6,052 articles
Local field
A local field in algebraic number theory is a field complete with respect to a discrete valuation and having a finite residue field, such as the p-adic numbers.
Local martingale
A local martingale is a stochastic process that becomes a true martingale when stopped at suitable stopping times increasing to infinity; every martingale is one, but not conversely.
Local mean decomposition
Local mean decomposition is an adaptive signal processing method that breaks modulated signals into product functions, yielding instantaneous amplitude and frequency without the Hilbert transform.
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.
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.
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.
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.
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.
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-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.
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.
Logarithm tables
Logarithm tables are printed lists pairing numbers with their logarithms so multiplication and division can be done by addition and subtraction, standard from John Napier's first table of 1614 until calculators spread in the 1970s.
Logarithmic derivative
The logarithmic derivative of a function f is f′/f, equal to the derivative of ln f; it measures how fast f changes relative to its current size.
Logarithmic integral function
The logarithmic integral, li(x), is a special function defined as the integral of 1/ln t for x > 1, used as the standard approximation to the prime counting function π(x).
Logarithmic potential
The logarithmic potential is the potential U(z) = ∫ log(1/|z−w|) dμ(w) for a compactly supported measure in the plane; its kernel is the Laplacian's two-dimensional fundamental solution, underlying logarithmic potential theory, capacity, and log gases.
Logarithmic spiral
The logarithmic spiral, or equiangular spiral, is a plane curve that cuts every ray from its pole at a constant angle, common in shells and galaxies.
Logarithmic transformation
A logarithmic transformation replaces each value of a variable with its logarithm, a statistical preprocessing step that stabilizes variance, reduces skewness, and turns multiplicative differences into additive ones.
Logic
Logic, also known as Logike, is the systematic study of valid inference, which patterns of reasoning preserve truth from premises to conclusion, now underpinning mathematics, philosophy, and computer science.
Logic Colloquium
The Logic Colloquium is the European Summer Meeting of the Association for Symbolic Logic, an annual logic conference first held in Oxford in 1956 and one of the ASL's two major meetings.
Logic in Computer Science (conference)
Logic in Computer Science (LICS) is an annual academic conference on logic in computer science, founded in 1986 and generally regarded as the field's most prestigious.
Logic model
A logic model, also called a theory of change or program theory, is a graphic depiction of a program linking resources, activities, and intended outcomes, widely used in program planning and evaluation.
Logical biconditional
The logical biconditional, also called biimplication, is the two-place propositional connective "P if and only if Q", true when P and Q have the same truth value.