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 "α"("G"). The effective number of signals transmitted per unit time step is the "k"th root of this number, "α"("G"). Using these concepts, the Shannon capacity may be defined as the limit (as "k" becomes arbitrarily large) of the effective number of signals per time step of arbitrarily long confusion-free codes. The computational complexity of the Shannon capacity is unknown, and even the value of the Shannon capacity for certain small graphs such as "C" (a cycle graph of seven vertices) remains unknown. A natural approach to this problem would be to compute a finite number of powers of the given