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MapReduce is a programming model and an associated implementation for processing and generating big data sets with a parallel and distributed algorithm on a cluster. [1] [2] [3]A MapReduce program is composed of a map procedure, which performs filtering and sorting (such as sorting students by first name into queues, one queue for each name), and a reduce method, which performs a summary ...
In number theory, the gcd-sum function, [1] also called Pillai's arithmetical function, [1] is defined for every by = = (,) or equivalently ...
In the data transformation stage, a series of rules or functions are applied to the extracted data in order to prepare it for loading into the end target. An important function of transformation is data cleansing, which aims to pass only "proper" data to the target. The challenge when different systems interact is in the relevant systems ...
A function object solves those problems since the function is really a façade for a full object, carrying its own state. Many modern (and some older) languages, e.g. C++, Eiffel, Groovy, Lisp, Smalltalk, Perl, PHP, Python, Ruby, Scala, and many others, support first-class function objects and may even make significant use of them. [3]
For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2. If the initial term of an arithmetic progression is a 1 {\displaystyle a_{1}} and the common difference of successive members is d {\displaystyle d} , then the n {\displaystyle n} -th term of the sequence ( a n {\displaystyle a_{n ...
The third normal form (3NF) is a normal form used in database normalization. 3NF was originally defined by E. F. Codd in 1971. [2]Codd's definition states that a table is in 3NF if and only if both of the following conditions hold:
Since PHP 4.0.1 create_function(), a thin wrapper around eval(), allowed normal PHP functions to be created during program execution; it was deprecated in PHP 7.2 and removed in PHP 8.0 [226] in favor of syntax for anonymous functions or "closures" [227] that can capture variables from the surrounding scope, which was added in PHP 5.3.
A Laurent series is a generalization of the Taylor series, allowing terms with negative exponents; it takes the form = and converges in an annulus. [6] In particular, a Laurent series can be used to examine the behavior of a complex function near a singularity by considering the series expansion on an annulus centered at the singularity.