the same in-planar hexagonal structure of the surface monolayer and RII, as well as the weakened intermolecular interaction in alkane mixtures. This is the first time that RII is found in such a binary even-even n-alkane mixture that neither of the components contains RII phase in the crystallization process. Furthermore, based on the variation of alkane molecule conformation and in-planar structure with temperature, the correlations between the phase transition temperature and composition have been discussed.     

Improved electrochemical immunosensor for myeloperoxidase in human serum based on nanogold/cerium dioxide-BMIMPF6/L-Cysteine composite film

An electrochemical immunosensing assay for myeloperoxidase (MPO) determination in human serum has been developed. Firstly, L-Cysteine was initially electropolymerized on an Au electrode to form L-Cysteine film. After that cerium dioxide (CeO2) dispersed in 1-butyl-3-methylimidazolium hexafluorophosphate (BMIMPF6) were immobilized on the L-Cysteine film. Then the negatively charged nanogold particles were adsorbed onto the membrane via the positive charge of CeO2, which aimed at assembling more antibody of MPO (anti-MPO). The resulting immunosensor showed a high sensitivity, broad linear response to the MPO concentration comprised between 10 ng/mL and 400 ng/mL with a detection limit of 0.06 ng/mL. Moreover, the surface morphology of the electrode was studied by means of a scanning electron microscope and the electrochemical properties of the fabricated immunosensor were further characterized by cyclic voltammetry. Also, factors influencing the performance of the resulting immunosensors were studied in detail.     

一道硕士研究生入学试题的推广

应用函数的单调性、拉格朗日中值定理、费马定理、柯西准则,对2007年黑龙江大学硕士研究生入学考试的一道试题给出四种解答,并给出这道试题的一种推广。     

一道级数习题的六种解法

应用约当不等式,函数的单调性以及数列极限的性质,对一道级数习题提供了六种解法.