edgepedia

Physical world and mathematics

42,772 articles

Gallium selenide

Gallium selenide (GaSe) is a layered semiconductor crystal, known since 1934, used for infrared and terahertz laser frequency conversion and studied as a two-dimensional optoelectronic material.

Gallium sulfide

Gallium sulfide (GaS) is a layered III–VI monochalcogenide semiconductor with a bulk band gap of 2.35 eV that widens above 3 eV in monolayer form, studied for photodetectors, transistors, and catalysis.

Gallium-67

Gallium-67 is a radioactive isotope of gallium with a 78.3-hour half-life, used since 1969 in gallium scintigraphy to image tumors and inflammation, later displaced largely by FDG PET.

Gallium-68

Gallium-68 (^68Ga) is a positron-emitting radioactive isotope of gallium with a half-life of about 68 minutes, used to label PET tracers for neuroendocrine tumors and prostate cancer.

Gallium(III) oxide

Gallium(III) oxide (Ga₂O₃) is a compound of gallium and oxygen whose stable β phase has a roughly 4.8 eV bandgap and melt-grown crystals, enabling high-voltage power devices and solar-blind ultraviolet detection.

Gallon

The gallon is a unit of volume in the British imperial and US customary systems, with the US gallon of 3.785 liters and the imperial gallon of 4.546 liters.

Galois cohomology

Galois cohomology is the cohomology theory of Galois groups, the right derived functors of the invariants functor, central to class field theory, the Brauer group, and Wiles's proof of Fermat's last theorem.

Galois connection

A Galois connection, also known as a Galois correspondence, is a pair of monotone maps between partially ordered sets where f(p) ≤ q holds exactly when p ≤ g(q), named for Évariste Galois.

Galois cover

A Galois cover is a cover of curves or schemes whose function field extension is a Galois extension, equivalently one with a transitive group of deck transformations.

Galois extension

A Galois extension is an algebraic field extension that is both normal and separable, equivalently the splitting field of a separable polynomial over the base field.

Galois group

A Galois group is the group of automorphisms of a field extension fixing the base field, introduced by Évariste Galois to study when equations are solvable by radicals.

Galois module

A Galois module, also known as a Galois representation, is an abelian group with a compatible action of a Galois group; the term also names the theory of rings of integers.

Galois representation

A Galois representation is a continuous homomorphism from the absolute Galois group of a field to invertible matrices, central to Wiles's proof of Fermat's last theorem.

Galois theory

Galois theory is the branch of algebra, created by Évariste Galois, that associates to each field extension a Galois group and proves that general polynomial equations of degree 5 and higher cannot be solved by radicals.

Galton–Watson process

The Galton–Watson process, or Bienaymé–Galton–Watson process, is a branching process in which each individual independently produces offspring from one fixed distribution, posed by Galton in 1873.

Galvani potential

The Galvani potential is the inner electric potential of a phase, the electrostatic potential a charged particle experiences inside it; it cannot be measured directly except between phases of identical composition.

Galvanic cell

A galvanic cell, also called a voltaic cell, is an electrochemical cell in which a spontaneous chemical reaction generates electrical energy; batteries and fuel cells are examples.

Galvanic corrosion

Galvanic corrosion, also called dissimilar-metal corrosion, is the accelerated corrosion of the more active of two dissimilar metals in electrical contact within a common electrolyte; a small anode against a large cathode corrodes most severely.

Galvanic replacement reaction

The galvanic replacement reaction is an electrochemical method in materials chemistry in which a more noble metal salt dissolves a less noble nanostructure, forming hollow particles like gold nanocages.

Galvanism

Galvanism, or galvanic stimulation, is the application of electric current to living tissue to make muscles contract, named for Luigi Galvani's 1791 experiments on frog legs in Bologna.

Galvanostatic intermittent titration technique

The galvanostatic intermittent titration technique (GITT) is an electrochemical method introduced by Weppner and Huggins in 1977 that applies current pulses to a battery electrode to measure chemical diffusion coefficients.

Gambler's fallacy

The gambler's fallacy, also called the Monte Carlo fallacy, is the mistaken belief that an outcome absent from a random sequence becomes more likely on the next trial.

Gambler's ruin

Gambler's ruin is a classical probability problem in which a gambler makes repeated unit bets, and the question is whether the fortune reaches a target before zero.

Gamchen

Gamchen (Вулкан Гамчен, Sopka Khamchenskaya) is a complex of four stratovolcanoes in Kamchatka's Eastern Volcanic Arc, 2,539 m high, last erupting 188 BCE (VEI 3), with fumaroles and a UNESCO setting.

Game semantics

Game semantics is a style of denotational semantics interpreting types as games and programs as strategies, arising in the early 1990s from the full abstraction problem for PCF.

Game theory

Game theory is the mathematical study of strategic interaction, a family of models founded on von Neumann's 1928 minimax theorem and Nash's 1950 equilibrium, now central to economics.

Gamma Aquilae

Gamma Aquilae, better known by its proper name Tarazed, is an orange bright giant star in Aquila and the constellation's second brightest star after Altair, about 395 light-years away.

Gamma Cassiopeiae

Gamma Cassiopeiae (Gamma Cas, Tsih) is a Be star at the center of Cassiopeia's W, prototype of a class with unusual X-rays from a white dwarf companion.

Gamma Cassiopeiae variable

A Gamma Cassiopeiae variable (GCAS) is an eruptive irregular variable star of spectral class B, named for Gamma Cassiopeiae, whose irregular brightness changes come from a gas disk.

Gamma Cygni

Gamma Cygni, known by its proper name Sadr, is a yellow-white supergiant of magnitude 2.23 at the center of the Northern Cross asterism in Cygnus, about 1,800 light-years away.