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Extension of the scalar spherical harmonics for use with vector fields
In mathematics, vector spherical harmonics (VSH) are an extension of the scalar spherical harmonics for use with vector fields. The components of the
Vector_spherical_harmonics
Special mathematical functions defined on the surface of a sphere
basis Spinor spherical harmonics Spin-weighted spherical harmonics Sturm–Liouville theory Table of spherical harmonics Vector spherical harmonics Zernike polynomials
Spherical_harmonics
Special functions on a sphere
The spinor spherical harmonics are the natural spinor analog of the vector spherical harmonics. While the standard spherical harmonics are a basis for
Spinor_spherical_harmonics
Scattering of an electromagnetic plane wave by a sphere
expanded into radiating spherical vector spherical harmonics. The internal field is expanded into regular vector spherical harmonics. By enforcing the boundary
Mie_scattering
This is a table of orthonormalized spherical harmonics that employ the Condon-Shortley phase up to degree ℓ = 10 {\displaystyle \ell =10} . Some of these
Table_of_spherical_harmonics
zonal spherical harmonics are special spherical harmonics that are invariant under the rotation through a particular fixed axis. The zonal spherical functions
Zonal_spherical_harmonics
Expressing a plane wave as a combination of spherical waves
imaginary unit, k is a real or complex wave vector of length k, r is a position vector of length r, jℓ are spherical Bessel functions, Pℓ are Legendre polynomials
Plane-wave_expansion
Coordinates comprising a distance and two angles
derivatives of a vector-valued function List of canonical coordinate transformations Sphere – Set of points equidistant from a center Spherical harmonic – Special
Spherical_coordinate_system
Differential operator in mathematics
\ell =0,1,2,\dots ,} and the corresponding eigenfunctions are the spherical harmonics of degree ℓ {\displaystyle \ell } on S N − 1 {\displaystyle S^{N-1}}
Laplace_operator
Radiation description framework
dependence of radiation is recovered. Multipole expansion Spherical harmonics Vector spherical harmonics Near and far field Quadrupole formula Hartle, James
Multipole_radiation
Tensor operator generalizes the notion of operators which are scalars and vectors
vectors. A special class of these are spherical tensor operators which apply the notion of the spherical basis and spherical harmonics. The spherical
Tensor_operator
Special functions
harmonics—are functions on the sphere. Unlike ordinary spherical harmonics, the spin-weighted harmonics are U(1) gauge fields rather than scalar fields: mathematically
Spin-weighted spherical harmonics
Spin-weighted_spherical_harmonics
Real-time rendering technique
standard lighting equations with spherical functions that have been projected into frequency space using the spherical harmonics as a basis. To take a simple
Spherical_harmonic_lighting
Solutions of the Laplace equation in spherical polar coordinates
In physics and mathematics, the solid harmonics are solutions of the Laplace equation in spherical polar coordinates, assumed to be (smooth) functions
Solid_harmonics
Basis used to express spherical tensors
mechanics and spherical harmonic functions. While spherical polar coordinates are one orthogonal coordinate system for expressing vectors and tensors using
Spherical_basis
Theoretical description of Earth's gravimetric shape
exactly spherical, mainly because of its rotation around the polar axis that makes its shape slightly oblate. However, a spherical harmonics series expansion
Geopotential spherical harmonic model
Geopotential_spherical_harmonic_model
Mathematical series
transformation of complex spherical harmonics to real form is by a unitary transformation, we can simply substitute real irregular solid harmonics and real multipole
Multipole_expansion
Topics referred to by the same term
VSH may refer to: Vector spherical harmonics Very smooth hash, in cryptography VSH News, a Pakistani television station XrossMediaBar (Sony codename: VSH)
VSH
Partial differential equation used in physics
expansions in spherical harmonics with coefficients proportional to the spherical Bessel functions. However, applying this expansion to each vector component
Electromagnetic_wave_equation
Formats used for Ambisonics
needs. Furthermore, there was no widely accepted formulation of spherical harmonics for acoustics, so one was borrowed from chemistry, quantum mechanics
Ambisonic data exchange formats
Ambisonic_data_exchange_formats
Polynomial whose Laplacian is zero
portal Harmonic function Spherical harmonics Zonal spherical harmonics Multilinear polynomial Walsh, J. L. (1927). "On the Expansion of Harmonic Functions
Harmonic_polynomial
Mathematical identities
alternatively use the left-most vector position. Comparison of vector algebra and geometric algebra Del in cylindrical and spherical coordinates – Mathematical
Vector_calculus_identities
Atomic model
often partially replaced by cubic harmonics for a number of reasons. These harmonics are usually named tesseral harmonics in the field of condensed matter
Cubic_harmonic
Type of vector space in math
polynomials or wavelets for instance, and in higher dimensions into spherical harmonics. For instance, if en are any orthonormal basis functions of L2[0
Hilbert_space
Coefficients in a series expansion of a potential
which the potential is being observed. We also use spherical coordinates throughout, e.g., the vector r ′ {\displaystyle \mathbf {r} '} has coordinates
Spherical_multipole_moments
Probability of a given process occurring in a particle collision
_{s}\right]} . All the field can be decomposed into the series of vector spherical harmonics (VSH). After that, all the integrals can be taken. In the case
Cross_section_(physics)
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
Functions in mathematics
referred to as "harmonics." Fourier analysis involves expanding functions on the unit circle in terms of a series of these harmonics. Considering higher
Harmonic_function
Differential equation important in physics
conditions, for which the solutions represent standing waves, or harmonics, analogous to the harmonics of musical instruments. The wave equation in one spatial
Wave_equation
System of currents that do not radiate into the far field
symmetry group O(3) as a certain multipole (or the corresponding vector spherical harmonic), but does not radiate to the far field. In photonics, anapoles
Anapole
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)
right. Spherical harmonics can represent any scalar field (function of position) that satisfies certain properties. A magnetic field is a vector field
Earth's_magnetic_field
Vector field on a pseudo-Riemannian manifold that preserves the metric tensor
mathematics and theoretical physics, a Killing vector field or Killing field (named after Wilhelm Killing) is a vector field on a Riemannian manifold or pseudo-Riemannian
Killing_vector_field
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
Three-dimensional orthogonal coordinate system
These Legendre functions are often referred to as toroidal harmonics. Toroidal harmonics have many interesting properties. If you make a variable substitution
Toroidal_coordinates
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
coefficient of a K-invariant vector in an irreducible representation of G. The key examples are the matrix coefficients of the spherical principal series, the
Zonal_spherical_function
Second-order partial differential equation
infinity, making A = 0. This does not affect the angular portion of the spherical harmonics. Stewart, James. Calculus : Early Transcendentals. 7th ed., Brooks/Cole
Laplace's_equation
Quantum number denoting orbital angular momentum
important role here via the connection to the angular dependence of the spherical harmonics for the different orbitals around each atom. The term "azimuthal
Azimuthal_quantum_number
Coefficients in angular momentum eigenstates of quantum systems
spherical harmonics and their complex conjugates. The addition of spins in quantum-mechanical terms can be read directly from this approach as spherical harmonics
Clebsch–Gordan_coefficients
Ocean shape without winds and tides
Earth's mantle. Spherical harmonics are often used to approximate the shape of the geoid. The current best such set of spherical harmonic coefficients is
Geoid
European Space Agency scientific satellite
; Murphy, D. W. (2007). "The local stellar velocity field via vector spherical harmonics". Astronomical Journal. 134 (1): 367–375. arXiv:0705.3267. Bibcode:2007AJ
Hipparcos
Coordinates comprising two distances and an angle
canonical coordinate transformations Vector fields in cylindrical and spherical coordinates Del in cylindrical and spherical coordinates Krafft, C.; Volokitin
Cylindrical_coordinate_system
Representation theory
the spherical transform was Selberg's trace formula. The classical Poisson summation formula combines the Fourier inversion formula on a vector group
Plancherel theorem for spherical functions
Plancherel_theorem_for_spherical_functions
Three-dimensional orthogonal coordinate system
{\partial ^{2}V}{\partial \phi ^{2}}}} As is the case with spherical coordinates and spherical harmonics, Laplace's equation may be solved by the method of separation
Oblate_spheroidal_coordinates
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
French polymath (1749–1827)
angular or spherical part. The solution to the spherical part of the equation can be expressed as a series of Laplace's spherical harmonics, simplifying
Pierre-Simon_Laplace
Topics referred to by the same term
postulate. Sylvester's theorem on partitions. Sylvester theorem on spherical harmonics. Sylvester's criterion, a characterization of positive-definite Hermitian
Sylvester's_theorem
Textbook by E. B. Wilson based on the lectures of J. W. Gibbs
for pairs of vectors. These are extended to a scalar triple product and a quadruple product. Pages 77–81 cover the essentials of spherical trigonometry
Vector_Analysis
Nonlinear optical process
analysis of second-harmonic generation is a plane wave of amplitude E(ω) traveling in a nonlinear medium in the direction of its k vector. A polarization
Second-harmonic_generation
Mathematical description of quantum state
functions in this case are the spherical harmonics. The Legendre polynomials are ingredients in the spherical harmonics. Most problems with rotational
Wave_function
Matrix of partial derivatives of a vector-valued function
In vector calculus, the Jacobian matrix (/dʒəˈkoʊbiən/, /dʒɪ-, jɪ-/) of a vector-valued function of several variables is the matrix of all its first-order
Jacobian matrix and determinant
Jacobian_matrix_and_determinant
Type of fluid flow
Laplace equation, and can be expanded in a series of solid spherical harmonics in spherical coordinates. As a result, the solution to the Stokes equations
Stokes_flow
Energy related to Earth's gravity
the geopotential is typically described by a series expansion into spherical harmonics (spectral representation). In this context the geopotential is taken
Geopotential
Classical statement of gravity as force
the force (in vector form, see below) over the extents of the two bodies. In this way, it can be shown that an object with a spherically symmetric distribution
Newton's law of universal gravitation
Newton's_law_of_universal_gravitation
by spherical harmonics whose spin l is at most equal to some j. The terms in the product of two spherical harmonics that involve spherical harmonics with
Fuzzy_sphere
Generalization of the one-dimensional normal distribution to higher dimensions
normal distribution to higher dimensions. One definition is that a random vector is said to be k-variate normally distributed if every linear combination
Multivariate normal distribution
Multivariate_normal_distribution
Raising and lowering operators in quantum mechanics
1119/1.1972354. Burkhardt, C. E.; Levanthal, J. (2004). "Lenz vector operations on spherical hydrogen atom eigenfunctions". American Journal of Physics.
Ladder_operator
Mathematical function
three dimensions, in Cartesian and spherical geometry, on surfaces and in volumes, on graphs, and in scalar, vector, and tensor forms. Without reference
Slepian_function
Geographic coordinate specifying north-south position
the sphere is along the radial vector. The latitude, as defined in this way for the sphere, is often termed the spherical latitude, to avoid ambiguity with
Latitude
Theorem used in quantum mechanics for angular momentum calculations
the spherical tensors as T q ( 1 ) = 4 π 3 r Y 1 q {\displaystyle T_{q}^{(1)}={\sqrt {\frac {4\pi }{3}}}rY_{1}^{q}} and Ylm are spherical harmonics, which
Wigner–Eckart_theorem
Laplace limit, concerning series solutions to Kepler's equation Laplacian vector field Laplace's equation Laplace operator Discrete Laplace operator Laplace–Beltrami
List of things named after Pierre-Simon Laplace
List_of_things_named_after_Pierre-Simon_Laplace
Integration over a non-flat region in 3D space
position which returns a scalar as a value), or a vector field (that is, a function which returns a vector as value). If a region R is not flat, then it is
Surface_integral
Coefficients coupled with angular momentum
remain. The 3-jm symbols give the integral of the products of three spherical harmonics ∫ Y l 1 m 1 ( θ , φ ) Y l 2 m 2 ( θ , φ ) Y l 3 m 3 ( θ , φ ) sin
3-j_symbol
Matrix representing a Euclidean rotation
prime example – in mathematics and physics – would be the theory of spherical harmonics. Their role in the group theory of the rotation groups is that of
Rotation_matrix
Branch of mathematics
expansion is the decomposition of a function on the sphere into spherical harmonics. Again, this is an orthogonal expansion, and orthogonality of the
Mathematical_analysis
Mathematical objects more general than vectors
+i(\mathbf {r} {\hat {\mathbf {A} }})} . Tensor Spherical harmonics Operator (physics) Laplace-Runge-Lenz vector Angular momentum operator Ladder operator Multipolar
Harmonic_tensors
Topological space that locally resembles Euclidean space
harmonic analysis, where one studies harmonic functions: the kernel of the Laplace operator. This leads to such functions as the spherical harmonics,
Manifold
Irreducible representation of the rotation group SO
(2013). "Appendix A: Spin-Weighted Spherical Harmonic Function" (PDF). Probing the Early Universe with the CMB Scalar, Vector and Tensor Bispectrum (PhD). Nagoya
Wigner_D-matrix
Result that expresses a function f(x + y) in terms of f(x) and f(y)
formal groups. Timeline of abelian varieties Addition theorem for spherical harmonics Mordell–Weil theorem "Addition theorems in the theory of special
Addition_theorem
Type of signal in signal processing
has spherical symmetry in n-dimensional space. Therefore, any orthogonal transformation of the vector will result in a Gaussian white random vector. In
White_noise
Quantum mechanical operator related to rotational symmetry
|\ell ,m\right\rangle =Y_{\ell ,m}(\theta ,\phi )} are the spherical harmonics. Runge–Lenz vector (used to describe the shape and orientation of bodies in
Angular_momentum_operator
Statement about integration on manifolds
In vector calculus and differential geometry the generalized Stokes theorem (sometimes with apostrophe as Stokes' theorem or Stokes's theorem), also called
Generalized_Stokes_theorem
Quantum mechanical model
wavefunction; Y l m ( θ , ϕ ) {\displaystyle Y_{lm}(\theta ,\phi )\,} is a spherical harmonic function; ħ is the reduced Planck constant: ℏ ≡ h 2 π . {\displaystyle
Quantum_harmonic_oscillator
Widely used scientific instrument aboard satellites and probes
magnetometers on spacecraft were made as vector sensors. However, the magnetometer electronics created harmonics which interfered with readings. Properly
Spacecraft_magnetometer
Discrete Fourier transform algorithm
5 / 2 log n ) {\textstyle O(n^{5/2}\log n)} generalization to spherical harmonics on the sphere S2 with n2 nodes was described by Mohlenkamp, along
Fast_Fourier_transform
Tensor in general relativity
standard results in vector calculus, this is readily converted to expressions valid in other coordinate charts, such as the polar spherical chart d s 2 = d
Tidal_tensor
Integral transform
{\displaystyle f\in L^{2}(S^{2})} on the sphere can be decomposed into spherical harmonics Y n k {\displaystyle Y_{n}^{k}} f = ∑ n = 0 ∞ ∑ k = − n n f ^ ( n
Funk_transform
Mechanical force towards or away from a point
(\mathbf {r} )=F(\mathbf {r} ){\hat {\mathbf {r} }}} where F is a force vector, F is a scalar valued force function (whose absolute value gives the magnitude
Central_force
Scalar measure of the rotational inertia with respect to a fixed axis of rotation
vector is directed along the unit vector k {\displaystyle \mathbf {k} } which is perpendicular to the plane of movement. Introduce the unit vectors e
Moment_of_inertia
In mathematical harmonic analysis, Harish-Chandra's Ξ function is a special spherical function on a semisimple Lie group, studied by Harish-Chandra (1966
Harish-Chandra's_Ξ_function
Number describing angular momentum along an axis
if it is in a magnetic field because in the absence of one, all spherical harmonics corresponding to the different arbitrary values of m l {\displaystyle
Magnetic_quantum_number
Family of distributions that generalize the multivariate normal distribution
general elliptical distributions (with finite variance), particularly for spherical distributions (which are defined below). Elliptical distributions are
Elliptical_distribution
Spectral density estimation technique
estimation on the sphere using Slepian functions constructed from spherical harmonics for applications in geophysics and cosmology among others. An extensive
Multitaper
Mathematics of smooth surfaces
tangential vector fields. Given a tangential vector field X and a tangent vector Y to S at p, the covariant derivative ∇YX is a certain tangent vector to S
Differential geometry of surfaces
Differential_geometry_of_surfaces
MayaVi, it now has more features. visualizes computational grids and scalar, vector, and tensor data an easy-to-use GUI can be imported as a Python module from
MayaVi
Electromagnetic phenomenon
interaction Spin magnetic moment Monopole Solid harmonics Axial multipole moments Cylindrical multipole moments Spherical multipole moments Laplace expansion Molecular
Dipole
Tensor field in Riemannian geometry
1007/BF01454201, S2CID 120009332 Sandberg, Vernon D (1978). "Tensor spherical harmonics on S 2 and S 3 as eigenvalue problems" (PDF). Journal of Mathematical
Riemann_curvature_tensor
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
Process of modeling orbits
the Earth, the gravitational field of the Earth is modeled with spherical harmonics which are expressed through the equation: f = − μ R 2 r ^ + ∑ n =
Orbit_modeling
Instantaneous rate of change of the function
instantaneous rate at which a function changes along a specified vector through a given point. If the vector is multiplied by a scalar, the corresponding directional
Directional_derivative
For a large class of boundary conditions, all solutions have the same gradient
Coulomb's law Method of images Green's function Uniqueness theorem Spherical harmonics L.D. Landau, E.M. Lifshitz (1975). The Classical Theory of Fields
Uniqueness theorem for Poisson's equation
Uniqueness_theorem_for_Poisson's_equation
Examination
multivariate calculus coordinate systems (rectangular, cylindrical, spherical) vector algebra and vector differential operators Fourier series partial differential
GRE_Physics_Test
Generalized sphere of dimension n (mathematics)
− 1 {\displaystyle j=n-1} in concordance with the spherical harmonics. The standard spherical coordinate system arises from writing R n {\displaystyle
N-sphere
yearly cycles. Gravity acceleration is a vector quantity, with direction in addition to magnitude. In a spherically symmetric Earth, gravity would point directly
Gravity_of_Earth
Method of environment mapping in computer graphics
represent a skylight is very complex; one recent process is computing the spherical harmonic basis that best represents the low frequency diffuse illumination
Cube_mapping
Fundamental study of potential theory
where x is a vector of length x pointing from the point mass toward the small body and x ^ {\displaystyle {\hat {\mathbf {x} }}} is a unit vector pointing
Gravitational_potential
Method in physics
+\mathbf {G} |_{\text{max}}} . In each MT sphere, the expansion into spherical harmonics is limited to a maximum number of angular momenta l max , α ≈ K max
Linearized augmented-plane-wave method
Linearized_augmented-plane-wave_method
Group of rotations in 3 dimensions
Representations of SO(3) Rigid body Rodrigues' rotation formula Spherical harmonics Spherical symmetry Three-dimensional rotation operator This is effected
3D_rotation_group
which generalizes into higher dimensions. Vector analysis also known as vector calculus, see vector calculus. Vector calculus a branch of multivariable calculus
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
VECTOR SPHERICAL-HARMONICS
VECTOR SPHERICAL-HARMONICS
Male
English
Short form of English Sylvester, VESTER means "from the forest."
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
Galician-Portuguese form of Roman Latin Victor, VITOR means "conqueror."
Male
English
 Anglicized form of Scottish Gaelic Eachann, HECTOR means "brown horse." Compare with another form of Hector.
Male
Arthurian
, sir Hector de Maris; (defender).
Boy/Male
Spanish
Victor.
Male
Portuguese
Portuguese form of Latin Hector, HEITOR means "defend; hold fast."
Boy/Male
English American
Doctor; teacher.
Boy/Male
Arthurian Legend
Father of Arthur.
Boy/Male
Australian, Basque, Czech, Czechoslovakian, Danish, Finnish, French, German, Hungarian, Latin, Polish, Slovenia, Swedish, Swiss, Ukrainian
The Conqueror; Victory; Victorious; Conquer
Male
Greek
(á¼ÎºÏ„ωÏ) Variant spelling of Greek Hektor, EKTOR means "defend; hold fast."
Boy/Male
Latin American Spanish
Conqueror.
Male
English
Roman Latin name VICTOR means "conqueror."Â
Boy/Male
Christian & English(British/American/Australian)
Conqueror
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
Boy/Male
Spanish American Shakespearean Greek Latin
Tenacious.
Male
Scandinavian
 Scandinavian form of Roman Latin Victor, VIKTOR means "conqueror." Compare with another form of Viktor.
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
Christian & English(British/American/Australian)
Steadfast
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.
VECTOR SPHERICAL-HARMONICS
VECTOR SPHERICAL-HARMONICS
Boy/Male
Tamil
Lord Shiva
Boy/Male
Hindu, Indian
Brave
Boy/Male
English
Near the Stream; Brook
Girl/Female
Hindu, Indian, Marathi, Tamil
Beautiful Angel; A Stone Slab
Boy/Male
Hindu
Worshipped by mynaka
Biblical
fraternity; brother of Jehovah
Boy/Male
Tamil
Tavasya | தாவாஸà¯à®¯
Strength
Girl/Female
Assamese, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Sindhi, Telugu
Peace
Girl/Female
Latin
From France or 'free one.' Feminine of Francis.
Boy/Male
Arabic, Australian, Muslim
Comfort; Sweet Smelling Plant
VECTOR SPHERICAL-HARMONICS
VECTOR SPHERICAL-HARMONICS
VECTOR SPHERICAL-HARMONICS
VECTOR SPHERICAL-HARMONICS
VECTOR SPHERICAL-HARMONICS
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.
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.
v. t.
To tamper with and arrange for one's own purposes; to falsify; to adulterate; as, to doctor election returns; to doctor whisky.
a.
Alt. of Spheric
n.
The province of a rector; a parish church, parsonage, or spiritual living, with all its rights, tithes, and glebes.
a.
Pertaining to a rector or a rectory; rectoral.
n.
Same as Radius vector.
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.
n.
The doctrine of the sphere; the science of the properties and relations of the circles, figures, and other magnitudes of a sphere, produced by planes intersecting it; spherical geometry and trigonometry.
a.
Spherical.
v. t.
To confer a doctorate upon; to make a doctor.
a.
Having the form of a sphere; like a sphere; globular; orbicular; as, a spherical body.
v. t.
To form into roundness; to make spherical, or spheral; to perfect.
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.
An African weaver bird (Textor alector).
n.
A belly, or protuberant part; a broad surface; as, the venter of a muscle; the venter, or anterior surface, of the scapula.
n.
A woman who wins a victory; a female victor.
n.
The turning factor of a quaternion.
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.
A term made up of the two parts / + /1 /-1, where / and /1 are vectors.