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Mathematical term
require the base field to be spherically complete. Any locally compact field is spherically complete. This includes, in particular, the fields Qp of p-adic
Spherically_complete_field
Special mathematical functions defined on the surface of a sphere
scientific fields. The table of spherical harmonics contains a list of common spherical harmonics. Since the spherical harmonics form a complete set of orthogonal
Spherical_harmonics
Assignment of a vector to each point in a subset of Euclidean space
also a vector field. For example, the gravitational field vectors for a spherically symmetric body would all point towards the sphere's center with the magnitude
Vector_field
Geometric system used in black hole physics
In physics, spherically symmetric spacetimes are commonly used to obtain analytic and numerical solutions to Einstein's field equations in the presence
Spherically symmetric spacetime
Spherically_symmetric_spacetime
US nuclear fusion reactor
magnetic field strength. Since the amount of fusion power produced is proportional to the square of the plasma pressure, the use of spherically shaped plasmas
National Spherical Torus Experiment
National_Spherical_Torus_Experiment
Coordinates comprising a distance and two angles
Precision optical measuring instrument Vector fields in cylindrical and spherical coordinates – Vector field representation in 3D curvilinear coordinate
Spherical_coordinate_system
Team sport played with sticks and a ball
allowed when playing with a field keep, or a player can exit the field, but you must wait until after the penalty corner is complete. Play is not stopped for
Field_hockey
Metric geometry
is called complete (or a Cauchy space) if every Cauchy sequence of points in M has a limit that is also in M. Intuitively, a space is complete if there
Complete_metric_space
Fusion power device
gives it an overall shape similar to a donut, complete with a large hole in the middle. The spherical tokamak reduces the size of the hole as much as
Spherical_tokamak
Field-equations in general relativity
field equations are non-linear, they cannot always be completely solved (i.e. without making approximations). For example, there is no known complete
Einstein_field_equations
Mathematical formal infinite series
{\displaystyle K[[T^{\Gamma }]]} into a spherically complete valued field with value group Γ {\displaystyle \Gamma } and residue field K {\displaystyle K} (justifying
Hahn_series
Relativistic generalization of Mordehai Milgrom's MOND paradigm
principle, TeVeS respects conservation laws; In the weak-field approximation of the spherically symmetric, static solution, TeVeS reproduces the MOND acceleration
Tensor–vector–scalar_gravity
Aspect of general relativity
The Schwarzschild solution, which describes spacetime surrounding a spherically symmetric non-rotating uncharged massive object. For compact enough objects
Solutions of the Einstein field equations
Solutions_of_the_Einstein_field_equations
In the mathematical field of graph theory, the sphericity of a graph is a graph invariant defined to be the smallest dimension of Euclidean space required
Sphericity_(graph_theory)
American physicist
He received his Ph.D. in physics in 1964 after completing a doctoral dissertation titled "Spherically symmetric cosmological models." His Ph.D. students
Curtis_Callan
Set of points equidistant from a center
many fields of mathematics. Spheres and nearly-spherical shapes also appear in nature and industry. Bubbles such as soap bubbles take a spherical shape
Sphere
Radio telescope in Guizhou, China
The Five-hundred-meter Aperture Spherical Telescope (FAST; Chinese: 五百米口径球面射电望远镜), nicknamed Tianyan (天眼, lit. "Sky's/Heaven's Eye"), is a radio telescope
Five-hundred-meter Aperture Spherical Telescope
Five-hundred-meter_Aperture_Spherical_Telescope
Function in algebra
a metric on the field K. If K is complete with respect to this metric, then it is called a complete valued field. If K is not complete, one can use this
Valuation_(algebra)
System of numbers with non-finite quantities
(being real closed with a convex valuation ring) but not spherically complete. Indeed, the field of Hahn series with real coefficients and value group (
Levi-Civita_field
Multiple exposure image of deep space in the constellation Ursa Major
Hubble Ultra-Deep Field, which was the most sensitive optical deep field image for years until the Hubble eXtreme Deep Field was completed in 2012. Images
Hubble_Deep_Field
(quantum mechanics) particle in a box particle in a ring particle in a spherically symmetric potential quantum harmonic oscillator hydrogen atom ring wave
List of mathematical topics in quantum theory
List_of_mathematical_topics_in_quantum_theory
Property of space that quantifies the magnetic influence at a given location
electromagnetism, magnetic field is a physical property of space that quantifies the magnetic influence at a given location. Magnetic fields deflect moving electric
Magnetic_field
Statistical test
list (link) Field, A. P. (2005). Discovering Statistics Using SPSS. Sage Publications. Mauchly, J. W. (1940). "Significance Test for Sphericity of a Normal
Mauchly's_sphericity_test
Tensor operator generalizes the notion of operators which are scalars and vectors
class of these are spherical tensor operators which apply the notion of the spherical basis and spherical harmonics. The spherical basis closely relates
Tensor_operator
Emission of electrons induced by an electrostatic field
Field electron emission, also known as field-induced electron emission, field emission (FE) and electron field emission, is the emission of electrons from
Field_electron_emission
Mathematical model of a wormhole
earliest-known complete mathematical model of a traversable wormhole. It is a static, spherically symmetric solution of the Einstein vacuum field equations
Ellis_drainhole
Solution to the Einstein field equations
the Schwarzschild metric is the most general spherically symmetric vacuum solution of the Einstein field equations. A Schwarzschild black hole or static
Schwarzschild_metric
Method of analysis applied to problems wave propagation
source of spherical wavelets and that the secondary wavelets emanating from different points mutually interfere. The sum of these spherical wavelets forms
Huygens–Fresnel_principle
Foundational law of electromagnetism relating electric field and charge distributions
Gauss's law if it is assumed, in addition, that the electric field from a point charge is spherically symmetric (this assumption, like Coulomb's law itself,
Gauss's_law
Natural number
The integers modulo 2 form the finite field F 2 {\displaystyle \mathbb {F} _{2}} , the smallest finite field. It has two elements, usually denoted 0
2
Limiting magnetic field strength for superconductivity
both by perfect conductivity (zero resistance) and by the complete expulsion of magnetic fields (the Meissner effect). Changes in either temperature or
Critical_field
Hypothetical phenomenon
Waugh, B.; Lake, Kayll (1989-09-15). "Shell-focusing singularities in spherically symmetric self-similar spacetimes". Physical Review D. 40 (6): 2137–2139
Naked_singularity
Chess variants played on spherical boards
Spherical chess is any of several chess variants played on boards composed of fields arranged on the surface of a sphere. A variant described by Don Miller
Spherical_chess
Interactive panoramic photo viewing format
as well as spherical panorama, interactive panorama or immersive panorama. VR photography is the art of capturing or creating a complete scene as a single
VR_photography
Scattering of an electromagnetic plane wave by a sphere
scattering field, is expanded into radiating spherical vector spherical harmonics. The internal field is expanded into regular vector spherical harmonics
Mie_scattering
Differential equation for the description of waves or standing wave
partial differential equation for the description of waves or standing wave fields such as mechanical waves (e.g. water waves, sound waves and seismic waves)
Wave_equation
American academic (1893–1988)
trained in biochemistry), he made several notable contributions to the field. Murray developed the “personology” theory of personality. Murray was also
Henry_Murray
Isotope of helium
helium - Cornell Chronicle". Yu, Xiaoquan; Mueller, Markus (2012). "Mean field theory of superglasses". Physical Review B. 85 (10) 104205. arXiv:1111.5956
Helium-4
Hypothetical FTL transportation by warping space
and Gianni Martire claim that, in principle, a class of subluminal, spherically symmetric warp drive spacetimes can be constructed based on physical
Alcubierre_drive
Special functions
the sphere. Unlike ordinary spherical harmonics, the spin-weighted harmonics are U(1) gauge fields rather than scalar fields: mathematically, they take
Spin-weighted spherical harmonics
Spin-weighted_spherical_harmonics
Circulation density in a vector field
infinitesimal spherical volume of field F {\displaystyle \mathbf {F} } , seen (up to the third order), as a rigid body with motion field equal to F {\displaystyle
Curl_(mathematics)
Time that it takes to complete one rotation relative to the background stars
determined from the rotation of the planet's magnetic field. For objects that are not spherically symmetrical, the rotation period is, in general, not
Rotation_period
Physical theory describing classical fields
more complete formulation using tensor fields was found. Instead of using two vector fields describing the electric and magnetic fields, a tensor field representing
Classical_field_theory
Compact astronomical body
Israel showed that any non-spinning, uncharged collapsing star gives a spherically symmetric black hole: any asymmetry must somehow vanish. In 1972, Richard
Black_hole
Approximation method in quantum physics
multi-configurational self-consistent field, configuration interaction, quadratic configuration interaction, and complete active space SCF (CASSCF). Still
Hartree–Fock_method
Coordinate system used in general relativity
are a pair of coordinate systems for a Schwarzschild geometry (e.g. a spherically symmetric black hole) which are adapted to radial null geodesics. Null
Eddington–Finkelstein coordinates
Eddington–Finkelstein_coordinates
Measure in 3-dimensional geometry
In geometry, a solid angle (symbol: Ω) is a measure of the amount of the field of view from some particular point that a given object covers. That is,
Solid_angle
American applied physicist and electrical engineer (1918–2007)
electrodynamics in 1948, with a dissertation titled A Theoretical Investigation of Spherically-Capped Conical Antennas advised by Ronold W. P. King. During the war
Charles_H._Papas
Directional variation in strength of radio waves
placed in front of the source, or over a cylindrical or spherical surface enclosing it. The far-field pattern of an antenna may be determined experimentally
Radiation_pattern
Description of gravity using discrete values
Quantum gravity (QG) is a field of theoretical physics that seeks unification of the theory of gravity with the principles of quantum mechanics. It deals
Quantum_gravity
Theory of gravitation as curved spacetime
holes relied on explicit solutions of Einstein's equations, notably the spherically symmetric Schwarzschild solution (used to describe a static black hole)
General_relativity
Physical constant for the strength of gravity induced by a mass
magnitude of the attractive force (F) between two bodies each with a spherically symmetric density distribution is directly proportional to the product
Gravitational_constant
Coordinate system
set of coordinates for the Schwarzschild metric—a spherically symmetric solution to the Einstein field equations in vacuum—introduced by Georges Lemaître
Lemaître_coordinates
Track and field event
The shot put is a track and field event involving "putting" (or throwing) a heavy spherical ball—the shot—as far as possible. For men, the sport has been
Shot_put
Magnetic confinement device used to produce thermonuclear fusion power
(/ˈtoʊkəmæk/; Russian: токамáк) is a machine which uses a powerful magnetic field generated by external magnets to confine plasma in the shape of an axially-symmetric
Tokamak
Hypothetical topological feature of spacetime
Relativity" For the combined field, gravity and electricity, Einstein and Rosen derived the following Schwarzschild static spherically symmetric solution φ 1
Wormhole
German mathematician (1826–1866)
contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first rigorous formulation
Bernhard_Riemann
related fields. Astronomy is concerned with the study of celestial objects and phenomena that originate outside the atmosphere of Earth. The field of astronomy
Glossary_of_astronomy
Hypothesis proposing a modification of Newton's laws
between the gravitational potential and the X-ray gas in this highly non-spherically-symmetric system. In MOND, one would expect the "missing mass" to be
Modified_Newtonian_dynamics
German physicist (1873–1916)
used rectangular coordinates to approximate the gravitational field around a spherically symmetric, non-rotating, non-charged mass. Schwarzschild, in contrast
Karl_Schwarzschild
Attraction of masses and energy
gravitational field, which can be conceptualized with Newtonian physics as exerting an attractive force on all objects. Assuming a spherically symmetrical
Gravity
Proposed theory of gravitation
situations in which no non-gravitational fields are present. The following Lagrangian contains the complete description of the Brans–Dicke theory: S =
Brans–Dicke_theory
Function describing an electron in an atom
counter rotating modes. There are only radial modes and the shape is spherically symmetric. Nodal planes, cones and spheres are surfaces on which the
Atomic_orbital
Variant of football played on a court
goalkeeping rules; from hockey, the substitution rules; and from handball, the field and goal sizes. The YMCA spread the game quickly throughout South America
Futsal
3D imaging technique
display using integral imaging is a type of light field display. The result is a visual reproduction complete with all significant depth cues, including parallax
Integral_imaging
Diagram of different points in spacetime
diagram of finite size, with infinity on the boundary of the diagram. For spherically symmetric spacetimes, every point in the Penrose diagram corresponds
Penrose_diagram
Vector field on a pseudo-Riemannian manifold that preserves the metric tensor
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
To be included in this list, the formats must all have been used in the field or for test shooting, and they must all use photochemical images that are
List of motion picture film formats
List_of_motion_picture_film_formats
Scanning microscopy using thin samples and transmitted electrons
STEM suitable for analytical techniques such as Z-contrast annular dark-field imaging, and spectroscopic mapping by energy dispersive X-ray (EDX) spectroscopy
Scanning transmission electron microscopy
Scanning_transmission_electron_microscopy
Electricity generation by nuclear fusion
J.; Stanic, M.; Tang, X.; Welch, D. R.; Witherspoon, F. D. (2012). "Spherically Imploding Plasma Liners as a Standoff Driver for Magnetoinertial Fusion"
Fusion_power
American manufacturer
surface was adapted to create spherically curved glass with the goals of eliminating blind spots and offering an expanded field of view. As of 2016[update]
Gentex_(automotive_supplier)
Quantum mechanical model
as in integer partition. The Schrödinger equation for a particle in a spherically-symmetric three-dimensional harmonic oscillator can be solved explicitly
Quantum_harmonic_oscillator
Number with a real and an imaginary part
associative, commutative, and distributive laws. This makes the complex numbers a field. The set of complex numbers is denoted by either of the symbols C {\displaystyle
Complex_number
Deviation from perfect paraxial optical behavior
The most common monochromatic aberrations are: Defocus Spherical aberration Coma Astigmatism Field curvature Image distortion Although defocus is technically
Optical_aberration
Symmetry of spatially mirrored systems
parity. The parity of the states of a particle moving in a spherically symmetric external field is determined by the angular momentum, and the particle state
Parity_(physics)
Australian and American mathematician (born 1975)
at the University of California, Los Angeles (UCLA). He was awarded the Fields Medal in 2006 for his contributions to partial differential equations, combinatorics
Terence_Tao
Eighth planet from the Sun
magnetic field surrounding the planet and discovered that the field was offset from the centre and tilted in a manner similar to the field around Uranus
Neptune
Elastic interaction of x-rays with electrons
Nobel Prize in Physics in 1914. After Von Laue's pioneering research the field developed rapidly, most notably by physicists William Lawrence Bragg and
X-ray_diffraction
2023 Chinese science fiction television series
Chinese adaptation was already underway at Tencent and took four years to complete. Shooting began in July 2020 and lasted 126 days. The Beijing Electron–Positron
Three-Body
Integral transform useful in probability theory, physics, and engineering
can be alternatively defined in a purely algebraic manner by applying a field of fractions construction to the convolution ring of functions on the positive
Laplace_transform
German physicist and astronomer, best known for his solution of Einstein's field equations, leading to the Schwarzschild radius. He was the director of the
Meanings of minor-planet names: 1–1000
Meanings_of_minor-planet_names:_1–1000
Semiconductor light source
giving a spherical light distribution, but rather a lambertian distribution. So, LEDs are difficult to apply to uses needing a spherical light field. Different
Light-emitting_diode
Elastostatics problem in linear elasticity
Finally, on the first days of January 1963, Fichera was able to give a complete proof of the existence of a unique solution for the problem with ambiguous
Signorini_problem
Technique for recording widescreen images onto a 4:3 frame
has an inherently wider horizontal field of view. Anamorphic lenses have more complex optics than standard spherical lenses which require more light, and
Anamorphic_format
Canonical solutions of the general Legendre equation
phase and normalization factor than given here (see spherical harmonics). When a 3-dimensional spherically symmetric partial differential equation is solved
Associated Legendre polynomials
Associated_Legendre_polynomials
May 2016 at the Wayback Machine – Military.com, 20 May 2016 "Army completes fielding of the M3A1 Multi-Role Anti-Armor Anti-Personnel Weapon System (MAAWS)"
List of equipment of the United States Army
List_of_equipment_of_the_United_States_Army
Optical device which transmits and refracts light
image quality, including spherical aberration, coma, and chromatic aberration. Spherical aberration occurs because spherical surfaces are not the ideal
Lens
Smith and his officers knew before they left Southampton that the drift ice field was larger in extent and more southernly than in previous years. Additionally
Iceberg_that_sank_the_Titanic
Debate about credit for general relativity
equations, which are unaffected by the trace term that was added to complete the field equations.) Reference to the final form of the equations appears only
General relativity priority dispute
General_relativity_priority_dispute
Family of linear transformations
the electromagnetic field tensor. Lorentz transformations can also be used to illustrate that the magnetic field B and electric field E are simply different
Lorentz_transformation
Deepest known point of Earth's seabed
system of underwater navigation at a depth exceeding 10,000 metres, during a field trial of the Tsaihungyuy (ultra-short baseline) system. Project leader Tsui
Challenger_Deep
Excited atomic quantum state with high principal quantum number (n)
lower electron shells filled with Z-1 electrons. An electron in the spherically symmetric Coulomb potential has potential energy: U C = − e 2 4 π ε 0
Rydberg_atom
Form of nitrocellulose used in small arms cartridges
propellant (trademarked as Ball Powder by Olin Corporation and marketed as spherical powder by Hodgdon Powder Company) is a form of nitrocellulose used in
Ball_propellant
German mathematician (1894–1971)
any simply connected complete Riemannian 3-manifold of constant sectional curvature is globally isometric to Euclidean, spherical, or hyperbolic space
Heinz_Hopf
Approach to controlled thermonuclear fusion using magnetic fields
considerable experimental attention. However, spherical tokamaks to date have been at low toroidal field and as such are impractical for fusion neutron
Magnetic_confinement_fusion
Notation in general relativity
tetrad formalism, where the tensors of the theory are projected onto a complete vector basis at each point in spacetime. Usually this vector basis is chosen
Newman–Penrose_formalism
German-born theoretical physicist (1879–1955)
assumption" that had to be postulated in addition to the field equations in order to complete the theory. Believing this to be a shortcoming in how general
Albert_Einstein
Painting attributed to Leonardo da Vinci
patron Giuliano de' Medici in 1514 and so may have convinced the artist to complete the commission at that time. Frank Zöllner has discussed Leo X as a possible
Salvator_Mundi_(painting)
Type of vector space in math
length and angle to be measured. Finally, Hilbert spaces are required to be complete, a property that stipulates the existence of enough limits in the space
Hilbert_space
Russian mathematician (born 1966)
Russian mathematician and geometer who is known for his contributions to the fields of geometric analysis, Riemannian geometry, and geometric topology. In 2005
Grigori_Perelman
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