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The concept of an almost periodic function (also called a quasiperiodic function) was studied by Bohr, including work of Bohl and Escanglon. [47] He introduced the notion of a superspace. Bohr showed that quasiperiodic functions arise as restrictions of high-dimensional periodic functions to an irrational slice (an intersection with one or more ...
Quasiperiodic behavior is almost but not quite periodic. [2] The term used to denote oscillations that appear to follow a regular pattern but which do not have a fixed period. The term thus used does not have a precise definition and should not be confused with more strictly defined mathematical concepts such as an almost periodic function or a ...
Bloch's theorem says that the eigenfunctions of a periodic Schrödinger equation (or other periodic linear equations) can be found in quasiperiodic form, and a related form of quasi-periodic solution for periodic linear differential equations is expressed by Floquet theory. Functions with an additive functional equation
A periodic function, also called a periodic waveform (or simply periodic wave), is a function that repeats its values at regular intervals or periods. The repeatable part of the function or waveform is called a cycle . [ 1 ]
Furthermore, the "spectre" tile is a "strictly chiral" aperiodic monotile: even if reflections are allowed, every tiling is non-periodic and uses only one chirality of the spectre. That is, there are no tilings of the plane that use both the spectre and its mirror image.
Fig 1. The top graph shows a non-periodic function () in blue defined only over the red interval from 0 to P. The function can be analyzed over this interval to produce the Fourier series in the bottom graph. The Fourier series is always a periodic function, even if original function () is not.
In electronics, acoustics, and related fields, the waveform of a signal is the shape of its graph as a function of time, independent of its time and magnitude scales and of any displacement in time. [1] [2] Periodic waveforms repeat regularly at a constant period. The term can also be used for non-periodic or aperiodic signals, like chirps and ...
An example of such a tiling is shown in the adjacent diagram (see the image description for more information). A tiling that cannot be constructed from a single primitive cell is called nonperiodic. If a given set of tiles allows only nonperiodic tilings, then this set of tiles is called aperiodic . [ 3 ]