Mathematics and statistics

Lower envelope of functions

The lower envelope of functions is the pointwise minimum of a collection of functions, together with the subdivision showing which function is lowest in each region; it describes Voronoi diagrams in computational geometry.

Lowest common denominator

The lowest common denominator (LCD), also called the least common denominator, is the least common multiple of the denominators in a set of fractions, used mainly to add and subtract fractions with unlike denominators.

Lp convergence of random variables

Lp convergence of random variables, also called convergence in mean of order p, is the mode of convergence where E[|Xn − X|^p] tends to zero as n grows.

Lp space

An Lp space, also called a Lebesgue space or Lp norm space, is a space of measurable functions whose p-th power is integrable, a central object of functional analysis.

LU decomposition

The LU decomposition, also called LU factorization or LR decomposition, expresses a matrix as the product of a lower triangular matrix L and an upper triangular matrix U.

Lubin–Tate formal group law

The Lubin–Tate formal group law, or Lubin–Tate group, is a formal group over the integers of a local field, introduced by Jonathan Lubin and John Tate in 1965.

Luca Pacioli

Luca Pacioli, also known as Fra Luca Pacioli, was an Italian Franciscan friar and mathematician whose 1494 Summa gave the first printed account of double-entry bookkeeping.

Lucas number

The Lucas numbers, also known as the Lucas series, are an integer sequence 2, 1, 3, 4, 7, 11, where each term is the sum of the two before it.

Lucas numbers

Lucas numbers form an integer sequence 2, 1, 3, 4, 7, 11, defined by the Fibonacci recurrence but with different starting values, named for Édouard Lucas.

Lucas sequence

A Lucas sequence is one of a pair of integer sequences defined by a recurrence with parameters P and Q, generalizing Fibonacci, Pell, and Mersenne numbers.

Lucky number

A lucky number is a positive integer surviving a position-based sieve invented at Los Alamos in 1956 as a variation of the sieve of Eratosthenes.

Ludwig Wittgenstein

Ludwig Josef Johann Wittgenstein was an Austrian-British philosopher, born in Vienna in 1889, whose Tractatus and Philosophical Investigations shaped analytic philosophy and ideas of meaning as use.

Łukasiewicz logic

Łukasiewicz logic, also called Lukasiewicz fuzzy logic, is a many-valued logic introduced by Polish logician Jan Łukasiewicz in 1920, with truth values between true and false.

Łukasiewicz–Moisil algebra

A Łukasiewicz–Moisil algebra, also known as an LM algebra, is a bounded distributive lattice with nuance operations, introduced by Grigore Moisil in 1940 as an algebraic counterpart of Łukasiewicz's many-valued logic.

Luzin space

A Luzin space, also called a Luzin topological space, is an uncountable T1-space without isolated points in which every nowhere-dense subset is countable, named for Nikolai Luzin.

Lyapunov equation

The Lyapunov equation is a matrix equation, AᵀP + PA = −Q, named for Aleksandr Lyapunov, whose positive definite solution certifies the stability of a linear dynamical system.

Lyapunov exponent (ODE stability)

A Lyapunov exponent measures the average exponential rate at which nearby trajectories of a dynamical system diverge or converge; a positive maximal exponent signals chaos, while negative exponents indicate contraction toward an attractor.

Lyapunov stability

Lyapunov stability is a mathematical notion of stability for an equilibrium point of a dynamical system: solutions starting sufficiently close remain close, introduced by Aleksandr Lyapunov in 1892.

Lyapunov–Schmidt reduction

Lyapunov–Schmidt reduction is a bifurcation-theory technique that replaces a large or infinite-dimensional equation near a singular point by a smaller finite-dimensional equation carrying all essential information about the bifurcation.

Lyndon word

A Lyndon word is a finite word over an ordered alphabet that is lexicographically smaller than all of its nontrivial rotations, introduced by Roger Lyndon in 1954.

M-estimation

M-estimation is a class of statistical estimators defined by minimizing a sum of an objective function over the data, generalizing maximum likelihood and least squares to estimate parameters robustly despite outliers.

M-estimator

An M-estimator is a statistical estimator defined as the minimizer of a sum of an objective function over the data, generalizing maximum likelihood and least squares.

M-matrix

An M-matrix is a real square matrix with nonpositive off-diagonal entries and nonnegative principal minors, named for Minkowski and used in numerical analysis, economics, and probability.

M/M/1 queue

The M/M/1 queue, also known as the MM1 Model, is a single-server queueing model with Poisson arrivals and exponential service times, stable only when the arrival rate stays below the service rate.

M/M/c queue

The M/M/c queue, or Erlang C model, is a queueing model with Poisson arrivals served by c identical parallel servers, published by A. K. Erlang in 1917.

Macaulay2

Macaulay2 is a free, open-source software system for research in algebraic geometry and commutative algebra, created by Daniel Grayson and Michael Stillman and funded by the National Science Foundation since 1992.

Macdonald polynomials

Macdonald polynomials are a two-parameter family of symmetric polynomials indexed by partitions, introduced by Ian G. Macdonald in 1987 to unify the Hall-Littlewood and Jack symmetric functions.

Machine epsilon

Machine epsilon is the smallest positive number that, when added to 1.0 in a floating-point system, produces a result different from 1.0, measuring the system's precision.

MacMahon partition analysis

MacMahon partition analysis is a combinatorial method introduced by Percy MacMahon in 1915 that counts solutions of linear Diophantine inequalities via the Omega operator, revived by George Andrews in the late 1990s.