Regular may refer to:
Arts, entertainment, and media
Music
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"Regular" (Badfinger song)
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Regular tuning
Among guitar tunings#Alternative, alternative guitar tunings, guitar-tunings, regular tunings have equal interval (music), musical intervals between the paired note (music), notes of their successive open string (music), open strings.
...
s of stringed instruments, tunings with equal intervals between the paired notes of successive open strings
Other uses
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Regular character, a main character who appears more frequently and/or prominently than a recurring character
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Regular division of the plane, a series of drawings by the Dutch artist M. C. Escher which began in 1936
Language
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Regular inflection, the formation of derived forms such as plurals in ways that are typical for the language
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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 ...
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Regular script
The regular script is the newest of the major Chinese script styles, emerging during the Three Kingdoms period , and stylistically mature by the 7th century. It is the most common style used in modern text. In its traditional form it is the t ...
, the newest of the Chinese script styles
Mathematics
Algebra and number theory
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Regular category
In category theory, a regular category is a category with limit (category theory), finite limits and coequalizers of all pairs of morphisms called kernel pairs, satisfying certain ''exactness'' conditions. In that way, regular categories recapture ...
, a kind of category that has similarities to both Abelian categories and to the category of sets
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Regular chains in computer algebra
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Regular element (disambiguation), certain kinds of elements of an algebraic structure
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Regular extension of fields
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Regular ideal (multiple definitions)
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Regular Lie group
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Regular matrix (disambiguation)
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Regular monomorphisms and
regular epimorphisms, monomorphisms (resp. epimorphisms) which equalize (resp. coequalize) some parallel pair of morphisms
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Regular numbers, numbers which evenly divide a power of 60
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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
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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
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Regular ring, a ring such that all its localizations have Krull dimension equal to the minimal number of generators of the maximal ideal
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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 eleme ...
, or absolutely flat ring (unrelated to the previous sense)
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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 ...
s in computer algebra
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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
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*-regular semigroup
Analysis
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Borel regular measure
In mathematics, an outer measure ''μ'' on ''n''-dimensional Euclidean space R''n'' is called a Borel regular measure if the following two conditions hold:
* Every Borel set ''B'' ⊆ R''n'' is ''μ''-measurable in the sense of Carath� ...
* 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
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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 reg ...
s, functions that are analytic and single-valued (unique) in a given region
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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 topol ...
, 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
In mathematics, the Laurent series of a complex function f(z) is a representation of that function as a power series which includes terms of negative degree. It may be used to express co ...
, of a Laurent series, the series of terms with positive powers
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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'', a ...
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 constraints in Hamiltonian mechanics
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Regularity of an elliptic operator
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Regularity theory of
elliptic partial differential equation
In mathematics, an elliptic partial differential equation is a type of partial differential equation (PDE). In mathematical modeling, elliptic PDEs are frequently used to model steady states, unlike parabolic PDE and hyperbolic PDE which gene ...
s
Combinatorics, discrete math, and mathematical computer science
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Regular algebra, or Kleene algebra
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Regular code, an algebraic code with a uniform distribution of distances between codewords
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Regular expression
A regular expression (shortened as regex or regexp), sometimes referred to as rational expression, is a sequence of characters that specifies a match pattern in text. Usually such patterns are used by string-searching algorithms for "find" ...
, a type of pattern describing a set of strings in computer science
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Regular graph
In graph theory, a regular graph is a Graph (discrete mathematics), graph where each Vertex (graph theory), vertex has the same number of neighbors; i.e. every vertex has the same Degree (graph theory), degree or valency. A regular directed graph ...
, a graph such that all the degrees of the vertices are equal
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Szemerédi regularity lemma, some random behaviors in large graphs
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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)
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Regular map (graph theory)
In mathematics, a regular map is a symmetric tessellation of a closed surface (topology), surface. More precisely, a regular map is a Manifold decomposition, decomposition of a two-dimensional manifold (such as a sphere, torus, or real project ...
, a symmetric tessellation of a closed surface
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Regular matroid, a matroid which can be represented over any field
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Regular paperfolding sequence, also known as the dragon curve sequence
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Regular tree grammar
Geometry
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Castelnuovo–Mumford regularity of a coherent sheaf
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Closed regular sets in solid modeling
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Irregularity of a surface in algebraic geometry
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Regular curves
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Regular grid
A regular grid is a tessellation of ''n''-dimensional Euclidean space by Congruence_(geometry), congruent parallelepiped#Parallelotope, parallelotopes (e.g. bricks). Its opposite is Unstructured grid, irregular grid.
Grids of this type appear on ...
, a tesselation of Euclidean space by congruent bricks
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Regular map (algebraic geometry), a map between varieties given by polynomials
* Regular point, a
non-singular point of an algebraic variety
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Regular point of a differentiable map, a point at which a map is a submersion
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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 ...
s, polygons with all sides and angles equal
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Regular polyhedron
A regular polyhedron is a polyhedron whose symmetry group acts transitive group action, transitively on its Flag (geometry), flags. A regular polyhedron is highly symmetrical, being all of edge-transitive, vertex-transitive and face-transitive. In ...
, a generalization of a regular polygon to higher dimensions
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Regular polytope
In mathematics, a regular polytope is a polytope whose symmetry group acts transitive group action, transitively on its flag (geometry), flags, thus giving it the highest degree of symmetry. In particular, all its elements or -faces (for all , w ...
, a generalization of a regular polygon to higher dimensions
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Regular skew polyhedron
Logic, set theory, and foundations
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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 Empty set, non-empty Set (mathematics), set ''A'' contains an element that is Disjoint sets, disjoin ...
, also called the Axiom of Foundation, an axiom of set theory asserting the non-existence of certain infinite chains of sets
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Partition regularity
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Regular cardinal, a cardinal number that is equal to its cofinality
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Regular modal logic
Probability and statistics
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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, ''s ...
, a stochastic matrix such that all the entries of some power of the matrix are positive
Topology
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Free regular set, a subset of a topological space that is acted upon disjointly under a given group action
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Regular homotopy
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Regular isotopy in knot theory, the equivalence relation of link diagrams that is generated by using the 2nd and 3rd Reidemeister moves only
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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'' have non-overlapping open neighborhoods. Thus ''p'' and ''C'' can ...
(or
) space, a topological space in which a point and a closed set can be separated by neighborhoods
Military
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Regular army
A regular army is the official army of a state or country (the official armed forces), contrasting with irregular forces, such as volunteer irregular militias, private armies, mercenaries, etc. A regular army usually has the following:
* a ...
, the official army of a state or country
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British Regulars, of the 18th and 19th centuries
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Regular Army (United States)
The Regular Army of the United States succeeded the Continental Army as the country's permanent, professional land-based military force. In modern times, the professional core of the United States Army continues to be called the Regular Army (of ...
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Regular Force, of the Canadian Forces
Organizations
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Regular Baptists, an 18th-century American and Canadian Baptist group
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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 ...
, members of a religious order subject to a rule of life
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Regular Masonic jurisdictions
In Freemasonry, regularity is one of the factors by which individual Grand Lodges judge whether to recognise one another for the purposes of allowing formal interaction at the Grand Lodge level and visitation by members of other jurisdictions. E ...
, or ''regularity'', refers to the constitutional mechanism by which Freemasonry Grand Lodges or Grand Orients give one another mutual recognition
People
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Moses Regular (born 1971), America football player
Science and social science
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Regular economy, an economy characterized by an excess demand function whose slope at any equilibrium price vector is non-zero
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Regular moon, a natural satellite that has low eccentricity and a relatively close and prograde orbit
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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
Constipation is a bowel dysfunction that makes bowel movements infrequent or hard to pass. The Human feces, stool is often hard and dry. Other symptoms may include abdominal pain, bloating, and feeling as if one has not completely passed the ...
* Regular
customer
In sales, commerce, and economics, a customer (sometimes known as a Client (business), client, buyer, or purchaser) is the recipient of a Good (economics), good, service (economics), service, product (business), product, or an Intellectual prop ...
, a person who frequently visits the same restaurant, pub, store, transit provider, etc.
* Regular
octane rating
An octane rating, or octane number, is a standard measure of a liquid fuel, fuel's ability to withstand Compression ratio, compression in an internal combustion engine without causing engine knocking. The higher the octane number, the more compres ...
of gasoline, as a differentiation from "premium" and similar variants
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Regular stance (or footedness) in boardsports, a stance in which the left foot leads (as compared to "goofy")
* Regular type, referring to
Roman type
In Latin script typography, roman is one of the three main kinds of Typeface, historical type, alongside blackletter and Italic type, italic. Sometimes called normal or regular, it is distinct from these two for its upright style (relative to the ...
, an upright style of typeface or computer font, as compared to italic and blackletter
See also
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Irregular (disambiguation)
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Regular set (disambiguation)
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