Regular

Regular and regularity may refer to:

Arts, entertainment, and media

Music

• "Regular" (Badfinger song)
• Regular tunings of stringed instruments, tunings with equal intervals between the paired notes of successive open strings

Other uses

• 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

Language

• Regular inflection, the formation of derived forms such as plurals in ways that are typical for the language
  • Regular verb
• Regular script, the newest of the Chinese script styles

Mathematics

Algebra and number theory

• 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 Lie group
• Regular matrix (disambiguation)
• 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

• 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 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

• 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

Geometry

• 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

• 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

• 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

• 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 $T_{3}$) space, a topological space in which a point and a closed set can be separated by neighborhoods

Military

• Regular army, the official army of a state or country
  • British Regulars, of the 18th and 19th centuries
  • Regular Army (United States)
  • Regular Force, of the Canadian Forces

Organizations

• Regular Baptists, an 18th-century American and Canadian Baptist group
• Regular clergy, members of a religious order subject to a rule of life
• Regular Masonic jurisdictions, or regularity, refers to the constitutional mechanism by which Freemasonry Grand Lodges or Grand Orients give one another mutual recognition

People

• Moses Regular (born 1971), America football player

Science and social science

• 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

• Regular bowel movements, the opposite of constipation
• Regular customer, a person who frequently visits the same restaurant, pub, store, transit provider, etc.
• Regular octane rating of gasoline, as a differentiation from "premium" and similar variants
• Regular stance (or footedness) in boardsports, a stance in which the left foot leads (as compared to "goofy")
• Regular type, referring to Roman type, an upright style of typeface or computer font, as compared to italic and blackletter
• Presumption of regularity, a legal principle

See also

• All pages with titles beginning with regular
• All pages with titles containing regular
• Irregular (disambiguation)
• Regular set (disambiguation)
• Quasiregular