综合题新编选登

题 79　已知P ,Q是椭圆C :x2a2 + y2b2 =1(a >b >0 )上两个动点 ,O为原点 ,直线OP的斜率为k ,而直线OP与OQ的斜率之积为m ,且 p =|OP| 2 + |OQ| 2 是一个与k无关的定值 .1)求m ,p的值 ;2 )若双曲线Γ的焦点在x轴上 ,渐近线方程为y =±mx ,椭圆C与双曲线Γ的离心率分别为e1,e2 ,求e2 -e1的取值范围 .解　OP的方程为 :y =kx ,与椭圆C的方程联立 ,可得 :x2 =a2 b2b2 +a2 k2 ,∴ |OP| 2 =x2 + y2 =(1+k2 )x2=a2 b2 (1+k2 )b2 +a2 k2 .同理可求得 :|OQ| 2 =a2 b2 [1+ (mk) 2 ]b2 +a2 ·(mk) 2=(k2 +m2 )a2 b2a2 m2 +b2 k2 .∴ p =|OP| …     

综合题新编选登

题167已知直三棱柱ABC-A1B1C1中有下列三个条件:①A1B⊥AC1;②A1B⊥B1C;③B1C1=A1C1.试利用①,②,③构造出一个你认为正确的命题,并加以证明.图1三棱柱解设C1A1=a,C1B1=b,C1C=c.A1B⊥AC1A1B·AC1=0(b-a c)(-a-c)=0-a·b a2-c2=0(1)A1B⊥B1CA1B·B1C=0(b-a c)(c-b)=0c2-b2 a·b=     

试题研讨(22)

试题(2004届第五次大联考试题)已知平面上一定点C(-1,0)和一定直线l:x=-4,P为该平面上一动点,作PQ( )l,垂足为Q, (PQ→ PC→)·(PQ→-2PC→)=0.     

试题研讨 (12)

题 1　 (2 0 0 3年 3月湖北省黄石二中、黄冈中学、华师一附中等八校联考题 ,杨志明命题 )　已知函数 f(t)对任意实数x、y都有f(x+ y) =f(x) + f(y) + 3xy(x+y+ 2 )+ 3 ,f(1) =1.(1)若t为自然数 ,试求f(t)的表达式 ;(2 )满足条件 f(t) =t的所有整数t能否构成等差数列 ?若能构成等差数列 ,求出此数列 ;若不能构成等差数列 ,请说明理由 ;(3 )若t为自然数 ,且当t≥ 4时 ,f(t) ≥mt2 + (4m+ 1)t+ 3m恒成立 ,求m的最大值 .命题溯源　此题是受 2 0 0 2年北京市朝阳区第二次模拟试题第 2 2题的启发 ,笔者自编而成 .此题与 2 0 0 2年济南市 6月份高…     

聚全氟乙丙膜电子束引发预辐射接枝AA和SSS制备阳离子交换膜的研究

利用电子束引发预辐射接枝技术,在聚全氟乙丙烯(FEP)薄膜上接枝丙烯酸(AA)和对苯乙烯磺酸钠(SSS),制备一种含羧酸基团和磺酸基团的阳离子交换膜,详细研究了反应温度、单体总浓度、pH值变化、辐照气氛及添加剂对接枝率的影响规律,明确了实验条件与接枝率的对应关系。FTIR测试证明了接枝产物是全氟乙丙烯和丙烯酸、对苯乙烯磺酸钠的接枝共聚物。     

Sensitivity of heavy-ion-induced single event burnout in SiC MOSFET

The energy deposition and electrothermal behavior of SiC metal-oxide-semiconductor field-effect transistor(MOSFET)under heavy ion radiation are investigated based on Monte Carlo method and TCAD numerical simulation.The Monte Carlo simulation results show that the density of heavy ion-induced energy deposition is the largest in the center of the heavy ion track.The time for energy deposition in SiC is on the order of picoseconds.The TCAD is used to simulate the single event burnout(SEB)sensitivity of SiC MOSFET at four representative incident positions and four incident depths.When heavy ions strike vertically from SiC MOSFET source electrode,the SiC MOSFET has the shortest SEB time and the lowest SEB voltage with respect to direct strike from the epitaxial layer,strike from the channel,and strike from the body diode region.High current and strong electric field simultaneously appear in the local area of SiC MOSFET,resulting in excessive power dissipation,further leading to excessive high lattice temperature.The gate-source junction area and the substrate-epitaxial layer junction area are both the regions where the SiC lattice temperature first reaches the SEB critical temperature.In the SEB simulation of SiC MOSFET at different incident depths,when the incident depth does not exceed the device's epitaxial layer,the heavy-ion-induced charge deposition is not enough to make lattice temperature reach the SEB critical temperature.     

含有1,4,7-三苄基-1,4,7-三氮杂环壬烷的两个双核铜配合物的合成、表征及其与DNA的相互作用

合成了2个含有1,4,7-三苄基-1,4,7-三氮杂环壬烷（Bn₃tacn）的双核铜配合物：[Cu₂（Bn₃tacn）₂（m-bdc）（CH₃CN）₃（H₂O）₂]ClO₄（1）和[Cu₂（Bn₃tacn）₂（OH）₂]（ClO₄）₂（2）。配合物1由间苯二甲酸采取单双齿方式桥连Cu（Ⅱ）离子,配合物2由OH桥连。配合物1和2晶体均属于单斜晶系,分别为P2₁/c空间群和C2/c空间群。分别对2个配合物进行了红外光谱、紫外-可见光谱和元素分析表征。研究了配合物1与DNA的相互作用,对配合物2进行了循环伏安测试。     

《大学物理实验》课程多媒体CAI教学模式的研究与实践

本文主要介绍《大学物理实验》课程利用多媒体ＣＡＩ方法实现教学模式的转变。     

Absolute small-angle measurement based on optical feedback interferometry

We present a simple but effective method for small-angle measurement based on optical feedback interferometry （or laser self-mixing interferometry）. The absolute zero angle can be defined at the biggest fringe amplitude point, so this method can also achieve absolute angle measurement. In order to verify the method, we construct an angle measurement system. The Fourier-transform method is used to analysis the interference signal. Rotation angles are experimentally measured with a resolution of 10^-6 rad and a measurement range of approximately from -0.0007 to ＋0.0007 rad.     

Theoretical Studies on the Proton Transfer Mechanism in Four-water Hydrated Glycine Complexes

The mp2/6-31++g**//b3lyp/6-31++g** method has been employed to study the proton transfer mechanism in 4H2O-glycine complexes(4W-G).Compared with bare glycine the four-water hydrated neutral glycine complexes(4W-GN) can turn into the corresponding zwitterionic glycine(4W-GZ) through proton transfer.The most stable conformation of 4W-GZ has a "double water-chain" structure and is more stable than its corresponding precursor 4W-GN by 0.97 KJ/mol though it is less stable than the most stable 4W-GN by 7.80 KJ/mol.It is a spontaneous reaction to form the most stable conformation of 4W-GZ,and the potential barrier is only 1.97 KJ/mol,so the probability of this reaction is very high and the most stable 4W-GZ may be detected in experiment or in the early stage of experiment.