These notes essentially tie up a few loose ends in Lecture 8; in particular, I exhibit examples of inefficiencies in first- and second-price auctions. I would also like to briefly comment on Questions 1 and 2 in Problem Set 2

第四章4-4特征值与特征向量(续) 4.4.2关于特征向量与特征子空间的一些性质 命题线性变换的属于不同特征值的特征向量线性无关。 证明设A为VK上的线性变换,,2,是两两不同的特征值,(1≤i≤t)是 属于特征子空间V的特征向量,设k,k2,k,∈K,使得k5+k252+…+k5=0,两 边用A作用(i=1,2,…,-1),于是得到方程组 5+52++=0,j0,1,t-1 其中入的方幂组成的矩阵为

1,指数函数希望能够在复平面内定义一个函 数f(z)具有实函数中的指数函数ex的三个性质: i)f(z)在复平面内解析; ii) f'(z) f(z) i)当m(z)=0时,f(z)=ex,其中x=re(z) 前面的例1中已经知道,函数

连续时间马氏链 仍记状态空间为S={0,1,2,…} 定义设随机过程X={X(t),t≥0}对于任意0≤to0就有 P{(tn+1)=in+1(to) io, X (t1) =i1,.,()= in} =P{X(tn+) in+()= in} 则称{X(t),t≥0}为连续参数马尔可夫链(简称连续参数马氏链)

Part I Vocabulary Structure(20%) Section a I. Ben was quite stubborn and it was almost impossible to him of his mistakes B. recognize C. forget D. convince

Revision: I. Expressions Directions: Turn the following English terms into Chinese without looking at your textbook I. sale by sample 2. G M.Q 3. sale by

第六章设备管理 6.1概述 6.2I/O软件的组成 6.3I/O硬件特点 6.4有关技术 6.5设备处理 6.6典型外部设备

Task Team of FUNDAMENTAL ACCOUntING hool of Business, Sun Y at-sen University Lesson 13 Managerial Accounting I: Concepts and Principles Self-Test I. True and False Questions Managerial accounting places less emphasis on precision and more emphasis on flexibility

ynamic order statistics OS-SELECT(i, S): returns the i th smallest element in the dynamic set S. OS-RANK(, S): returns the rank ofx E S in the sorted order of s s elements IDEA: Use a red-black tree for the set S, but keep subtree sizes in the nodes

Binary-search-tree sort 7∈ b Create an empty Bst for i=i to n do trEe-INSert(,AiD) Perform an inorder tree walk of t Example: