6,052 articles
Balayage
Balayage, French for "sweeping," is a potential theory operation replacing a charge inside a domain with a boundary distribution whose potential matches the original outside the domain.
Bald eagle search
Bald eagle search (BES) is a nature-inspired metaheuristic algorithm for continuous optimization and engineering design, introduced in 2020 and modeled on bald eagles hunting fish.
Banach algebra cohomology
Banach algebra cohomology, also called cohomology of Banach algebras, is the cohomology theory for Banach algebras using bounded cochains, introduced by Barry Edward Johnson in 1972.
Banach fixed-point theorem
The Banach fixed-point theorem, also called the Banach contraction principle or contraction mapping theorem, states that a contraction mapping on a complete metric space has a unique fixed point.
Banach function algebra
A Banach function algebra is a complete normed subalgebra of continuous functions that separates points and contains constants, studied with Gelfand theory as a commutative Banach algebra.
Banach space
A Banach space is a vector space with a norm under which every Cauchy sequence converges, named for Stefan Banach and central to functional analysis.
Banach–Tarski paradox
The Banach–Tarski paradox is a theorem of set-theoretic geometry, proved by Stefan Banach and Alfred Tarski in 1924, stating that a solid ball can be reassembled into two identical balls.
Band model (hyperbolic geometry)
The band model is a conformal model of the hyperbolic plane drawn as an infinite horizontal strip, obtained from the Poincaré disk model and analogous to the Mercator projection.
Banzhaf power index
The Banzhaf power index, also called the Penrose–Banzhaf index, measures voting power as the number of coalitions in which a voter can change the outcome, introduced by John F. Banzhaf III in 1965.
Bar chart
A bar chart, or bar graph, is a statistical graphic showing categorical data as rectangular bars with lengths proportional to their values, separated by gaps.
Bar complex
The bar complex of an associative algebra A is the chain complex whose n-th term is the tensor power A⊗(n+1), with a differential multiplying adjacent factors with alternating signs.
Barber paradox
The barber paradox is a logic puzzle asking whether a barber who shaves all and only men who do not shave themselves shaves himself, since no such barber can exist.
Bareiss algorithm
The Bareiss algorithm, also known as Montante's method, is a fraction-free form of Gaussian elimination that keeps integer matrices exact, published by Erwin Bareiss in 1968.
Bargmann transform
The Bargmann transform is a unitary integral transform, introduced by Valentine Bargmann in 1961, mapping functions on real space to holomorphic functions on complex space.
Barrier function
In potential theory, a barrier function is an auxiliary superharmonic function, positive inside a domain and vanishing at one boundary point; a barrier exists there exactly when the point is regular.
Barrier method (optimization)
A barrier method solves inequality-constrained optimization by adding a logarithmic barrier that keeps iterates strictly feasible, and it underlies the interior-point methods used in modern conic optimization software.
Bartlett's test
Bartlett's test, also called the Sphericity test, is a statistical test checking whether several groups have equal variances, commonly used to check an assumption of ANOVA.
Bartlett's test of sphericity
Bartlett's test of sphericity is a chi-square test, proposed by M. S. Bartlett in 1950, that checks whether a correlation matrix differs from the identity before exploratory factor analysis.
Barycentric coordinate system
A barycentric coordinate system, also called areal coordinates, locates a point as a weighted average of fixed reference points, introduced by August Ferdinand Möbius in 1827.
Base rate fallacy
The base rate fallacy, also called base rate neglect, is a cognitive error in which people judge probability from case-specific evidence while underweighting how common the event is.
Basel problem
The Basel problem, named for the Bernoulli family of Basel, asks for the exact sum of the reciprocals of the squares of the positive integers.
Basic Linear Algebra Subprograms
Basic Linear Algebra Subprograms (BLAS) is a specification of standard routines for vector and matrix operations in three levels, widely used by software such as LAPACK.
Basis (linear algebra)
A basis of a vector space is a linearly independent set that spans it, letting every vector be written uniquely as a combination of basis vectors.
Bathtub curve
The bathtub curve is a reliability engineering model showing a product population's failure rate over time, which falls early, stays constant, and rises as units wear out.
Baudhayana (बौधायन)
Baudhayana (बौधायन), also known as Bodhayana, was an Indian mathematician and Vedic priest of about 800 BCE, author of the Baudhayana Sulbasutra, which states the Pythagorean theorem.
Baum–Connes conjecture
The Baum–Connes conjecture, from operator algebras and noncommutative geometry, states that the assembly map is an isomorphism; it was posed by Paul Baum and Alain Connes in 1982.
Baum–Welch algorithm
The Baum–Welch algorithm, also called the forward–backward algorithm, is an expectation-maximization method that estimates the transition and emission probabilities of a hidden Markov model from unlabeled observations, with applications in speech recognition and computational biology.
Bayes A (genomic selection)
Bayes A is a Bayesian linear regression method for genomic selection, introduced by Meuwissen, Hayes, and Goddard in 2001, that gives each marker its own variance.
Bayes estimator
A Bayes estimator, or Bayesian estimate, is a decision rule minimizing posterior expected loss, depending on the chosen loss function and prior; squared error loss gives the posterior mean.
Bayes factor
The Bayes factor is the ratio of the marginal likelihoods of two competing statistical models, developed by Harold Jeffreys in 1935 to quantify scientific evidence.