透过“教材”关注“向量”

自新课程改革以来,向量正式从"幕后"走向"前台",成交衔接代数、几何与三角的纽带,把向量和向量法穿插、渗透和融合到其他知识点中,已成为数学试题中一道亮丽的风景.现在笔者通过对人教A版的教材例题或习题来谈谈向量与向量法的广泛应用.     

如何实现例题教学的“有效性”——从“参数分离法”说起

一、问题的提出原题(2012年浙江省上虞市城南中学高三理科数学期中试卷第20题)已知函数g(x)=ax2-2ax+1+b(a>0),在区间[2,3]上有最大值4,最小值1,设函数(fx)=g(x)/x.(1)求a,b的值;(2)     

An alternative phase modulator half-wave voltage measurement based on photonic link

We measure the half-wave voltage of LiNbO 3 phase modulators in a 26-GHz wideband frequency range, and then analyze it by the phase modulation photonic peak gain linked to the interferometric demodulation. The optical interferometer is constructed with two 50:50 couplers and two fiber arms with a 1-m difference in fiber length. The photonic link gain peaks are frequency dependent, as indicated by the differential time delay in the interferometer. The procedure described is a new and practical half-wave voltage measurement method that can accurately predict the nonlinear frequency characteristics of the phase modulator. Moreover, the method can be applied to various types of LiNbO 3 phase modulators.     

Optical bistability and multistability via amplitude and phase control in a Duplicated two-level system

We investigate the optical bistability(OB) in a duplicated two-level system contained in a ring cavity.The atoms are driven by two orthogonally polarized fields with a relative phase.The OB behavior of such a system can be controlled by the amplitude and the relative phase of the coupling field,and it is possible to switch between bistability and multistability by adjusting the relative phase.     

Design and preparation of LWIR narrow-band filter with wide rejection band

In this letter, using mult-half-wave structure and some chosen films optimized method, the long-wave infrared （LWIR） narrow-band pass filter is investigated, meanwhile the opposite of the substrate coated with long-wavelength pass film. The transmittance of design spectrum is more than 80% at wavelength region of 8.05 8.35 μm, and the average transmittance is less than 0.5% at wavelength region of less than 7.95 and 8.45 14 pro. The filter is prepared by thermal evaporation method, and plasma-assisted deposition technology. The experiment result shows that the average transmittance is about 75% in the transmission wavelength range, and the average transmittance of cut-off band is about 0.3%. The results show that multi-half-wave structure and some chosen films optimized method for the preparation LWIR narrow-band pass filter are feasible. The film system is simplified and is convenient to prepare the film.     

Influences of high-temperature annealing on atomic layer deposited Al2 O3/4H-SiC

High-temperature annealing of the atomic layer deposition (ALD) of Al2O3 films on 4H-SiC in O 2 atmosphere is studied with temperature ranging from 800℃ to 1000℃. It is observed that the surface morphology of Al2O3 films annealed at 800℃ and 900℃ is pretty good, while the surface of the sample annealed at 1000℃ becomes bumpy. Grazing incidence X-ray diffraction (GIXRD) measurements demonstrate that the as-grown films are amorphous and begin to crystallize at 900℃. Furthermore, C-V measurements exhibit improved interface characterization after annealing, especially for samples annealed at 900℃ and 1000℃. It is indicated that high-temperature annealing in O2 atmosphere can improve the interface of Al2O3 /SiC and annealing at 900℃ would be an optimum condition for surface morphology, dielectric quality, and interface states.     

Simultaneous effects of magnetic field and space porosity on compressible Maxwell fluid transport induced by a surface acoustic wave in a microchannel

Peristaltic motion induced by a surface acoustic wave of a viscous, compressible and electrically conducting Maxwell fluid in a confined parallel-plane microchannel through a porous medium is investigated in the presence of a constant magnetic field. The slip velocity is considered and the problem is discussed only for the free pumping case. A perturbation technique is employed to analyze the problem in terms of a small amplitude ratio. The phenomenon of a “backward flow” is found to exist in the center and at the boundaries of the channel. In the second order approximation, the net axial velocity is calculated for various values of the fluid parameters. Finally, the effects of the parameters of interest on the mean axial velocity, the reversal flow, and the perturbation function are discussed and shown graphically. We find that in the non-Newtonian regime, there is a possibility of a fluid flow in the direction opposite to the propagation of the traveling wave. This work is the most general model of peristalsis created to date with wide-ranging applications in biological, geophysical and industrial fluid dynamics.     

Molecular dynamics study of thermal stress and heat propagation in tungsten under thermal shock

Using molecular dynamics （MD） simulation, we study the thermal shock behavior of tungsten （W）, which has been used for the plasma facing material （PFM） of tokamaks. The thermo-elastic stress wave, corresponding to the collective displacement of atoms, is analyzed with the Lagrangian atomic stress method, of which the reliability is also analyzed. The stress wave velocity corresponds to the speed of sound in the material, which is not dependent on the thermal shock energy. The peak pressure of a normal stress wave increases with the increase of thermal shock energy. We analyze the temperature evolution of the thermal shock region according to the Fourier transformation. It can be seen that the “obvious” velocity of heat propagation is less than the velocity of the stress wave; further, that the thermo-elastic stress wave may contribute little to the transport of kinetic energy. The heat propagation can be described properly by the heat conduction equation. These results may be useful for understanding the process of the thermal shock of tungsten.     

Pressure-induced phase transitions of multiferroic BiFeO3

Pressure-induced phase transitions of multiferroic BiFeO3 have been investigated using synchrotron radiation X-ray diffraction with diamond anvil cell technique at room temperature. Present experimental data clearly show that rhombohedral （R3c） phase of BiFeO3 first transforms to monoclinic （C2/m） phase at 7 GPa, then to orthorhombic （Pnma） phase at 11 GPa, which is consistent with recent theoretical ab initio calculation. However, we observe another peak at 2θ=7° in the pressure range of 5-7 GPa that has not been reported previously. Further analysis reveals that this reflection peak is attributed to the orthorhombic （Pbam） phase, indicating the coexistance of monoclinic phase with orthorhombic phase in low pressure range.     

也谈零向量——与《关于零向量两个典型案例的思考与探究》一文作者商榷

文[1]发表在贵刊2012年第8期上,其中,案例1引2010年福建高考文科数学第18题为例,以人教A版《必修4》教材关于零向量的若干叙述为依据,给出了"零向量与非零向量不能垂直"的结论,宣判了这道高考题的答案是错误的!无独有偶,2009年湖北省高考理科数学第17题:已知向量a=