Function

Function may refer to:

Math, computing and engineering

Music

Other uses

See also

Minkowski's question mark function

In mathematics, the Minkowski question mark function (or the slippery devil's staircase), denoted by ?(x), is a function possessing various unusual fractal properties, defined by Hermann Minkowski (1904, pages 171–172). It maps quadratic irrationals to rational numbers on the unit interval, via an expression relating the continued fraction expansions of the quadratics to the binary expansions of the rationals, given by Arnaud Denjoy in 1938. In addition, it maps rational numbers to dyadic rationals, as can be seen by a recursive definition closely related to the Stern–Brocot tree.

Definition

If is the continued fraction representation of an irrational number x, then

whereas:

If is a continued fraction representation of a rational number x, then

Intuitive explanation

To get some intuition for the definition above, consider the different ways of interpreting an infinite string of bits beginning with 0 as a real number in [0,1]. One obvious way to interpret such a string is to place a binary point after the first 0 and read the string as a binary expansion: thus, for instance, the string 001001001001001001001001... represents the binary number 0.010010010010..., or 2/7. Another interpretation views a string as the continued fraction [0; a₁, a₂, … ], where the integers a_i are the run lengths in a run-length encoding of the string. The same example string 001001001001001001001001... then corresponds to [0; 2, 1, 2, 1, 2, 1, …] = √3 − 1/2. If the string ends in an infinitely long run of the same bit, we ignore it and terminate the representation; this is suggested by the formal "identity":

Function (mathematics)

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x². The output of a function f corresponding to an input x is denoted by f(x) (read "f of x"). In this example, if the input is −3, then the output is 9, and we may write f(−3) = 9. Likewise, if the input is 3, then the output is also 9, and we may write f(3) = 9. (The same output may be produced by more than one input, but each input gives only one output.) The input variable(s) are sometimes referred to as the argument(s) of the function.

Functions of various kinds are "the central objects of investigation" in most fields of modern mathematics. There are many ways to describe or represent a function. Some functions may be defined by a formula or algorithm that tells how to compute the output for a given input. Others are given by a picture, called the graph of the function. In science, functions are sometimes defined by a table that gives the outputs for selected inputs. A function could be described implicitly, for example as the inverse to another function or as a solution of a differential equation.

Cook

Cook may refer to:

Place name

Australia

New Zealand

United Kingdom

United States

Cook (crater)

Cook is a lunar crater that lies in the western part of the Mare Fecunditatis, just to the southeast of the prominent crater Colombo. To the southwest is Monge.

The interior of this crater has been flooded with lava, leaving only a low rim projecting above the surface. This rim is not quite circular, and has a somewhat hexagonal appearance. The low wall is worn in a few places, particularly along the northeastern rim. There is a tiny craterlet called Cook A on the interior floor near the southeast rim.

Satellite craters

By convention these features are identified on lunar maps by placing the letter on the side of the crater midpoint that is closest to Cook.

References

USS Donald Cook (DDG-75)

USS Donald Cook (DDG-75) is an Arleigh Burke-class guided missile destroyer in the United States Navy.

Named for Donald Cook, a Vietnam War prisoner of war who died in captivity, the destroyer was commissioned in 1998. It was one of the first U.S. warships to come to the aid of USS Cole after it was damaged by suicide bombers on 12 October 2000. In 2003, the ship fired Tomahawk missiles during Operation Iraqi Freedom.

On 16 February 2012, Secretary of the Navy Ray Mabus announced Donald Cook will be one of four ships to be homeported at Naval Station Rota, Spain. It was announced in January 2014 that the ship would arrive there in mid-February 2014. In Rota she forms part of Destroyer Squadron 60.

Service history

On 24 February 2012, Donald Cook was awarded the 2011 Battle Efficiency "E" award.

Private (web series)

Private is an American Web series produced by Alloy Entertainment based on the novels of the same name by Kate Brian.

The series was announced in May 2009, beginning with a contest allowing female readers the chance to audition for the role of Kiran Hayes. It was also announced that the series would adapt the first four books via 20 episodes, each with a standard length of four to six minutes.

A DVD with episodes of the series was released by Newvideo.

Contest

Private: The Casting Call was the contest in which three contestants competed for the role of Kiran Hayes in the Web adaptation of Private.

Episode list

References