MIT6_004s09_lec12

n � T � i=1 t=1 n T −1 � � i=1 t=1
φi (pi,t ) +
ψi (pi,t+1 − pi,t ).
Choosing the generator output schedules to minimize C , while respecting the con­ straints described above, is a convex optimization problem. The problem data are dt 2
6.079/6.975 December 10–11, 2009.
S. Boyd & P. Parrilo
Final exam
This is a 24 hour take-home final exam. Please turn it in to Professor Stephen Boyd, (Stata Center), on Friday December 11, at 5PM (or before). You may use any books, notes, or computer programs (e.g., Matlab, CVX), but you may not discuss the exam with anyone until December 11 after 5PM, after everyone has taken the exam. The only exception is that you can ask us for clarification, via email. Please address your emails to both professors and the TA. Please make a copy of your exam before handing it in. When a problem involves computation you must give all of the following: a clear discussion and justification of exactly what you did, the Matlab source code that produces the result, and the final numerical results or plots. Matlab files containing problem data are available on Stellar. All problems have equal weight. Some are easier than they might appear at first glance. And others are harder than they might appear at first glance. Be sure to check your email and the course web site on Stellar often during the exam, just in case we need to send out an important announcement. And one technical comment. For problems that require you to work out a numerical solution, you are welcome to use a solution method that involves solving more than just a single convex optimization problem. (Of course, only when this is necessary.)

Moving a magnet towards a coil produces a time-varying magnetic field inside the coil
Rotating a bar of magnet (or the coil) produces a time-varying magnetic field inside the coil
I=
V J · dA = σ E · dA = σ A l l ρl V =I = I = IR σA A
14
H
Ni = Φ
Reluctance of Magnetic Bar
Magnetic “OHM’s LAW”
l
Ni = Φ
φ
A
l = μA
15
Flux Density in a Toroidal Core
Electrical Circuit Analogy
Electromotive force (charge push)= Magneto-motive force (flux push)=
v=
i
+
V
E · dl
C
H · dl = Ienclosed
i
EQUIVALENT CIRCUITS
i
Ф
Electrical
Shield GMR Read Head
Recording Medium Horizontal Magnetized Bits Bit density is limited by how well the field can be localized in write head
9
Review: Ferromagnetic Materials

2
How are Financial Products Traded?
Introduction of basic knowledge of financial markets and quantitative analysis
Jake Xia MIT Course 18.S096 September 5, 2013
and
Vega
Markets, Exchanges, OTC, Regions
Money, Currencies Stocks, Equity Indices, IPOs, Primary/Secondary
Loans, Bonds, Credit Products
Commodity
Real Estate, Mortgages, ABS
Dealers, Market Makers, Brokers
Individuals, Retail Investors
Mutual Funds, Insurance Companies, Pension Funds, Asset Managers, SWFs Hedge Funds (various strategies), PE Governments, Policy Makers Corporate Hedgers, Liability Management
Special situations, distressed
Financial Mathematics:
1. Pricing Models:
relative value, arbitrage-free.
2. Risk Management:
human risk aversion, greed/fear.

ecture 5: Generalized Random Graphs and Small-World
Model
Daron Acemoglu and Asu Ozdaglar
MIT
September 23, 2009
1
Networks: Lecture 5
Naive intuition: Same distribution as node i . Example: Consider a graph with 4 nodes and links {1,2}, {2,3}, {3,4}. We have P (1) = P (2) = 1/2. If we randomly pick a link and then randomly pick an end of it, there is a 2/3 chance of finding a node with degree 2 and 1/3 chance of finding a node with degree 1. Reflects the fact that higher degree nodes are involved in a higher percentage of the links.
Clustering Average path lengths
Reading: Jackson, Sections 4.1.2, 4.1.4-4.1.6, 4.2.1, 4.2.6, 4.2.7. EK, Chapter 20.
2
Networks: Lecture 5
Configuration Model—1
Poisson degree distribution and low clustering.