Hilbert's basis theorem, in commutative algebra, stating every ideal in the ring of multivariate polynomials over a Noetherian ring is finitely generated
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Hilbert's irreducibility theorem, in number theory, concerning irreducible polynomials
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Hilbert's syzygy theorem, a result of commutative algebra in connection with the syzygy problem of invariant theory
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Hilbert's Theorem 90, an important result on cyclic extensions of fields that leads to Kummer theory
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Hilbert's Nullstellensatz, the basis of abstract algebra, establishing a fundamental relationship between geometry and algebra
David Hilbert | Liouville's theorem | Hilbert space | Chinese remainder theorem | Hilbert | Shannon–Hartley theorem | Quillen–Suslin theorem | Nyquist–Shannon sampling theorem | Hilbert transform | Hahn–Banach theorem | Fermat's Last Theorem | Buckingham π theorem | Thue–Siegel–Roth theorem | Szemerédi's theorem | Schottky's theorem | Rodrigo Hilbert | Riemann-Roch theorem | Pythagorean theorem | Nash embedding theorem | Müntz–Szász theorem | Malgrange–Ehrenpreis theorem | Kleene fixed-point theorem | Kakutani fixed-point theorem | Hilbert van der Duim | Hilbert's problems | Hilbert cube | Hilbert Circle Theatre | Gauss–Bonnet theorem | Doob's martingale convergence theorem | Dirichlet's theorem on arithmetic progressions |
Both appeared, alongside several other important theorems, in a well-known paper by József Beck.
Ciprian Foiaş, Béla Szőkefalvi-Nagy: Analyse harmonique des opérateurs de l'espace de Hilbert.
For the theorem named after Felix Bloch on wave functions of a particle in a periodic potential, see Bloch wave.
But it was proven much earlier by Yusuf Al-Mu'taman ibn Hűd, an eleventh-century king of Zaragoza.
Because this constraint is nonholonomic, Liouville's theorem does not apply, and although energy is conserved, the motion is dissipative in the sense that phase space volume is not conserved.
Probably Gauss first realized this, and used it to prove the impossibility of some constructions; only much later did Hilbert find a complete set of axioms for geometry.
The constant is irrational; this can be proven with Dirichlet's theorem on arithmetic progressions or Bertrand's postulate (Hardy and Wright, p. 113) or Ramare's theorem that every even integer is a sum of at most six primes.
In a 1969 paper, Dutch mathematician Nicolaas Govert de Bruijn proved several results about packing congruent rectangular bricks (of any dimension) into larger rectangular boxes, in such a way that no space is left over.
In 2008, he handled the play-by-play duties for the Wisconsin Interscholastic Athletic Association Division 7 championship game played at Camp Randall Stadium in Madison, Wisconsin, between Hilbert and Burlington Catholic Central.
Ajtai and Szemerédi proved the corners theorem, an important step toward higher dimensional generalizations of the Szemerédi theorem.
Shape theory: Many shape invariants (Borsuk groups, Quigley inward and approaching groups) of a compact metric space can be obtained as exterior homotopy groups of the exterior space determined by the open neighborhoods of a compact metric space embedded in the Hilbert cube.
Heiko Harborth raised the question of whether every planar graph has a straight line representation in which all edge lengths are integers.
The works of 17th century mathematician Pierre de Fermat engendered many theorems.
The trail begins at the CityDeck in Green Bay, Wisconsin, follows the Fox River south through De Pere, then deviatiating east, away from the river, were it follows a former railroad bed through Rockland, Wrightstown, Greenleaf, Holland, and ends at Ott Road in Hilbert.
The Gelfond–Schneider theorem answers affirmatively Hilbert's seventh problem.
While gravitational lensing preserves surface brightness, as dictated by Liouville's theorem, lensing does change the apparent solid angle of a source.
For maximal planar graphs, in which every face is a triangle, a greedy planar embedding can be found by applying the Knaster–Kuratowski–Mazurkiewicz lemma to a weighted version of a straight-line embedding algorithm of Schnyder.
The mathematical transform which shifts the phase of all components of some function by is called a Hilbert transform; the components of the magnetization vector can therefore be any Hilbert transform pair (the simplest of which is simply
Cousin's theorem states that for every gauge , such a -fine partition P does exist, so this condition cannot be satisfied vacuously.
Hilbert C*-modules were first introduced in the work of Irving Kaplansky in 1953, which developed the theory for commutative, unital algebras (though Kaplansky observed that the assumption of a unit element was not "vital").
The Hilbert spectrum (sometimes referred to as the Hilbert amplitude spectrum), named after David Hilbert, is a statistical tool that can help in distinguishing among a mixture of moving signals.
Hilbert van der Duim became World Allround Champion in 1980, being the first skater in four years to beat Eric Heiden in international competition.
In mathematical logic, the Hilbert–Bernays provability conditions, named after David Hilbert and Paul Bernays, are a set of requirements for formalized provability predicates in formal theories of arithmetic (Smith 2007:224).
Since the 1960s, following the work of Arthur Wightman and Rudolf Haag, also modern quantum field theory can be considered close to an axiomatic description.
Kellogg's theorem is a pair of related results in the mathematical study of the regularity of harmonic functions on sufficiently smooth domains by Oliver Dimon Kellogg.
This result may also be known as the Kolmogorov theorem; see Kolmogorov's theorem for disambiguation.
Kōmura's theorem, result on the differentiability of absolutely continuous Banach space-valued functions
The following lemma is usually known as Liouville's theorem (on diophantine approximation), there being several results known as Liouville's theorem.
For example, the first version of Montel's theorem stated above is the analog of Liouville's theorem, while the second version corresponds to Picard's theorem.
Morley's categoricity theorem, a theorem related to model theory, discovered by Michael D. Morley
Morton Shelly Hilbert (January 3, 1917 - December 24, 1998) was a professor of public health, environmentalist, and co-founder of Earth Day.
The problem of finding their solutions is equivalent to the Hilbert's tenth problem that is proven to be algorithmically unsolvable.
In 1900, David Hilbert posed the problem of proving their consistency using only finitistic methods as the second of his twenty-three problems.
In the 1990s, Alex Wilkie showed that one has the same result if instead of adding every analytic function, one just adds the exponential function to R to get the ordered real field with exponentiation, Rexp, a result known as Wilkie's theorem.
Poynting's theorem on conservation of energy in electromagnetic field
Then, for any sets U and V, by the Chinese remainder theorem, the numbers that are quadratic resides modulo every prime in U and nonresidues modulo every prime in V form a periodic sequence, so by Dirichlet's theorem on primes in arithmetic progressions this number-theoretic graph has the extension property.
Brauer's theorem on the representability of zero by forms over certain fields in sufficiently many variables
The theorem for compact Riemann surfaces can be deduced from the algebraic version using Chow's theorem and the GAGA principle: in fact, every compact Riemann surface is defined by algebraic equations in some complex projective space.
Theodor Estermann (1902–1991) proved in his book Complex Numbers and Functions the following relation: Let be a bounded region with continuous boundary .
In computational complexity theory, Savitch's theorem, proved by Walter Savitch in 1970, gives a relationship between deterministic and non-deterministic space complexity.
Stagnation zones theorems are closely related to pre-Liouville's theorems about evaluation of solutions fluctuation, which direct consequences are the different versions of the classic Liouville theorem about conversion of the entire doubly periodic function into the identical constant.
Syamadas Mukhopadhyaya (June 22, 1866 – May 8, 1937) was an Indian mathematician who introduced the four-vertex theorem and Mukhopadhyaya's theorem in plane geometry.
An earlier version of the result is already mentioned in 1671 by James Gregory.
The theorem was independently derived in 1853 by the German scientist Hermann von Helmholtz and in 1883 by Léon Charles Thévenin (1857–1926), an electrical engineer with France's national Postes et Télégraphes telecommunications organization.
WIS 57 was rerouted onto its current alignment between Hilbert and Askeaton in 1932, replacing a former routing to Hollandtown; the original routing was replaced by county roads.