Function

Function may refer to:

Math, computing and engineering

Function (mathematics), a relation that associates an input to a single output according to some rule

Function model, a structured representation of the functions, activities or processes

Function (engineering), related to the selected property of a system

Subroutine, also called a function, a sequence of instructions within a larger computer program

Function object, or functor or functionoid, a concept of object-oriented programming

Music

Diatonic function, a term in music theory

"Function" (song), a 2012 song by American rapper E-40 featuring YG, Iamsu! & Problem

"Function", song by Dana Kletter from Boneyard Beach (Dish album) 1995

Other uses

A social event

Function (biology), explaining why a feature survived selection

Function (language), in linguistics, a way of achieving an aim using language

Function Drinks, a beverage company based in Redondo Beach, California.

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 $[a_0; a_1, a_2, \ldots]$ is the continued fraction representation of an irrational number $x$ , then

whereas:

If $[a_0; a_1, a_2, \ldots, a_m]$ 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 $[0; a 1, a 2, \dots ]$ , 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 $[0; 2, 1, 2, 1, 2, 1, \dots] =$ √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.

Ko Samui

Ko Samui (or Koh Samui, Thai: เกาะสมุย, Thai pronunciation: [kɔ̀ sàmūj]) is an island off the east coast of the Kra Isthmus, Thailand. Geographically in the Chumphon Archipelago, it is administratively part of Surat Thani Province. Ko Samui is Thailand's second-largest island after Phuket, with an area of 228.7 km², a population of over 63,000 and a hotel occupancy rate of 73% as the number of visitors increases. Abundant tourist resources, sandy beaches, coral reefs, and coconut trees are present on the island.

History

The island was probably first inhabited about 15 centuries ago, settled by fishermen from the Malay Peninsula and southern China. It appears on Chinese maps dating back to 1687, under the name Pulo Cornam. The name samui is mysterious in itself. Perhaps it is an extension of the name of one of the native trees, mui. Some people believe that the word "samui" derives from the Malay word "saboey", or "safe haven", although there appears to be no credible corroboration of this. Ko is the Thai word for "island".