Spinodal decomposition both complete one cycle per second—but they represent different frequencies in the Fourier transform. Hence, frequency no longer measures the number of cycles per unit time, but is closely related.) If A(β) is the amplitude of a Fourier component of wavelength λ and wavenumber β = 2π/λ the spatial variation in composition can be expressed by the Fourier integral: in which the coefficients are defined by the inverse relationship: Substituting, we obtain on equating coefficients: This is an ordinary differential equation that has the solution: in which "A(β)" is the initial amplitude of the Fourier component of wave wavenumber β
Shannon capacity of a graph no two of these code words can be confused with each other. By using this method, in "n" steps of communication, the sender can communicate up to 5 messages, significantly more than the 2 that could be transmitted with the simpler one-digit code. The effective number of values that can be transmitted per unit time step is (5) = . In graph-theoretic terms, this means that the Shannon capacity of the 5-cycle is at least . As showed, this bound is tight: it is not possible to find a more complicated system of code words that allows even more different