Regular
Look up regular or regularity in Wiktionary, the free dictionary.
The term regular can mean normal or in accordance with rules. It may refer to:
People[edit]
- Moses Regular (born 1971), America football player
Arts, entertainment, and media[edit]
Music[edit]
- "Regular" (Badfinger song)
- Regular tunings of stringed instruments, tunings with equal intervals between the paired notes of successive open strings
Other uses in arts, entertainment, and media[edit]
- Regular character, a main character who appears more frequently and/or prominently than a recurring character
- Regular division of the plane, a series of drawings by the Dutch artist M. C. Escher which began in 1936
- Regular Show, an animated television sitcom
- The Regular Guys, a radio morning show
Language[edit]
- Regular inflection, the formation of derived forms such as plurals in ways that are typical for the language
- Regular script, the newest of the Chinese script styles
Mathematics[edit]
There are an extremely large number of unrelated notions of "regularity" in mathematics.
Algebra and number theory[edit]
(See also the geometry section for notions related to algebraic geometry.)
- Regular category, a kind of category that has similarities to both Abelian categories and to the category of sets
- Regular chains in computer algebra
- Regular element (disambiguation), certain kinds of elements of an algebraic structure
- Regular extension of fields
- Regular ideal (multiple definitions)
- Regular monomorphisms and regular epimorphisms, monomorphisms (resp. epimorphisms) which equalize (resp. coequalize) some parallel pair of morphisms
- Regular numbers, numbers which evenly divide a power of 60
- Regular p-group, a concept capturing some of the more important properties of abelian p-groups, but general enough to include most "small" p-groups
- Regular prime, a prime number p > 2 that does not divide the class number of the p-th cyclotomic field
- The regular representation of a group G, the linear representation afforded by the group action of G on itself
- Regular ring, a ring such that all its localizations have Krull dimension equal to the minimal number of generators of the maximal ideal
- von Neumann regular ring, or absolutely flat ring (unrelated to the previous sense)
- Regular semi-algebraic systems in computer algebra
- Regular semigroup, related to the previous sense
- *-regular semigroup
Analysis[edit]
- Borel regular measure
- Cauchy-regular function (or Cauchy-continuous function,) a continuous function between metric spaces which preserves Cauchy sequences
- Regular functions, functions that are analytic and single-valued (unique) in a given region
- Regular matrix (disambiguation)
- Regular measure, a measure for which every measurable set is "approximately open" and "approximately closed"
- The regular part, of a Laurent series, the series of terms with positive powers
- Regular singular points, in theory of ordinary differential equations where the growth of solutions is bounded by an algebraic function
- Regularity, the degree of differentiability of a function
- Regularity conditions arise in the study of first class constraints in Hamiltonian mechanics
- Regularity of an elliptic operator
- Regularity theory of elliptic partial differential equations
Combinatorics, discrete math, and mathematical computer science[edit]
- Regular algebra, or Kleene algebra
- Regular code, an algebraic code with a uniform distribution of distances between codewords
- Regular expression, a type of pattern describing a set of strings in computer science
- Regular graph, a graph such that all the degrees of the vertices are equal
- Szemerédi regularity lemma, some random behaviors in large graphs
- Regular language, a formal language recognizable by a finite state automaton (related to the regular expression)
- Regular map (graph theory), a symmetric tessellation of a closed surface
- Regular matroid, a matroid which can be represented over any field
- Regular paperfolding sequence, also known as the dragon curve sequence
- Regular tree grammar
- Regular string, a binary string in which the one-density in any long consecutive substring is close to the one-density in the whole
Geometry[edit]
- Castelnuovo–Mumford regularity of a coherent sheaf
- Closed regular sets in solid modeling
- Irregularity of a surface in algebraic geometry
- Regular curves
- Regular grid, a tesselation of Euclidean space by congruent bricks
- Regular map (algebraic geometry), a map between varieties given by polynomials
- Regular point, a non-singular point of an algebraic variety
- Regular point of a differentiable map, a point at which a map is a submersion
- Regular polygons, polygons with all sides and angles equal
- Regular polyhedron, a generalization of a regular polygon to higher dimensions
- Regular polytope, a generalization of a regular polygon to higher dimensions
- Regular skew polyhedron
Logic, set theory, and foundations[edit]
- Axiom of Regularity, also called the Axiom of Foundation, an axiom of set theory asserting the non-existence of certain infinite chains of sets
- Partition regularity
- Regular cardinal, a cardinal number that is equal to its cofinality
- Regular modal logic
Probability and statistics[edit]
- Regular conditional probability, a concept that has developed to overcome certain difficulties in formally defining conditional probabilities for continuous probability distributions
- Regular stochastic matrix, a stochastic matrix such that all the entries of some power of the matrix are positive
Topology[edit]
- Free regular set, a subset of a topological space that is acted upon disjointly under a given group action
- Regular homotopy
- Regular isotopy in knot theory, the equivalence relation of link diagrams that is generated by using the 2nd and 3rd Reidemeister moves only
- Regular space (or ) space, a topological space in which a point and a closed set can be separated by neighborhoods
Organizations[edit]
- Regular army for military usage
- Regular Baptists, an 18th-century American and Canadian Baptist group
- Regular clergy, members of a religious order subject to a rule of life
- Regular Force for usage in the Canadian Forces
- Regular Masonic jurisdictions, or regularity, refers to the constitutional mechanism by which Freemasonry Grand Lodges or Grand Orients give one another mutual recognition
Science and social science[edit]
- Regular bowel movements, the opposite of constipation
- Regular economy, an economy characterized by an excess demand function whose slope at any equilibrium price vector is non-zero
- Regular moon, a natural satellite that has low eccentricity and a relatively close and prograde orbit
- Regular solutions in chemistry, solutions that diverge from the behavior of an ideal solution only moderately
Other uses[edit]
- Regular customer, a person who visits the same restaurant, pub, store, or transit provider frequently
- Regular (footedness) in boardsports, a stance in which the left foot leads
See also[edit]
References[edit]
- ^ Axenovich, Maria; Person, Yury; Puzynina, Svetlana (2013). "A regularity lemma and twins in words". Journal of Combinatorial Theory. Series A. 120 (4): 733–743. doi:10.1016/j.jcta.2013.01.001. S2CID 5923754.
- ^ Guruswami, Venkatesan; He, Xiaoyu; Li, Ray (2022). "The zero-rate threshold for adversarial bit-deletions is less than 1/2". 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS). pp. 727–738. arXiv:2106.05250. doi:10.1109/FOCS52979.2021.00076. ISBN 978-1-6654-2055-6. S2CID 235377196.
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