edgepedia

Physical world and mathematics

42,772 articles

Ingrid Kogel-Knabner

Ingrid Kogel-Knabner, also written Ingrid Kögel-Knabner, is a German soil scientist and professor emeritus at the Technical University of Munich, elected to the US National Academy of Engineering in 2025.

Inherent chirality

Inherent chirality is a form of molecular chirality where the curved molecular scaffold itself is the stereogenic element, first named by Volker Böhmer and co-workers in 1994.

Inhomogeneous broadening

Inhomogeneous broadening is the widening of a spectroscopic line caused by emitters having different transition frequencies, arising from Doppler shifts in gases and structural disorder in solids.

Inhomogeneous cosmology

Inhomogeneous cosmology is the study of cosmological models whose spacetime is not assumed homogeneous and isotropic, spanning exact solutions such as Lemaître–Tolman–Bondi universes and the averaging, or backreaction, program.

Initial conditions of relativistic heavy-ion collisions

The initial conditions of relativistic heavy-ion collisions are the energy–momentum tensor and conserved charge currents handed to hydrodynamic simulations, modeled from nuclear geometry through the Glasma stage toward hydrodynamization.

Initial data construction in numerical relativity

Initial data construction in numerical relativity produces a spatial slice of spacetime satisfying Einstein's constraint equations, so an evolution code can start from a valid snapshot.

Initial mass function

The initial mass function (IMF) is the empirical distribution of the masses stars have at birth, counting how many stars form in each mass interval.

Initial singularity

The initial singularity, also called the Big-Bang singularity, is the hypothetical state of infinite density and temperature to which general relativity extrapolates the universe backward in time.

Initial value formulation (general relativity)

The initial value formulation, also called the Cauchy problem, of general relativity determines a spacetime from metric and extrinsic curvature data on a spacelike hypersurface, subject to four constraint equations.

Initiator full configuration interaction quantum Monte Carlo

Initiator full configuration interaction quantum Monte Carlo, introduced by Cleland and colleagues in 2010, is a variant of FCIQMC that removes the annihilation plateau at the cost of a small bias.

Injection seeding

Injection seeding is a laser technique in which light from a low-power seed laser is injected into a pulsed laser's cavity, forcing single-frequency output useful for lidar and spectroscopy.

Injective dimension

Injective dimension, denoted id(M), is the least number of injective modules needed to resolve a module over a ring, measured via Ext; finiteness characterizes Gorenstein and regular rings.

Injective function

An injective function, also called a one-to-one function or injection, maps distinct inputs to distinct outputs, so no value in the codomain is hit more than once.

Injective hull

An injective hull, also called an injective envelope, is the smallest injective module containing a given module M, unique up to isomorphism; every module has one.

Injective module

An injective module is a module J over a ring R such that every homomorphism from a submodule into J extends to the whole module, the dual of projectivity.

Inland Waters (journal)

Inland Waters is a peer-reviewed academic journal covering limnology and the management of inland aquatic ecosystems, official journal of the International Society of Limnology since 2011.

Inline holography

Inline holography is an optical imaging method in which the light illuminating a specimen also serves as the reference wave, so a hologram forms on a sensor without reference-beam optics.

INM-CM

INM-CM is the family of coupled Earth system climate models developed at the Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences in Moscow since 2000.

INMETRO

INMETRO, the National Institute of Metrology, Quality and Technology, is a Brazilian federal autarky created in 1973 that maintains measurement standards, accredits laboratories, and enforces legal metrology.

Inner automorphism

An inner automorphism of a group is conjugation by a fixed element, sending x to gxg⁻¹; the inner automorphisms form a normal subgroup of the automorphism group.

Inner core rotation

Inner core rotation is the spin of Earth's solid inner core relative to the mantle, inferred from tiny changes in seismic wave travel times since 1996.

Inner main belt

The inner main belt is the innermost zone of the main asteroid belt, between about 2.05 and 2.5 au, dominated by Vesta and a major source of meteorites.

Inner model

An inner model is a transitive class of sets containing all the ordinals and satisfying ZF, introduced by Kurt Gödel, whose constructible universe L gave the first relative consistency proofs in set theory.

Inner model theory

Inner model theory is the branch of set theory that constructs canonical inner models of ZFC satisfying large cardinal hypotheses, using fine structure theory, iteration trees, and extender models.

Inner product space

An inner product space, also called a pre-Hilbert space, is a vector space with an inner product that generalizes the dot product, giving lengths, angles, and orthogonality.

Innermost stable circular orbit

The innermost stable circular orbit (ISCO) is the smallest radius at which a body can stably orbit a compact object; inside it, circular motion is impossible and matter plunges inward.

Innovation process

The innovation process is the sequence of one-step-ahead prediction errors of a stochastic process, forming the basis of linear time series models, the Kalman filter's correction, and model-fit diagnostics.

Innovations process

The innovations process is the part of a noisy observation record carrying new information about an unobserved signal, the basis of the innovations approach to filtering.

Innovative trend analysis

Innovative trend analysis is a graphical method that detects trends in hydrological or climatic time series without assumptions about serial correlation, proposed by Zekâi Şen in 2012.

Inorganic chemistry

Inorganic chemistry is the branch of chemistry covering all compounds except organic, carbon-based ones, with subfields including coordination, organometallic, and solid-state chemistry, and industrial uses such as pigments and catalysts.