Mathematics and statistics

Olga Ladyzhenskaya (Ольга Александровна Ладыженская)

Olga Ladyzhenskaya (Ольга Александровна Ладыженская), born 1922 and died 2004, was a Russian mathematician known for proving global unique solvability of the 2D Navier-Stokes equations.

Omnibus test

An omnibus test is a statistical test of whether a set of effects or parameters is jointly significant, without identifying which individual component drives the result.

On-Line Encyclopedia of Integer Sequences

The On-Line Encyclopedia of Integer Sequences (OEIS), also called Sloane's OEIS, is a free online database of integer sequences, online since 1996 and holding over 400,000 entries.

One- and two-tailed tests

A one-tailed (one-sided) test places its entire rejection region in one tail, testing a directional effect, while a two-tailed (two-sided) test splits it between both tails.

One-way analysis of variance

The one-way analysis of variance (one-way ANOVA) is a statistical test of whether the means of three or more independent groups differ, defined by a single factor.

Ones' complement

Ones' complement is a method of representing signed integers in binary in which a negative number is formed by inverting every bit, used by early computers like the CDC 6600 and PDP-1.

Open ball

An open ball in a metric space is the set of all points within a given distance of a center, and it is always an open set.

Open cover

An open cover of a set in a topological space is a collection of open sets whose union contains it, and compactness means every open cover has a finite subcover.

Open map

An open map is a function between topological spaces that sends every open set to an open set; every homeomorphism is open, and non-constant holomorphic functions are open maps.

Open mapping theorem (functional analysis)

The open mapping theorem, or Banach–Schauder theorem, is a functional analysis result stating that every surjective bounded linear operator between Banach spaces sends open sets to open sets.

Open set

An open set is a subset of a topological space declared open by the topology, generalizing a region where every point has room around it.

OpenBLAS is an open-source, optimized implementation of the Basic Linear Algebra Subprograms (BLAS), based on Goto's GotoBLAS2 and including LAPACK, with hand-tuned assembly kernels for many CPU architectures.

OpenBUGS

OpenBUGS is an open source package for Bayesian analysis of complex statistical models using MCMC, the first open source version of the BUGS software family.

Operand

An operand is the number, variable, or data that an operator acts on in mathematics or computing, as in 7 + 5, where 7 and 5 are operands.

Operating characteristic curve

An operating characteristic curve is a graph used in acceptance sampling that plots the probability of accepting a lot against its true quality, as the fraction defective.

Operation (mathematics)

In mathematics, an operation is a function that takes a fixed number of elements of a set as inputs and returns one element of the same set.

Operator (mathematics)

In mathematics, an operator, or mathematical operator, is a mapping that takes one function or vector to another, most commonly a linear map on a vector space.

Operator K-theory

Operator K-theory is the branch of K-theory assigning K₀ and K₁ groups to C-algebras through projections and unitaries, central to classification and topological phases of matter.

Operator space theory

Operator space theory studies Banach spaces embedded in C-algebras, where matrix-level norms distinguish spaces that look identical as Banach spaces, merging C-algebra and Banach space theory.

Operator splitting

Operator splitting is a numerical time-integration method for ODEs and PDEs that applies sub-operators one after another, exact when they commute and otherwise carrying a splitting error.

Operator theory

Operator theory is the branch of functional analysis that studies linear operators, especially bounded linear maps between Hilbert and Banach spaces, and underlies the mathematics of quantum mechanics.

Opportunistic sampling

Opportunistic sampling is a form of nonprobability sampling that collects data from readily available sources, such as citizen-science records and museum specimens, rather than by a known random mechanism.

Optimal design (statistics)

Optimal design is a statistical method for choosing experiment settings, run allocations, or point weights so a criterion computed from the Fisher information matrix is optimized.

Optimal design of environmental monitoring networks

Optimal design of environmental monitoring networks is the statistical problem of choosing how many stations to operate and where, so measurements carry the most information per unit of budget.

Optimal stopping

Optimal stopping is the branch of probability theory that studies when to take a once-only action, such as selling an asset or exercising an option, to maximize expected reward.

Optional stopping theorem

The optional stopping theorem, also called the optional sampling theorem, is a martingale result due to J. L. Doob, showing no quitting strategy can beat a fair game.

OR gate

The OR gate, or OR circuit, is a digital logic circuit whose output is HIGH when at least one input is HIGH, implementing inclusive logical disjunction.

Oracle machine

An oracle machine, also called an oracle Turing machine, is a Turing machine that queries a fixed set as an oracle, introduced by Alan Turing in 1939.

Order (ring theory)

In ring theory, an order is a subring of the ring of integers of a number field that has finite index there, a concept introduced by Richard Dedekind.