Please print out this problem set and record your answers on the printed copy. Answers to this problem set are to be turned in at the box outside by 4: 10 Wednesday, October I Problem sets will not be accepted late Solutions will be posted on the web October 2

4.7.I Occurrence and microheterogeneity B-Lactoglobulin is a major protein in bovine milk, representing about 50% of total whey protein and 12% of the total protein of milk. It was among the first proteins to be crystallized, and since crystallizability was long considered to be a good criterion of homogeneity, B-Ig, which is a typical

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

Number Theory I Number theory is the study of the integers. Number theory is right at the core of math ematics; even Ug the Caveman surely had some grasp of the integers- at least the posi tive ones. In fact, the integers are so elementary that one might ask, What's to study?

1 The Number-Picking Game Here is a game that you and I could play that reveals a strange property of expectation. 3, First, you think of a probability density function on the natural numbers. Your distri- bution can be absolutely anything you like. For example, you might choose a uniform distribution on 1, 2, ... 6, like the outcome of a fair die roll. Or you might choose a bi- probability, provided that,...,n. You can even give every natural number a non-zero nomial distribution on 0, 1 he sum of all probabilities is 1

知识要点 1.全电流定律(安培环路定律) 其数学表达式为 a=i (11) 把该定律用于电机或变压器的多磁路耦合时,可简化为∑H=∑Ni 2.磁路欧姆定律

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

Diffusion: Read Plummer Chap. 7, sections 7.1-7.4,, 7.53, 7.5.8 Show that c(zt) Wroexpfzla)I,with a=2VDf, is a solution to Fick's second law of diffusion. ac(z, t) dc(zt) 2. a) What is the intrinsic carrier concentration in Si at 1100 C? b) Calculate the effective diffusivity (including first-order, charged-vacancy corrections)for As impurities in Si at 1100 C for two cases: 1)CAs=10 cm and ii)

I. Plot resolution and depth of field as a function of exposure wavelength for a projection aligner with 100nm< A <500nm. Assume NA=0.26. Recalculate on the same plot for NA=0.41. Discuss the implication of these plots for the technologist that must manufacture transistors with 0.5 um

1. You need to deposit a high quality (low electrical resistivity) Al film at a very high rate(v> I micron/min) and achieve good step coveage using sputter deposition. Referring to information in the class notes and text, answer the following three questions. (Grade will depend more on how you justify your design, rather than on its