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Fibonacci word
The Fibonacci word, also called the rabbit sequence, is an infinite binary sequence beginning 0100101001001, the fixed point of the substitution sending 0 to 01 and 1 to 0.
Fibration
A fibration is a continuous map between topological spaces with the homotopy lifting property; Serre fibrations, introduced in 1951, organize homotopy theory and yield long exact sequences of homotopy groups.
Fictitious domain method
The fictitious domain method is a numerical technique for solving partial differential equations on irregular or moving domains by embedding them in a larger, simply shaped one.
Fictitious play
Fictitious play is an iterative game-theory process in which each player best-responds to opponents' past play frequencies, used to model learning and compute Nash equilibria.
Fiducial inference
Fiducial inference is a statistical inference framework that produces a probability distribution for an unknown parameter without a prior, proposed by R. A. Fisher in 1930.
Fiedler vector
A Fiedler vector is an eigenvector of a graph's Laplacian matrix corresponding to the second smallest eigenvalue, known as the algebraic connectivity, and is central to spectral graph partitioning.
Field (mathematics)
In mathematics, a field is a set equipped with addition and multiplication satisfying the usual laws of arithmetic; the rational, real, and complex numbers are the familiar examples.
Field extension
A field extension is a pair of fields L/K where K is a subfield of L, the central object of Galois theory and its measure of size, the degree.
Field of fractions
The field of fractions of an integral domain is the smallest field containing it, built as the rationals are built from the integers; also called the quotient field.
Field of sets
A field of sets, also called an algebra of sets, is a collection of subsets of a set closed under finite union, intersection, and complementation.
Field-failure and early-life failure analysis
Field-failure and early-life failure analysis is the statistical study of how products fail in actual use, drawing on warranty claims, returns, and service records to forecast failures and costs.
Fields Medal
The Fields Medal (Fields Prize) is a mathematics prize awarded every four years at the International Congress of Mathematicians, first awarded in 1936 and limited to mathematicians under 40.
Filter (mathematics)
In mathematics, a filter is a non-empty family of subsets closed under finite intersections and upward inclusion and excluding the empty set, introduced by Henri Cartan in 1937.
Filter model
A filter model is a mathematical model of the untyped lambda-calculus whose elements are filters of intersection types, introduced by Barendregt, Coppo, and Dezani-Ciancaglini in 1983.
Filter stability and approximation in nonlinear filtering
Filter stability is the property of a nonlinear filter whereby its estimates become insensitive to the initial condition as observations accumulate, and it underpins accurate particle filter approximation.
Filtration (probability theory)
A filtration in probability theory is an increasing family of σ-algebras on a probability space, indexed by time, modeling the accumulation of information; it underlies martingales and stopping times.
Filtration method
The filtration method is a proof technique in modal logic that converts an infinite Kripke model of a formula into a finite one, proving the finite model property.
Fine–Gray model
The Fine–Gray model is a semiparametric proportional hazards regression model for the subdistribution hazard of a competing risk, proposed by Jason P. Fine and Robert J. Gray in 1999 and widely used as competing risks regression.
Finite difference
A finite difference, also known as the calculus of differences, is a difference between a function's values at nearby points, used to approximate derivatives numerically.
Finite difference method
The finite difference method (FDM) is a numerical technique for solving differential equations by replacing derivatives with difference quotients on a grid, turning the problem into algebraic equations solved simultaneously.
Finite field
A finite field, also called a Galois field, is a field with a finite number of elements. Its order is always a prime power, and one such field exists for each.
Finite field arithmetic
Finite field arithmetic, also called Galois field arithmetic, is arithmetic in a field with a finite number of elements rather than in infinite fields like the rationals.
Finite geometry
Finite geometry is the branch of geometry that studies geometric structures with finitely many points, notably projective and affine spaces over finite fields, with applications to coding theory and cryptography.
Finite group
A finite group is a group containing only finitely many elements, the count being its order. Finite groups model symmetries of finite objects and arise throughout mathematics and physics.
Finite model property
The finite model property (FMP) is a property of a logic: every satisfiable formula has a finite model, giving a standard route to proving decidability in modal logic.
Finite set
A finite set is a set whose elements can be counted with a natural number n; the number n is the set's cardinality, and any set that is not finite is infinite.
Finite-variable infinitary logic
Finite-variable infinitary logic, L^k∞ω, allows infinitely long conjunctions and disjunctions but limits formulas to at most k variables, and its union over all finite k is the main yardstick of expressiveness in finite model theory.
Finitely generated group
A finitely generated group is a group whose every element is a product of powers of elements from some finite generating set, a basic finiteness condition in group theory.
Finitely generated module
A finitely generated module is a module expressible as combinations of finitely many elements, the analog of a spanning set in linear algebra over general rings.
Finitism
Finitism is a position in the philosophy of mathematics, due to David Hilbert, restricting reasoning to finite, executable arguments; it underpinned his program for proving mathematics consistent.