Wireless Communications - MIT OpenCourseWare

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Stochastic Processes I - MIT OpenCourseWare

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Understanding Reference Semantics IV • If we increment x, then what’s really happening is: 1. The reference of name x is looked up. 2. The value at that reference is retrieved. 3. The 3+1 calculation occurs, producing a new data element 4 which is assigned to a fresh memory location with a new reference. 4.

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5 Introduction to harmonic functions

0) + iv(x 0;y 0) = f(z 0) = 1 2ˇ Z 2ˇ 0 f(z 0 + rei )d = 1 2ˇ Z 2ˇ 0 u(z 0 + rei ) + iv(z 0 + rei )d Looking at the real parts of this equation proves the theorem. Theorem. (Maximum principle)Suppose u(x;y) is harmonic on a open region A. (i)Suppose z 0 is in A. If uhas a relative maximum or minimum at z 0 then uis constant on a disk ...

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