掌握一种科学的语言和工具,学习一种理性的思维模式——新课程试卷函数试题命题和答题

新课程试卷文科第(21)题和理科第(20)题是同一类型的试题,利用导数讨论曲线的切线及有关的性质. 文科试题为:已知n>O,函数f(x)=x3-a,x∈[0, ∞).设x1>0,记曲线y=f(x)在点M(x1,f(x1))处的切线为l. (Ⅰ)求l的方程; (Ⅱ)设l与x轴的交点是(x2,0),证明: (1)x2≥a1/3; (2)若x1>a1/3,则a1/3<220,函数f(x)=1/x-     

谈数学教育中的“问题解决”

现在,“问题解决”风行数学教育界。在美国“问题解决”是继“现代数学”和“回到基础”之后在八十年代提出的又一新的口号。一九八二年英国数学教育的权威性文件——数学教学调查委员会报告,即以委员会主席名字命名的科克柯罗福特报告(Cockcroft Report)也正式提出了“问题解决”。本文拟就当今数学教育中“问题解决”的类型和意义做一个概略的介绍。     

用光学显微术和X-射线衍射法研究焦炭结构

用X-射线衍射测定了具有各种不同光学组织(从各向同性到直径大于60μm 的广域)的24种焦炭。研究了光学组织指数(OTI)与微晶高度和面间距之间的关系。对于光学组织中大于中粒锒嵌(1.5—5.0μm)的焦炭,其OTI 值随X-射线衍射指数的变化很小。对于光学组织中结构很小的焦炭,则微晶高度急剧下降和面间距增加。这些结果可以解释为当生成中粒锒嵌焦炭时,流动中间相融并,消除了缺陷。而光学组织尺寸较小的焦炭则是未经融并,因此缺陷残存于焦炭中,从而降低了结晶化程度。     

MIS结构光电探测器

本文重点谈一谈有关把MIS结构用于光探测的研究过程中所得到的一些结果。这种探测包括可见光及红外。文章在扼要地提到MIS结构受到光照后所引起的物理现象之后,叙述了这些现象怎样用到锑化铟红外探测上去,以及把扩展的MOS结构用作光扫描象读出。在MIS电容上加一个扩散二极管或整流二极管就可增加光电探测的可能性,还谈到了对这些器件所进行的研究和研究工作日     

Influence of Rashba SOI and Polaronic Effects on the Ground-State Energy of Electrons in Semiconductor Quantum Rings

The influence of Rashba spin-orbit interaction （SOI） and polaronic effect on the ground-state energy of electrons in semiconductor quantum rings （QRs） are studied by means of the Lee-Low-Pines variational method. Numerical calculations for GaAs QRs are performed and the results show that the ground-state energy of electrons splits into two branches as E（↑） and E（↓） under the Rashba SOI, which correspond to the spin-up state and spin-down state, respectively. The contribution of the Rashba SOI effect to the ground-state energy of electrons is related to the spin state of electrons and is closely linked to the inner and outer radii of a QR. However, it is independent of the height of the QR. The ground-state energy of electrons decreases due to the polaronic effect in QRs. The energy shift ＆#8710;Ee-LO of the ground-state of the electron induced by the polaronic effect decreases monotonically with increase of the height of a QR and fluctuates with the changes of the radii of QRs. The amplitude of the fluctuation is very sensitive and remarkable to the changes of the inner radius R1 and the outer radius R2.     

基于Pekar类型变分法的高斯函数型限定势阱量子点中电子的跃迁

分别选取抛物线型限定势阱和高斯函数型限定势阱描写盘状量子点中电子的横向限定势和纵向限定势,采用Pekar类型变分法推导出了电子的基态和激发态能量,并基于费米黄金规则讨论了在磁场作用下电子的跃迁几率。结果表明,高斯函数型限定势阱比抛物线型限定势阱更能精准反映量子点中真实的限定势;量子点的厚度对电子跃迁几率的影响显著;电声耦合强度α、磁场的回旋频率ω_c、抛物线型限定势阱范围R_0、高斯函数型限定势阱的阱深V_0和阱宽L等对电子跃迁几率Q的影响的量度和变化规律方面差异较大。     

A review:aluminum nitride MEMS contour-mode resonator

Over the past several decades, the technology of micro-electromechanical system (MEMS) has advanced. A clear need of miniaturization and integration of electronics components has had new solutions for the next generation of wireless communications. The aluminum nitride (AlN) MEMS contour-mode resonator (CMR) has emerged and become promising and competitive due to the advantages of the small size, high quality factor and frequency, low resistance, compatibility with integrated circuit (IC) technology, and the ability of integrating multi-frequency devices on a single chip. In this article, a comprehensive review of AlN MEMS CMR technology will be presented, including its basic working principle, main structures, fabrication processes, and methods of performance optimization. Among these, the deposition and etching process of the AlN film will be specially emphasized and recent advances in various performance optimization methods of the CMR will be given through specific examples which are mainly focused on temperature compensation and reducing anchor losses. This review will conclude with an assessment of the challenges and future trends of the CMR.     

极性晶体膜中电子—表面声子强耦合极化子的自陷能

采用Ｈｕｙｂｒｅｃｈｔｓ线性组合算符和变分法相结合的方法,研究了极性晶体膜内电子与体纵光学声子弱耦合、与表面光学声子强耦合系统的基态能量,得到了作为膜厚和耦合常数函数的极化子的自陷能,对ＫＣｌ晶体进行了数值计算,结果表明,不同支声子与电子相互作用对极化子自陷能的贡献大不相同     

CdF_2半导体中表面磁极化子的性质

本文讨论电子和表面光学声子耦合强、与体纵光学声子耦合弱时对ＣｄＦ２半导体表面磁极化子性质的影响．采用线性组合算符法和微扰法导出了ＣｄＦ２半导体中表面磁极化子的有效哈密顿量．在计及电子在反冲效应中发射和吸收不同波矢的声子之间的相互作用时,讨论了对ＣｄＦ２半导体中表面磁极化子性质的的影响．对ＣｄＦ２半导体进行数值计算,结果表明,ＣｄＦ２半导体中表面磁极化子的振动频率λ和诱生势Ｖｉｓ随坐标ｚ的增加而减小,随磁场Ｂ的增加而增加;诱生势Ｖｉｂ随坐标ｚ的增加而增加,但与外磁场Ｂ无关;有效势Ｖｅｆ随坐标ｚ和磁场Ｂ的增加