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
Oh Dear! What Can the Matter Be? basin it was the same water the next washed her face in – and nobody knew they were there. </poem> "Seven Old Ladies" was not the first parody, however. Long before that parody, the song had been parodied for political purposes. One such parody can be found in the "Wisconsin State Journal" of 1 March 1864. It was written to exhort parents, who during the U.S. Civil War had not taken much interest in public schooling in Madison, to visit the schools of their children. Its lyrics were: <poem> Oh, dear, what can the matter be? Oh, dear, what can