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In mathematics, a Poisson ring is a commutative ring on which an anticommutative and distributive binary operation [ ⋅ , ⋅ ] {\displaystyle [\cdot ,\cdot
Poisson_ring
Operation in Hamiltonian mechanics
In mathematics and classical mechanics, the Poisson bracket is an important binary operation in Hamiltonian mechanics, playing a central role in Hamilton's
Poisson_bracket
Algebraic structure with addition and multiplication
ring Lie ring Local ring Noetherian and artinian rings Ordered ring Poisson ring Reduced ring Regular ring Ring of periods SBI ring Valuation ring and discrete
Ring_(mathematics)
Poisson boundary Poisson bracket, see Hamiltonian mechanics header Poisson games Poisson manifold Poisson ring Poisson supermanifold Poisson–Charlier polynomials
List of things named after Siméon Denis Poisson
List_of_things_named_after_Siméon_Denis_Poisson
Mathematical structure in differential geometry
a field in mathematics, a Poisson manifold is a smooth manifold endowed with a Poisson structure. The notion of Poisson manifold generalises that of
Poisson_manifold
Historically important optical effect
In optics, the Arago spot, Poisson spot, or Fresnel spot is a bright point that appears at the center of a circular object's shadow due to Fresnel diffraction
Arago_spot
Canadian wrestler (born 1947)
Gilles Poisson (born 1946) is a Canadian retired professional wrestler, known by his ring name Pierre or Gilles "The Fish" Poisson, who competed in North
Gilles_Poisson
formalism known as the De Donder–Weyl theory as the algebra of generalized Poisson brackets defined on differential forms. A Gerstenhaber algebra is a graded-commutative
Gerstenhaber_algebra
Gravitational singularity of a rotating black hole
A ring singularity or ringularity is the gravitational singularity of a rotating black hole, or a Kerr black hole, that is shaped like a ring. When a
Ring_singularity
Novikov ring Poisson 1. 2. Poisson algebra. 3. A Poisson manifold generalizes a symplectic manifold. 4. A Poisson–Lie group, a Poisson manifold
Glossary of symplectic geometry
Glossary_of_symplectic_geometry
About polynomials in several variables
two conjectures are equivalent to the Poisson conjecture, that every endomorphism of the n-th complex Poisson algebra is an automorphism. In consequence
Jacobian_conjecture
Operation measuring the failure of two entities to commute
be commutative. There are different definitions used in group theory and ring theory. The commutator of two elements, g and h, of a group G, is the element
Commutator
is then used to determine the static Young's modulus of elasticity and Poisson's ratio of concrete. ASTM C469 describes about the instrument. Extensometer
Compressometer
Matrix algebra Non-associative algebra Octonion algebra Pre-Lie algebra Poisson algebra Process algebra Quadratic algebra Quadric geometric algebra Quaternion
List_of_algebras
German aerospace engineering award
Josef Singer 1995 Werner Albring [de] 1996 Harvard Lomax 1997 Philippe Poisson-Quinton [fr] 1998 Jürgen Zierep 1999 Hans G. Hornung 2000 Julius C. Rotta
Ludwig_Prandtl_Ring
Topics referred to by the same term
distinct regular shape Incidence rate ratio, a statistic derived from a Poisson regression model Individual Ready Reserve, a personnel status of the United
IRR
Algebra based on a vector space with a quadratic form
T ( V ) / I Q . {\displaystyle \operatorname {Cl} (V,Q)=T(V)/I_{Q}.} The ring product inherited by this quotient is sometimes referred to as the Clifford
Clifford_algebra
Concept in number theory
In number theory, the adele ring is a construction that combines all local versions of a global field into one object. For the rational numbers, these
Adele_ring
Branch of functional analysis
of a single operator. In general, operator algebras are non-commutative rings. An operator algebra is typically required to be closed in a specified operator
Operator_algebra
Ring that is also a vector space or a module
mathematics, an associative algebra A over a commutative ring (often a field) K is a ring A together with a ring homomorphism from K into the center of A. This
Associative_algebra
Topics referred to by the same term
a Z 2 {\displaystyle \mathbb {Z} _{2}} -graded algebra Lie algebras, Poisson algebras, and Jordan algebras, important examples of (potentially) nonassociative
Algebra_(disambiguation)
Austro-Hungarian con artist (1890–1947)
his mark in André Poisson—an insecure man who wished to rise up amongst the inner circles of the Parisian business community. As Poisson showed the keenest
Victor_Lustig
Property of some binary operations
mathematician Carl Gustav Jacob Jacobi. He derived the Jacobi identity for Poisson brackets in his 1862 paper on differential equations. The cross product
Jacobi_identity
Typically linear operator defined in terms of differentiation of functions
in an associative algebra structure on a deformation quantization of a Poisson algebra. A microdifferential operator is a type of operator on an open
Differential_operator
High-energy particle measurement tool
particle type = proton, since fluctuations in the number of photons follow Poisson statistics about the expected mean, so that the probability of e.g. a 22
Ring-imaging Cherenkov detector
Ring-imaging_Cherenkov_detector
Canadian-born professional wrestler (born 1983)
Tyson Smith (born October 16, 1983), better known by his ring name Kenny Omega (Japanese: ケニー・オメガ, Hepburn: Kenī Omega), is a Canadian-born professional
Kenny_Omega
with the most awards: Ben-Hur (1959), Titanic (1997), and The Lord of the Rings: The Return of the King (2003) each earned 11 Academy Awards. Films with
List of Academy Award–winning films
List_of_Academy_Award–winning_films
on symmetric multivector fields, which is more or less the same as the Poisson bracket on the cotangent bundle. It was invented by Jan Arnoldus Schouten
Schouten–Nijenhuis_bracket
Mathematics award
the universal Vassiliev invariant of knots, and formal quantization of Poisson manifolds." Curtis T. McMullen Harvard University, US "For his contributions
Fields_Medal
Brackets as used in mathematical notation
Nijenhuis–Richardson bracket, also known as algebraic bracket. Pochhammer symbol Poisson bracket Schouten–Nijenhuis bracket System of equations Russell, Deb. "When
Bracket_(mathematics)
Mass shooting in British Columbia, Canada
home". Vancouver Sun. Archived from the original on March 17, 2026. Jayme Poisson; Caroline Barghout (February 12, 2026). "Tragedy in Tumbler Ridge" (Podcast)
2026_Tumbler_Ridge_shooting
Mathematic theory
and study its properties. Using harmonic analysis, more precisely the Poisson summation formula, he proved the functional equation and meromorphic continuation
Tate's_thesis
Avenue in Paris, France
In 1765 the garden was remade in the Le Nôtre style by Abel François Poisson, the marquis de Marigny, brother of the Madame de Pompadour and Director-General
Champs-Élysées
Punctuation mark
than zero. They are often also used to denote the Poisson bracket between two quantities. In ring theory, braces denote the anticommutator where {a, b}
Bracket
Device for measuring or maintaining orientation
pages 72–83. The French mathematician Poisson mentions Bohnenberger's machine as early as 1813: Simeon-Denis Poisson (1813) "Mémoire sur un cas particulier
Gyroscope
Algebraic structure used in analysis
Particle physics and representation theory Orthogonal symmetric Lie algebra Poisson algebra Pre-Lie algebra Quantum groups Moyal algebra Quasi-Frobenius Lie
Lie_algebra
Branch of mathematics
T ) ≡ ∑ n = − ∞ ∞ s [ n ] ⋅ e − i 2 π f n T ⏞ Fourier series (DTFT) ⏟ Poisson summation formula = F { ∑ n = − ∞ ∞ s [ n ] δ ( t − n T ) } , {\displaystyle
Fourier_analysis
Electrical conductivity with exactly zero resistance
Kelvin Kirchhoff Larmor Lenz Liénard Lorentz Maxwell Neumann Ohm Ørsted Poisson Poynting Ritchie Savart Singer Steinmetz Tesla Thomson Volta Weber Wiechert
Superconductivity
Algebra over a field where binary multiplication is not necessarily associative
R-algebras, they thus include Cayley-Dickson algebras and many more. The Poisson algebras are considered in geometric quantization. They carry two multiplications
Non-associative_algebra
Species of fish
The ring-tailed cardinalfish (Ostorhinchus aureus) is a widespread fish species in the family Apogonidae found in the Red Sea and off East Africa to Papua
Ring-tailed_cardinalfish
Canadian professional wrestler (1948–1993)
defeated Gilles Poisson and Killer Kowalski to capture the Grand Prix Tag Team Championship. The team would continue into 1973, facing Poisson and Kowalksi
Dino_Bravo
Greek mythological artefact
she becomes engaged instead to a social upstart. The play by Philippe Poisson (1682–1743) was a one-act verse comedy first produced in 1729. There Mercury
Pandora's_box
Generalization of associativity properties
since found many applications, such as in deformation quantization of Poisson manifolds, the Deligne conjecture, or graph homology in the work of Maxim
Operad
Scottish professional wrestler
21 April 2005) was a Scottish professional wrestler, better known by the ring names Black Angus Campbell, Wild Angus, and Rasputin (whilst wearing a wrestling
Black_Angus_Campbell
Electromagnetic opposition to change
Aluminium ring moved by electromagnetic induction, thus demonstrating Lenz's law.
Lenz's_law
Theory for associative algebras over rings
homology (and cohomology) is a homology theory for associative algebras over rings. There is also a theory for Hochschild homology of certain functors. Hochschild
Hochschild_homology
(disambiguation), multiple people David Platt (disambiguation), multiple people David Poisson (disambiguation), multiple people David Pollock (disambiguation), multiple
List of people with given name David
List_of_people_with_given_name_David
Amazon satellite constellation and internet service
Successful Amazon Launch". newsroom.ulalaunch.com. Retrieved April 28, 2026. Poisson, Juliette (March 24, 2026). "Arianespace to launch another 32 Amazon Leo
Amazon_Leo
Historic pub in New York City
include Willa Cather, E.E. Cummings, Theodore Dreiser, William Faulkner, Ring Lardner, Edna St. Vincent Millay, Eugene O'Neill, John Dos Passos, and John
Chumley's
Area of mathematical analysis
and of the Poisson kernel, is often more delicate than Fourier methods alone can resolve. Thus questions about the convergence of Poisson integrals, the
Harmonic_analysis
English chemist and physicist (1791–1867)
breakthrough came when he wrapped two insulated coils of wire around an iron ring, and found that, upon passing a current through one coil, a momentary current
Michael_Faraday
Astronomical observatory in Chile
image. While it is possible to model and remove a streak, the residual Poisson noise lowers the signal-to-noise ratio of the corrected pixels too much
Vera_C._Rubin_Observatory
Theorem in queueing theory
come, first served discipline. A distributional relation for many FIFO/Poisson-class systems was derived by Keilson and Servi (1988) and further developed
Little's_law
Circular statistical graph of proportionality
the causes of mortality in the army in the East" by Florence Nightingale A ring chart, also known as a sunburst chart or a multilevel pie chart, is used
Pie_chart
Nigerian world champion boxer (1929–1971)
Tiger was inducted into the International Boxing Hall of Fame in 1991. The Ring magazine named him Fighter of the Year in 1962 and 1965, while the Boxing
Dick_Tiger
Titanium alloy
Retrieved 2026-07-14. SAE AMS4928W, Titanium Alloy Bars, Wire, Forgings, Rings, and Drawn Shapes 6Al - 4V Annealed, Warrendale, PA: SAE International,
Ti-6Al-4V
Medical imaging technique
distribution. Research has shown that Bayesian methods that involve a Poisson likelihood function and an appropriate prior probability (e.g., a smoothing
Positron_emission_tomography
2017 film by Bill Condon
Harry Potter film (Deathly Hallows – Part 2) and all three The Lord of the Rings films (which also starred Ian McKellen). It is currently the eighth-biggest
Beauty and the Beast (2017 film)
Beauty_and_the_Beast_(2017_film)
Formal power series
a counter-term to normalise the derivative operator acting on xn. The Poisson generating function of a sequence an is PG ( a n ; x ) = ∑ n = 0 ∞ a
Generating_function
Branch of discrete mathematics
via Google Books. Translation from Russian ed. White, Arthur T. (1987). "Ringing the Cosets". The American Mathematical Monthly. 94 (8): 721–746. doi:10
Combinatorics
Differential algebra
In abstract algebra, the Weyl algebras are abstracted from the ring of differential operators with polynomial coefficients. They are named after Hermann
Weyl_algebra
2019 death in custody in New York, US
Archived from the original on November 13, 2019. Retrieved November 13, 2019. Poisson, Jayme; Merlan, Anna (November 20, 2019). "Understanding the 'Jeffrey Epstein
Death_of_Jeffrey_Epstein
Mathematical transform that expresses a function of time as a function of frequency
which has Fourier series coefficients proportional to those samples by the Poisson summation formula: f P ( x ) ≜ ∑ n = − ∞ ∞ f ( x + n P ) = 1 P ∑ k = −
Fourier_transform
Product of numbers from 1 to n
Factorials are used extensively in probability theory, for instance in the Poisson distribution and in the probabilities of random permutations. In computer
Factorial
American professional wrestler (born 1955)
Don't Call Me Fake, on January 23, 2018. On April 28, 2020, Dark Side of the Ring aired a second season episode that focuses on Schultz's wrestling career
David Schultz (professional wrestler)
David_Schultz_(professional_wrestler)
Hard, dense and stiff chemical compound
strength of 344 MPa, an ultimate compression strength of about 2.7 GPa and a Poisson's ratio of 0.31 . The speed of a longitudinal pressure wave (the speed of
Tungsten_carbide
Algebraic structure used in theoretical physics
bracket, there may also be an "ordinary" product, thus giving rise to the Poisson superalgebra and the Gerstenhaber algebra. Such gradings are also observed
Lie_superalgebra
Equation of statistical mechanics
emerges from time-reversible microscopic laws. Vlasov equation The Vlasov–Poisson equation Landau kinetic equation Fokker–Planck equation Williams–Boltzmann
Boltzmann_equation
Mistress and advisor to Henry IV of France
York, NY: St. Martin's Publishing Group. p. 147. ISBN 978-1-250-14086-9. Poisson, Georges (2013). La Grande Histoire du Louvre. Perrin. p. 465. Desclozeaux
Gabrielle_d'Estrées
Concepts from linear algebra
general domains towards the end of the 19th century, while Poincaré studied Poisson's equation a few years later. At the start of the 20th century, David Hilbert
Eigenvalues_and_eigenvectors
History of research by Augustin-Jean Fresnel
to Robert H. Silliman, Poisson eventually accepted the wave theory shortly before his death in 1840. Among the French, Poisson's reluctance was an exception
Fresnel's_physical_optics
Discrete dynamical system on polygons in the projective plane and on their moduli space
link with the Poisson–Lie groups, dimer models and other so-called cluster-integrable systems. These methods allow to retrieve the Poisson bracket and Hamiltonians
Pentagram_map
List of albums by Michel Legrand
Winner (Un cœur gros comme ça) (1961) Retour a New York (1962) Comme un poisson dans l'eau (1962) Eva (1962) Une grosse tete (1962) My Life to Live (Vivre
Michel_Legrand_discography
Lithography using 13.5 nm UV light
measured for a 48 nm pitch EUV-printed metal pattern. With the natural Poisson distribution due to the random arrival and absorption times of the photons
EUV_lithography
English singer-songwriter (born 1988)
On 30 April 2012, a tribute to Adele was held at New York City's (Le) Poisson Rouge called Broadway Sings Adele, starring various Broadway actors such
Adele
6th-century BC tyrant of Samos
liturgique du thème de l'anneau jeté a la mer et retrouvé dans le ventre d'un poisson." In: Revue De L'histoire Des Religions 66 (1912): 49-80. Accessed May
Polycrates
Tower in Paris, France
Paris, Mayor Anne Hidalgo proposed keeping the Olympic rings on the tower permanently. The rings, which measure 95 feet (29 m) wide and 43 feet (13 m)
Eiffel_Tower
Extinct giant shark species
megalodon its scientific name in his seminal 1833–1843 work Recherches sur les poissons fossiles (Research on fossil fish). He named it Carcharias megalodon in
Megalodon
German mathematician (1805–1859)
at the Academy had also put Dirichlet in close contact with Fourier and Poisson, who raised his interest in theoretical physics, especially Fourier's analytic
Peter Gustav Lejeune Dirichlet
Peter_Gustav_Lejeune_Dirichlet
Town in New Brunswick, Canada
Things: The Monuments of Canada. Retrieved November 12, 2014. Cormier & Poisson 2009, pp. 138–139. "Local Governments Establishment Regulation – Local
Shediac
Awards ceremony for film, TV, and digital media of 2025
Sister Nancy Story Dale Heslip, Blue Rodeo: Lost Together Jean-François Poisson, Who Killed the Montreal Expos? Ali Weinstein, Your Tomorrow Larry Weinstein
14th_Canadian_Screen_Awards
Compact astronomical body
Archived from the original on 3 September 2019. Retrieved 28 June 2020. Poisson, Eric; Israel, Werner (1990). "Internal Structure of Black Holes". Physical
Black_hole
Chemical element with atomic number 74 (W)
industry makes rings of sintered tungsten carbide, tungsten carbide/metal composites, and also metallic tungsten. WC/metal composite rings use nickel as
Tungsten
Description of gravity using discrete values
gravity (NG) Newton's law of universal gravitation Gauss's law for gravity Poisson's equation for gravity History of gravitational theory General relativity
Quantum_gravity
Psychedelic drug
Better evidence was produced in 1965 by French pharmacologist Jacques Poisson, who isolated DMT as a sole alkaloid from leaves, provided and used by
Dimethyltryptamine
Line integral of the electric field
voltages. By Gauss's law, the potential can also be found to satisfy Poisson's equation: ∇ ⋅ E = ∇ ⋅ ( − ∇ V E ) = − ∇ 2 V E = ρ / ε 0 {\displaystyle
Electric_potential
Hexagonal lattice made of carbon atoms
These ripples, when amplified by vacancy defects, induce a negative Poisson's ratio into graphene, resulting in the thinnest auxetic material known
Graphene
German polymath and scholar (1777–1855)
a basic theory of magnetic potential, based on Lagrange, Laplace, and Poisson; it seems rather unlikely that he knew the previous works of George Green
Carl_Friedrich_Gauss
index theorems based on spectral triples and deformation quantization of Poisson structures. An elliptic operator D on a compact smooth manifold defines
Cyclic_homology
Branch of mathematics
In deformation quantization, the commutative algebra of functions on a Poisson manifold is replaced by a noncommutative product depending on a formal
Noncommutative_geometry
Equations describing classical electromagnetism
Kelvin Kirchhoff Larmor Lenz Liénard Lorentz Maxwell Neumann Ohm Ørsted Poisson Poynting Ritchie Savart Singer Steinmetz Tesla Thomson Volta Weber Wiechert
Maxwell's_equations
Study of discrete mathematical structures
polynomial rings over finite fields to be models of the affine spaces over that field, and letting subvarieties or spectra of other rings provide the
Discrete_mathematics
Street in Manhattan, New York
Richard Amos, brother of Charles Christopher Amos, member of the Culper Spy Ring in New York City during the American Revolutionary War Eva Amurri, actor
Christopher_Street
American animated film by Disney
D23. Retrieved April 30, 2026. Tobenkin, David (January 2, 1995). "Disney rings in the new year with Belle: Studio plans to launch FCC-friendly show based
Beauty and the Beast (1991 film)
Beauty_and_the_Beast_(1991_film)
Canadian professional wrestler (1932 – 1989)
December 28, 1989) was a Canadian professional wrestler, best known by his ring name Paddy Ryan, who competed in North American and international promotions
Earl_Patrick_Freeman
processes such as Poisson processes, Cox processes and binomial processes. If I {\displaystyle {\mathcal {I}}} is a generating ring of S {\displaystyle
Simple_point_process
Production of voltage by a varying magnetic field
on August 29, 1831, he wrapped two wires around opposite sides of an iron ring or "torus" (an arrangement similar to a modern toroidal transformer).[citation
Electromagnetic_induction
Analytic function on the upper half-plane with a certain behavior under the modular group
\lambda \Vert ^{2}z}} converges when Im(z) > 0, and as a consequence of the Poisson summation formula can be shown to be a modular form of weight n/2. It is
Modular_form
Topological space that locally resembles Euclidean space
19th century mathematics was analytical mechanics, as developed by Siméon Poisson, Jacobi, and William Rowan Hamilton. The possible states of a mechanical
Manifold
Rape of a single victim by two or more violators
Ramalingam (2013). "Informatics about fear to report rapes using bumped-up Poisson model". American Journal of Biostatistics. 3 (1): 17–29. doi:10.3844/amjbsp
Gang_rape
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