Introduction 1. Definition: Fis a fictitious force which is supposed to be responsible for the motion of dislocation. Fll Criterion: The work done on crystal by stress must be equal to that done on dislocation by force F. 2. Principle of derivation of F: Macroscopic work=microscopic work (or deformation work)

Introduction A primary goal of your efforts in this course will be to gather empirical data so as to prove(or disprove) your hypothesis Typically the data that you gather will not directly satisfy this goal Rather, it will be necessary to \reduce\the data. to put it into an appropriate form, so that you can

How can the paradox with the spring be plained? In other words, which of the following statements is true 1. Equilibrium can be derived from the equiv alence of the external and the internal work 2. Equilibrium is an artifact of our imagina- tion

DEFINITION OF A HYPOTHESIS Hypothesis A tentative explanation that accounts for facts and can be tested by further investigation; a theory Something taken to be true for the purpose of argument or investigation; an assumption .Experiment test under controlled conditions that is made to demonstrate

Rank deficiencies Ranks deficiencies are combinations of parameters that can not be separately estimated In GPs. there are several rank deficiencies UTl, Longitudes of all the stations and the nodes of the satellite orbits, effectively can not be separated In theory, orbit perturbations by the moon/sun on the GPs

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