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A nonzero constant P for which this is the case is called a period of the function. If there exists a least positive [2] constant P with this property, it is called the fundamental period (also primitive period, basic period, or prime period.) Often, "the" period of a function is used to mean its fundamental period.
Two properties are crucial regarding photoionization. On the one hand, the ionization energy (also called ionization potential, IP), refers to the energy necessary to remove one electron from a molecule; the lowest IP, corresponding to the ejection of a first electron, is the most biologically relevant factor. On the other hand, the ...
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. [citation needed] The smallest p for which a periodic sequence is p-periodic is called its least period [1] or exact period.
This is a list of some well-known periodic functions. The constant function f (x) = c, where c is independent of x, is periodic with any period, but lacks a fundamental period. A definition is given for some of the following functions, though each function may have many equivalent definitions.
For r between 1 and 3, the value 0 is still periodic but is not attracting, while the value is an attracting periodic point of period 1. With r greater than 3 but less than 1 + 6 , {\displaystyle 1+{\sqrt {6}},} there are a pair of period-2 points which together form an attracting sequence, as well as the non-attracting period-1 points ...
The function's integral is equal to over any set because the function is equal to zero almost everywhere. If G = { ( x , f ( x ) ) : x ∈ ( 0 , 1 ) } ⊂ R 2 {\displaystyle G=\{\,(x,f(x)):x\in (0,1)\,\}\subset \mathbb {R} ^{2}} is the graph of the restriction of f {\displaystyle f} to ( 0 , 1 ) {\displaystyle (0,1)} , then the box-counting ...
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The smallest such value of m for a given x is called the period of the orbit. The point x itself is called a periodic point . The cycle detection problem in computer science is the algorithmic problem of finding the first periodic point in an orbit, and the period of the orbit.