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Necklace (combinatorics), an equivalence classes of cyclically ordered sequences of symbols modulo certain symmetries; Cyclic (mathematics), a list of mathematics articles with "cyclic" in the title; Cyclic group, a group generated by a single element; Cyclic permutation, a basic permutation (all permutations are products of cycles)
A set with a cyclic order is called a cyclically ordered set or simply a cycle. [nb] Some familiar cycles are discrete, having only a finite number of elements : there are seven days of the week , four cardinal directions , twelve notes in the chromatic scale , and three plays in rock-paper-scissors .
Normally, pronunciation is given only for the subject of the article in its lead section. For non-English words and names, use the pronunciation key for the appropriate language. If a common English rendering of the non-English name exists (Venice, Nikita Khrushchev), its pronunciation, if necessary, should be indicated before the non-English one.
Pronunciation is the way in which a word or a language is spoken. This may refer to generally agreed-upon sequences of sounds used in speaking a given word or language in a specific dialect ("correct" or "standard" pronunciation) or simply the way a particular individual speaks a word or language. [1] (Pronunciation ⓘ)
This definition of periodicity can be extended to other geometric shapes and patterns, as well as be generalized to higher dimensions, such as periodic tessellations of the plane. A sequence can also be viewed as a function defined on the natural numbers , and for a periodic sequence these notions are defined accordingly.
Gradients of convex functions are cyclically monotone. In fact, the converse is true. Suppose U {\displaystyle U} is convex and f : U ⇉ R n {\displaystyle f:U\rightrightarrows \mathbb {R} ^{n}} is a correspondence with nonempty values.
A cyclically ordered group is a group together with a cyclic order preserved by the group structure. Every cyclic group can be given a structure as a cyclically ordered group, consistent with the ordering of the integers (or the integers modulo the order of the group). Every finite subgroup of a cyclically ordered group is cyclic. [22]
Square brackets are used with phonetic notation, whether broad or narrow [17] – that is, for actual pronunciation, possibly including details of the pronunciation that may not be used for distinguishing words in the language being transcribed, but which the author nonetheless wishes to document. Such phonetic notation is the primary function ...