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":

Structural functionalism

Structural functionalism, or simply functionalism, is a framework for building theory that sees society as a complex system whose parts work together to promote solidarity and stability. This approach looks at society through a macro-level orientation, which is a broad focus on the social structures that shape society as a whole, and believes that society has evolved like organisms. This approach looks at both social structure and social functions. Functionalism addresses society as a whole in terms of the function of its constituent elements; namely norms, customs, traditions, and institutions. A common analogy, popularized by Herbert Spencer, presents these parts of society as "organs" that work toward the proper functioning of the "body" as a whole. In the most basic terms, it simply emphasizes "the effort to impute, as rigorously as possible, to each feature, custom, or practice, its effect on the functioning of a supposedly stable, cohesive system". For Talcott Parsons, "structural-functionalism" came to describe a particular stage in the methodological development of social science, rather than a specific school of thought. The structural functionalism approach is a macrosociological analysis, with a broad focus on social structures that shape society as a whole.

Ritmo

Ritmo is the title of the fifth album by the British singer-songwriter Judie Tzuke, released in September 1983. The album peaked at number 26 in the UK.

The album was Tzuke's second and final studio album to be released during her contract with Chrysalis Records. Originally only released on vinyl album and cassette, it was remastered and released on compact disc in 1994 by BGO Records.

Track listing

All tracks by Judie Tzuke, Mike Paxman and Paul Muggleton, except where indicated

Personnel

Nebiolo Printech

Nebiolo Printech S.p.A. is a manufacturer of printing presses and paper and formerly a type foundry. Nebiolo & Co. was created when Giovanni Nebiolo bought out the type foundry of G. Narizzano in Turin, Italy, in 1852. In 1908 the company merged with the Urania Company and operated under the name Augustea and began to buy out many smaller foundries. In 1916 it was again renamed Società Nebiolo. Fiat bought the press manufacturing business in 1978, turning the type business over to Italiana Caratteri. In 1992 it became Nebiolo Printech S.p.A. and continues to manufacture presses under that name today.

Type Foundry

Nebiolo created a large library of typefaces, which remain popular today, although the company never entered photocomposition. It also built a type caster that competed with the Ludlow Typograph. Nebiolo types were distributed in the United States by Continental Type Founders Association. The designer Aldo Novarese became art director in 1952. The matrices for Nebiolo types are still being used by Schriften-Service D. Stempel GmbH.