恒成立,能成立,恰成立

证不等式的恒成立、能成立与恰成立求参数范围问题是一种常见的题型，也是高考的热点之一．这三类问题既有区别又有联系。在教学过程中很多学生容易混淆，它们的意义和转化方法是不同的．本文结合实例来辨析这三种问题的区别和联系．

“恒成立”“能成立”“恰成立”问题

"恒成立","能成立","恰成立"问题在教材中虽然没有专门设计,但这些内容是高中内容的重点、难点,同时也是高考和数学竞赛的热点,又因为它们的解法多样,所以这三类问题考生容易混淆不清,笔者认为分离变量法和函数法具有思路清、操作强、易掌握等特点,所以在解决"恒成立","能成立","恰成立"问题是很好的方法。

含参不等式的恒成立、恰成立与能成立

本文举例说明了不等式成立的几种不同形式的解答方向，以增强辨析能力，提高数学素养．

恒成立、能成立问题处理策略

确界是高等数学中的一个重要概念.在解决恒成立和能成立问题时,有时仅用最值很难说清楚,而若用确界来解决就显得方便得多.文章通过对两道高考题的分析,探讨确界在解恒成立、能成立问题中的妙用.

Electrochemical synthesis, characterization and thermal properties of niobium ethoxide

Niobium(V) ethoxide(Nb(OEt)5) was synthesized by electrochemical reaction of ethanol with niobium plate as the sacrificial anode,stainless steel as the cathode and tetraethylammonium chloride(TEAC) as the conductive additive.The condensates were isolated by vacuum distillation under 5 kPa.The product was characterized by Fourier transform infrared(FT-IR) spectra,Raman spectra and nuclear magnetic resonance(NMR) spectra.The results indicate that the product is niobium ethoxide.Thermal properties of niobium ethoxide were analysed by TG/DTG.Vapour pressure was calculated from the Langmuir equation and the enthalpy of vaporization was calculated from the vapour pressure-temperature data using the Clausius-Clapeyron equation.The concentrations of impurity metallic elements in the sample were detected by ICP-MS.It is shown that the purity can reach 99.997%.The volatility and purity of the niobium ethoxide ensure that it could be a good precursor for chemical vapor deposition and atomic layer deposition of niobium oxide layers.

Detection and Separation of Event-related Potentials from Multi-Artifacts Contaminated EEG by Means of Independent Component Analysis

Event-related potentials (ERP) is an important type of brain dynamics in human cognition research. However, ERP is often submerged by the spontaneous brain activity EEG, for its relatively tiny scale. Further more, the brain activities collected from scalp electrodes are often inevitably contaminated by several kinds of artifacts, such as blinks, eye movements, muscle noise and power line interference. A new approach to correct these disturbances is presented using independent component analysis (ICA). This technique can effectively detect and extract ERP components from the measured electrodes recordings even if they are heavily contaminated. The results compare favorably to those obtained by parametric modeling. Besides, auto-adaptive projection of decomposed results to ERP components was also given. Through experiments, ICA proves to be highly capable of ERP extraction and S/N ratio improving.

Preparation,Characterization of Dawson-type Heteropoly Acid Cerium（Ⅲ） Salt and Its Catalytic Performance on the Synthesis of n-Butyl Acetate

A novel cerium(Ⅲ) salt of Dawson type tungstophosphoric acid(Ce2P2W18O62·16H2O) was prepared by doping cerous nitrate in H6P2W18O62·13H2O powder and characterized by thermogravimetry and differential thermal analyses(TG/DTA),Fourier transform infrared spectroscopy(FT-IR),X-ray powder diffraction(XRD),pyridine infrared spectroscopy(Py-IR) and scanning electron microscopy(SEM).Its catalytic activity was evaluated by the probe reaction of synthesis of n-butyl acetate with acetic acid and n-butanol.The effects of various parameters such as molar ratio of n-butanol to acetic acid,reaction temperature,reaction time,and catalyst amount have been studied by single factor experiment.The results show that Ce2P2W18O62·16H2O behaved as an excellent heterogeneous catalyst in the synthesis of n-butyl acetate.The optimum synthetic conditions were determined as follows︰molar ratio of n-butanol to acetic acid at 2.0︰1.0,mass of the catalyst being 1.44% of the total reaction mixture,reaction temperature of 120 ℃ and reaction time of 150 min.Under above conditions,the conversion of acetic acid was above 97.8%.The selectivity of n-butyl acetate based on acetic acid was,in all cases,nearly 100%.The catalysts could be recycled and still exhibited high catalytic activity with 90.4% conversion after five cycles of reaction.It was found by means of TG-DTA and Py-IR that the catalyst deactivation was due to the adsorption of a complex of by-product on the active sites on catalysts surface or the catalyst loss in its separation from the products.Compared with using sulfuric acid as catalyst,the present procedure with Ce2P2W18O62·16H2O is a green productive technology due to simple process,higher yield,catalyst recycling and no corrosion for the production facilities.

An Improved Fixed-point Algorithm for Independent Component Analysis of Functional MRI Data

The fixed-point algorithm and infomax algorithm are two of the most popular algorithms in independent component analysis(ICA).However,it is hard to take both stability and speed into consideration in processing functional magnetic resonance imaging(fMRI)data.In this paper,an optimization model for ICA is presented and an improved fixed-point algorithm based on the model is proposed.In the new algorithms a small step size is added to increase the stability.In order to accelerate the convergence,an improvement on Newton method is made,which makes cubic convergence for the new algorithm.Applying the algorithm and two other algorithms to invivo fMRI data,the results show that the new algorithm separates independent components stably,which has faster convergence speed and less computation than the other two algorithms.The algorithm has obvious advantage in processing fMRI signal with huge data.