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

Notes for Recitation 14 Counting Rules Rule 1(Generalized Product Rule). Let be a set of length-k sequences. If there are: n1 possible first entries, n2 possible second entries for each first entry, n3 possible third entries for each combination of first and second entries, etc. then:

Key to practice exercise I. GRAMMAR 1.C 2.A在 hope,Ibet结构后的that-分句中可使用一般现在时表示将来的动作。如: bet it rains tomorrow. 3.B.主句中若有 require, demand, suggest insist order, prefer, propose recommend, request等动词,其后的that分句中应使用be型虚拟式,即动次原形或 should+动词原形

Keynes简化的线性函数形式为: Y=a+by Keynes提出其理论是在三十年代,当时 他主要是以个人的偶然的观察为依据 3五十年代后,经济学家为了检验这个假 说,对实际统计资料进行统计分析,在 此基础上总结出了几种新的消费函数形 式,相应提出了各种有关消费的假说

一、单项选择题 1.氧气湿化瓶的处理不妥的是 A.装入冷开水 B.水量为2/3满 C.通气管浸入液面以下 D.氧气雾化吸入时瓶内不放水E.湿化瓶内的水定时更换

Chapter 3 Least Squares Methods for Estimating B Methods for estimat ing B Least squares estimation Maximum like lihood estimation Met hod of moments est imation Least a bsolute deviat ion est imation 3.1 Least squares estimation The criterion of the least squares estimation is

后缀suffix 常见的构成名词的后缀 -ability ability stability availability -age leakage shortage shrinkage drainage -a/ denial dismissal renewal withdrawal burial -an American Russian Asian Indian African -ance admittance attendance endurance -ant accountant attendant contestant pollutant

Lecture 16: Intracellular drug delivery Last time nano- and micro-particle drug carriers Delivery to tissues from systemic circulation Today. Intracellular drug delivery Reading A.S. Hoffman et aL., Design of \smart polymers that can direct intracellular drug delivery, Polym. Adv. Technol. 13, 992-999(2002) Ph gradients and drug delivery: cancer res. 56, 1194(1996): adv drug deliv rev 25, 3 (1997); see asokan minireview

Lecture 3: Degradable Materials with Biological Recognition Last time: Theory of hydrolytic polymer erosion Enzymatic degradation of polymers Designing Biodegradable Macromolecules Today: Biological recognition in vivo Engineering biological recognition of biomaterials: cell adhesion/migration Reading: S.E. Sakiyama-Elbert and J.A. Hubbell, 'Functional Biomaterials: Design of Novel

本部分由 Math Type工具制作,若要修改,请确定安装了 MathType 第二十章重积分 §2重积分化累次积分 313.5(1) k+1 (2)1(3)(4)=a4(5)-(e2-1)(6 (k+1)(m+1+-)