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 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, 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'', a radio morning show

Language

* Regular inflection, 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, 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 monomorphism ...

s and

regular epimorphism In category theory, an epimorphism (also called an epic morphism or, colloquially, an epi) is a morphism ''f'' : ''X'' → ''Y'' that is right-cancellative in the sense that, for all objects ''Z'' and all morphisms , : g_1 \circ f = g_2 \circ f \ ...

s, 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 matrix (disambiguation) * Regular measure, a measure for which every measurable set is "approximately open" and "approximately closed" * The

regular part In mathematics, the regular part of a Laurent series consists of the series of terms with positive powers.. That is, if :f(z) = \sum_^ a_n (z - c)^n, then the regular part of this Laurent series is :\sum_^ a_n (z - c)^n. In contrast, the series of ...

, 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 vanishi ...

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 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 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, 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 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 instrumen ...

, 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 set Solid modeling (or solid modelling) is a consistent set of principles for mathematical and computer modeling of three-dimensional shapes '' (solids)''. Solid modeling is distinguished from related areas of geometric modeling and computer graphi ...

s 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 curve In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that ap ...

s * Regular grid, 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 In mathematics, a submersion is a differentiable map between differentiable manifolds whose differential is everywhere surjective. This is a basic concept in differential topology. The notion of a submersion is dual to the notion of an immersion. ...

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 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 In combinatorics, a branch of mathematics, partition regularity is one notion of largeness for a collection of sets. Given a set X, a collection of subsets \mathbb \subset \mathcal(X) is called ''partition regular'' if every set ''A'' in the coll ...

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 normal ...

Probability and statistics

Regular conditional probability In probability theory, regular conditional probability is a concept that formalizes the notion of conditioning on the outcome of a random variable. The resulting conditional probability distribution is a parametrized family of probability measures c ...

, 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 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 In the mathematical field of topology, a regular homotopy refers to a special kind of homotopy between immersions of one manifold in another. The homotopy must be a 1-parameter family of immersions. Similar to homotopy classes, one defines two imme ...

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 instrumen ...

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 for military usage * Regular Baptists, 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 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 A regular economy is an economy characterized by an excess demand function which has the property that its slope at any equilibrium price vector is non-zero. In other words, if we graph the excess demand function against prices, then the excess dem ...

, 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 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'' (8 ...

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) Footedness is the natural preference of one's left or right foot for various purposes. It is the foot equivalent of handedness. While purposes vary, such as applying the greatest force in a certain foot to complete the action of kick as opposed to ...

in boardsports, a stance in which the left foot leads

References

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