42,772 articles
Highland
A highland is a broad elevated region of hills, mountains, or plateau standing above surrounding lowland; no universal altitude defines it, only elevation, relief, and contrast with neighboring lowlands.
Highly accelerated life test
A highly accelerated life test (HALT) is a qualitative reliability engineering method that stresses electronics with extreme temperatures and vibration to expose design weaknesses, without predicting product life.
Highly charged ion
A highly charged ion is an atom stripped of many or all of its electrons, serving as a laboratory for quantum electrodynamics, plasma diagnostics, and next-generation optical clocks.
Highly charged ion optical clock
A highly charged ion optical clock is an atomic clock using an ion with many electrons removed; the first, based on Ar¹³⁺, was demonstrated in 2022.
Highly composite number
A highly composite number, also called an anti-prime or maximally divisible number, is a positive integer with more divisors than any smaller one, first analyzed by Ramanujan in 1915.
Highstand systems tract
The highstand systems tract (HST) is, in sequence stratigraphy, the upper tract of a sequence, deposited when high, slowly rising sea level lets sediment supply outpace accommodation.
Hiʻiaka (moon)
Hiʻiaka is the outer and larger of Haumea's two known moons, discovered in 2005 and named for the Hawaiian goddess of Hawaii island and hula dancers.
Hijri year (التقويم الهجري)
The Hijri year (التقويم الهجري), also called Anno Hegirae, is the year of the Islamic lunar calendar, counted from the Hijra of 622 CE and designated AH.
Hikurangi subduction margin
The Hikurangi subduction margin is the plate boundary off New Zealand's East Coast where the Pacific plate subducts beneath the Australian plate, a major earthquake and tsunami hazard source.
Hilbert C*-module
A Hilbert C-module is a right module over a C-algebra with an algebra-valued inner product, generalizing Hilbert spaces and central to KK-theory and noncommutative geometry.
Hilbert class field
The Hilbert class field of a number field K is its unique maximal unramified abelian extension, with Galois group isomorphic to K's ideal class group.
Hilbert cube
The Hilbert cube is the compact subset of the Hilbert space l₂ whose coordinates are bounded by (1/2)ⁿ, a standard model space in infinite-dimensional topology.
Hilbert curve
The Hilbert curve is a continuous, nowhere differentiable space-filling fractal curve described by David Hilbert in 1891, whose locality makes it a standard tool for indexing multidimensional data in databases and geospatial systems.
Hilbert matrix
The Hilbert matrix is the square matrix with entries 1/(i + j − 1), the standard example of a badly ill-conditioned matrix in numerical linear algebra.
Hilbert scheme
The Hilbert scheme is a fundamental parameter space in algebraic geometry that parametrizes fixed closed sub-schemes of a scheme or projective space having a fixed Hilbert polynomial.
Hilbert space
A Hilbert space is a complete vector space with an inner product, formulated from David Hilbert's work on integral equations and central to quantum mechanics and signal processing.
Hilbert space fragmentation
Hilbert space fragmentation is a phenomenon in quantum many-body physics where an interacting system's Hilbert space splits into exponentially many dynamically disconnected Krylov sectors, letting clean systems evade thermalization.
Hilbert symbol
The Hilbert symbol, also called the norm residue symbol, is a pairing on a local field that tests whether an element is a norm, central to reciprocity laws.
Hilbert system
The Hilbert system, also called the Hilbert calculus, is a formal proof system for logic with many axiom schemas and few rules, usually just modus ponens.
Hilbert transform
The Hilbert transform is a linear integral operator, named for David Hilbert, that shifts each frequency component of a signal in phase by 90 degrees.
Hilbert-space formulation of quantum states
In the Hilbert-space formulation of quantum mechanics, a physical state is a ray in a complex Hilbert space, unifying Schrödinger's wave mechanics and Heisenberg's matrix mechanics.
Hilbert–Bernays provability conditions
The Hilbert–Bernays provability conditions, given by Hilbert and Bernays in Grundlagen der Mathematik (1939), are conditions on a formalized provability predicate sufficient for proving Gödel's second incompleteness theorem.
Hilbert–Pólya conjecture
The Hilbert–Pólya conjecture in number theory proposes that the Riemann zeta function's non-trivial zeros are eigenvalues of a self-adjoint operator, which would prove the Riemann hypothesis.
Hilbert's axioms
Hilbert's axioms, also called Hilbert's axiom system, are a rigorous axiomatization of Euclidean geometry presented by David Hilbert in his 1899 monograph Grundlagen der Geometrie.
Hilbert's basis theorem
Hilbert's basis theorem is a theorem of David Hilbert, proved in 1890, stating that if a ring R is Noetherian, then the polynomial ring R[x] is also Noetherian.
Hilbert's fifth problem
Hilbert's fifth problem, posed by David Hilbert in 1900, asks whether every locally Euclidean topological group is a Lie group, answered affirmatively in 1952 by Gleason, Montgomery, and Zippin.
Hilbert's Nullstellensatz
Hilbert's Nullstellensatz, German for "zero locus theorem," is David Hilbert's 1893 theorem bridging commutative algebra and algebraic geometry: over an algebraically closed field, ideals of polynomials correspond precisely to the sets of their common zeros.
Hilbert's paradox of the Grand Hotel
Hilbert's paradox of the Grand Hotel, also known as Hilbert's Hotel, is a thought experiment in which a fully occupied infinite hotel still makes room for new guests.
Hilbert's problems
Hilbert's problems, also listed as the List of Hilbert's problems, are 23 mathematical problems David Hilbert presented at the 1900 Paris congress; several, including the Riemann Hypothesis, remain unsolved.
Hilbert's program
Hilbert's program was David Hilbert's 1920s proposal to secure mathematics by proving formal axiomatic systems consistent using finitary methods; Gödel's incompleteness theorems showed it could not succeed.