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A (purely) periodic sequence (with period p), or a p-periodic sequence, is a sequence a 1, a 2, a 3, ... satisfying . a n+p = a n. for all values of n. [1] [2] [3] If a sequence is regarded as a function whose domain is the set of natural numbers, then a periodic sequence is simply a special type of periodic function.
Any function that consists only of periodic functions with the same period is also periodic (with period equal or smaller), including: addition, subtraction, multiplication and division of periodic functions, and; taking a power or a root of a periodic function (provided it is defined for all ).
Periodic points of f(z) = z*z−0.75 for period =6 as intersections of 2 implicit curves. The degree of the equation () = is 2 n; thus for example, to find the points on a 3-cycle we would need to solve an equation of degree 8. After factoring out the factors giving the two fixed points, we would have a sixth degree equation.
A periodic motion is a closed curve in phase space. That is, for some period, ′ = (,), = (). The textbook example of a periodic motion is the undamped pendulum.. If the phase space is periodic in one or more coordinates, say () = (+), with a vector [clarification needed], then there is a second kind of periodic motions defined by
Similarly, right division of b by a (written b / a) is the solution y to the equation y ∗ a = b. Division in this sense does not require ∗ to have any particular properties (such as commutativity, associativity, or an identity element). A magma for which both a \ b and b / a exist and are unique for all a and all b (the Latin square ...
The United States on Monday called out Russia and China at the United Nations Security Council for "shamelessly protecting" and emboldening North Korea to further violate U.N. sanctions as ...
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