Recall from lecture 22 °Flow value:f=f(s,V) Cut: Any partition (S, T)of y such that s E S andt∈T Lemma. f=f(s, T) for any cut(S, T) Corollary. f(s, T) for any cut(S, T) Residual graph: The graph G=(v, ef) with strictly positive residual capacities c u, v) c(u,)-f(2y)>0

Graphs(review) Definition. a directed graph(digraph G=(, E)is an ordered pair consisting of a set y of vertices(singular: vertex) a sete c× of edges. In an undirected graphG=(V, E), the edge set e consists of unordered pairs of vertices In either case, we have El=O(v2).Moreover if G is connected, then E2v-l, which

1 If the voltage across a 5F capacitor is 2te -V, find the current and the power 2 In 5s, the voltage across a 40mF capacitor changes from 160v to 220V. Calculating the average current through the capacitor

3-1 解： 由螺纹副受力分析可得其效率公式及自锁条件： 由=tan/tan(+v)，≤v 可知当螺纹升角一定时，螺纹工作面的牙型斜角愈大， 则 fv（或v）愈大，效率愈低，但自锁性愈好。在几种牙型的螺纹中，三角形螺纹牙 型斜角最大（=30°），故当量摩檫因素 fv 大，自锁性最好，但效率低

1 质量 的质点受力 的作用，且力方向不变．t=0 s时从v0=10 m·s-1 开始作直线运动（v0方向与力向相同），求： (1)0~2 s内，力的冲量I；(2)t=2 s时质点的速 率v2．(式中力的单位为N，时间单位为s．)

I Let L= 1.25 H in Fig. 6-11, and determine v(t)if v(0) 1(02)=20A L 0.05F ig 6-11 For prob. I 2(a)What value of L in the circuit of Fig 6-11 will result in a transient response of the form, v(t)

Definition A real-valued function V: X H R defined on state space X of a system with behavior set B and state r:B×[0,∞)→ X is called a Lyapunov function if tHv(t)=v(a(t))=v(a(z(), t)) is a non-increasing function of time for every z E B according to this definition, Lyapunov

Consider a digraph G = (V, E) with edge-weight function w : E → R. The weight of path p = v1 → v2 → L → vk is defined to be

例能源利用系统的预测 v1能源利用量;2能源价格; 3能源生产率;4环境质量;v v—工业产值;6就业机会;

2.4r.v.函数的分布 问题已知r.v.X的d.f.或分布律