Problem set 1 Micro Theory S. Wang Question1.1. Show that“f(X)=f(x),Vx∈R,A>1” implies“f(A)= Af(x),Vx∈R,A>0.” estion 1.2. Use a Lagrange function to solve c(w1, w2, y) for the following problem

Problem set 3 Micro Susen Wang Try to do most problems in MWG(1995), Chapters 7-9 Question 3.1.(Mixed-Strategy Nash Equilibrium). A principal hires an agent to perform some service at a price(which is supposed to equal the cost of the service The principal and the agent have initial

• Brief introduction – Hardware, software, login and policy • How to write and run program on multiple CPUs – Simple MPI programming – Resources on MPI documentation • Demonstration of software installed – SPRNG, BLAS, NAMD2, GAMESS, PGI

Then =1-91=1(3+:2)(3+2n 可=-1-3)=1(4-+2)(1-2+a With 1 0 O: Thus, in equilibrium, we must have ai=.2. In fact, the two firms must sit in the middle By Proposition 2.1, Pi=p?=c Discussion

1. Introduction 2. Applications 3. Characteristics of Serial I/O 4. Characteristics of Parallel I/O 5. Introduction to MPI-2 Parallel I/O 6. MPI-2 File Structure 7. Initializing MPI-2 File I/O 8. Defining A View 9. Data Access - Reading Data 10.Data Access - Writing Data 11.Closing MPI-2 File I/O

18.1 Introduction 18.2 C++ 18.3 A Simple Program: Adding Two Integers 18.4 C++ Standard Library 18.5 Header Files 18.6 Inline Functions 18.7 References and Reference Parameters 18.8 Empty Parameter Lists 18.9 Default Arguments 18.10 Unary Scope Resolution Operator 18.11 Function Overloading 18.12 Function Templates 18.13 Introduction to Object Technology and the UML 18.14 Wrap-Up

then there exists AE R\ such that (Kuhn-Tucker condition) G(s') =0 and 1. Lagrange Method for Constrained Optimization FOC: D.L(,\)=0. The following classical theorem is from Takayama(1993, p.114). Theorem A-4 (Sufficieney). Let f and, i= ,..m, be quasi-concave, where Theorem A-1. (Lagrange). For f: and G\\, consider the following G=(.8 ) Let r' satisfy the Kuhn-Tucker condition and the FOC for (A.2). Then, x' problem is a global maximum point if max f() (1)Df(x') =0, and f is locally twice continuously differentiable,or

⚫ Introduction to Linux ⚫ History of UNIX and Linux ⚫ Login, logout and changing the password ⚫ Basic Linux command ⚫ Linux hierarchical file system ⚫ Linux shell environment ⚫ Editors: vi, pico, emacs, joe, nano ⚫ Basic shell scripts ⚫ Compiling, link and run C, C++, Fortran programs ⚫ Foreground and Background jobs ⚫ File transfer from other PCs in different platform ⚫ Linux distributions

◆ Background of Mobile Ad Hoc Networks ◆ Thesis part I ◼ A Trusted Routing Protocol for Security Issues of Mobile Ad Hoc Networks ◆ Thesis part II ◼ A Coalitional Game Model for Security Issues of Wireless Networks ◆ Thesis part III ◼ A Coalitional Game Model for Selfishness Issues of Wireless Networks

Production Plans with Multiple Outputs Lety≡(m,,…,ym) be a net output vector, YArn be a convex set,G:Y→R be twice differentiable Production possibility set:{y∈Y|G(y)≤0} Assumption 1.1. Gy (y)>0, Vi,yEY. Proposition 1. 12. Production frontier yEY G(y)=0 contains technologically efficient production plans Definition 1.1. Marginal rate of transformation