Physical world and mathematics

Local realism

Local realism is the conjunction of locality, that influences cannot propagate faster than light, and realism, that outcomes are fixed before observation; Bell's theorem and the 2015 Delft experiment support its rejection.

Local regression

Local regression, best known as LOWESS or loess, is a nonparametric method fitting a smooth curve by low-degree polynomials to nearby observations, introduced by William Cleveland in 1979.

Local ring

A local ring, also known as a quasi-local or quasilocal ring, is a ring with exactly one maximal ideal, the basic algebraic tool for studying geometric objects near a single point.

Local Volume

The Local Volume is the region of space around the Milky Way containing about 1000 known galaxies within 11 megaparsecs, organized into seven mostly dwarf groups and used to test cosmology.

Local-density approximation

The local-density approximation (LDA) is an approximation to the exchange-correlation energy in density-functional theory that treats each point as a uniform electron gas of the same density.

Localization (ring theory)

Localization is a construction in commutative algebra that inverts a multiplicative set S in a ring, producing fractions S⁻¹A; at a prime ideal it yields a local ring.

Localization microscopy

Localization microscopy, also called single-molecule localization microscopy (SMLM), is a fluorescence microscopy technique that reconstructs super-resolution images by pinpointing individual fluorescent molecules, reaching resolutions near 10–30 nm.

Localized surface plasmon resonance

Localized surface plasmon resonance (LSPR) is the collective oscillation of conduction electrons in metallic nanoparticles, producing strong absorption and scattering peaks used for sensing, surface-enhanced Raman spectroscopy, and photothermal catalysis.

Locally compact group

A locally compact group, also called a locally compact topological group, is a topological group where every point has a compact neighborhood. It is the standard setting for Haar measure and harmonic analysis.

Locally compact space

A locally compact space is a Hausdorff topological space where every point has a compact neighborhood, a weakening of compactness exemplified by Euclidean space Rn.

Locally convex topological vector space

A locally convex space (LCS) is a topological vector space whose topology is generated by a family of seminorms, the standard setting for duality theory in functional analysis.

Location test

A location test is a statistical hypothesis test that compares the location parameter, such as the mean or median, of distributions, using parametric tests like the t-test or nonparametric rank tests.

LOCC

LOCC, or local operations and classical communication, is the class of operations in quantum information theory where separated parties act locally and exchange classical messages.

Lock-in (vortex shedding)

Lock-in, also called synchronization, is the regime of vortex-induced vibration in which vortex shedding locks to a structure's natural frequency over a range of flow velocities.

Locus (mathematics)

In mathematics, a locus (plural: loci) is the set of all points, and only those points, satisfying a stated condition, typically forming a curve or surface.

Lodestone

A lodestone is a rare piece of magnetite ore that is naturally magnetized, thought to be struck by lightning, and used for centuries to magnetize compass needles.

Loess

Loess (Löss) is wind-deposited silt sediment, typically 60–90% silt-sized, that covers roughly 6.6% of land and forms some of the world's most fertile soils.

Loewner equation

The Loewner equation is a differential equation describing the growth of a slit in a planar domain via conformal maps, introduced by Charles Loewner in 1923.

LOFAR

LOFAR (LOw Frequency ARray) is a European radio telescope operating at 10 to 240 MHz, the largest of its kind at the lowest observable frequencies.

Oct 22, 2026

LOFAR radio air-shower imaging

LOFAR radio air-shower imaging is the detection of extensive air showers from the radio pulses they emit, using the LOFAR radio telescope and its dense antenna core in the Netherlands.

Log

A log, or logarithm, is the exponent a fixed base must be raised to produce a number, turning multiplication into addition; Napier published it in 1614.

Log scheme

A log scheme is a scheme equipped with a logarithmic structure, a sheaf of commutative monoids recording boundary or degeneration data, introduced by Kato in 1989.

Log-linear model

A log-linear model is a statistical model for the expected cell counts of a contingency table, treating all variables jointly as responses to describe associations rather than predict one variable.

Log-normal distribution

The log-normal distribution is a continuous probability distribution of a positive random variable whose logarithm is normally distributed, common in reliability, aerosol science, pharmacology, and finance.

Log-Pearson type III distribution

The log-Pearson type III distribution (LP-III or LP3) is a probability distribution used in flood frequency analysis, the standard method in the United States since 1967.

Log-rank test

The log-rank test is a nonparametric hypothesis test comparing survival distributions of two or more groups from censored time-to-event data, widely used in cancer trials.

Log-Sobolev inequality

The log-Sobolev inequality is a functional inequality, introduced by Leonard Gross in 1975, bounding entropy by gradient energy and used for mixing time bounds and concentration of measure.

Log–log plot

A log–log plot, or log–log graph, is a two-dimensional graph with logarithmic scales on both axes, making power-law relationships y = ax^b appear as straight lines.

Logarithm

A logarithm, the inverse of exponentiation, is the exponent a base must be raised to in order to produce a given number, invented by John Napier in 1614.