42,772 articles
Klaus Wagner
Klaus Wagner (1910–2000) was a German mathematician who worked in graph theory, known for his 1937 planarity theorem and his conjecture proved by Robertson and Seymour.
Kleene star
The Kleene star, also called Kleene closure, is an operation that maps a language L to all strings formed by concatenating zero or more strings from L.
Kleene's O
Kleene's O is a set of natural numbers, called ordinal notations, that names the constructive ordinals; it was introduced by Stephen Cole Kleene in 1938.
Kleene's recursion theorem
Kleene's recursion theorem, also called the fixed point theorem, is a result in computability theory published by Stephen Kleene in 1938, implying self-reproducing programs called quines.
Klein bottle
The Klein bottle is a closed, one-sided surface with no inside or outside, described by Felix Klein in 1882 and impossible to place in space without self-intersection.
Klein four-group
The Klein four-group is the smallest non-cyclic group, a 4-element abelian group in which every element is its own inverse, isomorphic to C2 × C2.
Klein tunneling of light
Klein tunneling of light is the optical analog of the relativistic quantum effect in which light crosses a barrier with perfect transmission, realized through refractive-index patterning in photonic systems.
Klein–Gordon equation
The Klein–Gordon equation is the relativistic wave equation for free spinless particles, proposed in 1926 and describing scalar particles like the pion and Higgs boson.
Klein–Nishina formula
The Klein–Nishina formula, also called the Klein–Nishina cross section, is the quantum-mechanical expression for the differential cross section of Compton scattering, derived by Oskar Klein and Yoshio Nishina in 1928.
Kleinian group
A Kleinian group is a discrete group of Möbius transformations of the sphere, equivalently isometries of hyperbolic 3-space, created by Poincaré and Klein in the 1880s.
Kleisli category
A Kleisli category is a category built from a monad, keeping the base category's objects and taking morphisms X to Y to be morphisms X to T(Y).
Klerksdorp sphere
Klerksdorp spheres, also called Ottosdal objects, are small pyrite concretions in 3-billion-year-old rock near Ottosdal, South Africa, often promoted as out-of-place artifacts despite geologists classifying them as natural.
Klimaschutzgesetz
The Klimaschutzgesetz, formally the Bundes-Klimaschutzgesetz, is a German federal law enacted in 2019 that sets binding greenhouse gas targets, including 65% below 1990 levels by 2030.
KLM protocol
The KLM protocol is a 2001 scheme for quantum computation using only linear optical elements, single-photon sources, and photo-detectors, proposed by Knill, Laflamme, and Milburn in a Nature paper.
Kloosterman sum
A Kloosterman sum is an exponential sum over invertible residues modulo an integer, introduced by Hendrik Kloosterman in 1926 to represent integers by quaternary quadratic forms.
Klystron
A klystron, also called a klystron tube, is a vacuum tube that amplifies signals at microwave frequencies by velocity-modulating an electron beam, used in radar and particle accelerators.
KM3NeT
KM3NeT (Cubic Kilometre Neutrino Telescope) is a European research infrastructure of deep-sea neutrino detectors in the Mediterranean, operating ARCA off Sicily and ORCA off Toulon, France.
KMS state
A KMS state, also known as a KMS condition, is a state on a C-algebra with time evolution whose analytic boundary condition characterizes thermal equilibrium at inverse temperature beta.
Knapsack problem
The knapsack problem, also called the rucksack problem, is a combinatorial optimization problem in which the most valuable items are packed within a fixed capacity, solvable by dynamic programming.
Kneser graph
The Kneser graph K(n, k) has the k-subsets of {1, ..., n} as vertices, with edges between disjoint sets; introduced by Lovász in 1978, K(5, 2) is the Petersen graph.
Knight's tour
A knight's tour, or knight's tour problem, is a sequence of chess knight moves visiting every square exactly once; a closed tour returns a knight's move from the start.
Knill error correction
Knill error correction is a fault-tolerant quantum error correction method proposed by Emanuel Knill, which corrects an encoded quantum state by teleporting it through a verified Bell state.
Knizhnik–Zamolodchikov equations
The Knizhnik–Zamolodchikov equations, or KZ equations, are a holonomic system of linear partial differential equations written down by Vladimir Knizhnik and Alexander Zamolodchikov in 1984 for conformal blocks of the Wess–Zumino–Witten model.
Knockout reactions
A knockout reaction is a direct nuclear reaction in which a projectile such as a proton or electron ejects a nucleon from a nucleus, revealing how that particle was bound.
Knoevenagel condensation
The Knoevenagel condensation is an organic reaction in which an active methylene compound condenses with an aldehyde or ketone to form a carbon–carbon double bond, typically an α,β-unsaturated carbonyl.
Knoevenagel reaction
The Knoevenagel reaction is an organic condensation in which an activated methylene compound adds to an aldehyde or ketone and loses water to give an electron-poor alkene.
Knot (unit)
The knot, historically called the Admiralty Knot, is a unit of speed equal to one nautical mile per hour, about 1.15 mph, used worldwide in maritime and air navigation.
Knot theory
Knot theory, also called the theory of knots, is the branch of mathematics studying closed loops in 3-dimensional space, asking when two knots are equivalent without cutting.
Knowledge base
A knowledge base is a structured store of facts, rules, and relationships that computers query and reason over, spanning expert systems like MYCIN and modern knowledge graphs such as Google's.
Knowledge in pieces
Knowledge in pieces (KiP) is an epistemological perspective in physics education research, begun by Andrea diSessa in 1983, holding that intuitive physics knowledge consists of many small, context-sensitive elements.