Problem 1. An undirected graph G has width w if the vertices can be arranged in a se- quence V1,2,3,…,Vn such that each vertex v; is joined by an edge to at most w preceding vertices. (Vertex vj precedes if i.) Use induction to prove that every graph with width at most w is (w+1)-colorable

Problem 1. The following two parts are not related. Try them, to make sure you un- derstand the jargon of random variables distributions, probability density functions, etc. Ask your TA if you don't understand/remember what some phrase means. (a)Suppose X1, X2, and X3 are three mutually independent random variables, each having the uniform distribution

An explorer is trying to reach the Holy Grail, which she believes is located in a desert shrine d days walk from the nearest oasis. In the desert heat, the explorer must drink continuously. She can carry at most 1 gallon of water, which is enough for 1 day. However, she is free to create water caches out in the desert. For example, if the shrine were 2/3 of day's walk into the desert, then she could recover

In this example, the domain is the set fa,b, c, d, el and the range is the set Y= (1, 2, 3, 4, 5/. Related elements are joined by an arrow. This relation is a function because every element on the left is related to exactly one element on the right. In graph-theoretic

1 Independent Events Suppose that we flip two fair coins simultaneously on opposite sides of room. Intu- itively, the way one coin lands does not affect the way the other coin lands. The mathe- matical concept that captures this intuition is called independence. In particular, events A and B are independent if and only if:

Natural expansion of forest Expansion of forest through natural succession on land that until These terms have been adopted for use in the Global Forest then was under another land use( e.g. forest succession on land Resources Assessment 2000. Further information on definitions previously used for agriculture). It implies a transformation from

Forest resources n 2001, FAO published the Global Forest close collaboration among international Resources assessment 2000 forest-related processes such as those related most comprehensive such survey ever to criteria and indicators for sustainable undertaken. Largely based on information forest management; provided by the countries themselves and a the involvement of countries remote sensing survey of tropical countries

一、健康的含义 1、健康与疾病是一个连续体 2、医学模式的改变 A、神灵模式 B、机械模式 C、生物医学模式 D、生物-心理-社会医学模式

1本章学习目的 通过本章的学习,要重点掌握沉降和过滤这两种机械分离 操作的原理、过程计算、典型设备的结构与特性,能够根 据生产工艺要求,合理选择设备类型和尺寸。 2本章应掌握的内容 a沉降分离(包括重力沉降和离心沉降)的原理、过程计 算、旋风分离器的选型

一.(16分)选择题(每题只许选一个答案) (1)孔板流量计的孔流系数C当R增大时,其值 A总在增大B先减小,后保持为定值总在减小D不定 (2)某液体在内径为do的水平管路中稳定流动,其平均流速为,当它以相同的体积流量通 过等长的内径为d2(d2=do2)的管子时,若流体为层流,则压降p为原来的倍