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
Cycles of the Kings the king they served. This they did in poems that blended the mythological and the historical to a greater or lesser degree. The resulting stories form what has come to be known as the Historical Cycle, or more correctly Cycles, as there are a number of independent groupings. The kings that are included range from the almost entirely mythological Labraid Loingsech, who allegedly became High King of Ireland around 431 BC, to the entirely historical Brian Boru. However, the greatest glory of the Historical Cycle is the "Buile Shuibhne" ("The Frenzy of Sweeney"), a 12th-century tale told in verse and