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In object-oriented programming, the singleton pattern is software design pattern that restricts the instantiation of a class to a singular instance.
The carrier (underlying set) associated with a unit type can be any singleton set. There is an isomorphism between any two such sets, so it is customary to talk about the unit type and ignore the details of its value. One may also regard the unit type as the type of 0-tuples, i.e. the product of no types.
In software engineering, the initialization-on-demand holder (design pattern) idiom is a lazy-loaded singleton. In all versions of Java, the idiom enables a safe, highly concurrent lazy initialization of static fields with good performance. [1] [2]
In coding theory, the Singleton bound, named after Richard Collom Singleton, is a relatively crude upper bound on the size of an arbitrary block code with block length , size and minimum distance . It is also known as the Joshibound [ 1 ] proved by Joshi (1958) and even earlier by Komamiya (1953) .
A set such as {{,,}} is a singleton as it contains a single element (which itself is a set, but not a singleton). A set is a singleton if and only if its cardinality is 1. In von Neumann's set-theoretic construction of the natural numbers, the number 1 is defined as the singleton {}.
[12] [6] In philosopher Nick Bostrom's 2014 work Superintelligence: Paths, Dangers, Strategies, he cited the Baruch Plan as part of an argument that a future power possessing superintelligence that obtained a sufficient strategic advantage would employ it to establish a benign 'singleton' or form of global unity.
The 5th roots of unity in the complex plane form a group under multiplication. Each non-identity element generates the group. In abstract algebra, a generating set of a group is a subset of the group set such that every element of the group can be expressed as a combination (under the group operation) of finitely many elements of the subset and their inverses.
In computer graphics, the centripetal Catmull–Rom spline is a variant form of the Catmull–Rom spline, originally formulated by Edwin Catmull and Raphael Rom, [1] which can be evaluated using a recursive algorithm proposed by Barry and Goldman. [2]