Class expectations This is a graduate level class. There is no final exam Grading in the class is based on homework (75%) and on a final written report(25%) The report will be revised during semester and should be 2000-3000 words(8-10 double spaced pages)

Questions: Why do we select fuzzy controllers in many real-world- systems? How much of the success can be attributed to the use of the mathematical model and conventional control design approach? How much should be attributed to the clever heuristic tuning that the control engineer uses upon implementation?

How p53 and Rb pathway function may be disrupted in cancer cells Components of the pathway which are found altered in human cancers are shown in red on the diagram above p53 and Rb themselves may be inactivated by gene mutation (loss of both copies or also as in familial retinoblastoma and Li-Fraumeni syndrome where there are inherited mutations in one copy of Rb or p53 gene respectively. Alternatively

If the system reaches a statistical steady state the covariance matrix would be constant. The system would have to be invariant

The estimate of x based on N data points can then be made without reprocessing the first N, points. Their effect can be included simply by starting with pseudo observation which is equal to the estimate based on the first N points having a variance equal to the variance of the estimate based on N The same is true of the variance of the estimate based on N

Special case: [(P)] is rational: In this solution formula we can carry out the indicated integrations in literal form in the case in which [(P)] is rational. In our work, we deal in practical way only with rational,sn, and, so this function will be rational if D(p)is rational This will be true of every desired operation except predictor. Thus except in the case of prediction, the above

Blessed are the young, for they shall inherit the national debt Herbert hoover When a government spends more than it collects in taxes, it borrows from the private sector to finance the budget deficit. The accumulation of past borrowin is the government debt. Debate about the appropriate amount of government debt in the United States is as old as the country itself. Alexander Hamilton be- lieved thata national debt, if it is not excessive, will be to us a national blessing, whereas James Madison argued that \a public debt is a public curse \Indeed, the location of the nations capital was chosen as part of a deal in which the federal

Question 1 A)Yes. The sale of the machine is part of the project initiative. Therefore, the proceeds from the sale of the equipment should be counted. )No. The R&D expenditure is a sunk cost that should not be included in the project evaluation

Introduction Packaging can be unnecessarily expensive in a couple of ways: 1. Inadequate design results in shipment damage 2. Over-design or poor design (more protection than is required or materials being incorrectlyused) results in excessive material cost. The procedure can be broken down into seven basic steps

For general applications in 3D, often need to perform 3 separate rotations to relate our inertial frame to our body frame Especially true for aircraft problems There are many ways to do this set of rotations -with the variations be based on the order of the rotations All would be acceptable