6,052 articles
Orthogonal polynomials
Orthogonal polynomials are sequences of polynomials whose distinct members are orthogonal under a weighted inner product; introduced by Legendre in 1783, they underlie Gaussian quadrature, quantum mechanics, and approximation theory.
Orthogonality
Orthogonality is the generalization of perpendicularity to inner product spaces, where two elements are orthogonal when their inner product is zero; it underlies Fourier series and least squares.
Orthographic projection
Orthographic projection, also called orthogonal projection, is a parallel projection method for representing three-dimensional objects in two dimensions, the primary method used in engineering drawings of manufactured parts.
Osprey optimization algorithm
The osprey optimization algorithm (OOA) is a population-based metaheuristic for continuous and engineering optimization, introduced by Mohammad Dehghani and Pavel Trojovský in 2023, modeling how ospreys hunt fish.
OSQP
OSQP (Operator Splitting Quadratic Program) is an open-source numerical optimization package, written in C, that solves convex quadratic programs using the alternating direction method of multipliers.
Ostrowski's theorem
Ostrowski's theorem is a 1916 result in number theory stating that every nontrivial absolute value on the rational numbers is equivalent to the usual real one or a p-adic one.
Outcome test (discrimination)
The outcome test is a statistical method for detecting discrimination that compares post-decision success rates across groups rather than decision rates, introduced by Gary Becker in 1957.
Outer product
The outer product of two vectors multiplies every entry of one by every entry of the other, producing an m by n matrix of rank one, written u v^T.
Outerplanar graph
An outerplanar graph is a graph drawable in the plane without edge crossings and with all vertices on the outer face; every outerplanar graph is planar, but K4 is not.
Outlier
An outlier is an observation that lies an abnormal distance from other values in a sample, which may signal an error, fraud, or a real extreme value.
Oval
An oval is a closed plane curve resembling the outline of an egg or an ellipse; unlike the ellipse, it has no single precise mathematical definition in ordinary usage.
Overall survival
Overall survival (OS) is the time from diagnosis, treatment start, or randomization until death from any cause, widely called the gold standard endpoint in cancer trials.
Overdetermined system
An overdetermined system is a system of equations, typically linear, with more equations than unknowns, arising in curve fitting and satellite positioning and usually solved by least squares.
Overlapping circles grid
An overlapping circles grid is a geometric pattern of congruent circles centered on a lattice, with radii large enough that neighbors overlap, often built on a triangular lattice.
Overlapping domain decomposition
Overlapping domain decomposition solves a partial differential equation by splitting its domain into overlapping subdomains, solving local problems in parallel, and exchanging interface data until they combine.
Overshoot (signal)
Overshoot in signal processing is the excursion of a reconstructed or filtered signal above its true value near a transition, paired with an undershoot below it.
Overview of statistics and probability journals
Statistics and probability journals are the peer-reviewed periodicals where statistical theory, methods, and applications are published, led by titles like JASA, Biometrika, and the Annals of Statistics.
Ovoid (projective geometry)
An ovoid in finite projective geometry is a set of q²+1 points in PG(3,q) with no three collinear, used to build inversive planes, generalized quadrangles, and error-correcting codes.
P (complexity)
P, also called PTIME, is the class of decision problems solvable by a deterministic Turing machine in time bounded by a polynomial in the input length.
P versus NP problem
The P versus NP problem asks whether every problem whose solutions can be checked quickly can also be solved quickly, one of the Clay Mathematics Institute's $1 million Millennium Prize Problems.
P-adic analysis
P-adic analysis, also known as ultrametric calculus, is the branch of analysis over the p-adic number fields, created by Kurt Hensel around 1899 and central to modern number theory.
P-adic exponential function
The p-adic exponential is the classical exponential power series interpreted over the p-adic numbers, where it converges only on a small disk around the origin, unlike the real exponential.
p-adic field
A p-adic field, also called a p-adic local field, is a field that is a finite extension of the p-adic numbers for a prime p, studied in algebraic number theory.
P-adic Hodge theory
P-adic Hodge theory is a branch of arithmetic geometry that compares the p-adic cohomology theories, étale, de Rham, and crystalline, of algebraic varieties over p-adic fields.
p-adic integer
A p-adic integer is an element of the ring Z_p, written in base p with digits extending infinitely to the left; it completes the ordinary integers under the p-adic norm.
P-adic L-function
A p-adic L-function is a p-adically valued analytic function that interpolates special values of classical L-functions such as the Riemann zeta function, introduced by Kubota and Leopoldt in 1964.
P-adic number
A p-adic number, or p-adic, is a number obtained by completing the rational numbers with a distance based on divisibility by a prime p, introduced by Kurt Hensel in 1897.
p-adic numbers
The p-adic numbers are a family of number systems, one for each prime p, built by completing the rational numbers; introduced by Kurt Hensel in 1897.
P-adic valuation
The p-adic valuation, also called the p-adic order, measures how deeply a rational number is divisible by a fixed prime p, taking the value infinity at 0.
P-chart
The p-chart is an attribute control chart in statistical process control that monitors the proportion of defective units in samples of varying size, using binomial control limits.