Theory of Equivalence Relations (A, R) (E1) For all x : xRx. (E2) For all x, y : If xRy then yRx. (E3) For all x, y, z : If xRy and yRz then xRz. Logic in Computer Science – p.2/16

16.322 Stochastic Estimation and Control Professor Vander Velde 1. P(ABCD.=P(A)P(B A)P(C|AB)P(D 1 ABC) Derive this by letting A=CD. Then P(BCD)= P(CD)P(B ICD)= P(C)P(DIC)P(DICD) 2. If A,, A2r.. is a set of mutually exclusive and collectively exhaustive events, then

1、最小差错概率准则 由于噪声的干扰,所以在发送x时,不一定判 为r;,而可能判为其他符号,这就是错误判决。当 然,我们希望差错概率最小,在数字通信中最直 观和最合理的准则是“最小差错概率”准则

1范围 本方法适用于地面水、饮用水、污水、电子电镀、生化等一般工业废水中NO3N的测 定。 本方法的检出限为0.21mg/LNO3-N。线性测量范围为1.00~1000mg/lno3-n 试验了sO2、pO4、Cr、Br、I、Ac、HCO3、CO32、C2O42、nO2、s2、+、nH4、 A13+、Ca2+、Mg2+、Zn2+、Cu2+、Pb2、Fe2+、Fe+对测定的干扰,其中s2、r明显干扰,Br 大于57倍,NO2大于32倍,C大于250倍时有干扰,其他均无干扰

一、例题精解 【例题15.1】在图15.1(a)中,u1是输入电压的波形。试画出对应于u1的输出电压u、 电阻R上的电压u和二极管D上电压u的波形。二极管的正向压降可忽略不计

1)某盛有液体的圆筒容器,容器轴心线为铅垂向,液面水平,如附图中虚 线所示。当容器以等角速度ω绕容器轴线旋转,液面呈曲面状。试证明 ①液面为旋转抛物面 ③液相内某一点(r,z)的压强20+P

例1采用3M色谱柱对A、B二组分进行分离,此时测得非滞 留组分的tu值为0.9min, A组分的保留时间(t(A)为15.1minB组分的t为18.0min,要 使二组分达到基线分离 (R=1.5),问最短柱长应选择多少米(设B组分的峰宽为1.1 min)?

1.在银电极上,C,Br和均可进行下述反应。 ag+=10-6mol/leaa.790.09log10-0.445V E AgCL,Ag=.222 V, E AgBr,Ag=0.071V, E Aglr,Ag-0.152V) Ag(s)+X= AgX(s)+e\ 试问:(1)若Br和的起始浓度都是0.05mol/l,可否用恒电位电解法分离r和?

The Normal Distribution: the distribution of a continuous r.v. whose value depends on a number of factors, yet no single factor dominates the other. 1. Properties of the normal distribution: 1)The normal distribution curve is symmetrical around its mean valueu. 2)The PDF of the distribution is the highest at its mean value but tails off at its extremities

1 At a frequency of 796 Hz, compute Zo,u and for a line having the following parameters: F2230 u H/km,=0.0055 u F, r-6./km, g negligible. 2 At certain frequency, transmission line has Zo=5560°andy=0.005+j0.03np/km The line is 60 km long. A sinusoidal voltage of 100V at the specified frequency is applied to one end. Find: