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Typically linear operator defined in terms of differentiation of functions
differential operators also exist, such as the Schwarzian derivative. Given a nonnegative integer m, an order- m {\displaystyle m} linear differential operator is
Differential_operator
Operator characterizing the phase of a system
In quantum field theory, an order operator or an order field is a quantum field version of Landau's order parameter whose expectation value characterizes
Order_operator
an operator is also in C. Note that C does not support operator overloading. When not overloaded, for the operators &&, ||, and , (the comma operator),
Operators_in_C_and_C++
Performing order of mathematical operations
Common operator notation (for a more formal description) Hyperoperation Logical connective#Order of precedence Operator associativity Operator overloading
Order_of_operations
Type of differential operator
elliptic equations. Let L {\displaystyle L} be a linear differential operator of order m on a domain Ω {\displaystyle \Omega } in Rn given by L u = ∑ | α
Elliptic_operator
mathematical field of differential geometry, the Paneitz operator is a fourth-order differential operator defined on a Riemannian manifold of dimension n. It
Paneitz_operator
Type of functional equation (mathematics)
pseudo-differential equations use pseudo-differential operators instead of differential operators. A differential algebraic equation (DAE) is a differential
Differential_equation
Feature of some programming languages
comparison operator (operator<=>), all the order operators can be defined by just defining that operator. The three-way comparison operator exists in many
Operator_overloading
First-order differential linear operator on spinor bundle, whose square is the Laplacian
a Dirac operator is a first-order differential operator that is a formal square root, or half-iterate, of a second-order differential operator such as
Dirac_operator
Order-preserving mathematical function
or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory. In calculus,
Monotonic_function
Methods of mathematical approximation
Hamiltonian from the very beginning and never specifies a perturbation operator as such. Møller–Plesset perturbation theory uses the difference between
Perturbation_theory
Linear operator equal to its own adjoint
In mathematics, a self-adjoint operator on a complex vector space V {\displaystyle V} with inner product ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot
Self-adjoint_operator
Differential equation that is linear with respect to the unknown function
nonnegative integer n is the order of the operator (if an(x) is not the zero function). Let L be a linear differential operator. The application of L to a
Linear_differential_equation
Type of operator ordering in quantum field theory
annihilation operators, is usually said to be normal ordered (also called Wick order) when all creation operators are to the left of all annihilation operators in
Normal_order
Existence and uniqueness of solutions to initial value problems
{\displaystyle t} and Lipschitz continuous in y {\displaystyle y} , this integral operator is a contraction (See detailed proof below) and so the Banach fixed-point
Picard–Lindelöf_theorem
Elliptic differential operators in geometry mathematics
differential geometry there are a number of second-order, linear, elliptic differential operators bearing the name Laplacian. This article provides an
Laplace operators in differential geometry
Laplace_operators_in_differential_geometry
Logical connective AND
\wedge } ) is the truth-functional operator of conjunction or logical conjunction. The logical connective of this operator is typically represented as ∧ {\displaystyle
Logical_conjunction
solved the factorization problem for a bivariate hyperbolic operator of the second order (see Hyperbolic partial differential equation), constructing
Invariant factorization of LPDOs
Invariant_factorization_of_LPDOs
Operator generalizing the Laplacian in differential geometry
In differential geometry, the Laplace–Beltrami operator is a generalization of the Laplace operator to functions defined on submanifolds in Euclidean space
Laplace–Beltrami_operator
Gauge field loop operator
in terms of these loops. In pure gauge theory they play the role of order operators for confinement, where they satisfy what is known as the area law.
Wilson_loop
Field of mathematical control theory
fact, the fractional integral operator 1 s λ {\displaystyle {\frac {1}{s^{\lambda }}}} is different from any integer-order rational transfer function G
Fractional-order_control
Differential equation containing derivatives with respect to only one variable
second-order linear ordinary differential equation. Their solutions are based on eigenvalues and corresponding eigenfunctions of linear operators defined
Ordinary differential equation
Ordinary_differential_equation
Conditional operator in computer programming
In computer programming, the ternary conditional operator is a conditional expression with three parts: the Boolean condition, the then-expression, and
Ternary_conditional_operator
Branch of ordinary differential equations
{\displaystyle E} corresponds to the energy levels of the Schrödinger operator L = − d 2 d x 2 + V ( x ) {\displaystyle L=-{\frac {d^{2}}{dx^{2}}}+V(x)}
Floquet_theory
Differential operator in mathematics
In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean
Laplace_operator
Class of numerical techniques
one needs to substitute Taylor Series expansions up to order 3 into the discrete Laplace operator. Similar to continuous subharmonic functions one can define
Finite_difference_method
Class of ordinary differential equations
correspond to the eigenvalues and eigenfunctions of a Hermitian differential operator in an appropriate Hilbert space of functions with inner product defined
Sturm–Liouville_theory
Type of constraint on solutions to differential equations
^{2}y+y=0,} where ∇ 2 {\displaystyle \nabla ^{2}} denotes the Laplace operator, the Dirichlet boundary conditions on a domain Ω ⊂ Rn take the form y (
Dirichlet_boundary_condition
Technique for solving linear ordinary differential equations
Reduction of order (or d’Alembert reduction) is a technique in mathematics for solving second-order linear ordinary differential equations. It is employed
Reduction_of_order
Economic activity
A tour operator is a business that typically combines and organizes accommodations, meals, sightseeing and transportation components, in order to create
Tour_operator
Binary operator in computer programming
The null coalescing operator is a binary operator that is part of the syntax for a basic conditional expression in several programming languages, such
Null_coalescing_operator
Method of describing higher-order polyhedra
a series, these operators allow many higher order polyhedra to be generated. Conway defined the operators a (ambo), b (bevel), d (dual), e (expand), g
Conway_polyhedron_notation
Mathematical operator
In mathematics, a closure operator on a set S is a function cl : P ( S ) → P ( S ) {\displaystyle \operatorname {cl} :{\mathcal {P}}(S)\rightarrow {\mathcal
Closure_operator
Feature of a typed formal language that builds new types from old ones
proper types in order to distinguish them from the types of the type operators in their own calculus, which are called kinds. Type operators may bind type
Type_constructor
Numerical method for solving physical or engineering problems
theorem) but may be proved in a distributional sense as well. We define a new operator or map ϕ ( u , v ) {\displaystyle \phi (u,v)} by using integration by parts
Finite_element_method
Differential operator used in vector calculus
A vector operator is a differential operator used in vector calculus. Vector operators include: Gradient is a vector operator that operates on a scalar
Vector_operator
Programming languages binary operator
the C and C++ programming languages, the comma operator (represented by the token ,) is a binary operator that evaluates its first operand and discards
Comma_operator
Space of all possible states that a system can take
values in phase-space quantization are obtained isomorphically to tracing operator observables with the density matrix in Hilbert space: they are obtained
Phase_space
spaces equipped with an Archimedean matrix order. Operator space Choi M.D., Effros, E.G. Injectivity and operator spaces. Journal of Functional Analysis 1977
Operator_system
Bottom-up parser that interprets an operator-precedence grammar
an operator-precedence parser is a bottom-up parser that interprets an operator-precedence grammar. For example, most calculators use operator-precedence
Operator-precedence_parser
Property determining how equal-precedence operators are grouped
programming language theory, the associativity of an operator is a property that determines how operators of the same precedence are grouped in the absence
Operator_associativity
Determinant of the matrix of first derivatives of a set of functions
(where L {\displaystyle L} is a linear differential operator with respect to x {\displaystyle x} of order less than n {\displaystyle n} ) on some interval
Wronskian
Type of differential equation
_{i}u)+\sum _{i}b^{i}\partial _{i}u+cu} denotes a second-order partial differential operator in divergence form. We say a u ∈ H 0 1 ( U ) {\displaystyle
Partial_differential_equation
Existence and uniqueness theorem for certain partial differential equations
ISBN 0-691-04361-2 Hörmander, L. (1983), The analysis of linear partial differential operators I, Grundl. Math. Wissenschaft., vol. 256, Springer, doi:10.1007/978-3-642-96750-4
Cauchy–Kovalevskaya_theorem
Image edge detection algorithm
The Sobel operator, sometimes called the Sobel–Feldman operator or Sobel filter, is used in image processing and computer vision, particularly within
Sobel_operator
Operator in quantum mechanics
quantum mechanics, the momentum operator is the operator associated with the linear momentum. The momentum operator is, in the position representation
Momentum_operator
Computational operation
"Binary Operators". Haxe - The Cross-platform Toolkit. Retrieved 2026-01-20. "Operators". Microsoft. 30 June 2021. Retrieved 2021-07-19. The % operator is
Modulo
Operator of the electric power distribution system
A distribution network operator (DNO), also known as a distribution system operator (DSO), is the operator of the electric power distribution system which
Distribution_network_operator
Gauge symmetry cannot be spontaneously broken
local operator can act as an order operator for confinement. Instead, to get around the theorem requires constructing nonlocal gauge invariant operators, whose
Elitzur's_theorem
Measure of the "size" of linear operators
mathematics, the operator norm measures the "size" of certain linear operators by assigning each a real number called its operator norm. Formally, it
Operator_norm
Approach to finding numerical solutions of ordinary differential equations
science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with
Euler_method
Type of calculus problem
integral can be considered an operator which maps one function into another, such that the solution is a fixed point of the operator. The Banach fixed point
Initial_value_problem
Type of problem involving ODEs or PDEs
problems, in the linear case, involves the eigenfunctions of a differential operator. To be useful in applications, a boundary value problem should be well
Boundary_value_problem
Method for solving continuous operator problems (such as differential equations)
Galerkin methods are a family of methods for converting a continuous operator problem, such as a differential equation, commonly in a weak formulation
Galerkin_method
Former telephony occupation
(BLV), in which an operator checked whether a line was busy or out of order, and busy line interruption (BLI), in which the operator interrupted an existing
Switchboard_operator
Property of differential equations describing physical phenomena
posed must be non-characteristic with respect to the partial differential operator), then on certain regions, there necessarily exist solutions which are
Well-posed_problem
Type of ordinary differential equation
inhomogeneous. A linear differential equation can be represented as a linear operator acting on y(x) where x is usually the independent variable and y is the
Homogeneous differential equation
Homogeneous_differential_equation
Type of differential operator
analysis a pseudo-differential operator is an extension of the concept of differential operator. Pseudo-differential operators are used extensively in the
Pseudo-differential_operator
Branch of mathematical analysis
differentiation operator D {\displaystyle D} D f ( x ) = d d x f ( x ) , {\displaystyle Df(x)={\frac {d}{dx}}f(x)\,,} and of the integration operator J {\displaystyle
Fractional_calculus
also has an induced matrix order. For operator algebras, there is still the additional ring structure. Gilles Pisier Operator system Paulsen, Vern (2002)
Operator_space
Basic programming language construct
In computer programming, an operator is a programming language construct that provides functionality that may not be possible to define as a user-defined
Operator (computer programming)
Operator_(computer_programming)
Mathematical mapping in quantum mechanics
transformation is a transformation that maps spin operators onto fermionic creation and annihilation operators. It was proposed by Pascual Jordan and Eugene
Jordan–Wigner_transformation
Mathematical operator in quantum optics
mechanics study of optical phase space, the displacement operator for one mode is the shift operator in quantum optics, D ^ ( α ) = exp ( α a ^ † − α ∗
Displacement_operator
Additionally, in order for J {\displaystyle {\mathcal {J}}} to be an operator ideal, it must contain the class of all finite-rank Banach space operators. Let L
Operator_ideal
Topic in mathematics
In mathematics, a Hilbert–Schmidt operator, named after David Hilbert and Erhard Schmidt, is a bounded operator A : H → H {\displaystyle A\colon H\to
Hilbert–Schmidt_operator
Solution method for linear differential equations
energies are good approximations to the actual eigenvalues of the Schrödinger operator. Specifically, the error in the energies is small compared to the typical
WKB_approximation
Mathematical symbol for "less than"
left operand precedes the right operand in document order; otherwise it returns false. In PHP, operator <<<OUTPUT is used to denote the beginning of a heredoc
Less-than_sign
Programming language construct
In computer science, a relational operator is a programming language construct or operator that defines syntactically a relationship between two entities
Relational_operator
are three main types of operators (mutation, crossover and selection), which must work in conjunction with one another in order for the algorithm to be
Genetic_operator
Company offering air-side aviation services at an airport
A fixed-base operator (FBO) is an organization granted the right by an airport to operate at the airport and provide aeronautical services such as fueling
Fixed-base_operator
Generalized function whose value is zero everywhere except at zero
position operator are called the eigenkets and are denoted by φy = |y⟩. Similar considerations apply to any other (unbounded) self-adjoint operator with continuous
Dirac_delta_function
Electric power coordinator
organization (RTO) in the United States is an electric power transmission system operator (TSO) that coordinates, controls, and monitors a multi-state electric grid
Regional transmission organization (North America)
Regional_transmission_organization_(North_America)
Operator for offsetting time series elements
In time series analysis, the lag operator (L) or backshift operator (B) operates on an element of a time series to produce the previous element. For example
Lag_operator
Technique for solving hyperbolic partial differential equations
and P a linear differential operator P : C ∞ ( X ) → C ∞ ( X ) {\displaystyle P:C^{\infty }(X)\to C^{\infty }(X)} of order k. In a local coordinate system
Method_of_characteristics
Type of differential equation subject to a particular solution methodology
and two functions I and J which are continuous on D, an implicit first-order ordinary differential equation of the form I ( x , y ) d x + J ( x , y )
Exact_differential_equation
Computing operation which compares two values
strcmp in C), a method (such as compareTo in Java), or an operator (such as the spaceship operator <=> in Perl, PHP and C++). Most processors have instruction
Three-way_comparison
Generalization of the BRST formalism
graded supercommutative algebra (with a unit 1) with a second-order nilpotent operator Δ of degree −1. More precisely, it satisfies the identities ( a
Batalin–Vilkovisky_formalism
Boundary condition for generalized functions
In mathematical analysis, the trace operator extends the notion of the restriction of a function to the boundary of its domain to "generalized" functions
Trace_operator
(on a complex Hilbert space) continuous linear operator
functional analysis, a normal operator on a complex Hilbert space H {\displaystyle H} is a continuous linear operator N : H → H {\displaystyle N\colon
Normal_operator
Specific operation in theoretical physics
meta-operator is sometimes used to refer to a specific operation over a combination of operators, as in the example of path-ordering. A meta-operator is
Meta-operator
The following is a list of current and former operators of the Airbus A380, the world's largest passenger aircraft. The first flight was on April 27,
List_of_Airbus_A380_operators
Procedure of ordering a product operators
theoretical physics, path-ordering is the procedure (or a meta-operator P {\displaystyle {\mathcal {P}}} ) that orders a product of operators according to the
Path-ordering
Mathematical approach to quantum physics
derivative ∂μ∂νEn, simply applying the differential operator ∂μ to the result of the first order derivative ⟨ n | ∂ ν H | n ⟩ {\displaystyle \langle n|\partial
Perturbation theory (quantum mechanics)
Perturbation_theory_(quantum_mechanics)
Catholic lay religious order
Palestinian Authority, the Order has never received one. For awards purposes, amateur radio operators consider the Order a separate "entity"—but stations
Sovereign Military Order of Malta
Sovereign_Military_Order_of_Malta
Aviation license
An air operator's certificate (AOC) is the approval granted by a civil aviation authority (CAA) to an aircraft operator to allow it to use aircraft for
Air_operator's_certificate
Procedure for solving differential equations
{\displaystyle Lx(t)=F(t)} by means of considering the second-order linear differential operator L to be the net force, thus the total impulse imparted to
Variation_of_parameters
Class of operator mapping
In mathematics, a nonlocal operator is a mapping that maps a space of functions on a topological space to another space of functions on some domain in
Nonlocal_operator
Logical operator in modal logic
modal operator) is a logical connective for modal logic. It is an operator which forms propositions from propositions. In general, a modal operator has
Modal_operator
Function that takes one or more functions as an input or that outputs a function
functions are first-order functions. In mathematics higher-order functions are also termed operators or functionals. The differential operator in calculus is
Higher-order_function
Expansion of the time evolution operator
time-ordered. It is useful to introduce an operator T {\displaystyle {\mathcal {T}}} , called the time-ordering operator, and to define U n ( t , t 0 ) = ( −
Dyson_series
Analog of the continuous Laplace operator
In mathematics, the discrete Laplace operator is an analog of the continuous Laplace operator, defined so that it has meaning on a graph or a discrete
Discrete_Laplace_operator
Concept in computability theory
μ-operator, minimization operator, or unbounded search operator searches for the least natural number with a given property. Adding the μ-operator to
Mu_operator
In mathematics, Jordan operator algebras are real or complex Jordan algebras with the compatible structure of a Banach space. When the coefficients are
Jordan_operator_algebra
Technique for solving differential equations
when one separates variables for first-order equations, one in fact moves the dx denominator of the operator to the side with the x variable, and the
Separation_of_variables
commercial operators of the Airbus A350. There were 632 A350 aircraft in service with 44 operators as of March 20, 2025[update]. The top 10 largest operators are
List_of_Airbus_A350_operators
Method of solution for inhomogeneous ODEs
but instead of using a particular kind of differential operator (the annihilator) in order to find the best possible form of the particular solution
Method of undetermined coefficients
Method_of_undetermined_coefficients
Markov process is a second-order elliptic operator. The infinitesimal generator of Brownian motion is the Laplace operator and the transition probability
Stochastic analysis on manifolds
Stochastic_analysis_on_manifolds
Mathematical homomorphism
In mathematics, the Verschiebung or Verschiebung operator V is a homomorphism between affine commutative group schemes over a field of nonzero characteristic
Verschiebung_operator
Second-order differential operator
d'Alembert operator (denoted by a box: ◻ {\displaystyle \Box } ), also called the d'Alembertian, wave operator, box operator or sometimes quabla operator (cf
D'Alembert_operator
Legal/criminal procedural television franchise
Law & Order is a media franchise composed of a number of related American television series created by Dick Wolf and produced by Wolf Entertainment. They
Law_&_Order_(franchise)
ORDER OPERATOR
ORDER OPERATOR
Surname or Lastname
English
English : variant of Cordier.Catalan : occupational name for a maker of cord or string, from an agent derivative of Catalan corda ‘string’, ‘cord’.
Boy/Male
Arabic, Australian, Muslim
Order
Girl/Female
Greek
Order.
Boy/Male
Greek
Order.
Surname or Lastname
English
English : topographic name for someone who lived at the edge of a village or by some other boundary, Middle English border, from Old French bordure ‘edge’.
Girl/Female
Indian, Traditional
Order
Boy/Male
Australian, French, German, Greek
Order
Boy/Male
Arabic
Order; Discipline
Boy/Male
Muslim
Order, Decree
Girl/Female
Australian, French, German, Greek, Italian
Order
Male
Swedish
Old Swedish form of Old Norse Oddr, ODDER means "point of a weapon."
Boy/Male
Indian
Order, Decree
Boy/Male
Greek
Order.
Boy/Male
Tamil
Pradarsh | பà¯à®°à®¤à®°à¯à®·
Appearance, Order
Pradarsh | பà¯à®°à®¤à®°à¯à®·
Girl/Female
German, Greek
Order
Boy/Male
Greek
Order.
Girl/Female
Indian, Telugu
Order
Boy/Male
Muslim
Order. Discipline.
Boy/Male
Hindu, Indian, Punjabi, Sikh
Order
Girl/Female
Indian, Marathi, Sindhi
Order
ORDER OPERATOR
ORDER OPERATOR
Male
Irish
Variant spelling of Irish Gaelic Bruadair, BRUADAR means "dream."Â
Girl/Female
Arabic, Muslim, Sindhi
Daughter of Sa'ad; She was a Queen of Irqan
Girl/Female
Muslim
Censure
Male
Iranian/Persian
(سیاوش) Variant spelling of Persian Siyavash, SIAVASH means "possesses black stallions." In the ancient epic poem Shahnameh, this is the name of a king, the son of Shah Kavakhous, a Shah of the Pishdak Dynasty.
Boy/Male
British, Czech, Czechoslovakian, English, Teutonic
Rich; Wealthy; Prosperous
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Name of a Grammarian
Girl/Female
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Telugu
Lady
Surname or Lastname
English, of Welsh origin
English, of Welsh origin : Anglicized form of Welsh ap Adda ‘son of Adda’, a byform of Adam.
Boy/Male
Hindu, Indian, Traditional
Noble Partition
Girl/Female
Indian
Wish, Desire, Will of (Allah)
ORDER OPERATOR
ORDER OPERATOR
ORDER OPERATOR
ORDER OPERATOR
ORDER OPERATOR
n.
A command; a mandate; a precept; a direction.
n.
Rank; degree; thus, the order of a curve or surface is the same as the degree of its equation.
v. t.
To make a border for; to furnish with a border, as for ornament; as, to border a garment or a garden.
n.
That which prescribes a method of procedure; a rule or regulation made by competent authority; as, the rules and orders of the senate.
n.
To put in order; to reduce to a methodical arrangement; to arrange in a series, or with reference to an end. Hence, to regulate; to dispose; to direct; to rule.
n.
An ecclesiastical grade or rank, as of deacon, priest, or bishop; the office of the Christian ministry; -- often used in the plural; as, to take orders, or to take holy orders, that is, to enter some grade of the ministry.
n.
To admit to holy orders; to ordain; to receive into the ranks of the ministry.
n.
Conformity with law or decorum; freedom from disturbance; general tranquillity; public quiet; as, to preserve order in a community or an assembly.
n.
A body of persons having some common honorary distinction or rule of obligation; esp., a body of religious persons or aggregate of convents living under a common rule; as, the Order of the Bath; the Franciscan order.
n.
The disposition of a column and its component parts, and of the entablature resting upon it, in classical architecture; hence (as the column and entablature are the characteristic features of classical architecture) a style or manner of architectural designing.
n.
The placing of words and members in a sentence in such a manner as to contribute to force and beauty or clearness of expression.
v. i.
To give orders; to issue commands.
a.
Being on duty; keeping order; conveying orders.
n.
A number of things or persons arranged in a fixed or suitable place, or relative position; a rank; a row; a grade; especially, a rank or class in society; a group or division of men in the same social or other position; also, a distinct character, kind, or sort; as, the higher or lower orders of society; talent of a high order.
n.
To give an order to; to command; as, to order troops to advance.
v. t.
To be, or to have, contiguous to; to touch, or be touched, as by a border; to be, or to have, near the limits or boundary; as, the region borders a forest, or is bordered on the north by a forest.
n.
An assemblage of genera having certain important characters in common; as, the Carnivora and Insectivora are orders of Mammalia.
n.
Right arrangement; a normal, correct, or fit condition; as, the house is in order; the machinery is out of order.
n.
Hence: A commission to purchase, sell, or supply goods; a direction, in writing, to pay money, to furnish supplies, to admit to a building, a place of entertainment, or the like; as, orders for blankets are large.
n.
To give an order for; to secure by an order; as, to order a carriage; to order groceries.