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Mohr–Mascheroni theorem Summary Mohr–Mascheroni_theorem In mathematics, the Mohr–Mascheroni theorem states that any geometric construction that can be performed by a compass and straightedge can be performed by a compass alone. It must be understood that "any geometric construction" refers to figures that contain no st... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Moore determinant of a Hermitian matrix Summary Moore_determinant_over_a_division_algebra In mathematics, the Moore determinant is a determinant defined for Hermitian matrices over a quaternion algebra, introduced by Moore (1922). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Moore plane Summary Moore_plane In mathematics, the Moore plane, also sometimes called Niemytzki plane (or Nemytskii plane, Nemytskii's tangent disk topology), is a topological space. It is a completely regular Hausdorff space (also called Tychonoff space) that is not normal. It is named after Robert Lee Moore and Vikt... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mordell–Weil theorem Summary Mordell–Weil_theorem In mathematics, the Mordell–Weil theorem states that for an abelian variety A {\displaystyle A} over a number field K {\displaystyle K} , the group A ( K ) {\displaystyle A(K)} of K-rational points of A {\displaystyle A} is a finitely-generated abelian group, called the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Morlet wavelet Summary Morlet_wavelet In mathematics, the Morlet wavelet (or Gabor wavelet) is a wavelet composed of a complex exponential (carrier) multiplied by a Gaussian window (envelope). This wavelet is closely related to human perception, both hearing and vision. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Morrey–Campanato space Summary Morrey–Campanato_space In mathematics, the Morrey–Campanato spaces (named after Charles B. Morrey, Jr. and Sergio Campanato) L λ , p ( Ω ) {\displaystyle L^{\lambda ,p}(\Omega )} are Banach spaces which extend the notion of functions of bounded mean oscillation, describing situations wher... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Morrey–Campanato space Summary Morrey–Campanato_space The seminorm of the Morrey spaces is given by ( λ , p ) p = sup 0 < r < diam ( Ω ) , x 0 ∈ Ω 1 r λ ∫ B r ( x 0 ) ∩ Ω | u ( y ) | p d y . {\displaystyle {\bigl (}_{\lambda ,p}{\bigr )}^{p}=\sup _{0 n {\displaystyle \lambda >n} , the space contains only the 0 funct... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Morrey–Campanato space Summary Morrey–Campanato_space The seminorm of the Campanato space is given by ( λ , p ) p = sup 0 < r < diam ( Ω ) , x 0 ∈ Ω 1 r λ ∫ B r ( x 0 ) ∩ Ω | u ( y ) − u r , x 0 | p d y {\displaystyle {\bigl (}_{\lambda ,p}{\bigr )}^{p}=\sup _{0 A r n {\displaystyle |\Omega \cap B_{r}(x_{0})|>Ar^{n}... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Morse–Palais lemma Summary Morse–Palais_lemma In mathematics, the Morse–Palais lemma is a result in the calculus of variations and theory of Hilbert spaces. Roughly speaking, it states that a smooth enough function near a critical point can be expressed as a quadratic form after a suitable change of coordinates. The Mo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mostow–Palais theorem Summary Mostow–Palais_theorem In mathematics, the Mostow–Palais theorem is an equivariant version of the Whitney embedding theorem. It states that if a manifold is acted on by a compact Lie group with finitely many orbit types, then it can be embedded into some finite-dimensional orthogonal repres... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Star product (quantization) Summary Star_product_(quantization) In mathematics, the Moyal product (after José Enrique Moyal; also called the star product or Weyl–Groenewold product, after Hermann Weyl and Hilbrand J. Groenewold) is an example of a phase-space star product. It is an associative, non-commutative product,... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Muller–Schupp theorem Summary Muller–Schupp_theorem In mathematics, the Muller–Schupp theorem states that a finitely generated group G has context-free word problem if and only if G is virtually free. The theorem was proved by David Muller and Paul Schupp in 1983. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Munn semigroup Summary Munn_semigroup In mathematics, the Munn semigroup is the inverse semigroup of isomorphisms between principal ideals of a semilattice (a commutative semigroup of idempotents). Munn semigroups are named for the Scottish mathematician Walter Douglas Munn (1929–2008). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Freedman–He–Wang conjecture Summary Möbius_energy In mathematics, the Möbius energy of a knot is a particular knot energy, i.e., a functional on the space of knots. It was discovered by Jun O'Hara, who demonstrated that the energy blows up as the knot's strands get close to one another. This is a useful property becaus... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Freedman–He–Wang conjecture Summary Möbius_energy They also showed the minimum energy of any knot conformation is achieved by a round circle.Conjecturally, there is no energy minimizer for composite knots. Robert B. Kusner and John M. Sullivan have done computer experiments with a discretized version of the Möbius ener... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Freedman–He–Wang conjecture Summary Möbius_energy For example, the inversion in the sphere { v ∈ R 3: | v − a | = ρ } {\displaystyle \{\mathbf {v} \in \mathbf {R} ^{3}\colon |\mathbf {v} -\mathbf {a} |=\rho \}} is defined by x → a + ρ 2 | x − a | 2 ⋅ ( x − a ) . {\displaystyle \mathbf {x} \to \mathbf {a} +{\rho ^{2} \o... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Freedman–He–Wang conjecture Summary Möbius_energy Define its energy by E ( γ ) = ∬ { 1 | γ ( u ) − γ ( v ) | 2 − 1 D ( γ ( u ) , γ ( v ) ) 2 } | γ ˙ ( u ) | | γ ˙ ( v ) | d u d v , {\displaystyle E(\gamma )=\iint \left\{{\frac {1}{|\gamma (u)-\gamma (v)|^{2}}}-{\frac {1}{D(\gamma (u),\gamma (v))^{2}}}\right\}|{\dot {\g... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Freedman–He–Wang conjecture Summary Möbius_energy Moreover, the energy of any line is 0, the energy of any circle is 4 {\displaystyle 4} . In fact, let us use the arc-length parameterization. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Freedman–He–Wang conjecture Summary Möbius_energy Denote by ℓ {\displaystyle \ell } the length of the curve γ {\displaystyle \gamma } . Then E ( γ ) = ∫ − ℓ / 2 ℓ / 2 d x ∫ x − ℓ / 2 x + ℓ / 2 d y . {\displaystyle E(\gamma )=\int _{-\ell /2}^{\ell /2}{}dx\int _{x-\ell /2}^{x+\ell /2}\leftdy.} Let γ 0 ( t ) = ( cos t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nagata's conjecture on algebraic curves Summary Nagata's_conjecture_on_curves In mathematics, the Nagata conjecture on curves, named after Masayoshi Nagata, governs the minimal degree required for a plane algebraic curve to pass through a collection of very general points with prescribed multiplicities. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nagata–Biran conjecture Summary Nagata–Biran_conjecture In mathematics, the Nagata–Biran conjecture, named after Masayoshi Nagata and Paul Biran, is a generalisation of Nagata's conjecture on curves to arbitrary polarised surfaces. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nagell–Lutz theorem Summary Nagell–Lutz_theorem In mathematics, the Nagell–Lutz theorem is a result in the diophantine geometry of elliptic curves, which describes rational torsion points on elliptic curves over the integers. It is named for Trygve Nagell and Élisabeth Lutz. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nakai conjecture Summary Nakai_conjecture In mathematics, the Nakai conjecture is an unproven characterization of smooth algebraic varieties, conjectured by Japanese mathematician Yoshikazu Nakai in 1961. It states that if V is a complex algebraic variety, such that its ring of differential operators is generated by th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Narasimhan–Seshadri theorem Summary Narasimhan–Seshadri_theorem In mathematics, the Narasimhan–Seshadri theorem, proved by Narasimhan and Seshadri (1965), says that a holomorphic vector bundle over a Riemann surface is stable if and only if it comes from an irreducible projective unitary representation of the fundament... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Narasimhan–Seshadri theorem Summary Narasimhan–Seshadri_theorem Donaldson (1983) gave another proof using differential geometry, and showed that the stable vector bundles have an essentially unique unitary connection of constant (scalar) curvature. In the degree zero case, Donaldson's version of the theorem says that a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Narumi polynomials Summary Narumi_polynomials In mathematics, the Narumi polynomials sn(x) are polynomials introduced by Narumi (1929) given by the generating function ∑ s n ( x ) t n / n ! = ( t log ( 1 + t ) ) a ( 1 + t ) x {\displaystyle \displaystyle \sum s_{n}(x)t^{n}/n!=\left({\frac {t}{\log(1+t)}}\right)^{a}(1... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
N-transform Summary N-transform In mathematics, the Natural transform is an integral transform similar to the Laplace transform and Sumudu transform, introduced by Zafar Hayat Khan in 2008. It converges to both Laplace and Sumudu transform just by changing variables. Given the convergence to the Laplace and Sumudu tran... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Navier–Stokes existence and smoothness The Navier–Stokes equations Navier–Stokes_existence_and_smoothness > The Navier–Stokes equations In mathematics, the Navier–Stokes equations are a system of nonlinear partial differential equations for abstract vector fields of any size. In physics and engineering, they are a syst... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Navier–Stokes existence and smoothness The Navier–Stokes equations Navier–Stokes_existence_and_smoothness > The Navier–Stokes equations Let v ( x , t ) {\displaystyle \mathbf {v} ({\boldsymbol {x}},t)} be a 3-dimensional vector field, the velocity of the fluid, and let p ( x , t ) {\displaystyle p({\boldsymbol {x}},t)}... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Navier–Stokes existence and smoothness The Navier–Stokes equations Navier–Stokes_existence_and_smoothness > The Navier–Stokes equations Since in three dimensions, there are three equations and four unknowns (three scalar velocities and the pressure), then a supplementary equation is needed. This extra equation is the c... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Navier–Stokes existence and smoothness The Navier–Stokes equations Navier–Stokes_existence_and_smoothness > The Navier–Stokes equations {\displaystyle \nabla \cdot \mathbf {v} =0.} Due to this last property, the solutions for the Navier–Stokes equations are searched in the set of solenoidal ("divergence-free") function... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Navier–Stokes existence and smoothness The Navier–Stokes equations Navier–Stokes_existence_and_smoothness > The Navier–Stokes equations For this flow of a homogeneous medium, density and viscosity are constants. Since only its gradient appears, the pressure p can be eliminated by taking the curl of both sides of the Na... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Navier–Stokes existence and smoothness The Navier–Stokes equations Navier–Stokes_existence_and_smoothness > The Navier–Stokes equations In this case the Navier–Stokes equations reduce to the vorticity-transport equations. Now, we are going to look at nonlinearity. The Navier–Stokes equations are nonlinear because the t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Navier–Stokes existence and smoothness The Navier–Stokes equations Navier–Stokes_existence_and_smoothness > The Navier–Stokes equations This means that the equations cannot be solved using traditional linear techniques, and more advanced methods must be used instead. Nonlinearity is important in the Navier–Stokes equat... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Navier–Stokes existence and smoothness The Navier–Stokes equations Navier–Stokes_existence_and_smoothness > The Navier–Stokes equations One way to understand the nonlinearity of the Navier–Stokes equations is to consider the term (v · ∇)v in the equations. This term represents the acceleration of the fluid, and it is a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Navier–Stokes existence and smoothness The Navier–Stokes equations Navier–Stokes_existence_and_smoothness > The Navier–Stokes equations The nonlinear nature of the Navier–Stokes equations can be seen in the term ( v ⋅ ∇ ) v {\displaystyle (\mathbf {v} \cdot \nabla )\mathbf {v} } , which represents the acceleration of t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Navier–Stokes existence and smoothness The Navier–Stokes equations Navier–Stokes_existence_and_smoothness > The Navier–Stokes equations The pressure in a fluid depends on the density and the gradient of the pressure, and this term is therefore nonlinear in the pressure. One example of the nonlinear nature of the Navier... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Navier–Stokes existence and smoothness The Navier–Stokes equations Navier–Stokes_existence_and_smoothness > The Navier–Stokes equations This results in a pressure gradient, with higher pressure near the obstacle and lower pressure farther away. To see this more explicitly, consider the case of a circular obstacle of ra... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Navier–Stokes existence and smoothness The Navier–Stokes equations Navier–Stokes_existence_and_smoothness > The Navier–Stokes equations The Navier–Stokes equations in this case are: ∂ v ∂ t + ( v ⋅ ∇ ) v = − 1 ρ ∇ p + ν Δ v {\displaystyle {\frac {\partial \mathbf {v} }{\partial t}}+(\mathbf {v} \cdot \nabla )\mathbf {v... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Navier–Stokes existence and smoothness The Navier–Stokes equations Navier–Stokes_existence_and_smoothness > The Navier–Stokes equations This results in a nonlinear term ( v ⋅ ∇ ) v {\displaystyle (\mathbf {v} \cdot \nabla )\mathbf {v} } in the Navier–Stokes equations that is proportional to the velocity of the fluid. A... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Navier–Stokes existence and smoothness The Navier–Stokes equations Navier–Stokes_existence_and_smoothness > The Navier–Stokes equations Since the velocity is higher near the obstacle, the mass flow rate through a surface near the obstacle will be higher than the mass flow rate through a surface farther away from the ob... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Navier–Stokes existence and smoothness The Navier–Stokes equations Navier–Stokes_existence_and_smoothness > The Navier–Stokes equations This system of ordinary differential equations can be solved using techniques such as the finite element method or spectral methods. Such method can be applied as: we can use a variety... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Neukirch–Uchida theorem Summary Neukirch–Uchida_theorem In mathematics, the Neukirch–Uchida theorem shows that all problems about algebraic number fields can be reduced to problems about their absolute Galois groups. Jürgen Neukirch (1969) showed that two algebraic number fields with the same absolute Galois group are ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Neumann boundary condition Summary Neumann_problem In mathematics, the Neumann (or second-type) boundary condition is a type of boundary condition, named after Carl Neumann. When imposed on an ordinary or a partial differential equation, the condition specifies the values of the derivative applied at the boundary of th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Neumann polynomial Summary Neumann_polynomial ( − α n − k ) ( 2 t ) n + 1 − 2 k , {\displaystyle O_{n}^{(\alpha )}(t)={\frac {\alpha +n}{2\alpha }}\sum _{k=0}^{\lfloor n/2\rfloor }(-1)^{n-k}{\frac {(n-k)!}{k! }}{-\alpha \choose n-k}\left({\frac {2}{t}}\right)^{n+1-2k},} and they have the "generating function" ( z 2 ) α... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Neumann–Dirichlet method Summary Neumann–Dirichlet_method In mathematics, the Neumann–Dirichlet method is a domain decomposition preconditioner which involves solving Neumann boundary value problem on one subdomain and Dirichlet boundary value problem on another, adjacent across the interface between the subdomains. On... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Neumann–Poincaré operator Summary Neumann–Poincaré_operator In mathematics, the Neumann–Poincaré operator or Poincaré–Neumann operator, named after Carl Neumann and Henri Poincaré, is a non-self-adjoint compact operator introduced by Poincaré to solve boundary value problems for the Laplacian on bounded domains in Eucl... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nevanlinna invariant Summary Nevanlinna_invariant In mathematics, the Nevanlinna invariant of an ample divisor D on a normal projective variety X is a real number connected with the rate of growth of the number of rational points on the variety with respect to the embedding defined by the divisor. The concept is named ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elementary symmetric mean Summary Elementary_symmetric_mean In mathematics, the Newton inequalities are named after Isaac Newton. Suppose a1, a2, ..., an are real numbers and let e k {\displaystyle e_{k}} denote the kth elementary symmetric polynomial in a1, a2, ..., an. Then the elementary symmetric means, given by S ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Newton polygon Summary Newton_polygon In mathematics, the Newton polygon is a tool for understanding the behaviour of polynomials over local fields, or more generally, over ultrametric fields. In the original case, the local field of interest was essentially the field of formal Laurent series in the indeterminate X, i.... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Newton polygon Summary Newton_polygon The exponents r {\displaystyle r} here are certain rational numbers, depending on the branch chosen; and the solutions themselves are power series in K ] {\displaystyle K]} with Y = X 1 d {\displaystyle Y=X^{\frac {1}{d}}} for a denominator d {\displaystyle d} corresponding to the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Newton polytope Summary Newton_polytope In mathematics, the Newton polytope is an integral polytope associated with a multivariate polynomial. It can be used to analyze the polynomial's behavior when specific variables are considered negligible relative to the others. Specifically, given a vector x = ( x 1 , … , x n ) ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Newton polytope Summary Newton_polytope {\displaystyle \operatorname {Newt} (f)=\left\{\sum _{k}\alpha _{k}\mathbf {a} _{k}:\sum _{k}\alpha _{k}=1\;\&\;\forall j\,\,\alpha _{j}\geq 0\right\}\!.} The Newton polytope satisfies the following homomorphism-type property: Newt ( f g ) = Newt ( f ) + Newt ( g ) {\displa... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Single layer potential Summary Newtonian_kernel In mathematics, the Newtonian potential or Newton potential is an operator in vector calculus that acts as the inverse to the negative Laplacian, on functions that are smooth and decay rapidly enough at infinity. As such, it is a fundamental object of study in potential t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Single layer potential Summary Newtonian_kernel In modern potential theory, the Newtonian potential is instead thought of as an electrostatic potential. The Newtonian potential of a compactly supported integrable function f is defined as the convolution where the Newtonian kernel Γ in dimension d is defined by Here ωd ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Single layer potential Summary Newtonian_kernel {\displaystyle \Gamma (x)=-1/(4\pi |x|).} The Newtonian potential w of f is a solution of the Poisson equation which is to say that the operation of taking the Newtonian potential of a function is a partial inverse to the Laplace operator. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Single layer potential Summary Newtonian_kernel Then w will be a classical solution, that is twice differentiable, if f is bounded and locally Hölder continuous as shown by Otto Hölder. It was an open question whether continuity alone is also sufficient. This was shown to be wrong by Henrik Petrini who gave an example ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Single layer potential Summary Newtonian_kernel The solution is not unique, since addition of any harmonic function to w will not affect the equation. This fact can be used to prove existence and uniqueness of solutions to the Dirichlet problem for the Poisson equation in suitably regular domains, and for suitably well... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Single layer potential Summary Newtonian_kernel It satisfies the Poisson equation in the sense of distributions. Moreover, when the measure is positive, the Newtonian potential is subharmonic on Rd. If f is a compactly supported continuous function (or, more generally, a finite measure) that is rotationally invariant, ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Single layer potential Summary Newtonian_kernel When the measure μ is associated to a mass distribution on a sufficiently smooth hypersurface S (a Lyapunov surface of Hölder class C1,α) that divides Rd into two regions D+ and D−, then the Newtonian potential of μ is referred to as a simple layer potential. Simple layer... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Noether inequality Summary Noether_inequality In mathematics, the Noether inequality, named after Max Noether, is a property of compact minimal complex surfaces that restricts the topological type of the underlying topological 4-manifold. It holds more generally for minimal projective surfaces of general type over an a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Noether's normalization lemma Summary Noether_normalization_lemma In mathematics, the Noether normalization lemma is a result of commutative algebra, introduced by Emmy Noether in 1926. It states that for any field k, and any finitely generated commutative k-algebra A, there exist algebraically independent elements y1,... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Noether's normalization lemma Summary Noether_normalization_lemma Then the inclusion map S ↪ A {\displaystyle S\hookrightarrow A} induces a surjective finite morphism of affine varieties X → A k d {\displaystyle X\to \mathbb {A} _{k}^{d}}: that is, any affine variety is a branched covering of affine space. When k is in... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Novikov–Veselov equation Summary Novikov–Veselov_equation In mathematics, the Novikov–Veselov equation (or Veselov–Novikov equation) is a natural (2+1)-dimensional analogue of the Korteweg–de Vries (KdV) equation. Unlike another (2+1)-dimensional analogue of KdV, the Kadomtsev–Petviashvili equation, it is integrable vi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Novikov–Veselov equation Summary Novikov–Veselov_equation The equation is named after S.P. Novikov and A.P. Veselov who published it in Novikov & Veselov (1984). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Néron–Ogg–Shafarevich criterion Summary Néron–Ogg–Shafarevich_criterion In mathematics, the Néron–Ogg–Shafarevich criterion states that if A is an elliptic curve or abelian variety over a local field K and ℓ is a prime not dividing the characteristic of the residue field of K then A has good reduction if and only if th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nørlund–Rice integral Summary Nørlund–Rice_integral In mathematics, the Nørlund–Rice integral, sometimes called Rice's method, relates the nth forward difference of a function to a line integral on the complex plane. It commonly appears in the theory of finite differences and has also been applied in computer science a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
O'Nan–Scott theorem Summary O'Nan–Scott_theorem In mathematics, the O'Nan–Scott theorem is one of the most influential theorems of permutation group theory; the classification of finite simple groups is what makes it so useful. Originally the theorem was about maximal subgroups of the symmetric group. It appeared as an... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
O'Nan–Scott theorem Summary O'Nan–Scott_theorem A complete version of the theorem with a self-contained proof was given by M.W. Liebeck, Cheryl Praeger and Jan Saxl. The theorem is now a standard part of textbooks on permutation groups. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Odlyzko–Schönhage algorithm Summary Odlyzko–Schönhage_algorithm In mathematics, the Odlyzko–Schönhage algorithm is a fast algorithm for evaluating the Riemann zeta function at many points, introduced by (Odlyzko & Schönhage 1988). The main point is the use of the fast Fourier transform to speed up the evaluation of a f... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Oka's coherence theorem Summary Oka_coherence_theorem In mathematics, the Oka coherence theorem, proved by Kiyoshi Oka (1950), states that the sheaf O := O C n {\displaystyle {\mathcal {O}}:={\mathcal {O}}_{\mathbb {C} _{n}}} of germs of holomorphic functions on C n {\displaystyle \mathbb {C} ^{n}} over a complex manif... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Ornstein isomorphism theorem Summary Bernoulli_flow In mathematics, the Ornstein isomorphism theorem is a deep result in ergodic theory. It states that if two Bernoulli schemes have the same Kolmogorov entropy, then they are isomorphic. The result, given by Donald Ornstein in 1970, is important because it states that m... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Ornstein–Uhlenbeck operator Summary Ornstein–Uhlenbeck_operator In mathematics, the Ornstein–Uhlenbeck operator is a generalization of the Laplace operator to an infinite-dimensional setting. The Ornstein–Uhlenbeck operator plays a significant role in the Malliavin calculus. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Ornstein–Uhlenbeck processes Summary Ornstein–Uhlenbeck_process In mathematics, the Ornstein–Uhlenbeck process is a stochastic process with applications in financial mathematics and the physical sciences. Its original application in physics was as a model for the velocity of a massive Brownian particle under the influe... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Ornstein–Uhlenbeck processes Summary Ornstein–Uhlenbeck_process The Ornstein–Uhlenbeck process is a stationary Gauss–Markov process, which means that it is a Gaussian process, a Markov process, and is temporally homogeneous. In fact, it is the only nontrivial process that satisfies these three conditions, up to allowin... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Ostrowski–Hadamard gap theorem Summary Ostrowski–Hadamard_gap_theorem In mathematics, the Ostrowski–Hadamard gap theorem is a result about the analytic continuation of complex power series whose non-zero terms are of orders that have a suitable "gap" between them. Such a power series is "badly behaved" in the sense tha... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Paley construction Summary Paley_construction In mathematics, the Paley construction is a method for constructing Hadamard matrices using finite fields. The construction was described in 1933 by the English mathematician Raymond Paley. The Paley construction uses quadratic residues in a finite field GF(q) where q is a ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Paley–Wiener integral Summary Paley–Wiener_integral In mathematics, the Paley–Wiener integral is a simple stochastic integral. When applied to classical Wiener space, it is less general than the Itō integral, but the two agree when they are both defined. The integral is named after its discoverers, Raymond Paley and No... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Paley–Zygmund inequality Summary Paley–Zygmund_inequality In mathematics, the Paley–Zygmund inequality bounds the probability that a positive random variable is small, in terms of its first two moments. The inequality was proved by Raymond Paley and Antoni Zygmund. Theorem: If Z ≥ 0 is a random variable with finite var... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Paley–Zygmund inequality Summary Paley–Zygmund_inequality Proof: First, E = E } ] + E } ] . {\displaystyle \operatorname {E} =\operatorname {E} \}}]+\operatorname {E} \}}].} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Paley–Zygmund inequality Summary Paley–Zygmund_inequality The first addend is at most θ E {\displaystyle \theta \operatorname {E} } , while the second is at most E 1 / 2 P ( Z > θ E ) 1 / 2 {\displaystyle \operatorname {E} ^{1/2}\operatorname {P} (Z>\theta \operatorname {E} )^{1/2}} by the Cauchy–Schwarz ine... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pansu derivative Summary Pansu_derivative In mathematics, the Pansu derivative is a derivative on a Carnot group, introduced by Pierre Pansu (1989). A Carnot group G {\displaystyle G} admits a one-parameter family of dilations, δ s: G → G {\displaystyle \delta _{s}\colon G\to G} . If G 1 {\displaystyle G_{1}} and G 2 {... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Parker–Sochacki method Summary Parker–Sochacki_method In mathematics, the Parker–Sochacki method is an algorithm for solving systems of ordinary differential equations (ODEs), developed by G. Edgar Parker and James Sochacki, of the James Madison University Mathematics Department. The method produces Maclaurin series so... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Parry–Daniels map Summary Parry–Daniels_map In mathematics, the Parry–Daniels map is a function studied in the context of dynamical systems. Typical questions concern the existence of an invariant or ergodic measure for the map.It is named after the English mathematician Bill Parry and the British statistician Henry Da... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Parry–Sullivan invariant Summary Parry–Sullivan_invariant In mathematics, the Parry–Sullivan invariant (or Parry–Sullivan number) is a numerical quantity of interest in the study of incidence matrices in graph theory, and of certain one-dimensional dynamical systems. It provides a partial classification of non-trivial ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Parseval–Gutzmer formula Summary Parseval–Gutzmer_formula In mathematics, the Parseval–Gutzmer formula states that, if f {\displaystyle f} is an analytic function on a closed disk of radius r with Taylor series f ( z ) = ∑ k = 0 ∞ a k z k , {\displaystyle f(z)=\sum _{k=0}^{\infty }a_{k}z^{k},} then for z = reiθ on the ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Peano surface Summary Peano_surface In mathematics, the Peano surface is the graph of the two-variable function f ( x , y ) = ( 2 x 2 − y ) ( y − x 2 ) . {\displaystyle f(x,y)=(2x^{2}-y)(y-x^{2}).} It was proposed by Giuseppe Peano in 1899 as a counterexample to a conjectured criterion for the existence of maxima and m... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Jordan measure Summary Jordan_measure In mathematics, the Peano–Jordan measure (also known as the Jordan content) is an extension of the notion of size (length, area, volume) to shapes more complicated than, for example, a triangle, disk, or parallelepiped. It turns out that for a set to have Jordan measure it should b... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Jordan measure Summary Jordan_measure For historical reasons, the term Jordan measure is now well-established for this set function, despite the fact that it is not a true measure in its modern definition, since Jordan-measurable sets do not form a σ-algebra. For example, singleton sets { x } x ∈ R {\displaystyle \{x\}... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pearcey integral Summary Pearcey_integral In mathematics, the Pearcey integral is defined as Pe ( x , y ) = ∫ − ∞ ∞ exp ( i ( t 4 + x t 2 + y t ) ) d t . {\displaystyle \operatorname {Pe} (x,y)=\int _{-\infty }^{\infty }\exp(i(t^{4}+xt^{2}+yt))\,dt.} The Pearcey integral is a class of canonical diffraction integral... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pell numbers Summary Pell_number In mathematics, the Pell numbers are an infinite sequence of integers, known since ancient times, that comprise the denominators of the closest rational approximations to the square root of 2. This sequence of approximations begins 1/1, 3/2, 7/5, 17/12, and 41/29, so the sequence of Pel... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pell numbers Summary Pell_number Both the Pell numbers and the companion Pell numbers may be calculated by means of a recurrence relation similar to that for the Fibonacci numbers, and both sequences of numbers grow exponentially, proportionally to powers of the silver ratio 1 + √2. As well as being used to approximate... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Perkel graph Summary Perkel_graph In mathematics, the Perkel graph, named after Manley Perkel, is a 6-regular graph with 57 vertices and 171 edges. It is the unique distance-regular graph with intersection array (6, 5, 2; 1, 1, 3). The Perkel graph is also distance-transitive. It is also the skeleton of an abstract reg... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Perrin pseudoprime Summary Perrin_numbers In mathematics, the Perrin numbers are defined by the recurrence relation P(n) = P(n − 2) + P(n − 3) for n > 2,with initial values P(0) = 3, P(1) = 0, P(2) = 2.The sequence of Perrin numbers starts with 3, 0, 2, 3, 2, 5, 5, 7, 10, 12, 17, 22, 29, 39, ... (sequence A001608 in th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Peters polynomials Summary Peters_polynomials In mathematics, the Peters polynomials sn(x) are polynomials studied by Peters (1956, 1956b) given by the generating function ∑ n = 0 + ∞ s n ( x ) t n n ! = ( 1 + t ) x ( 1 + ( 1 + t ) λ ) μ {\displaystyle \displaystyle \sum _{n=0}^{+\infty }s_{n}(x){\frac {t^{n}}{n! }}={\... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Peterson–Stein formula Summary Peterson–Stein_formula In mathematics, the Peterson–Stein formula, introduced by Franklin P. Peterson and Norman Stein (1960), describes the Spanier–Whitehead dual of a secondary cohomology operation. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Peter–Weyl theorem Summary Peter-Weyl_theorem In mathematics, the Peter–Weyl theorem is a basic result in the theory of harmonic analysis, applying to topological groups that are compact, but are not necessarily abelian. It was initially proved by Hermann Weyl, with his student Fritz Peter, in the setting of a compact ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Peter–Weyl theorem Summary Peter-Weyl_theorem Let G be a compact group. The theorem has three parts. The first part states that the matrix coefficients of irreducible representations of G are dense in the space C(G) of continuous complex-valued functions on G, and thus also in the space L2(G) of square-integrable funct... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Peter–Weyl theorem Summary Peter-Weyl_theorem The second part asserts the complete reducibility of unitary representations of G. The third part then asserts that the regular representation of G on L2(G) decomposes as the direct sum of all irreducible unitary representations. Moreover, the matrix coefficients of the irr... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weak integral Summary Weak_integral In mathematics, the Pettis integral or Gelfand–Pettis integral, named after Israel M. Gelfand and Billy James Pettis, extends the definition of the Lebesgue integral to vector-valued functions on a measure space, by exploiting duality. The integral was introduced by Gelfand for the c... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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