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Look up scalar in Wiktionary, the free dictionary. Scalar may refer to: Scalar (mathematics), an element of a field, which is used to define a vector space...

of physics, a Lorentz scalar is a scalar expression whose value is invariant under any Lorentz transformation. A Lorentz scalar may be generated from...

A scalar boson is a boson whose spin equals zero. A boson is a particle whose wave function is symmetric under particle exchange and therefore follows...

Scalar quantities or simply scalars are physical quantities that can be described by a single pure number (a scalar, typically a real number), accompanied...

specifically in linear algebra, a scalar is an element of a field which is used to define a vector space through the operation of scalar multiplication: a vector...

together and multiplied ("scaled") by numbers called scalars. The operations of vector addition and scalar multiplication must satisfy certain requirements...

physics, a scalar field is a function associating a single number to each point in a region of space – possibly physical space. The scalar may either...

In mathematics, scalar multiplication is one of the basic operations defining a vector space in linear algebra (or more generally, a module in abstract...

In the mathematical field of Riemannian geometry, the scalar curvature (or the Ricci scalar) is a measure of the curvature of a Riemannian manifold. To...

are scalar theories because the gravitational field is a scalar. Other proposed alternatives include scalar–tensor theories that contain a scalar field...

coordinate vectors), and returns a single number. In Euclidean geometry, the scalar product of two vectors is the dot product of their Cartesian coordinates...

the electrostatic potential or electric field potential, is a field of scalar quantities through space, often denoted with the letter φ {\displaystyle...

scalar magnitude by writing it as a 1 = a 1 b ^ {\displaystyle \mathbf {a} _{1}=a_{1}\mathbf {\hat {b}} } where a 1 {\displaystyle a_{1}} is a scalar...

In pragmatics, scalar implicature, or quantity implicature, is an implicature that attributes an implicit meaning beyond the explicit or literal meaning...

theoretical physics, scalar field theory can refer to a relativistically invariant classical or quantum theory of scalar fields. A scalar field is invariant...

nonzero, non-scalar quaternions, or positive scalar quaternions, have exactly two roots, while 0 has exactly one root (0), and negative scalar quaternions...

the scalar projection of a vector a {\displaystyle \mathbf {a} } on (or onto) a vector b , {\displaystyle \mathbf {b} ,} also known as the scalar resolute...

Scalar processors are a class of computer processors that process only one data item at a time. Typical data items include integers and floating point...

In mathematical physics, scalar potential describes the situation where the difference in the potential energies of an object in two different positions...

physics theory. In the Standard Model, the Higgs particle is a massive scalar boson that couples to (interacts with) particles whose mass arises from...

scalar matrix; that is, a scalar multiple λ of the identity matrix I. Its effect on a vector is scalar multiplication by λ. For example, a 3×3 scalar...

In Riemannian geometry, a branch of mathematics, the prescribed scalar curvature problem is as follows: given a closed, smooth manifold M and a smooth...

In theoretical physics, a scalar–tensor theory is a field theory that includes both a scalar field and a tensor field to represent a certain interaction...

Scalar theories of gravitation are field theories of gravitation in which the gravitational field is described using a scalar field, which is required...

two groups can be distinguished by whether they write the derivative of a scalar with respect to a vector as a column vector or a row vector. Both of these...

context of applications to general relativity, the Kretschmann scalar is a quadratic scalar invariant. It was introduced by Erich Kretschmann. The Kretschmann...

single scalar quantity. The term may also be used to refer to elements of vector spaces, that can be added together and multiplied ("scaled") by scalars. In...

different products, the scalar-valued scalar triple product and, less often, the vector-valued vector triple product. The scalar triple product (also called...

In general relativity, a scalar field solution is an exact solution of the Einstein field equation in which the gravitational field is due entirely to...

The scalar timing or scalar expectancy theory (SET) is a model of the processes that govern behavior controlled by time. The model posits an internal...

Scalable Vector Graphics (SVG) is an XML-based vector graphics format for defining two-dimensional graphics, having support for interactivity and animation...

Scalar control of an AC electrical motor is a way to achieve the variable speed operation by manipulating the supply voltage or current ("magnitude") and...

called an inner product. The inner product of two vectors in the space is a scalar, often denoted with angle brackets such as in ⟨ a , b ⟩ {\displaystyle \langle...

§ Generalizations below for more). A scalar field smoothly assigns a scalar value to every point in a space. The scalar is a mathematical number representing...

In astrophysics and cosmology scalar field dark matter is a classical, minimally coupled, scalar field postulated to account for the inferred dark matter...

In high energy physics, a scalar meson is a meson with total spin 0 and even parity (usually noted as JP=0+). In contrast, pseudoscalar mesons have odd...

often called scalars (from scale) to distinguish them from vectors. The operation of multiplying a vector by a scalar is called scalar multiplication...

In vector calculus, the gradient of a scalar-valued differentiable function f {\displaystyle f} of several variables is the vector field (or vector-valued...

of scalars, f ! M = Hom R ⁡ ( S , M ) {\displaystyle f^{!}M=\operatorname {Hom} _{R}(S,M)} , the coinduced module, formed by co-extension of scalars, and...

In theoretical physics, scalar electrodynamics is a theory of a U(1) gauge field coupled to a charged spin 0 scalar field that takes the place of the...

covariates are functional or scalar: (i) scalar responses with functional covariates, (ii) functional responses with scalar covariates, (iii) functional...

It is an example of a scalar–tensor theory, a gravitational theory in which the gravitational interaction is mediated by a scalar field as well as the...

vectors and scalars to span a four-dimensional space. For a quaternion q = a + bi + cj + dk, Hamilton used two projections: S q = a, for the scalar part of...

different objects such as vectors, scalars, and even other tensors. There are many types of tensors, including scalars and vectors (which are the simplest...

magnitude and direction are needed to define it (velocity vector). The scalar absolute value (magnitude) of velocity is called speed, a quantity that...

languages) have been engineered specifically to generalize operations on scalars to apply transparently to vectors, matrices, and higher-dimensional arrays...

example, scalar multiplication of vector spaces takes a scalar and a vector to produce a vector, and scalar product takes two vectors to produce a scalar. Binary...

scalar chromodynamics, also known as scalar quantum chromodynamics or scalar QCD, is a gauge theory consisting of a gauge field coupled to a scalar field...

In general relativity, optical scalars refer to a set of three scalar functions { θ ^ {\displaystyle \{{\hat {\theta }}} (expansion), σ ^ {\displaystyle...

within the framework of super Yang–Mills theory, including fermionic and scalar fields, gave rise, in the case of N = 1 or 2 supersymmetry, to the constraint...

scalar field or a vector field. The value of the line integral is the sum of values of the field at all points on the curve, weighted by some scalar function...

act on scalar and vector fields in three different ways, giving rise to three different differential operations: first, it can act on scalar fields by...

self-interaction of a scalar field. Other types of quartic interactions may be found under the topic of four-fermion interactions. A classical free scalar field φ {\displaystyle...

differential geometry, a constant scalar curvature Kähler metric (cscK metric) is a Kähler metric on a complex manifold whose scalar curvature is constant. A special...

Tensor–vector–scalar gravity (TeVeS), developed by Jacob Bekenstein in 2004, is a relativistic generalization of Mordehai Milgrom's Modified Newtonian...

Koyama, Kazuya; Arroja, Frederico (2010). "Pathological behaviour of the scalar graviton in Hořava–Lifshitz gravity". Journal of High Energy Physics. 2010...

new opmask registers for masking most AVX-512 instructions. Adds a new scalar memory mode that automatically performs a broadcast. Adds room for explicit...

Magnetic scalar potential, ψ, is a physical quantity in classical electromagnetism analogous to electric potential. It is used to specify the magnetic...

A command hierarchy or chain of command is a group of people who carry out orders based on others' authority within the group. Certain aspects of a command...

surface, one may integrate over this surface a scalar field (that is, a function of position which returns a scalar as a value), or a vector field (that is,...

called scalars. The first operation, vector addition, takes any two vectors v and w and outputs a third vector v + w. The second operation, scalar multiplication...

vector spaces, which respects the basic operations of vector addition and scalar multiplication. A standard example of a linear map is an m × n {\displaystyle...

gravitational field in the Einstein–Cartan theory is proportional to the Ricci scalar: L G = 1 2 κ R | g | {\displaystyle {\mathcal {L}}_{\mathrm {G} }={\frac...

fields, which include scalar and vector fields as special cases. For example, if there are m {\displaystyle m} real-valued scalar fields, φ 1 , … , φ m...

the advection–diffusion equation, drift–diffusion equation, or (generic) scalar transport equation. The general equation in conservative form is ∂ c ∂ t...

This two-stage decomposition applies equally well to vector as well as scalar quantizers. Because quantization is a many-to-few mapping, it is an inherently...

Newman–Penrose (NP) formalism of general relativity, Weyl scalars refer to a set of five complex scalars { Ψ 0 , Ψ 1 , Ψ 2 , Ψ 3 , Ψ 4 } {\displaystyle \{\Psi...

In cosmological perturbation theory, the scalar–vector–tensor decomposition is a decomposition of the most general linearized perturbations of the...

instruction-level parallelism within a single processor. In contrast to a scalar processor, which can execute at most one single instruction per clock cycle...

the sum of a scalar and a vector. It can also be represented as the product of its tensor and its versor. Hamilton invented the term scalars for the real...

an additional scalar boson and the massless graviton, ensuring that general relativity is recovered at low energies. The additional scalar particle appears...

the electromagnetic field. The Standard Model has a unique fundamental scalar field, the Higgs field, the quanta of which are called Higgs bosons. The...

in contrast to scalar processors, whose instructions operate on single data items only, and in contrast to some of those same scalar processors having...

2015-4082. Rodal, José (May 2019). "A Machian wave effect in conformal, scalar--tensor gravitational theory". General Relativity and Gravitation. 51 (5):...

{\displaystyle A^{\mu }} identified with the electromagnetic vector potential; and a scalar field ϕ {\displaystyle \phi } . Then decompose the 5D metric so that the...

second (alternatively spelled meter per second) is the unit of both speed (a scalar quantity) and velocity (a vector quantity, which has direction and magnitude)...

is a generalization of the notion of vector space in which the field of scalars is replaced by a (not necessarily commutative) ring. The concept of a module...

{\mathcal {R}}={\mathcal {R}}^{ab}{}_{ab}.} This is equivalent to the Ricci scalar and is the only linear invariant that can be constructed. Similar to the...

into a vector field, which is irrelevant for our purposes, and a scalar field. This scalar mode exerts an extra attraction in the massive case compared to...

space where every point is at the same potential. This usually refers to a scalar potential (in that case it is a level set of the potential), although it...

In particle physics, the hypothetical dilaton is a particle of a scalar field φ {\displaystyle \varphi } that appears in theories with extra dimensions...

a square matrix of second-order partial derivatives of a scalar-valued function, or scalar field. It describes the local curvature of a function of many...

Bi-scalar tensor vector gravity theory (BSTV) is an extension of the tensor–vector–scalar gravity theory (TeVeS). TeVeS is a relativistic generalization...

Scalar–tensor–vector gravity (STVG) is a modified theory of gravity developed by John Moffat, a researcher at the Perimeter Institute for Theoretical Physics...

variable Object (computer science) Property (object-oriented programming) Scalar (mathematics) State (computer science) Temporary variable Variable interpolation...

– represented by a scalar, vector, spinor, or tensor – that has a value for each point in space and time. An example of a scalar field is a weather map...

In mathematical physics, vanishing scalar invariant (VSI) spacetimes are Lorentzian manifolds in which all polynomial curvature invariants of all orders...

AQUAL Tensor–vector–scalar Nonsymmetric gravitation Scalar–tensor theories Brans–Dicke Scalar–tensor–vector Conformal gravity Scalar theories Nordström...

generalizes the gradient of a scalar-valued function in several variables, which in turn generalizes the derivative of a scalar-valued function of a single...

}^{a}} and B μ {\displaystyle B_{\mu }} and the scalar field φ {\displaystyle \varphi } . The scalar potential is given by V ( φ ) = − μ 2 φ † φ + λ (...

different function, f, of the Ricci scalar, R. The simplest case is just the function being equal to the scalar; this is general relativity. As a consequence...

In differential geometry, Vermeil's theorem essentially states that the scalar curvature is the only (non-trivial) absolute invariant among those of prescribed...

is a quantity that behaves like a scalar, except that it changes sign under a parity inversion while a true scalar does not. A pseudoscalar, when multiplied...

six parameters: baryon density parameter; dark matter density parameter; scalar spectral index; two parameters related to curvature fluctuation amplitude;...

2026. Buoli, Alice (1 January 2014). "Beyond the border: exploring cross-scalar socio-spatial dynamics of conflict, resistance and encounter at the Ceuta–Morocco...

definitions are for the scalar and tensor case respectively known as advection and convection. For example, for a macroscopic scalar field ϕ ( x , t ) {\displaystyle...

relativistic scalar fields play a prominent role in modern physics, the Klein–Gordon is likewise indispensable in many areas. For example, such scalar fields...

marching squares is an algorithm that generates contours for a two-dimensional scalar field (rectangular array of individual numerical values). A similar method...

operates on a scalar field, producing a vector field. Divergence is a vector operator that operates on a vector field, producing a scalar field. Curl is...

Scalar-Tensor theories (or DHOST theories) are theories of modified gravity. They have a Lagrangian containing second-order derivatives of a scalar field...

λ {\displaystyle \lambda } ⁠, where ⁠ λ {\displaystyle \lambda } ⁠ is a scalar, then v {\displaystyle \mathbf {v} } is called an eigenvector of ⁠ A {\displaystyle...

particles according to the Yukawa potential. Specifically, it is between a scalar field (or pseudoscalar field) ϕ {\displaystyle \phi } and a Dirac field...

divergence is a vector operator that operates on a vector field, producing a scalar field giving the rate that the vector field alters the volume in an infinitesimal...

operands. Supercomputing moved away from the SIMD approach when inexpensive scalar multiple instruction, multiple data (MIMD) approaches based on commodity...

surface integral to obtain the value of the solution of the homogeneous scalar wave equation at an arbitrary point P in terms of the values of the solution...

The saxion is the scalar superpartner of the axion, and part of a chiral superfield. The axion represents the CP violating theory of the Standard Model...

Double-dot product) is a binary operation that takes two matrices and returns a scalar. It is often denoted ⟨ A , B ⟩ F {\displaystyle \langle \mathbf {A} ,\mathbf...

The pressuron is a hypothetical scalar particle which couples to both gravity and matter theorised in 2013. Although originally postulated without self-interaction...

conservative force) as mentioned above, it can be written as the gradient of a scalar potential, called the gravitational potential: g = − ∇ ϕ . {\displaystyle...

of positive Yamabe type, meaning that it must admit a metric of positive scalar curvature. Higher-dimensional gravity appears in string theory and M-theory...

Riemann tensor has only one independent component, which means that the Ricci scalar completely determines the Riemann tensor. There is only one valid expression...

the usual Einstein–Hilbert action where the Lagrangian is just the Ricci scalar. The equation of motion upon varying the metric is called the Bach tensor...

to have the same units, like torque (a vector product) versus energy (a scalar product). In another instance in the early 2000s, the International Committee...

form the product of any scalar with any vector, giving a map R × V → V {\displaystyle \mathbb {R} \times V\rightarrow V} . A scalar product is a bi-linear...

AQUAL Tensor–vector–scalar Nonsymmetric gravitation Scalar–tensor theories Brans–Dicke Scalar–tensor–vector Conformal gravity Scalar theories Nordström...

extensive), their transformation properties (i.e. whether the quantity is a scalar, vector, matrix or tensor), and whether the quantity is conserved. List...

denote an ensemble average. There are both scalar and tensor modes of fluctuations.[clarification needed] Scalar modes have the power spectrum defined as...

increasingly general cases, beginning with the case in which the parameter is a scalar and its estimator is unbiased. All versions of the bound require certain...

AQUAL Tensor–vector–scalar Nonsymmetric gravitation Scalar–tensor theories Brans–Dicke Scalar–tensor–vector Conformal gravity Scalar theories Nordström...

In mathematics, restriction of scalars (also known as "Weil restriction") is a functor which, for any finite extension of fields L/k and any algebraic...

done is given by the dot product of the two vectors, where the result is a scalar. When the force F is constant and the angle θ between the force and the...

of a vector ‖ A ‖ {\displaystyle \|\mathbf {A} \|} and the dot product (scalar product) of two vectors A·B, apply to vectors in any dimension, while identities...

consisting of a set together with operations of multiplication and addition and scalar multiplication by elements of a field and satisfying the axioms implied...

of the fifth dimension in Randall–Sundrum models. The mechanism uses a scalar field that propagates throughout the five-dimensional bulk. On each of the...

+x_{k}^{2}\right)-\left(x_{k+1}^{2}+\dots +x_{n}^{2}\right),} which is called the scalar square of the vector x. For Euclidean spaces, k = n, implying that the quadratic...

classical field theory is the massless scalar field (note that the name scalar is unrelated to scale invariance). The scalar field, φ(x, t) is a function of...

\mathbb {C} } ), any element of the center of a group must act as a scalar operator (a scalar multiple of the identity) on M. The lemma is named after Issai...

In mathematics, vector spherical harmonics (VSH) are an extension of the scalar spherical harmonics for use with vector fields. The components of the VSH...

dissimilar objects: a vector can be multiplied by a scalar to form another vector (an operation known as scalar multiplication), and the inner product operation...

Proca theory Chern–Simons theory Spinor and scalar Yukawa model Scalar and gauge Scalar electrodynamics Scalar chromodynamics Yang–Mills–Higgs Spinor and...

(finite or otherwise) in the quantities x, y and z sin α, sinh γ, log x A scalar is a physical quantity that has magnitude but no direction. Symbols for...

number of fundamental data types. The most commonly used and discussed are scalars, arrays, hashes, filehandles, and subroutines: String values (literals)...

suitable scaling. Let f ( x ; θ ) {\displaystyle f(x;\theta )} denote the scalar function computed by a given neural network with parameters θ {\displaystyle...

AQUAL Tensor–vector–scalar Nonsymmetric gravitation Scalar–tensor theories Brans–Dicke Scalar–tensor–vector Conformal gravity Scalar theories Nordström...

It can be seen that the vector form of the equation is the same as the scalar form given earlier, except that F is now a vector quantity, and the right...

{\displaystyle \mathbf {v} } be arbitrary vectors in an inner product space over the scalar field F , {\displaystyle \mathbb {F} ,} where F {\displaystyle \mathbb {F}...

Carlos A. R.; Radu, Eugen (2015). "Asymptotically flat black holes with scalar hair: A review". International Journal of Modern Physics D. 24 (9): 1542014–1542219...

, … , x n ) {\displaystyle \psi (x_{1},\ldots ,x_{n})} , also called a scalar field, the gradient is the vector field: ∇ ψ = ( ∂ ∂ x 1 , … , ∂ ∂ x n )...

done by gravity. On a real staircase, the height above the ground is a scalar potential field: one has to go upward exactly as much as one goes downward...

Since voltage is the difference in electric potential, it is a physical scalar quantity. A voltmeter can be used to measure the voltage between two points...

The inflaton field is a hypothetical scalar field that is conjectured to have driven cosmic inflation in the very early universe. The field, originally...

semidirect products Product of rings Ideal operations, for product of ideals Scalar multiplication Matrix multiplication Inner product, on an inner product...

and ultrasonic components. The two basic types of network analyzers are scalar network analyzer (SNA)—measures amplitude properties only vector network...

or a human brain) along with measured or computed data. The data may be scalar (such as the concentration of a chemical agent in the brain), vector or...

represented as a two-dimensional graph of an independent scalar input versus the dependent scalar output (known as a transfer curve or characteristic curve)...

AQUAL Tensor–vector–scalar Nonsymmetric gravitation Scalar–tensor theories Brans–Dicke Scalar–tensor–vector Conformal gravity Scalar theories Nordström...

AQUAL Tensor–vector–scalar Nonsymmetric gravitation Scalar–tensor theories Brans–Dicke Scalar–tensor–vector Conformal gravity Scalar theories Nordström...

indexed arrays, and a suite of fundamental scalar types. BSON originated in 2009 at MongoDB. Several scalar data types are of specific interest to MongoDB...

scalar quantity. It relates the vector area element (a vector normal to the surface) with the normal force acting on it. The pressure is the scalar proportionality...

semantics of the program. Loop-invariant code motion (also called hoisting or scalar promotion) is a compiler optimization that performs this movement automatically...

of the scalar field φ {\displaystyle \varphi } is a scalar, which is symbolically expressed by the scalar multiplication of ∇2 and the scalar field φ...

determinant of the metric tensor matrix, R {\displaystyle R} is the Ricci scalar, and κ = 8 π G c − 4 {\displaystyle \kappa =8\pi Gc^{-4}} is the Einstein...

geometry, which was resolved in the 1980s. It is a statement about the scalar curvature of Riemannian manifolds: Let (M,g) be a closed smooth Riemannian...

scalar curvature cannot exist on such manifolds. A particular consequence is that the torus cannot support any Riemannian metric of positive scalar curvature...

contrasted with scalar fields, which associate a number or scalar to every point in space, and are also contrasted with simple lists of scalar fields, which...

only the moment of inertia about an axis perpendicular to the plane, a scalar value, matters. If a body is allowed to rotate in all three dimensions,...

(R+2)+S_{boundary}} where GN is the two-dimensional Newton constant, R is the Ricci scalar of the metric gμν, and the cosmological constant is chosen such that the...

to scalar theories of gravitation (while Einstein explored tensor theories). Nordström's first attempt to propose a suitable relativistic scalar field...

pure quaternions with zero scalar part) is performed, it results in a quaternion with a scalar and vector part. The scalar and vector part of this Hamilton...

is the watt (symbol W), equal to one joule per second (J/s). Power is a scalar quantity. The output power of a motor is the product of the torque that...

leptons), which are believed to be the fundamental components of matter, or scalar fields, like the Higgs particles, which are used to introduced mass in a...

general relativity, the Carminati–McLenaghan invariants or CM scalars are a set of 16 scalar curvature invariants for the Riemann tensor. This set is usually...

growth processes) D.M.T. Benincasa, F. Dowker, The Scalar Curvature of a Causal Set; arXiv:1001.2725; (Scalar curvature, actions) G. Brightwell; M. Luczak;...

distinguished from quintessence which has w ≠ − 1 {\displaystyle w\neq -1} . A scalar field ϕ {\displaystyle \phi } can be viewed as a sort of perfect fluid with...

AQUAL Tensor–vector–scalar Nonsymmetric gravitation Scalar–tensor theories Brans–Dicke Scalar–tensor–vector Conformal gravity Scalar theories Nordström...

field can be simply expressed as the gradient of a certain scalar function, called a scalar potential. The potential energy is related to, and can be obtained...

Standard Model of Particle Physics there are five elementary bosons: One scalar boson (spin = 0) H0 Higgs boson – the particle that contributes to the phenomenon...

one-form, or a covector) is a linear map from a vector space to its field of scalars (often, the real numbers or the complex numbers). If V is a vector space...

mathematically as a vector field, and the transported material is described by a scalar field showing its distribution over space. Advection requires currents in...

AQUAL Tensor–vector–scalar Nonsymmetric gravitation Scalar–tensor theories Brans–Dicke Scalar–tensor–vector Conformal gravity Scalar theories Nordström...

The Cauchy formula for repeated integration, named after Augustin-Louis Cauchy, allows one to compress n antiderivatives of a function into a single integral...

hypothesis. Potential flow describes the velocity field as the gradient of a scalar function: the velocity potential. As a result, a potential flow is characterized...

In general relativity, curvature invariants are a set of scalars formed from the Riemann, Weyl and Ricci tensors – which represent curvature, hence the...

field, a specific type of the above algebraic structure Scalar field, assignment of a scalar to each point in a mathematical space Spinor field, assignment...

all  x ∈ H  and all scalar  c ∈ F , {\displaystyle f(cx)={\overline {c}}f(x)\quad {\text{ for all }}x\in H{\text{ and all scalar }}c\in \mathbb {F} ,}...

made a number of highly influential contributions to the study of positive scalar curvature. By an elementary but novel combination of the Gauss equation...

Similarity Measures Name Meaning Formula Formula (Scalar) Similarity Correlation Euclidean Distance Distance between ends of vectors | a − b | {\displaystyle...

with the property that the vector space operations (vector addition and scalar multiplication) are also continuous functions. Such a topology is called...

of its properties are strongly linked to the geometry associated to the scalar fields in the chiral multiplets. After the simplest form of this supergravity...

may be conveniently here labelled the 'vector approach', the other the 'scalar approach'. The vector definition refers to the full spherical integral of...

(2011). "Linking covariant and canonical LQG: new solutions to the Euclidean Scalar Constraint". Physical Review D. 86 (2) 024017. arXiv:1109.1290. Bibcode:2012PhRvD...

types of supermultiplets: a chiral supermultiplet consisting of a complex scalar field and its Majorana spinor superpartner, and a vector supermultiplet...

Tomboulis (1997) later extended this work. By looking at an equivalent scalar-tensor theory, Biswas, Mazumdar and Siegel (2005) looked at bouncing FRW...

manifolds, and is the negative L2-gradient flow of the (normalized) total scalar curvature, restricted to a given conformal class: it can be interpreted...

real-valued function. The Laplace operator therefore maps a scalar function to another scalar function. If the right-hand side is specified as a given function...

arguments is multiplied by the same scalar, then the function's value is multiplied by some power of this scalar; the power is called the degree of homogeneity...

, {\displaystyle V,} but whose scalar multiplication involves conjugation of the scalars. In other words, the scalar multiplication of V ¯ {\displaystyle...

reconstruct the spacetime's semi-Riemannian metric, at least up to a positive scalar factor. In mathematical terms, this defines a conformal structure or conformal...

AQUAL Tensor–vector–scalar Nonsymmetric gravitation Scalar–tensor theories Brans–Dicke Scalar–tensor–vector Conformal gravity Scalar theories Nordström...

the electromagnetic field can be derived. It combines both an electric scalar potential and a magnetic vector potential into a single four-vector. As...

to address these challenges. In 2021 the VFS for Git was superseded by Scalar. This box: view talk edit Version market share As a percentage of desktop...

AQUAL Tensor–vector–scalar Nonsymmetric gravitation Scalar–tensor theories Brans–Dicke Scalar–tensor–vector Conformal gravity Scalar theories Nordström...

AQUAL Tensor–vector–scalar Nonsymmetric gravitation Scalar–tensor theories Brans–Dicke Scalar–tensor–vector Conformal gravity Scalar theories Nordström...

opposing flows of positive energy. An example comes from considering a scalar field in D-dimensional Minkowski space. Consider a Lagrangian density given...

composed of two chips - one for the scalar portion of the processor, and the other for the vector portion. The scalar chip was also notable for including...

semitones is 5–6–7 (T5(A)) since 0 + 5 = 5, 1 + 5 = 6, and 2 + 5 = 7. In scalar transposition, every pitch in a collection is shifted up or down a fixed...

dependent on only two real parameters: the time t {\displaystyle t} , and the scalar-valued displacement d = x → ⋅ n → {\displaystyle d={\vec {x}}\cdot {\vec...

that point in space. Because the force field is conservative, there is a scalar potential energy per unit mass, Φ, at each point in space associated with...

the quaternion is the sum of a scalar function and another scalar function multiplying the vector part. These two scalar functions are series sums of multinomials...

frequency (symbol ω), also called angular speed and angular rate, is a scalar measure of the angle rate (the angle per unit time) or the temporal rate...

elements of K scalars. If v1,...,vn are vectors and a1,...,an are scalars, then the linear combination of those vectors with those scalars as coefficients...

relativity. The simplest generalization of Newton's approach would be a scalar field theory with the gravitational potential represented by a single number...

algebra or geometric algebra that extends the idea of scalars and vectors. Considering a scalar as a degree-zero quantity and a vector as a degree-one...

inner node is the maximal scalar value given in the subgrid belonging to the node. Nodes are not traversed if their scalar values are smaller than the...

reportedly pitched by Ubisoft Annecy as a multiplayer project using Ubisoft Scalar technology. Codename Stardust was also rumored to be a remake of the original...

AQUAL Tensor–vector–scalar Nonsymmetric gravitation Scalar–tensor theories Brans–Dicke Scalar–tensor–vector Conformal gravity Scalar theories Nordström...

\gamma _{ij}} into the theory, one has a great number of new tensors and scalars at one's disposal. One can set up other field equations other than Einstein's...

AQUAL Tensor–vector–scalar Nonsymmetric gravitation Scalar–tensor theories Brans–Dicke Scalar–tensor–vector Conformal gravity Scalar theories Nordström...

certain generalized scalar curvature. As such, Schoen and Yau's approach originated in their study of Riemannian manifolds of positive scalar curvature, which...

which other parts move), "rhythmic harmony", "harmony by imitation", and "scalar clusters" (see below for explanation of these terms). "By Western standards...

direction of the flow of a substance or property. In vector calculus, flux is a scalar quantity, defined as the surface integral of the perpendicular component...

complement the scalar matrices, and leaves one degree of freedom: any such map is determined by its value on scalars, which is one scalar parameter and...

physics, quintessence is a hypothetical form of dark energy, more precisely a scalar field minimally coupled to gravity, postulated as an explanation of the...

the total energy of matter and gravitation is proportional to the Ricci scalar of three-space up to the linear order of perturbation. Independently in...

form Aest, where t is time, s is a complex parameter, and A is a complex scalar. In any linear time-invariant system, all of the currents and voltages can...

linear mapping from a vector space V {\displaystyle V} into its field of scalars (that is, it is an element of the dual space V ∗ {\displaystyle V^{*}}...

is thus an algebraic structure with an addition, a multiplication, and a scalar multiplication (the multiplication by the image of the ring homomorphism...

generalization of the four-dimensional metric tensor. It additionally includes a scalar field called graviscalar (or radion) and a vector field called graviphoton...

geometrical objects can be classified into scalars, vectors, and other tensors of rank 2 or higher. (Technically, scalars, such as electrical potential are tensors...

object-oriented programming, data-management tasks act on objects that combine scalar values into objects. For example, consider an address book entry that represents...

out to be unique to non-unitary theories; an example is the biharmonic scalar. This property should be viewed as even more special than scale without...

invariants are scalar quantities constructed from tensors that describe the curvature of a space or spacetime. Because they are scalars, their values do...

vectors), since positions can be added (vector addition) and scaled in length (scalar multiplication) to obtain another position vector in the space. The notion...

{\displaystyle x} conditioned on y {\displaystyle y} . When x {\displaystyle x} is a scalar variable, the MSE expression simplifies to E ⁡ { ( x ^ − x ) 2 } {\displaystyle...

particular cases of this law. In case of a conservative body force with scalar potential : ϕ {\displaystyle \phi } : ρ g = − ∇ ϕ {\displaystyle \rho \mathbf...

If the vector is multiplied by a scalar, the corresponding directional derivative is multiplied by the same scalar. Some elementary texts instead use...

In algebra, an Okubo algebra or pseudo-octonion algebra is an 8-dimensional non-associative algebra similar to the one studied by Susumu Okubo. Okubo algebras...

subspace on which the scalar product g is positive-definite (resp. negative-definite), and r is the dimension of the radical of the scalar product g or the...

transformation is conformal whenever the Jacobian at each point is a positive scalar times a rotation matrix (orthogonal with determinant one). Some authors...

(representing a constant energy density filling space homogeneously) and scalar fields (dynamic quantities having energy densities that vary in time and...

LTO consortium. 2006 – Advanced Digital Information Corporation (ADIC), Scalar brand tape libraries, StorNext filesystem and de-duplication technology...

that distinguishes between generations of quarks and leptons. Branons, scalar fields predicted in brane world models. Composite Higgs, models that consider...

The Wavelet Scalar Quantization algorithm (WSQ) is a compression algorithm used for gray-scale fingerprint images. It is based on wavelet theory and has...

one quantizes a real scalar field, then one finds that there is only one kind of annihilation operator; therefore, real scalar fields describe neutral...

directions. This article mostly focuses on the scalar wave equation describing waves in scalars by scalar functions u = u ( x , y , z , t ) {\displaystyle...

The Individual Deprivation Measure (IDM) is a new, gender-sensitive and multidimensional measure of poverty developed to assess deprivation at the individual...

He was the son of John Heysham Gibbon. His contributions to scalar timing (1971) and scalar expectancy theory (1977) are considered major theoretical contributions...

A min/max kd-tree is a k-d tree with two scalar values—a minimum and a maximum—assigned to its nodes. The minimum/maximum of an inner node is equal to...

anticommutation relations obeyed by fermionic fields. Examples include scalar fields, describing spin-0 particles such as the Higgs boson, and gauge fields...

a tensor field is a generalization of a scalar field and a vector field that assigns, respectively, a scalar or vector to each point of space. If a tensor...

digital Morse theory is a digital adaptation of continuum Morse theory for scalar volume data. The term was first promulgated by DB Karron based on the work...

describe the motion of a continuum. The length of the flow velocity vector is scalar, the flow speed. It is also called velocity field; when evaluated along...

apply the linear operator before or after the operations of addition and scalar multiplication. In more technical words, linear operators are morphisms...

a scalar field is a scalar field, and the Fourier transform of a vector field is a vector field of same dimension. Now consider the following scalar and...

In probability theory, a probability density function (PDF), density function, or simply density of an absolutely continuous random variable, is a function...

extracting a polygonal mesh of an isosurface from a three-dimensional discrete scalar field (the elements of which are sometimes called voxels). The applications...

employee efficiency and less role conflict within an organisation.     The scalar principle asserts that there are clear and formal lines of hierarchal authority...

glueballs can have total angular momentum J = 0 (which are either scalar or pseudo-scalar) or J = 2. Triple-gluon glueballs can have total angular momentum...

self-interacting scalar field was derived. This showed that, apart from mass, electrical charge and angular momentum, black holes can carry a finite scalar charge...

bosons are different from the other kinds of bosons: first, fundamental scalar bosons (the Higgs boson); second, mesons, which are composite bosons, made...

is a differential operator given by the divergence of the gradient of a scalar function on Euclidean space. It is usually denoted by the symbols ⁠ ∇ ⋅...

the same file). Custom data types are allowed, but YAML natively encodes scalars (such as strings, integers, and floats), lists, and associative arrays...

isotropic liquid it reduces to a number, the so-called scalar coupling. In 1D NMR, the scalar coupling leads to oscillations in the free induction decay...

a pair of points) which can be made equal by scaling (by some positive scalar multiplier). Two vectors sharing the same direction are said to be codirectional...

topological ring such that scalar multiplication and addition are continuous. A module topology is the finest topology such that scalar multiplication and addition...

In mathematics, a relative scalar (of weight w) is a scalar-valued function whose transform under a coordinate transform, x ¯ j = x ¯ j ( x i ) {\displaystyle...

AQUAL Tensor–vector–scalar Nonsymmetric gravitation Scalar–tensor theories Brans–Dicke Scalar–tensor–vector Conformal gravity Scalar theories Nordström...

four-dimensional spacetime are encoded into seven (or ten) Ricci scalars which consist of three real scalars { Φ 00 , Φ 11 , Φ 22 } {\displaystyle \{\Phi _{00},\Phi...

formulations. Versions of Maxwell's equations based on the electric and magnetic scalar potentials are preferred for explicitly solving the equations as a boundary...

conforming methods. As an example, consider the continuity equation for a scalar unknown ρ {\displaystyle \rho } in a spatial domain Ω {\displaystyle \Omega...

Machine learning). The deviation is typically simply a differences of scalars; it can also be generalized to the vector lengths of a displacement, as...

media cannot in general be represented as a scalar quantity. Defining α {\displaystyle \alpha } as a scalar implies both that applied electric fields can...

a k-blade or a simple k-vector is a generalization of the concept of scalars and vectors to include simple bivectors, trivectors, etc. Specifically...

representation with two complex components called isospin), which is a scalar under Lorentz transformations. Its electric charge is zero; its weak isospin...

Tau neutrino Tau antineutrino Bosons Gauge Photon Gluon W and Z bosons Scalar Higgs boson Ghost fields Faddeev–Popov ghosts Hypothetical Superpartners...

pions are considerably less than that of the other mesons, such as the scalar or vector mesons. If their current quarks were massless particles, it could...

articles: Dot product – also known as the "scalar product", a binary operation that takes two vectors and returns a scalar quantity. The dot product of two vectors...

which gain an extra sign-flip under improper rotations compared to a true scalar or tensor. Physical examples of pseudovectors include angular velocity,...

Elliptic curve scalar multiplication is the operation of successively adding a point along an elliptic curve to itself repeatedly. It is used in elliptic...

AQUAL Tensor–vector–scalar Nonsymmetric gravitation Scalar–tensor theories Brans–Dicke Scalar–tensor–vector Conformal gravity Scalar theories Nordström...

physical constants. His framework replaces the fine-structure constant by a scalar field. However, this framework for changing constants did not incorporate...

components that are well-behaved under Lorentz transformations. These include scalars, spinors, tensors and spinor-tensors. The article considers four-vectors...

When the condition number is exactly one (which can only happen if A is a scalar multiple of a linear isometry), then a solution algorithm can find (in principle...

This operation is called scalar multiplication, but its result is not named "scalar product" to avoid confusion, since "scalar product" is often used as...

AQUAL Tensor–vector–scalar Nonsymmetric gravitation Scalar–tensor theories Brans–Dicke Scalar–tensor–vector Conformal gravity Scalar theories Nordström...

study of fluid dynamics and continuum mechanics, a velocity potential is a scalar potential used in potential flow theory. It was introduced by Joseph-Louis...

positive scalar, representing its length squared, while the square of any bivector is a negative scalar. The quotient of a vector with itself is the scalar 1...

events. In quantum field theory, the theory of a free (or non-interacting) scalar field is a useful and simple example which serves to illustrate the concepts...

additions become matrix sums and multiplications by coefficients become scalar multiplications. If the series converges for | x | < r {\displaystyle |x|<r}...

to Sanders and McGaugh, one problem with AQUAL (or any scalar–tensor theory in which the scalar field enters as a conformal factor multiplying Einstein's...

In complex analysis, Liouville's theorem states that every bounded entire function must be constant. That is, every holomorphic function f {\displaystyle...

David Hestenes, who advocated its importance to relativistic physics. The scalars and vectors have their usual interpretation and make up distinct subspaces...

Cartesian and spherical geometry, on surfaces and in volumes, on graphs, and in scalar, vector, and tensor forms. Without reference to any of these particularities...

1D function is represented as a curve on the 2D Cartesian plane, but a scalar-valued function of two variables is a surface in 3D, while curves can also...

Mayeul Arminjon (2006). "Space Isotropy and Weak Equivalence Principle in a Scalar Theory of Gravity". Brazilian Journal of Physics. 36 (1B): 177–189. arXiv:gr-qc/0412085...

which the skew symmetric tensor field was replaced by a vector field, is scalar–tensor–vector gravity (STVG). STVG, like Milgrom's Modified Newtonian Dynamics...

the force can be written in terms of the gradient of a function called a scalar potential: F = − ∇ U . {\displaystyle \mathbf {F} =-\mathbf {\nabla } U\...

is used to select between packed and scalar operation (0: packed, 1:scalar) For a given operation, all the scalar/packed variants belong to the same AVX-512...

where the dependent variable y(x,t) is called the density of the conserved (scalar) quantity, and a(y) is called the current coefficient, usually corresponding...

{\displaystyle R_{\mu \nu }} is the Ricci tensor, R {\displaystyle R} is the Ricci scalar, T μ ν {\displaystyle T_{\mu \nu }} is the energy–momentum tensor, κ {\displaystyle...

(2). A particular choice of the scalar and vector potentials is a gauge (more precisely, gauge potential) and a scalar function ψ used to change the gauge...

field strengths ∫ M i ω k {\displaystyle \int _{M_{i}}\omega ^{k}} are scalars and thus coordinate system invariant. In many cases, it is desirable for...

Additionally, the low scalar performance of the machine meant that after the switch had taken place and the machine was running scalar instructions, the performance...

stress–energy tensor, by adding a kind of gravitational contribution, namely the scalar field. According to Yilmaz's critics, this additional term is not well-defined...

dimensions whose Lagrangian is constructed out of the metric tensor and a scalar field and leads to second order equations of motion.[clarification needed]...

infinite-dimensional vectors. The input of a vector-valued function could be a scalar or a vector (that is, the dimension of the domain could be 1 or greater...

distance or range between the two points. It is a signed scalar quantity, formulated as the scalar projection of the relative velocity vector onto the LOS...

whose curl is a given vector field. This is analogous to a scalar potential, which is a scalar field whose gradient is a given vector field. Formally, given...

denotes the vector dot product, and V {\displaystyle V} is the electric scalar potential. This emf is the work done on a unit charge by the source's nonelectrostatic...

cumbersome, especially if one wants to determine E as a function of position. A scalar function called the electric potential can help. Electric potential, also...

considered according to the surface orientation described by the sign of the scalar product r ^ ⋅ n ^ {\displaystyle {\hat {r}}\cdot {\hat {n}}} . Thus one...

containing that direction. A further trace of the Ricci curvature yields the scalar curvature. In general relativity, the Ricci curvature tensor enters the...

The name paravector is used for the combination of a scalar and a vector in any Clifford algebra, known as geometric algebra among physicists. This name...

field, but is indistinguishable from a scalar in four dimensions, as shown in Kaluza–Klein theory. The scalar field ϕ {\displaystyle \phi } comes from...

groups had been proposed earlier by Kenneth G. Wilson and Giorgio Parisi in scalar field theory (see also Quantum triviality). The applicability to perturbatively...

scalar floating-point operations to be mixed without the performance hit from explicit MMX/floating-point mode switching. SSE introduced both scalar and...

extension of the product rule that ∇ ⋅ (ψ X ) = ∇ψ ⋅X + ψ ∇⋅X: Let φ and ψ be scalar functions defined on some region U ⊂ Rd, and suppose that φ is twice continuously...

potential and scalar potential are used for magnetic vector potential and electric potential, respectively. In mathematics, vector potential and scalar potential...

is the classical equation of motion for a free scalar field, but also the quantum equation for a scalar particle wave-function. This meant that quantizing...

Tau neutrino Tau antineutrino Bosons Gauge Photon Gluon W and Z bosons Scalar Higgs boson Ghost fields Faddeev–Popov ghosts Hypothetical Superpartners...

ISBN 978-0-7167-5016-1. A. Bakopoulos; P. Kanti (2016). "Novel Ansatzes and Scalar Quantities in Gravito-Electromagnetism". General Relativity and Gravitation...

AQUAL Tensor–vector–scalar Nonsymmetric gravitation Scalar–tensor theories Brans–Dicke Scalar–tensor–vector Conformal gravity Scalar theories Nordström...

identifying 0-forms and 3-forms with scalar fields, and 1-forms and 2-forms with vector fields: grad takes a scalar field (0-form) to a vector field (1-form);...

spin-statistics relation, which requires that all integer spin particles be bosons. Scalar boson Maxwell's equations Proca action Barianti, G.; Gabathuler, E. (October...

matrix: Interchanging two rows. Multiplying a row by a non-zero scalar. Adding a scalar multiple of one row to another. If the matrix is associated to...

through the center of mass unless otherwise specified. The following are scalar moments of inertia. In general, the moment of inertia is a tensor; see below...

behavioral and register-transfer level sources, approximately 93% of the CPU scalar and vector units, over 700,000 gates, were synthesized. SID was an artificial...

energy is a scalar quantity, the canonical conjugate to time. In special relativity energy is also a scalar (although not a Lorentz scalar but a time component...

clause is not a window function, but rather an aggregate or single-row (scalar) function. As an example, here is a query which uses a window function to...

E} are scalar position coefficients D 0 {\displaystyle D_{0}} is the common scalar quantity D m n {\displaystyle D_{mn}} is the respective scalar quantities...

describing the motion of a family of ideal observers, the Raychaudhuri scalar is the scalar field obtained by taking the trace of the tidal tensor corresponding...

of a moving electric point charge in terms of a vector potential and a scalar potential in the Lorenz gauge. Stemming directly from Maxwell's equations...

potential of its position in a gravitational field. Mathematically, is a scalar quantity attached to the conservative gravitational field and equals the...

in Electroweak interactions Gauge bosonsSpin = 1, 2 [‡] Force carriers Scalar bosonsSpin = 0 Three generations Up (u), Down (d) Charm (c), Strange (s)...

ω is the angular velocity, and ⋅ {\displaystyle \cdot } represents the scalar product. Algebraically, the equation may be rearranged to compute torque...

called a field, and an operation called scalar multiplication between elements of the field (called scalars), and elements of the vector space (called...

estimation. The algorithm uses a random rotation of input vectors, applies scalar quantizers to the rotated coordinates, and, for inner-product estimation...

{\displaystyle \times } to denote elliptic curve point multiplication by a scalar. For Alice to sign a message m {\displaystyle m} , she follows these steps:...

cones—is a subset of a real vector space that is closed under positive scalar multiplication; that is, C {\displaystyle C} is a cone if x ∈ C {\displaystyle...

a gauge theory with a spontaneous symmetry breaking. In this gauge, the scalar fields responsible for the Higgs mechanism are transformed into a basis...

Tau neutrino Tau antineutrino Bosons Gauge Photon Gluon W and Z bosons Scalar Higgs boson Ghost fields Faddeev–Popov ghosts Hypothetical Superpartners...

vectors defined by "one vector is the product of the other by a nonzero scalar". In other words, this amounts to defining a projective space as the set...

the average velocity (a vector), whose magnitude is the average speed (a scalar quantity), over the motion on this time interval. A displacement may be...

product"), which takes a pair of coordinate vectors as input and produces a scalar The Kronecker product, which takes a pair of matrices as input and produces...

gravity available. A singularity in general relativity can be defined by the scalar invariant curvature becoming infinite or, better, by a geodesic being incomplete...

natural description of a 1-subspace is the scalar multiplication of one non-zero vector v to all possible scalar values. 1-subspaces specified by two vectors...

Instability of the Cauchy Horizon for the Spherically Symmetric Einstein-Maxwell-Scalar Field Equations in 2001, under the supervision of Demetrios Christodoulou...

common domain of f and v the scalar ( ∇ v f ) p {\displaystyle \left(\nabla _{\mathbf {v} }f\right)_{p}} . For a scalar function f and vector field v...

of bosonic partners of fermions are prefixed with s-, because they are scalar particles. For example, if the electron existed in a supersymmetric theory...

choice of norm | α | {\displaystyle |\alpha |} on the field of scalars. When the scalar field is R {\displaystyle \mathbb {R} } (or more generally a subset...

parameter is the tensor to scalar ratio. The simplest inflation models, those without fine-tuning, predict a tensor to scalar ratio near 0.1 . Inflation...

In physics, action is a scalar quantity that describes how the balance of kinetic versus potential energy of a physical system changes with trajectory...

a strange attractor (see strange attractor below). If the variable is a scalar, the attractor is a subset of the real number line. Describing the attractors...

operations, such as vector element-wise addition/multiplication and vector scalar addition/multiplication, process multiple bytes of data in a single CPU...

AQUAL Tensor–vector–scalar Nonsymmetric gravitation Scalar–tensor theories Brans–Dicke Scalar–tensor–vector Conformal gravity Scalar theories Nordström...

AQUAL Tensor–vector–scalar Nonsymmetric gravitation Scalar–tensor theories Brans–Dicke Scalar–tensor–vector Conformal gravity Scalar theories Nordström...

interpretation of an imaginary mass, the mass is not quantized. Rather, the scalar field is; even for tachyonic quantum fields, the field operators at spacelike...

microprocessors it will eventually nearly universally displace single-variable scalar control (volts-per-Hertz, V/f control). Technische Universität Darmstadt's...

parity of the signature of the scalar product on V, that is, the sign of the determinant of the matrix of the scalar product with respect to any basis...

the four-gradient and f {\displaystyle f} is any harmonic scalar function: that is, a scalar function obeying ⁠ ∂ μ ∂ μ f = 0 {\displaystyle \partial _{\mu...

y(\mathbf {x} )\cdot \mathbf {\hat {n}} (\mathbf {x} ),} and f is a given scalar function. It becomes clear that the boundary must be sufficiently smooth...

For particles that are real scalars (such as an axion), there is a fermion superpartner as well as a second, real scalar field. For axions, these particles...

OCLC 7462032. Crispino, L. C. B.; Higuchi, A.; Matsas, G. E. A. (November 1999). "Scalar radiation emitted from a source rotating around a black hole". Classical...

{Ric} _{g}={\frac {1}{2}}R_{g}g} where R g {\displaystyle R_{g}} is the scalar curvature of g {\displaystyle g} . That is, the Ricci curvature becomes...

1 {\displaystyle \lim _{x\rightarrow \infty }F(x)=1} . In the case of a scalar continuous distribution, it gives the area under the probability density...

often consists of pairs of an input vector (or scalar) and the corresponding output vector (or scalar), where the answer key is commonly denoted as the...

2026. Buoli, Alice (1 January 2014). "Beyond the border: exploring cross-scalar socio-spatial dynamics of conflict, resistance and encounter at the Ceuta–Morocco...

conservation laws), and employs a unit vector field, a dynamical and non-dynamical scalar field, a free function and a non-Einsteinian metric in order to yield AQUAL...

(user-centered design). variable In computer programming, a variable, or scalar, is a storage location (identified by a memory address) paired with an associated...

field configurations. In the quantum field theory of (as example) a quantum scalar field ϕ ^ ( x ) {\displaystyle {\hat {\phi }}(x)} , in complete analogy...

represent energy flows is the gyrator–capacitor model. Magnetic reluctance is a scalar extensive quantity. The unit for magnetic reluctance is inverse henry, H−1...

the power gain. This is a real-value (or scalar) quantity, the phase information being dropped. The scalar logarithmic (decibel or dB) expression for...

q=a+ib+jc+kd} its scalar part a is the real number q − i q i − j q j − k q k 4 {\displaystyle {\frac {q-iqi-jqj-kqk}{4}}} . Likewise the scalar part of −qi...

equations (ODEs), Lyapunov functions, named after Aleksandr Lyapunov, are scalar functions that may be used to prove the stability of an equilibrium of an...

from a vector space V is said to be linearly dependent, if there exist scalars a 1 , a 2 , … , a k , {\displaystyle a_{1},a_{2},\dots ,a_{k},} not all...

student in physics and received M.S. in 1969 and Ph.D. in 1972. His thesis Scalar Quantum Field Theory in a Closed Universe of Constant Curvature was supervised...

integral through a gradient field can be evaluated by evaluating the original scalar field at the endpoints of the curve. The theorem is a generalization of...

contribute to the action, but are not dynamical variables. A scalar field source is another scalar field h that contributes a term to the (Lorentz) Lagrangian:...

which are called vectors) over a field K (the elements of which are called scalars). In other words, a bilinear form is a function B : V × V → K that is linear...

fixed, un → φ(x), a scalar field, and ω ( k ) ∝ k a {\displaystyle \omega (k)\propto ka} . This amounts to classical free scalar field theory, an assembly...

linear algebra, a subset of a vector space that is closed under addition and scalar multiplication Flat (geometry), a Euclidean subspace Affine subspace, a...

between scalar and vector registers. In keeping with the "load/store" model of the PowerPC's RISC design, the vector registers, like the scalar registers...

the Nash embedding theorem. A basic example of maps between manifolds are scalar-valued functions on a manifold, f : M → R {\displaystyle \scriptstyle f\colon...

space to the entire manifold, and many special metrics such as constant scalar curvature metrics and Kähler–Einstein metrics are constructed intrinsically...

non-interacting real scalar fields, with equal masses m. This system is described by an action that is the sum of the (usual) action for each scalar field φ i {\displaystyle...

R_{\mu \nu }} is the Ricci curvature tensor, and R {\displaystyle R} is the scalar curvature. This is a symmetric divergenceless second-degree tensor that...

Davis in the Department of Applied Maths and Theoretical Physics, studying Scalar Fields and the Accelerated Expansion of the Universe. She spotted signs...

scalar device. As the name implies, vector processors deal with multiple pieces of data in the context of one instruction. This contrasts with scalar...

Models (FLMs) with scalar responses, analogous to extending linear regression model to polynomial regression model. For a scalar response Y {\displaystyle...

and above, the handwritten scalar code provides a doubling to tripling of performance over compiler output. The Thumb-2 scalar code provides about 10% benefit...

Władysław Ślebodziński, evaluates the change of a tensor field (including scalar functions, vector fields and one-forms), along the flow defined by another...

\Lambda } is an n {\displaystyle n} -dimensional symmetric matrix, then the scalar quantity ε T Λ ε {\displaystyle \varepsilon ^{T}\Lambda \varepsilon } is...

electric field is conservative, and hence is given by the gradient of a scalar potential, V(r) E ( r ) = − ∇ V ( r ) . {\displaystyle \mathbf {E} (\mathbf...

light, if the symmetry is not exact) scalar particles appear in the spectrum of possible excitations. There is one scalar particle—called a Nambu–Goldstone...

under the name Bimetric gravity or both scalar and vector fields can be added, as in Tensor–vector–scalar gravity. The name "Einstein-aether theory"...

sesquilinear norm. Note that the adjoint of an operator depends on the scalar product considered on the n {\displaystyle n} dimensional complex or real...

given an initial velocity field, there exists a vector velocity and a scalar pressure field, which are both smooth and globally defined, that solve the...

perpendicular to the plane of the flow, and can therefore be considered a scalar field. The dynamics of vorticity are fundamentally linked to drag through...

Yang–Mills theories (such as quantum chromodynamics) the ghosts are complex scalar fields (spin 0), but they anti-commute (like fermions). In general, anti-commuting...

root of minus one in the scalar field C by h to avoid confusion with the i in the quaternion group. Commutativity of the scalar field with the quaternion...

values of a , b {\displaystyle a,b} and d {\displaystyle d} . For example in scalar ϕ 4 {\displaystyle \phi ^{4}} theory in 4 dimensions, the loop integral...

simply the same as the above distribution for a scalar-valued random variable with each occurrence of the scalar x replaced by the vector x = [ x 1 x 2 ⋯ x...

independent systems if these logarithmic expressions exist. For any numbers (scalars) a and b we know that the exponential function satisfies ea+b = ea eb....

that are scalars, vectors, and tensors, must be represented by scalar, vector, and tensor operators, respectively. Whether something is a scalar, vector...

In the physical sciences, the wavenumber (or wave number), also known as repetency, is the spatial frequency of a wave. Ordinary wavenumber is defined...

with positive scalar curvature. If the injectivity radius of a compact n-dimensional Riemannian manifold is ≥ π then the average scalar curvature is at...

{\textstyle m=n=1} , M {\textstyle \mathbf {M} } is the 1-dimensional linear scalar function f x h {\textstyle \mathbb {f} _{x}\mathbb {h} } , where f x {\textstyle...

or landing on a planet or moon, or an in-space orbital maneuver. It is a scalar that has the units of speed. As used in this context, it is not the same...

s = 0   . {\displaystyle ~s=0~.} It corresponds to the space of massive scalar fields. Let M be the hyperboloid sheet defined by:   P 0 2 − P 1 2 − P 2...

being listed in this article. To start with the geometry, the Bombieri scalar product for homogeneous polynomials with N variables can be defined as follows...

overview perspective The improvised and provisional use of infinitesimals or big-O notation; vector calculus computations by analogy with scalar calculus...

actualized by pushing it over the edge. In physics, a potential may refer to the scalar potential or to the vector potential. In either case, it is a field defined...

Rotational velocity is the vector quantity whose magnitude equals the scalar rotational speed. In the special cases of spin (around an axis internal...

{\Sigma }}\,.} Let f : Ω → R {\displaystyle f:\Omega \to \mathbb {R} } be a scalar field. Then ∫ Ω ∇ → f = ∫ ∂ Ω n → f {\displaystyle \int _{\Omega }{\vec...

are velocity, rapidity, and celerity which is proper velocity. Speed is a scalar, being the magnitude of the velocity vector which in relativity is the four-velocity...

_{2}=\mathbf {p} _{1}+(-\mathbf {p} _{2}).} Scalar multiplication has been defined for non-negative integer scalar multipliers as k p = [ ( a k ) mod 2 k r...

}=\sum _{\mu }P_{\nu \mu }u_{\mu }} on each section u of E. Here Pνμ is the scalar differential operator defined by P ν μ = ∑ α P ν μ α ∂ ∂ x α . {\displaystyle...

two Euclidean vectors. The dot product takes in two vectors and returns a scalar, while the cross product returns a pseudovector. Both of these have various...

attributes of a Higgs boson. This also means it is the first elementary scalar particle discovered in nature. Elementary bosons responsible for the four...

_{\text{area}}(\mathbf {E} \times \mathbf {H} )\cdot d\mathbf {A} .} The result is a scalar since it is the surface integral of the Poynting vector. 2024 world electricity...

automatic parallelization, where a computer program is converted from a scalar implementation, which processes a single pair of operands at a time, to...

supersymmetry (SUSY). It is a sfermion, which means it is a spin-0 boson (scalar boson). While the top quark is the heaviest known quark, the stop squark...

2007. In ethics, Norcross defends a version of act utilitarianism known as scalar utilitarianism, which is the theory that there are no right or wrong actions...

prefixing an 's' to the name of its superpartner, denoting that it is a scalar particle with spin 0. For instance, the electron's superpartner is the selectron...

the Scalar again as they enter the airspace over the Southern United States. Using explosives from the plane's armory, the squad breach the Scalar's chamber...

The chameleon is a hypothetical scalar particle that couples to matter more weakly than gravity, postulated as a dark energy candidate. Due to a non-linear...

algorithms. If homogeneous coordinates of a point are multiplied by a non-zero scalar then the resulting coordinates represent the same point. Since homogeneous...

renaming done in the previous paper removes all false dependencies for scalars. In 1988, Barry Rosen, Mark N. Wegman, and Kenneth Zadeck replaced the...

In calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions z and y in terms of the derivatives...

{\displaystyle \mathbf {v} } ⁠, ⁠ w {\displaystyle \mathbf {w} } ⁠ and any complex scalar ⁠ c {\displaystyle c} ⁠, ( u + v ) H A w = u H A w + v H A w , ( c   u )...

{\displaystyle \phi } is a complex scalar field, ψ {\displaystyle \psi } is a Weyl spinor. There is also the auxiliary complex scalar field F {\displaystyle F}...

inconsistency is offered by inflation theory in which a homogeneous and isotropic scalar energy field dominates the universe at some very early period (before baryogenesis)...

the UTF-16 code space), 1,114,112 valid code points in Unicode (1,112,064 scalar values and 2,048 surrogates). Ludology – Number of games: Approximately...

scalar field or a vector field. The value of the line integral is the sum of values of the field at all points on the curve, weighted by some scalar function...

Retrieved November 28, 2023. Liberation Schools. (n.d.). Retrieved from http://scalar.usc.edu/works/pictures-and-progress-the-black-panther-1966-2016/liberation-schools...

(sing.: modulus; more properly moduli fields) is sometimes used to refer to scalar fields whose potential energy function has continuous families of global...

\right)^{\text{T}}=c(\mathbf {A} ^{\text{T}}).} The transpose of a scalar is the same scalar. Together with the preceding property, this implies that the transpose...

scalars. linear independence Property of being not linearly dependent. linear map A function between vector spaces which respects addition and scalar...

that it would support VFS for Git. VFS for Git has been superseded by Scalar. Scalar was then integrated into the Microsoft Git project. Free and open-source...

non-Riemannian gravity and Einstein–Proca–Weyl theories extended to a class of scalar gravity theories". Class. Quantum Gravity. 16 (7): 2471–2478. arXiv:gr-qc/9905022...

Tachyon condensation is a process in which a tachyonic field—usually a scalar field—with a complex mass acquires a vacuum expectation value and reaches...

of inner products – producing a scalar from a pair of vectors – can be generalized by allowing a broader range of scalar values and, perhaps simultaneously...

potentials of a compact Kähler manifold whose critical points are constant scalar curvature Kähler metrics. The Mabuchi functional was introduced by Toshiki...

replica method to compute quantities like traces, spectral densities, or scalar products between eigenvectors. Many physical phenomena, such as the spectrum...

contexts (such as descriptions of camera sensors), pixel refers to a single scalar element of a multi-component representation (called a photosite in the camera...

fields, and possibly the space and time coordinates themselves. For one scalar field φ(x, t), the Hamiltonian density is defined from the Lagrangian density...

definitions have not been widely adopted.[better source needed] The simplest scalar data types, such as integer and floating-point numbers, are nearly always...

setting the teeth of a saw so each tooth protrudes to the side of the blade Scalar expectancy theory, a model of the processes that govern behavior controlled...

x^{k}}}} where |g| is the absolute value of the determinant of the matrix of scalar coefficients of the metric tensor g i k {\displaystyle g_{ik}} . These are...

squared Euclidean distance in a Euclidean space. Élie Cartan calls Q(x) the scalar square of x. The symmetric bilinear form B acting on two vectors x, y ∈...

CP1/TP1 Causal order Scalar SOCT4 Forward transformation (IT) Yes No CP2/TP2 CP1/TP1 Causal order + Continuous total order Scalar SOCT2 Forward Transformation(IT)...

therefore electrically uncharged—and unchargeable. Electric potential is a scalar quantity. That is, it has only magnitude and not direction. It may be viewed...

quantity Physical quantity – Measurable property of a material or system Scalar (mathematics) – Elements of a field, e.g. real numbers, in the context of...

vector of length S = 0, and only one spin projection (Sz = 0), called a scalar meson or spin-0 singlet. Because mesons are made of one quark and one antiquark...

and object properties in 7.4 The types expressible also expanded, with scalar types (integer, float, string, and boolean) in 7.0; iterable type, nullable...

Clifford Cl1,3(R) algebras, but STA uses real number scalars while Dirac algebra uses complex number scalars[citation needed]. The STA space–time split is similar...

Harbour has six scalar types: Nil, String, Date, Logical, Numeric, Pointer, and four complex types: Array, Object, CodeBlock, and Hash. A scalar holds a single...

the inlet conditions and the physical boundaries can coincide with the scalar control volume boundaries. This makes it possible to introduce the boundary...

map the Earth's magnetic field, the satellite had two magnetometers. The scalar (Cesium vapor) and vector magnetometers gave Magsat a capability beyond...

graphical analysis tool designed for viewing scientific data. It can visualize scalar and vector fields on 2D and 3D structured and unstructured meshes. VisIt...

vector addition and scalar multiplication. Some authors use "linear function" only for linear maps that take values in the scalar field; these are more...

X {\displaystyle \mathbf {X} } and Y {\displaystyle \mathbf {Y} } is a scalar random variable which is realized repeatedly in a time series, then the...

usually employed to generalize the definitions of monotone and concave/convex scalar functions to monotone and concave/convex Hermitian valued functions. These...

this is only the time derivative of volume, a scalar quantity, the volumetric flow rate is also a scalar quantity. The change in volume is the amount that...

any smooth vector or scalar field in R 3 {\displaystyle \mathbb {R} ^{3}} . When g {\displaystyle \mathbf {g} } is a uniform scalar field, the standard...

quantities are built out of scalars, four-vectors, four-tensors, and spinors. In particular, a Lorentz covariant scalar (e.g., the space-time interval)...

stellar nucleosynthesis. The universe contains a mysterious energy—possibly a scalar field—called dark energy, the density of which does not change over time...

group approach. However, in 2014, Frewer et al. refuted these results. For scalars (most notably temperature), the self-similar logarithmic law of the wall...

drive complexity with BLDC drives typically being with simple single-phase scalar-controlled voltage-regulated trapezoidal current waveform output involving...

Subtract, Returning High Half. The instructions are added in vector and scalar forms. A set of AArch64 load and store instructions that can provide a memory...

true or false. A char takes up 32 bits of space and represents a Unicode scalar value: a Unicode codepoint that is not a surrogate. IEEE 754 floating point...

AQUAL Tensor–vector–scalar Nonsymmetric gravitation Scalar–tensor theories Brans–Dicke Scalar–tensor–vector Conformal gravity Scalar theories Nordström...

provide kind). These functions are important for portable numerical software: Scalar variables corresponding to the five intrinsic types are specified as follows:...

Biot–Savart law Gauss's law for magnetism Magnetic dipole Magnetic flux Magnetic scalar potential Magnetic vector potential Magnetization Permeability Right-hand...

The Lagrangian in scalar-tensor theory can be expressed in the Jordan frame or in the Einstein frame, which are field variables that stress different aspects...

combination of vectors in B is equal to the zero vector, then all the scalars coefficients of the combination must be zero. If B is a basis for V, then...

pure states of constituent quark flavors, whereas pseudovector mesons and scalar mesons tend to be expressed as composites of mixed states. Since the development...

{d_{k}}}}+sB\right)V\end{aligned}}} Here, s {\displaystyle s} is a real number ("scalar"), and B {\displaystyle B} is the linear bias matrix defined by B = ( 0...

quantity that is invariant under Lorentz transformations is known as a Lorentz scalar. Writing the Lorentz transformation and its inverse in terms of coordinate...

handle. Although most GPU hardware has moved away from 4D instructions to scalar SIMT pipelines, modern compute kernels using SoA instead of AoS can still...

plane, with prescribed jump discontinuities across the contour. Classical scalar forms go back to Riemann and Hilbert, and modern matrix-valued Riemann–Hilbert...

⟩ {\displaystyle \langle u,v\rangle } gives a real number. The dot (or scalar) product is a typical example of an inner product. This allows one to define...

In physics and engineering, a phasor (a portmanteau of phase vector) is a complex number representing a sinusoidal function whose amplitude A and initial...

were the Versal adaptive compute acceleration platforms, which combine scalar, adaptable, and intelligent engines connected through a Network on Chip...

compound data type is a data type that consists of programming language scalar data types and other composite types that may be heterogeneous and hierarchical...

permeability of flat spacetime, εo and μo respectively by multiplying them by a scalar function, K: ε 0 → ε = K ε 0 ; μ 0 → μ = K μ 0 {\displaystyle \varepsilon...

"slow roll inflation" in which no tunnelling occurs, and the inflationary scalar field instead graphs as a gentle slope. In 2014, researchers at the Chinese...

diagrams. In a d {\displaystyle d} -dimensional field theory with a real scalar field ϕ {\displaystyle \phi } and action S [ ϕ ] {\displaystyle S[\phi ]}...

one-dimensional subspaces of V. More generally, any subset S of V closed under scalar multiplication defines a subset of P(V) formed by the lines contained in...

dubious. Quantity (i) A well-known class of quantity implicatures are the scalar implicatures. Prototypical examples include words specifying quantities...

algebra of U(1)) Yang–Mills theory coupled to a real scalar field ϕ {\displaystyle \phi } . This scalar field takes on values in a real 1D affine representation...

per ampere-meter, equivalently henry per meter. Typically μ would be a scalar, but for an anisotropic material, μ could be a second rank tensor. However...

long-lived (narrow in the jargon of particle spectroscopy) states: the scalar (0++) state D*± sJ(2317) and the vector (1+) meson D*± sJ(2460), observed...

vector scalar product (a scalar). Quaternion multiplication is noncommutative (because of the cross product, which anti-commutes), while scalar–scalar and...

Coleman-Weinberg approach, SVT gives the meaning to the symmetry-breaking relativistic scalar field as describing small fluctuations of background superfluid which can...

is what a clock reads. In classical, non-relativistic physics, it is a scalar quantity (often denoted by the symbol t {\displaystyle t} ) and, like length...

proposed to solve the cuspy halo problem. It would consist of extremely light scalar particles with masses on the order of ≈ 10 − 22 {\displaystyle \approx 10^{-22}}...

output of an engine. Although they are dimensionally equivalent, energy (a scalar) and torque (a Euclidean vector) are distinct physical quantities. Both...

{1}x_{2}-y_{1}y_{2}-z_{1}z_{2}.} Positivity of scalar product: An important property is that the scalar product of two similarly directed time-like vectors...

equivalent tensile stress, σ v {\displaystyle \sigma _{\text{v}}} . This is a scalar value of stress that can be computed from the Cauchy stress tensor. In this...

but there is no 4x16-bit popcnth yet there is 2x32-bit popcntw and 64-bit scalar popcntd. Likewise, prtyw is SWAR half-word 4x16-bit but there is no prtyb...

differencing, multiplication by the scalar 1 is the multiplicative identity operation, and multiplication by the scalar 0 takes every element to the edgeless...

X^{m}\,X^{n}} This quantity is sometimes called the Raychaudhuri scalar. The expansion scalar measures the fractional rate at which the volume of a small ball...

analyze, and data is much more difficult to collect. A tidal height is a scalar quantity and varies smoothly over a wide region. A flow is a vector quantity...

factor for circular accelerators. The radiated power is actually a Lorentz scalar, given in covariant form as P = − 2 3 q 2 m 2 c 3 d p μ d τ d p μ d τ ....

are often created from a continuous sequence of quarter notes in a mostly scalar, stepwise or arpeggio-based part called a "walking bass line". In Latin...

combination of the two. Alternative semantics Focus Free choice inference Scalar implicature Rooth 1992; Rooth 2016. Chierchia, Fox & Spector 2012; Chierchia...

disproved conjecture on absolute stability of nonlinear control system with one scalar nonlinearity, which belongs to the sector of linear stability. Kalman's...

location or distribution of physical quantities which may be, for example, scalars, vectors, or tensors. Mathematical expressions involving these quantities...

Tau neutrino Tau antineutrino Bosons Gauge Photon Gluon W and Z bosons Scalar Higgs boson Ghost fields Faddeev–Popov ghosts Hypothetical Superpartners...