Dirac-delta fimction

The Dirac delta fimction 8(f) localizes the integration onto the dividing surface f = 0. The gradient of the dividing surface (Vf) is in the fiill phase space, p is the generalized velocity vector in phase space with components q, Pq xj, p, ) = 1,..., N, and 0(y) is the unit step function which restricts the flux to be in one direction only. The term Vf p is proportional to the velocity perpendicular to the dividing smface. The numerator is the unidirectional flux and the denominator is the partition function of reactants. 

In control theory the impulse response, g(t), is the response of a (linear) system to a Dirac delta input. The Laplace transform of the delta fimction is... 

Figure 3.4. (a) Dirac delta comb (or Shah fimction) of period l/rr (b) its Fourier transform, another Dirac comb of period x. 

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