Mathematics and statistics

Non-uniform rational B-spline

A non-uniform rational B-spline, or NURBS, is a mathematical representation of curves and surfaces built from control points, weights, and a knot vector, created for computer 3D modeling.

Non-uniform sampling (statistics)

Non-uniform sampling in statistics is a sampling design that selects population units with unequal probabilities, concentrating effort where measured quantities are largest or most variable.

Non-unique factorization is the phenomenon in rings of algebraic integers and factorization monoids where an element has essentially different irreducible factorizations, classically 6 = 2·3 = (1+√−5)(1−√−5) in Z[√−5], measured by invariants like elasticity.

Nonagon

A nonagon, also called an enneagon or 9-gon, is a polygon with nine sides and nine angles totaling 1260°; the regular form cannot be constructed with compass and straightedge.

Noncommutative geometry

Noncommutative geometry, developed principally by Alain Connes, extends geometry, topology, and calculus to spaces described by noncommuting algebras, with the spectral triple as its central object.

Noncommutative integration

Noncommutative integration is a branch of operator algebra theory extending measure and integration theory to von Neumann algebras, reducing to classical integration when the algebra is abelian.

Nondeterministic finite automaton

A nondeterministic finite automaton (NFA) is a finite-state machine whose transitions can lead to several next states at once; it recognizes exactly the regular languages, like a deterministic automaton.

Nondeterministic Turing machine

A nondeterministic Turing machine is a mathematical model of computation that can choose among several possible transitions at each step, and it underlies the complexity class NP.

Nonlinear autoregressive distributed lag model

The nonlinear autoregressive distributed lag (NARDL) model is a single-equation error correction model, introduced in 2014, that estimates separate effects of positive and negative changes in each explanatory variable.

Nonlinear mixed-effects model

A nonlinear mixed-effects model (NLME model) is a statistical model for repeated-measures data in which some parameters vary between individuals, and the standard tool of pharmacometrics.

Nonlinear programming

Nonlinear programming, also known as nonlinear optimization, is the branch of mathematical optimization dealing with problems whose objective function, constraints, or both are nonlinear, generalizing linear programming.

Nonlinear regression

Nonlinear regression is a form of regression analysis in which the expected response is modeled by a function nonlinear in the unknown parameters, estimated by iterative least squares algorithms such as Levenberg-Marquardt.

Nonlinear Schrödinger equation

The nonlinear Schrödinger equation (NLS) is a partial differential equation combining dispersion and nonlinear self-interaction, with focusing and defocusing regimes, and applications in optics, water waves, and Bose–Einstein condensation.

Nonlinear system

A nonlinear system is a system whose equations describe behavior where output is not proportional to input; when the equations evolve in time it is called a dynamical system.

Nonparametric statistics

Nonparametric statistics, also known as distribution-free methods, is the branch of statistics that analyzes data without assuming a specific distribution, using rank-based tests, bootstrap resampling, and density estimation.

Nonprobability sampling

Nonprobability sampling is a survey method that selects units by convenience, judgment, or quotas rather than randomly, making it cheaper but harder to measure for error.

Nonstandard analysis

Nonstandard analysis is a rigorous formulation of mathematical analysis using actual infinitesimal and infinitely large numbers instead of epsilon-delta limits, introduced by Abraham Robinson at Princeton in 1960.

Nonuniform sampling (statistics)

Nonuniform sampling, also called varying probability sampling, is a statistical design that selects units with unequal probabilities, weighted by their inclusion probabilities, to estimate totals more precisely.

NOR logic

NOR logic is the Boolean operation, written A ↓ B, that outputs true only when all inputs are false; its NOR gate is a universal gate.

Norm (mathematics)

In mathematics, a norm, or vector norm, is a function on a vector space that assigns each vector a length, satisfying positivity, homogeneity, and the triangle inequality.

Norm of a field element

The norm of a field element, N of alpha, is the determinant of the multiplication-by-alpha map for a finite field extension, taking values in the base field K.

Normal (geometry)

A normal, or normal vector, in geometry is a vector or line perpendicular to a curve or surface at a point, used in differential geometry and computer graphics.

Normal coordinates

Normal coordinates are local coordinates on a manifold, built from the exponential map at a point, in which the metric is Euclidean and geodesics through the center are straight lines.

Normal curvature

Normal curvature is the component of a curve's curvature along the normal of the surface it lies on, measuring how the surface itself bends the curve.

Normal derivative

The normal derivative measures a function's rate of change in the direction perpendicular to a boundary, and prescribing it yields the Neumann boundary condition, named after Carl Neumann.

Normal distribution

The normal distribution, also called the Gaussian distribution or bell curve, is a symmetric continuous probability distribution defined by a mean and a standard deviation, central to statistics.

Normal extension

A normal extension is an algebraic field extension E/F in which every irreducible polynomial over F with a root in E has all its roots in E; together with separability, normality makes the extension Galois.

Normal family

A normal family is a family of functions in which every sequence has a subsequence converging uniformly on compact subsets, introduced by Paul Montel in 1907.

Normal form theory

Normal form theory is a body of methods in dynamical systems that simplifies differential equations near an equilibrium or periodic orbit via successive near-identity coordinate transformations.