The term regular can mean normal or in accordance with rules. It may refer to:

People

Moses Regular Moses Regular Jr. (born October 30, 1971) is a former American football tight end who played one season with the New York Giants of the National Football League. He played college football at Missouri Valley College and attended Gateway High Scho ...

(born 1971), America football player

Arts, entertainment, and media

Music

* "Regular" (Badfinger song) *

Regular tuning Among alternative guitar-tunings, regular tunings have equal musical intervals between the paired notes of their successive open strings. ''Guitar tunings'' assign pitches to the open strings of guitars. Tunings can be ...

s of stringed instruments, tunings with equal intervals between the paired notes of successive open strings

Other uses in arts, entertainment, and media

Regular character In fiction, a character (or speaker, in poetry) is a person or other being in a narrative (such as a novel, play, radio or television series, music, film, or video game). The character may be entirely fictional or based on a real-life p ...

, 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 ''Regular Show'' (known as ''Regular Show in Space'' during its eighth season) is an American animated sitcom created by J. G. Quintel for Cartoon Network. It ran from September 6, 2010, to January 16, 2017, over the course of eight seasons a ...

'', an animated television sitcom * ''

The Regular Guys ''The Regular Guys'' was a terrestrial radio show that started in Los Angeles, California, by DJs Larry Wachs and Eric Von Haessler. The show added Atlanta based DJs "Southside" Steve Rickman and "Action Plan" Tim Andrews when the show resumed in ...

'', a radio morning show

Language

Regular inflection In linguistic morphology, inflection (or inflexion) is a process of word formation in which a word is modified to express different grammatical categories such as tense, case, voice, aspect, person, number, gender, mood, animacy, and defini ...

, the formation of derived forms such as plurals in ways that are typical for the language **

Regular verb A regular verb is any verb whose conjugation follows the typical pattern, or one of the typical patterns, of the language to which it belongs. A verb whose conjugation follows a different pattern is called an irregular verb. This is one instance ...

Regular script Regular script (; Hepburn: ''kaisho''), also called (), (''zhēnshū''), (''kǎitǐ'') and (''zhèngshū''), is the newest of the Chinese script styles (popularized from the Cao Wei dynasty c. 200 AD and maturing stylistically around the ...

, the newest of the Chinese script styles

Mathematics

There are an extremely large number of unrelated notions of "regularity" in mathematics.

Algebra and number theory

(See also the geometry section for notions related to algebraic geometry.) *

Regular category In category theory, a regular category is a category with finite limits and coequalizers of a pair of morphisms called kernel pairs, satisfying certain ''exactness'' conditions. In that way, regular categories recapture many properties of abelian ...

, a kind of category that has similarities to both Abelian categories and to the category of sets *

Regular chain In computer algebra, a regular chain is a particular kind of triangular set in a multivariate polynomial ring over a field. It enhances the notion of characteristic set. Introduction Given a linear system, one can convert it to a triangular s ...

s in computer algebra * Regular element (disambiguation), certain kinds of elements of an algebraic structure *

Regular extension In field theory, a branch of algebra, a field extension L/k is said to be regular if ''k'' is algebraically closed in ''L'' (i.e., k = \hat k where \hat k is the set of elements in ''L'' algebraic over ''k'') and ''L'' is separable over ''k'', or ...

of fields *

Regular ideal In mathematics, especially ring theory, a regular ideal can refer to multiple concepts. In operator theory, a right ideal \mathfrak in a (possibly) non-unital ring ''A'' is said to be regular (or modular) if there exists an element ''e'' in ''A'' ...

(multiple definitions) *

Regular monomorphism In the context of abstract algebra or universal algebra, a monomorphism is an injective homomorphism. A monomorphism from to is often denoted with the notation X\hookrightarrow Y. In the more general setting of category theory, a monomorphi ...

s and regular epimorphisms, monomorphisms (resp. epimorphisms) which equalize (resp. coequalize) some parallel pair of morphisms *

Regular number Regular numbers are numbers that evenly divide powers of 60 (or, equivalently, powers of 30). Equivalently, they are the numbers whose only prime divisors are 2, 3, and 5. As an example, 602 = 3600 = 48 ×&nb ...

s, numbers which evenly divide a power of 60 *

Regular p-group In mathematical finite group theory, the concept of regular ''p''-group captures some of the more important properties of abelian ''p''-groups, but is general enough to include most "small" ''p''-groups. Regular ''p''-groups were introduced by . ...

, a concept capturing some of the more important properties of abelian ''p''-groups, but general enough to include most "small" ''p''-groups *

Regular prime In number theory, a regular prime is a special kind of prime number, defined by Ernst Kummer in 1850 to prove certain cases of Fermat's Last Theorem. Regular primes may be defined via the divisibility of either class numbers or of Bernoulli num ...

, a prime number ''p'' > 2 that does not divide the class number of the ''p''-th cyclotomic field * The

regular representation In mathematics, and in particular the theory of group representations, the regular representation of a group ''G'' is the linear representation afforded by the group action of ''G'' on itself by translation. One distinguishes the left regular rep ...

of a group G, the linear representation afforded by the group action of G on itself *

Regular ring In commutative algebra, a regular local ring is a Noetherian local ring having the property that the minimal number of generators of its maximal ideal is equal to its Krull dimension. In symbols, let ''A'' be a Noetherian local ring with maximal ide ...

, 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 In mathematics, a von Neumann regular ring is a ring ''R'' (associative, with 1, not necessarily commutative) such that for every element ''a'' in ''R'' there exists an ''x'' in ''R'' with . One may think of ''x'' as a "weak inverse" of the element ...

, or absolutely flat ring (unrelated to the previous sense) *

Regular semi-algebraic system In computer algebra, a regular semi-algebraic system is a particular kind of triangular system of multivariate polynomials over a real closed field. Introduction Regular chains and triangular decompositions are fundamental and well-developed t ...

s in computer algebra *

Regular semigroup In mathematics, a regular semigroup is a semigroup ''S'' in which every element is regular, i.e., for each element ''a'' in ''S'' there exists an element ''x'' in ''S'' such that . Regular semigroups are one of the most-studied classes of semigroup ...

, related to the previous sense * *-regular semigroup

Analysis

Borel regular measure Borel may refer to: People * Borel (author), 18th-century French playwright * Borel (1906–1967), pseudonym of the French actor Jacques Henri Cottance * Émile Borel (1871 – 1956), a French mathematician known for his founding work in the areas ...

* Cauchy-regular function (or

Cauchy-continuous function In mathematics, a Cauchy-continuous, or Cauchy-regular, function is a special kind of continuous function between metric spaces (or more general spaces). Cauchy-continuous functions have the useful property that they can always be (uniquely) extende ...

,) a continuous function between metric spaces which preserves Cauchy sequences *

Regular function In algebraic geometry, a morphism between algebraic varieties is a function between the varieties that is given locally by polynomials. It is also called a regular map. A morphism from an algebraic variety to the affine line is also called a regular ...

s, functions that are analytic and single-valued (unique) in a given region *

Regular matrix (disambiguation) Regular matrix may refer to: Mathematics * Regular stochastic matrix, a stochastic matrix such that all the entries of some power of the matrix are positive * The opposite of irregular matrix, a matrix with a different number of entries in each row ...

Regular measure In mathematics, a regular measure on a topological space is a measure for which every measurable set can be approximated from above by open measurable sets and from below by compact measurable sets. Definition Let (''X'', ''T'') be a topologi ...

, 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 point In mathematics, in the theory of ordinary differential equations in the complex plane \Complex, the points of \Complex are classified into ''ordinary points'', at which the equation's coefficients are analytic functions, and ''singular points'', at ...

s, 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 constraint A first class constraint is a dynamical quantity in a constrained Hamiltonian system whose Poisson bracket with all the other constraints vanishes on the constraint surface in phase space (the surface implicitly defined by the simultaneous vanis ...

s in Hamiltonian mechanics * Regularity of an elliptic operator

Combinatorics, discrete math, and mathematical computer science

Regular algebra In mathematics, a Kleene algebra ( ; named after Stephen Cole Kleene) is an idempotent (and thus partially ordered) semiring endowed with a closure operator. It generalizes the operations known from regular expressions. Definition Various ine ...

, or Kleene algebra *

Regular code In coding theory, the weight enumerator polynomial of a binary linear code specifies the number of words of each possible Hamming weight. Let C \subset \mathbb_2^n be a binary linear code length n. The weight distribution is the sequence of numb ...

, an algebraic code with a uniform distribution of distances between codewords *

Regular expression A regular expression (shortened as regex or regexp; sometimes referred to as rational expression) is a sequence of characters that specifies a search pattern in text. Usually such patterns are used by string-searching algorithms for "find" or ...

, a type of pattern describing a set of strings in computer science *

Regular graph In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency. A regular directed graph must also satisfy the stronger condition that the indegree and outdegree o ...

, a graph such that all the degrees of the vertices are equal **

Szemerédi regularity lemma Szemerédi's regularity lemma is one of the most powerful tools in extremal graph theory, particularly in the study of large dense graphs. It states that the vertices of every large enough graph can be partitioned into a bounded number of parts so ...

, some random behaviors in large graphs *

Regular language In theoretical computer science and formal language theory, a regular language (also called a rational language) is a formal language that can be defined by a regular expression, in the strict sense in theoretical computer science (as opposed to ...

, a formal language recognizable by a finite state automaton (related to the regular expression) *

Regular map (graph theory) In mathematics, a regular map is a symmetric tessellation of a closed surface. More precisely, a regular map is a decomposition of a two-dimensional manifold (such as a sphere, torus, or real projective plane) into topological disks such tha ...

, a symmetric tessellation of a closed surface *

Regular matroid In mathematics, a regular matroid is a matroid that can be represented over all fields. Definition A matroid is defined to be a family of subsets of a finite set, satisfying certain axioms. The sets in the family are called "independent sets". On ...

, a matroid which can be represented over any field *

Regular paperfolding sequence In mathematics the regular paperfolding sequence, also known as the dragon curve sequence, is an infinite sequence of 0s and 1s. It is obtained from the repeating partial sequence by filling in the question marks by another copy of the whole sequen ...

, also known as the dragon curve sequence *

Regular tree grammar In theoretical computer science and formal language theory, a regular tree grammar is a formal grammar that describes a set of directed trees, or terms. A regular word grammar can be seen as a special kind of regular tree grammar, describing a se ...

* Regular string, a binary string in which the one-density in any long consecutive substring is close to the one-density in the whole string

Geometry

Castelnuovo–Mumford regularity In algebraic geometry, the Castelnuovo–Mumford regularity of a coherent sheaf ''F'' over projective space \mathbf^n is the smallest integer ''r'' such that it is r-regular, meaning that :H^i(\mathbf^n, F(r-i))=0 whenever i>0. The regularity of a ...

of a coherent sheaf * Closed regular sets in solid modeling *

Irregularity of a surface In mathematics, the irregularity of a complex surface ''X'' is the Hodge number h^= \dim H^1(\mathcal_X), usually denoted by ''q.'' The irregularity of an algebraic surface is sometimes defined to be this Hodge number, and sometimes defined to be th ...

in algebraic geometry * Regular curves *

Regular grid A regular grid is a tessellation of ''n''-dimensional Euclidean space by congruent parallelotopes (e.g. bricks). Its opposite is irregular grid. Grids of this type appear on graph paper and may be used in finite element analysis, finite volume ...

, a tesselation of Euclidean space by congruent bricks *

Regular map (algebraic geometry) In algebraic geometry, a morphism between algebraic varieties is a function between the varieties that is given locally by polynomials. It is also called a regular map. A morphism from an algebraic variety to the affine line is also called a regula ...

, 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 polygon In Euclidean geometry, a regular polygon is a polygon that is Equiangular polygon, direct equiangular (all angles are equal in measure) and Equilateral polygon, equilateral (all sides have the same length). Regular polygons may be either convex p ...

s, polygons with all sides and angles equal **

Regular polyhedron A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags. A regular polyhedron is highly symmetrical, being all of edge-transitive, vertex-transitive and face-transitive. In classical contexts, many different equival ...

, a generalization of a regular polygon to higher dimensions **

Regular polytope In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry. All its elements or -faces (for all , where is the dimension of the polytope) — cells, f ...

, a generalization of a regular polygon to higher dimensions *

Regular skew polyhedron In geometry, the regular skew polyhedra are generalizations to the set of regular polyhedra which include the possibility of nonplanar faces or vertex figures. Coxeter looked at skew vertex figures which created new 4-dimensional regular polyhedra ...

Logic, set theory, and foundations

Axiom of Regularity In mathematics, the axiom of regularity (also known as the axiom of foundation) is an axiom of Zermelo–Fraenkel set theory that states that every non-empty set ''A'' contains an element that is disjoint from ''A''. In first-order logic, the axi ...

, 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 In set theory, a regular cardinal is a cardinal number that is equal to its own cofinality. More explicitly, this means that \kappa is a regular cardinal if and only if every unbounded subset C \subseteq \kappa has cardinality \kappa. Infinite ...

, a cardinal number that is equal to its cofinality *

Regular modal logic In modal logic, a regular modal logic is a modal logic containing (as axiom or theorem) the duality of the modal operators: \Diamond A \leftrightarrow \lnot\Box\lnot A and closed under the rule \frac. Every normal modal logic In logic, a norma ...

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 In mathematics, a stochastic matrix is a square matrix used to describe the transitions of a Markov chain. Each of its entries is a nonnegative real number representing a probability. It is also called a probability matrix, transition matrix, ...

, a stochastic matrix such that all the entries of some power of the matrix are positive

Topology

Free regular set In mathematics, a group action on a space is a group homomorphism of a given group into the group of transformations of the space. Similarly, a group action on a mathematical structure is a group homomorphism of a group into the automorphism ...

, a subset of a topological space that is acted upon disjointly under a given group action * Regular homotopy *

Regular isotopy The term regular can mean normal or in accordance with rules. It may refer to: People * Moses Regular (born 1971), America football player Arts, entertainment, and media Music * "Regular" (Badfinger song) * Regular tunings of stringed instrume ...

in knot theory, the equivalence relation of link diagrams that is generated by using the 2nd and 3rd Reidemeister moves only *

Regular space In topology and related fields of mathematics, a topological space ''X'' is called a regular space if every closed subset ''C'' of ''X'' and a point ''p'' not contained in ''C'' admit non-overlapping open neighborhoods. Thus ''p'' and ''C'' can ...

(or

T_3

) space, a topological space in which a point and a closed set can be separated by neighborhoods

Organizations

Regular army A regular army is the official army of a state or country (the official armed forces), contrasting with irregulars, irregular forces, such as volunteer irregular militias, private armies, mercenary, mercenaries, etc. A regular army usually has the ...

for military usage *

Regular Baptists Regular Baptists are "a moderately Calvinistic Baptist sect that is found chiefly in the southern U.S., represents the original English Baptists before the division into Particular and General Baptists, and observes closed communion and foot washi ...

, an 18th-century American and Canadian Baptist group *

Regular clergy Regular clergy, or just regulars, are clerics in the Catholic Church who follow a rule () of life, and are therefore also members of religious institutes. Secular clergy are clerics who are not bound by a rule of life. Terminology and history The ...

, members of a religious order subject to a rule of life *

Regular Force In the Canadian Armed Forces, a Regular Force unit or person is part of the full-time military, as opposed to being part of the Primary Reserve which has more flexibility. There are many bases and wings across Canada, and factors like trade, career ...

for usage in the Canadian Forces *

Regular Masonic jurisdictions :''This article deals with organization in ''Craft'' or ''Blue Lodge'' Freemasonry. See the appropriate article for information on organization in appendant Masonic bodies such as York Rite and Scottish Rite.'' In Freemasonry, regularity is one ...

, or ''regularity'', refers to the constitutional mechanism by which Freemasonry Grand Lodges or Grand Orients give one another mutual recognition

Science and social science

* Regular bowel movements, the opposite of

constipation Constipation is a bowel dysfunction that makes bowel movements infrequent or hard to pass. The stool is often hard and dry. Other symptoms may include abdominal pain, bloating, and feeling as if one has not completely passed the bowel movement ...

* Regular economy, an economy characterized by an excess demand function whose slope at any equilibrium price vector is non-zero *

Regular moon In astronomy, a regular moon is a natural satellite following a relatively close and prograde orbit with little orbital inclination or eccentricity. They are believed to have formed in orbit about their primary, as opposed to irregular moons, whic ...

, a natural satellite that has low eccentricity and a relatively close and prograde orbit *

Regular solution In chemistry, a regular solution is a solution whose entropy of mixing is equal to that of an ideal solution with the same composition, but is non-ideal due to a nonzero enthalpy of mixing.P. Atkins and J. de Paula, ''Atkins' Physical Chemistry'' ( ...

s in chemistry, solutions that diverge from the behavior of an ideal solution only moderately

Other uses

* Regular

customer In sales, commerce, and economics, a customer (sometimes known as a client, buyer, or purchaser) is the recipient of a good, service, product or an idea - obtained from a seller, vendor, or supplier via a financial transaction or exchange for ...

, 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

References

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