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 (engineering)

In engineering, a function is interpreted as a specific process, action or task that a system is able to perform.

In engineering design

In the lifecycle of engineering projects, there are usually distinguished subsequently: Requirements and Functional specification documents. The Requirements usually specifies the most important attributes of the requested system. In the Design specification documents, physical or software processes and systems are frequently the requested functions.

In products

For advertising and marketing of technical products, the number of functions they can perform is often counted and used for promotion. For example a calculator capable of the basic mathematical operations of addition, subtraction, multiplication, and division, would be called a "four-function" model; when other operations are added, for example for scientific, financial, or statistical calculations, advertisers speak of "57 scientific functions", etc. A wristwatch with stopwatch and timer facilities would similarly claim a specified number of functions. To maximise the claim, trivial operations which do not significantly enhance the functionality of a product may be counted.

Aim (musician)

Aim (born Andrew Turner) is a British musician, DJ and producer, who was born in Barrow-in-Furness, Cumbria. Aim's sound is a blend of funky electronic music and hip hop beats, a sound which typified the Grand Central Records label. Much of Aim's work is instrumental, though his records include collaborations with other artists who provide vocals, including Stephen Jones of Babybird, Diamond D, Souls of Mischief, QNC and Kate Rogers.

Aim has also worked as remixer, mixing songs for a variety of artists including Ian Brown, Saint Etienne, The Charlatans, Lil' Kim, Thunderbugs, Archive, Down to the Bone, Texas and former label-mates Rae & Christian.

History

Andy Turner's first musical output was in a fledgling indie band called The Chelsea Flower Show. His father was a jazz drummer and instrument shop owner and after the demise of the band, Turner followed in his father's footsteps, opening a record shop called Speed Limit Records. It was here that he began to hone his skills on the decks, helping him to embark upon a serious music career. Enthused by the burgening rave seen in the North West of England and regular trips to The_Haçienda nightclub, with Gripper he co-hosted several successful club and rave nights in his hometowm, including Yummy and Euphoria, and has continued to DJ regularly ever since. This includes at London's famous Fabric, for which he did a CD as part of the Fabric Live series.

List of Latin-script trigraphs

A number of trigraphs are found in the Latin script, most of these used especially in Irish orthography.

A

⟨aai⟩ is used in Dutch to write the sound /aːi̯/.

⟨abh⟩ is used in Irish to write the sound /əu̯/, or in Donegal, /oː/, between broad consonants.

⟨adh⟩ is used in Irish to write the sound /əi̯/, or in Donegal, /eː/, between broad consonants, or an unstressed /ə/ at the end of a word.

⟨aei⟩ is used in Irish to write the sound /eː/ between a broad and a slender consonant.

⟨agh⟩ is used in Irish to write the sound /əi̯/, or in Donegal, /eː/, between broad consonants.

⟨aim⟩ is used in French to write the sound /ɛ̃/ (/ɛm/ before a vowel).

⟨ain⟩ is used in French to write the sound /ɛ̃/ (/ɛn/ before a vowel). It also represents /ɛ̃/ in Tibetan Pinyin, where it is alternatively written än.

⟨aío⟩ is used in Irish to write the sound /iː/ between broad consonants.

⟨amh⟩ is used in Irish to write the sound /əu̯/, or in Donegal, /oː/, between broad consonants.

AIM (motorcycle)

AIM motorcycles were sports machines built in Italy between 1974 and 1982 using 49cc and 124cc Sachs and Franco Morini two-stroke engines.

See also

References

External links