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Vector field
mathematical fields of the calculus of variations and differential geometry, the variational vector field is a certain type of vector field defined on the
Variational_vector_field
Differential calculus on function spaces
The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and
Calculus_of_variations
Certain vector fields are the sum of an irrotational and a solenoidal vector field
theorem of vector calculus states that certain differentiable vector fields can be resolved into the sum of an irrotational (curl-free) vector field and a
Helmholtz_decomposition
Deep learning generative model to encode data representation
graphical models and variational Bayesian methods. In addition to being seen as an autoencoder neural network architecture, variational autoencoders can also
Variational_autoencoder
Element in Riemannian geometry
_{t}\right)} in which H(ft) is the mean curvature vector of the immersion ft and Wt denotes the variation vector field ∂ ∂ t f t . {\displaystyle {\frac {\partial
First variation of area formula
First_variation_of_area_formula
Property of space that quantifies the magnetic influence at a given location
magnetic field may vary with location, it is described mathematically by assigning a vector to each point of space, making it a vector field. There are
Magnetic_field
Scientific principles enabling the use of the calculus of variations
suspended at both ends—a catenary—can be solved using variational calculus, and in this case, the variational principle is the following: The solution is a function
Variational_principle
Physical quantities taking values at each point in space and time
In science, a field or field quantity is a physical quantity – represented by a scalar, vector, spinor, or tensor – that has a value for each point in
Field_(physics)
Circulation density in a vector field
In vector calculus, the curl, also known as rotor, is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional
Curl_(mathematics)
Calculus of vector-valued functions
Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional
Vector_calculus
Vector operator in vector calculus
In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the rate that the vector field alters
Divergence
Physical theory describing classical fields
constitutes a vector field. As the day progresses, the directions in which the vectors point change as the directions of the wind change. The first field theories
Classical_field_theory
Type of mathematical inequality
finite-dimensional variational inequality problem associated with K {\displaystyle K} consist of finding a n {\displaystyle n} -dimensional vector x {\displaystyle
Variational_inequality
Integration over a non-flat region in 3D space
scalar field (that is, a function of position which returns a scalar as a value), or a vector field (that is, a function which returns a vector as value)
Surface_integral
Computer vision framework
Gradient vector flow (GVF), a computer vision framework introduced by Chenyang Xu and Jerry L. Prince, is the vector field that is produced by a process
Gradient_vector_flow
Mathematical methods used in Bayesian inference and machine learning
set of samples, variational Bayes provides a locally-optimal, exact analytical solution to an approximation of the posterior. Variational Bayes can be seen
Variational_Bayesian_methods
Set of methods for supervised statistical learning
Wenzel developed two different versions, a variational inference (VI) scheme for the Bayesian kernel support vector machine (SVM) and a stochastic version
Support_vector_machine
Definite integral of a scalar or vector field along a path
curve (commonly arc length or, for a vector field, the scalar product of the vector field with a differential vector in the curve). This weighting distinguishes
Line_integral
Architectural motif in neural networks for aggregating information
downsamples and aggregates information that is dispersed among many vectors into fewer vectors. It has several uses. It removes redundant information, thus reducing
Pooling_layer
within Earth) and the centrifugal force (from the Earth's rotation). It is a vector quantity, whose direction coincides with a plumb bob and strength or magnitude
Gravity_of_Earth
Mathematical identities
three-dimensional Cartesian coordinate variables, the gradient is the vector field: grad ( f ) = ∇ f = ( ∂ ∂ x , ∂ ∂ y , ∂ ∂ z ) f = ∂ f ∂ x i + ∂
Vector_calculus_identities
Manifold with supersymmetry structure
variational calculus on graded manifolds, J. Math. Pures Appl. 63 (1984) 283 G. Giachetta, L. Mangiarotti, G. Sardanashvily, Advanced Classical Field
Graded_manifold
Classical field theories on fiber bundles
a finite-dimensional space of fields. Nowadays, it is well known that[citation needed] jet bundles and the variational bicomplex are the correct domain
Covariant classical field theory
Covariant_classical_field_theory
Application of Lagrangian mechanics to field theories
for vector fields, tensor fields, and spinor fields. In physics, fermions are described by spinor fields. Bosons are described by tensor fields, which
Lagrangian_(field_theory)
Result concerning ideals of commutative rings
algebra that a vector space over an infinite field or a finite field of large cardinality is not a finite union of its proper vector subspaces. The following
Prime_avoidance_lemma
Electric and magnetic fields produced by moving charged objects
field is a pair of vector fields consisting of one vector for the electric field and one for the magnetic field at each point in space. The vectors may
Electromagnetic_field
Technique for the generative modeling of a continuous probability distribution
space and by flow matching. Diffusion process Markov chain Variational inference Variational autoencoder Review papers Yang, Ling (2024-09-06),
Diffusion_model
Vector field reconstruction is a method of creating a vector field from experimental or computer-generated data, usually with the goal of finding a differential
Vector_field_reconstruction
Instruction set extension by Intel
AVX-512 are 512-bit extensions to the 256-bit Advanced Vector Extensions SIMD instructions for x86 instruction set architecture (ISA) proposed by Intel
AVX-512
Formulation of classical mechanics
thinking along the lines of the variational calculus, but did not publish. These ideas in turn lead to the variational principles of mechanics, of Fermat
Lagrangian_mechanics
Formalism in classical field theory based on Hamiltonian mechanics
again the overdots are partial time derivatives, the variational derivative with respect to the fields δ H δ ϕ i = ∂ H ∂ ϕ i − ∇ ⋅ ∂ H ∂ ( ∇ ϕ i ) , {\displaystyle
Hamiltonian_field_theory
Algebra based on a vector space with a quadratic form
unital associative algebra that contains and is generated by a vector space V over a field K, where V is equipped with a quadratic form Q : V → K. The Clifford
Clifford_algebra
Type of derivative in differential geometry
change of a tensor field (including scalar functions, vector fields and one-forms), along the flow defined by another vector field. This change is coordinate
Lie_derivative
Theorem in calculus
In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem relating the flux of a vector field through
Divergence_theorem
Branch of mathematics
vector spaces. Linear maps are mappings between vector spaces that preserve the vector-space structure. Given two vector spaces V and W over a field F
Linear_algebra
Vector used in astronomy
In classical mechanics, the Laplace–Runge–Lenz vector (LRL vector) is a vector used chiefly to describe the shape and orientation of the orbit of one
Laplace–Runge–Lenz_vector
Vector calculus construction
dependent vector field is a construction in vector calculus which generalizes the concept of vector fields. It can be thought of as a vector field which moves
Time_dependent_vector_field
Theorem in vector calculus
theorem in vector calculus on three-dimensional Euclidean space and real coordinate space, R 3 {\displaystyle \mathbb {R} ^{3}} . Given a vector field, the
Stokes'_theorem
Method in natural language processing
representation is a real-valued vector that encodes the meaning of the word in such a way that the words that are closer in the vector space are expected to be
Word_embedding
Specification of a derivative along a tangent vector of a manifold
presents an introduction to the covariant derivative of a vector field with respect to a vector field, both in a coordinate-free language and using a local
Covariant_derivative
Assignment of a tensor continuously varying across a region of space
speed) and a vector (a magnitude and a direction, like velocity), a tensor field is a generalization of a scalar field and a vector field that assigns
Tensor_field
Physical theory with fields invariant under the action of local "gauge" Lie groups
there necessarily arises a corresponding field (usually a vector field) called the gauge field. Gauge fields are included in the Lagrangian to ensure
Gauge_theory
Collection of random variables
variables is usually called a random field instead. The values of a stochastic process are not always numbers and can be vectors or other mathematical objects
Stochastic_process
Fundamental mechanical principles
developed a variational form for classical mechanics known as the Hamilton–Jacobi equation. In 1915, David Hilbert applied the variational principle to
Action_principles
the vector field as positive in the variational inequality, and negative in the corresponding projected dynamical system. Differential variational inequality
Projected_dynamical_system
Concept in calculus of variations
In the calculus of variations, a field of mathematical analysis, the functional derivative (or variational derivative) relates a change in a functional
Functional_derivative
Algebraic object with geometric applications
of algebraic objects associated with a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors. There
Tensor
Theoretical attempts to unify the forces of nature
feasible basis for the variational principle resulted in a field equation having the form of Einstein's general-relativistic field equation with a cosmological
Classical unified field theories
Classical_unified_field_theories
Straight path on a curved surface or a Riemannian manifold
allows one to construct a vector field for any Ehresmann connection on the tangent bundle. For the resulting vector field to be a spray (on the deleted
Geodesic
Method used to normalize the range of independent variables
of stochastic gradient descent. In support vector machines, it can reduce the time to find support vectors. Feature scaling is also often used in applications
Feature_scaling
Study of vector bundles, principal bundles, and fibre bundles
mathematical physics, gauge theory is the general study of connections on vector bundles, principal bundles, and fibre bundles. Gauge theory in mathematics
Gauge_theory_(mathematics)
Four-dimensional number system
Quaternions can be used to represent vectors in three-dimensional space, which provides a definition of the quotient of two vectors. Quaternions were first described
Quaternion
Differential operator in mathematics
returned vector field is equal to the vector field of the scalar Laplacian applied to each vector component. The vector Laplacian of a vector field A {\displaystyle
Laplace_operator
Neural network that learns efficient data encoding in an unsupervised manner
basic autoencoder, to be detailed below. Variational autoencoders (VAEs) belong to the families of variational Bayesian methods. Despite the architectural
Autoencoder
Overview of mechanics based on the least action principle
which they follow.[clarification needed] This is provided by various variational principles: behind each set of equations there is a principle that expresses
Analytical_mechanics
Paradigm in machine learning that uses no classification labels
learning rule, Boltzmann learning rule, Contrastive Divergence, Wake Sleep, Variational Inference, Maximum Likelihood, Maximum A Posteriori, Gibbs Sampling,
Unsupervised_learning
Concepts from linear algebra
algebra, an eigenvector (/ˈaɪɡən-/ EYE-gən-) or characteristic vector is a (nonzero) vector that has its direction unchanged (or reversed) by a given linear
Eigenvalues_and_eigenvectors
Right inverse of a fiber bundle map
{\displaystyle x\in B} . In particular, a vector field on a smooth manifold M {\displaystyle M} is a choice of tangent vector at each point of M {\displaystyle
Section_(fiber_bundle)
Formulation of classical mechanics using momenta
Hamiltonian induces a special vector field on the symplectic manifold, known as the Hamiltonian vector field. The Hamiltonian vector field induces a Hamiltonian
Hamiltonian_mechanics
Probabilistic programming language for Bayesian inference
MCMC engine Variational inference algorithms: Automatic Differentiation Variational Inference Pathfinder: Parallel quasi-Newton variational inference Optimization
Stan_(software)
Branch of mathematics
for medicine and biology. Vector analysis, also called vector calculus, is a branch of mathematical analysis dealing with vector-valued functions. Scalar
Mathematical_analysis
Machine learning methods using multiple input modalities
by the token representation of an image, which is then converted by a variational autoencoder to an image. Parti is an encoder–decoder transformer, where
Multimodal_learning
Equations describing classical electromagnetism
magnetic field is a solenoidal vector field. The Maxwell–Faraday version of Faraday's law of induction describes how a time-varying magnetic field corresponds
Maxwell's_equations
Vector space on which a distance is defined
physical world. If V {\displaystyle V} is a vector space over K {\displaystyle K} , where K {\displaystyle K} is a field equal to R {\displaystyle \mathbb {R}
Normed_vector_space
magnetic field for orientation and navigation. At any location, the Earth's magnetic field can be represented by a three-dimensional vector. A typical
Earth's_magnetic_field
Multivariate derivative (mathematics)
In vector calculus, the gradient of a scalar-valued differentiable function f {\displaystyle f} of several variables is the vector field (or vector-valued
Gradient
Calculus on stochastic processes
The main flavours of stochastic calculus are the Itô calculus and its variational relative the Malliavin calculus. For technical reasons the Itô integral
Stochastic_calculus
Quantum field theory enjoying conformal symmetry
Killing vector fields z n ∂ z {\displaystyle z^{n}\partial _{z}} . Strictly speaking, it is possible for a two-dimensional conformal field theory to
Conformal_field_theory
Vector field on tangent bundle
In differential geometry, a spray is a vector field H on the tangent bundle TM that encodes a quasilinear second order system of ordinary differential
Spray_(mathematics)
Function in mathematics
a means for taking directional derivatives of vector fields, measuring the deviation of a vector field from being parallel in a given direction. Connections
Connection_(mathematics)
Field theory involving topological effects in physics
mathematical physics, a topological quantum field theory (or topological field theory or TQFT) is a quantum field theory that computes topological invariants
Topological quantum field theory
Topological_quantum_field_theory
Mathematics concept
fundamental vector field must necessarily live in the vertical bundle, and vanish in any horizontal bundle. David Bleecker, Gauge Theory and Variational Principles
Vertical and horizontal bundles
Vertical_and_horizontal_bundles
Vector behavior under coordinate changes
Briefly, a contravariant vector is a list of numbers that transforms oppositely to a change of basis, and a covariant vector is a list of numbers that
Covariance and contravariance of vectors
Covariance_and_contravariance_of_vectors
Mathematical measure of a function's variability
_{\Omega }\|\nabla u(x)\|^{2}\,dx,} where ∇u : Ω → Rn denotes the gradient vector field of the function u. Since it is the integral of a non-negative quantity
Dirichlet_energy
Mathematical approach to quantum physics
be evaluated for large-expansion parameters, most efficiently by the variational method. In practice, convergent perturbation expansions often converge
Perturbation theory (quantum mechanics)
Perturbation_theory_(quantum_mechanics)
Overview of and topical guide to machine learning
kernel density estimation Variable rules analysis Variational message passing Varimax rotation Vector quantization Vicarious (company) Viterbi algorithm
Outline_of_machine_learning
4D relativistic energy and momentum
four-dimensional spacetime. Momentum is a vector in three dimensions; similarly four-momentum is a four-vector in spacetime. The contravariant four-momentum
Four-momentum
Setting of relativistic physics in geometric algebra
Dirac matrices over the field of real numbers; explicit matrix representation is unnecessary for STA. Products of the basis vectors generate a tensor basis
Spacetime_algebra
Modified theory of gravity developed by John Moffat
Scalar–tensor–vector gravity theory, also known as MOdified Gravity (MOG), is based on an action principle and postulates the existence of a vector field, while
Scalar–tensor–vector_gravity
Formulation of classical mechanics
\delta \xi =\delta \xi (t)} a vector field along ξ {\displaystyle \xi } . (For each t , {\displaystyle t,} the vector δ ξ ( t ) {\displaystyle \delta
Hamilton–Jacobi_equation
Method of data analysis
space are a sequence of p {\displaystyle p} unit vectors, where the i {\displaystyle i} -th vector is the direction of a line that best fits the data
Principal_component_analysis
Branch of applied mathematics
symplectic geometry and vector bundles). Within mathematics proper, the theory of partial differential equation, variational calculus, Fourier analysis
Mathematical_physics
Approximation of physical behavior
Using a non-interacting or effective field Hamiltonian, − m ∑ i s i {\displaystyle -m\sum _{i}s_{i}} , the variational free energy is F V = F 0 + ⟨ ( − J
Mean-field_theory
Type of physical quantity
sign with improper rotation Variational principle – Scientific principles enabling the use of the calculus of variations Sharipov, R.A. (1996). Course
Pseudotensor
Computer processor which works on arrays of several numbers at once
one-dimensional arrays of data called vectors. When integrated as a hardware component the vector processor is often called a vector processing unit (VPU). This
Vector_processor
rotational-flow form of Luke's variational principle. For the Clebsch representation to be possible, the vector field v {\displaystyle {\boldsymbol {v}}}
Clebsch_representation
Lovelock, David; Hanno Rund (1989) [1975]. Tensors, Differential Forms, and Variational Principles. Dover. ISBN 978-0-486-65840-7. Synge, John L; Schild, Alfred
Glossary_of_tensor_theory
Candidate unified theory of physics
Lagrangian formulation of classical field theory, the physical equations for causal fermion systems are formulated via a variational principle, the so-called causal
Causal_fermion_systems
Vector space with a notion of nearness
A topological vector space is a vector space that is also a topological space with the property that the vector space operations (vector addition and scalar
Topological_vector_space
Set of objects whose state must satisfy limits
methods to be solved in a reasonable time. Constraint programming (CP) is the field of research that specifically focuses on tackling these kinds of problems
Constraint satisfaction problem
Constraint_satisfaction_problem
Construct allowing differentiation of tangent vector fields of manifolds
so it permits tangent vector fields to be differentiated as if they were functions on the manifold with values in a fixed vector space. Connections are
Affine_connection
Light motion in curved spacetime
that combines the light-like particle and the gravitational field. Standard variational procedure according to Hamilton's principle is applied to action
Fermat's and energy variation principles in field theory
Fermat's_and_energy_variation_principles_in_field_theory
Application of mathematical methods to other fields
(broadly construed, to include representations, asymptotic methods, variational methods, and numerical analysis); and applied probability. These areas
Applied_mathematics
Electromagnetic quantum-mechanical effect in regions of zero magnetic and electric field
classical gravitational potential) and a stationary magnetic field as the curl of a vector potential (then a new concept – the idea of a scalar potential
Aharonov–Bohm_effect
Computational fluid dynamics tools
through time. The fluid parcels are labelled by some (time-independent) vector field x0. (Often, x0 is chosen to be the position of the center of mass of
Lagrangian and Eulerian specification of the flow field
Lagrangian_and_Eulerian_specification_of_the_flow_field
Italian mathematician (born 1989)
Ambrosio and Alessio Figalli. Her dissertation, Flows of non-smooth vector fields and degenerate elliptic equations: With applications to the Vlasov-Poisson
Maria_Colombo_(mathematician)
Unified field theory
space and time; a 4-vector A μ {\displaystyle A^{\mu }} identified with the electromagnetic vector potential; and a scalar field ϕ {\displaystyle \phi
Kaluza–Klein_theory
Tensor field in Riemannian geometry
and X ( M ) {\displaystyle {\mathfrak {X}}(M)} be the space of all vector fields on M {\displaystyle M} . We define the Riemann curvature tensor as a
Riemann_curvature_tensor
Field of higher mathematics
The calculus of variations is sometimes regarded as part of geometric analysis, because differential equations arising from variational principles have
Geometric_analysis
Change in speed due only to gravity
source. It is a vector oriented toward the field source, of magnitude measured in acceleration units. The gravitational acceleration vector depends only
Gravitational_acceleration
VARIATIONAL VECTOR-FIELD
VARIATIONAL VECTOR-FIELD
Boy/Male
American, British, Christian, Danish, Dutch, English, Finnish, French, German, Greek, Hindu, Indian, Irish, Jamaican, Latin, Romanian, Slovenia, Spanish, Swedish, Swiss, Tamil, Ukrainian
Victorious; Conqueror; Winner; Champion; One who Conquers; Victory
Male
English
Short form of English Sylvester, VESTER means "from the forest."
Male
Greek
(á¼ÎºÏ„ωÏ) Variant spelling of Greek Hektor, EKTOR means "defend; hold fast."
Male
Portuguese
Galician-Portuguese form of Roman Latin Victor, VITOR means "conqueror."
Boy/Male
English American
Doctor; teacher.
Boy/Male
Christian & English(British/American/Australian)
Conqueror
Male
Arthurian
, sir Hector de Maris; (defender).
Boy/Male
Spanish
Victor.
Boy/Male
Spanish American Shakespearean Greek Latin
Tenacious.
Male
English
 Anglicized form of Scottish Gaelic Eachann, HECTOR means "brown horse." Compare with another form of Hector.
Surname or Lastname
Scottish
Scottish : Anglicized form of the Gaelic personal name Eachann (earlier Eachdonn, already confused with Norse Haakon), composed of the elements each ‘horse’ + donn ‘brown’.English : found in Yorkshire and Scotland, where it may derive directly from the medieval personal name. According to medieval legend, Britain derived its name from being founded by Brutus, a Trojan exile, and Hector was occasionally chosen as a personal name, as it was the name of the Trojan king’s eldest son. The classical Greek name, HektÅr, is probably an agent derivative of Greek ekhein ‘to hold back’, ‘hold in check’, hence ‘protector of the city’.German, French, and Dutch : from the personal name (see 2 above). In medieval Germany, this was a fairly popular personal name among the nobility, derived from classical literature. It is a comparatively rare surname in France.
Male
English
Roman Latin name VICTOR means "conqueror."Â
Boy/Male
Latin American Spanish
Conqueror.
Male
Russian
(Cyrillic Виктор): Slavic form of Roman Latin Victor, VIKTOR means "conqueror." In use by the Bulgarians, Russians and Serbians. Compare with another form of Viktor.
Boy/Male
American, Australian, British, Chinese, Christian, Danish, Dutch, English, French, German, Greek, Italian, Latin, Portuguese, Shakespearean, Spanish
Steadfast; Anchor; Holds Fast; Star; Coined from Esther Vanhomrigh; Tenacious; Defend; Hold Fast; Coined from Esther Vanho
Male
Portuguese
Portuguese form of Latin Hector, HEITOR means "defend; hold fast."
Male
Scandinavian
 Scandinavian form of Roman Latin Victor, VIKTOR means "conqueror." Compare with another form of Viktor.
Boy/Male
Australian, Basque, Czech, Czechoslovakian, Danish, Finnish, French, German, Hungarian, Latin, Polish, Slovenia, Swedish, Swiss, Ukrainian
The Conqueror; Victory; Victorious; Conquer
Boy/Male
Arthurian Legend
Father of Arthur.
Boy/Male
Christian & English(British/American/Australian)
Steadfast
VARIATIONAL VECTOR-FIELD
VARIATIONAL VECTOR-FIELD
Girl/Female
Hindu
Male
Hungarian
Hungarian form of German Frideric, FREDEK means "peaceful ruler."
Girl/Female
American, Anglo, Australian, British, Christian, English, German, Latin, Swedish
Ruler of the Home; Star; Home Ruler; Myrtle Leaf; Female Version of Henry; Abbreviation for Henrietta and Harriette; Little
Boy/Male
British, English
Lighthearted Friend
Boy/Male
Indian
gives life.
Girl/Female
Bengali, Hindu, Indian, Kannada, Marathi, Sindhi, Tamil, Telugu
Meditation
Boy/Male
Hindu, Indian
Celestial Heavenly
Boy/Male
Arabic, Muslim
Understanding; Knowledge; Know-how
Boy/Male
Hindu
Supreme spirit, Lord of the lords, A name of Lord Rama
Boy/Male
Arabic, Muslim
Restorer
VARIATIONAL VECTOR-FIELD
VARIATIONAL VECTOR-FIELD
VARIATIONAL VECTOR-FIELD
VARIATIONAL VECTOR-FIELD
VARIATIONAL VECTOR-FIELD
v. t.
To confer a doctorate upon; to make a doctor.
n.
A belly, or protuberant part; a broad surface; as, the venter of a muscle; the venter, or anterior surface, of the scapula.
n.
The chief elective officer of some universities, as in France and Scotland; sometimes, the head of a college; as, the Rector of Exeter College, or of Lincoln College, at Oxford.
a.
Of or pertaining to victory, or a victor' being a victor; bringing or causing a victory; conquering; winning; triumphant; as, a victorious general; victorious troops; a victorious day.
n.
A mathematical instrument, consisting of two rulers connected at one end by a joint, each arm marked with several scales, as of equal parts, chords, sines, tangents, etc., one scale of each kind on each arm, and all on lines radiating from the common center of motion. The sector is used for plotting, etc., to any scale.
n.
A directed quantity, as a straight line, a force, or a velocity. Vectors are said to be equal when their directions are the same their magnitudes equal. Cf. Scalar.
n.
A woman who wins a victory; a female victor.
a.
Pertaining to a rector or a rectory; rectoral.
n.
The act of varying; a partial change in the form, position, state, or qualities of a thing; modification; alternation; mutation; diversity; deviation; as, a variation of color in different lights; a variation in size; variation of language.
n.
The province of a rector; a parish church, parsonage, or spiritual living, with all its rights, tithes, and glebes.
n.
An astronomical instrument, the limb of which embraces a small portion only of a circle, used for measuring differences of declination too great for the compass of a micrometer. When it is used for measuring zenith distances of stars, it is called a zenith sector.
n.
An African weaver bird (Textor alector).
n.
A pregnant woman; a mother; as, A has a son B by one venter, and a daughter C by another venter; children by different venters.
n.
Any mechanical contrivance intended to remedy a difficulty or serve some purpose in an exigency; as, the doctor of a calico-printing machine, which is a knife to remove superfluous coloring matter; the doctor, or auxiliary engine, called also donkey engine.
n.
A contrivance for removing superfluous ink or coloring matter from a roller. See Doctor, 4.
v. t.
To tamper with and arrange for one's own purposes; to falsify; to adulterate; as, to doctor election returns; to doctor whisky.
n.
A term made up of the two parts / + /1 /-1, where / and /1 are vectors.
n.
The ratio of one vector to another in length, no regard being had to the direction of the two vectors; -- so called because considered as a stretching factor in changing one vector into another. See Versor.
n.
Same as Radius vector.
n.
The turning factor of a quaternion.