Physical world and mathematics

Ornstein–Uhlenbeck process

The Ornstein–Uhlenbeck process, introduced by Uhlenbeck and Ornstein in 1930, is a mean-reverting stochastic process that is Gaussian, Markovian, and stationary, used to model Brownian-particle velocity and interest rates.

Ornstein–Zernike equation

The Ornstein–Zernike equation, or OZ equation, connects the total and direct correlation functions of a classical fluid through a convolution, introduced in 1914 to describe critical opalescence and scattering.

Orogenic gold deposit

An orogenic gold deposit is gold mineralization deposited from low-salinity, aqueous-carbonic fluids rising along crustal faults during mountain building, supplying an estimated 75% of all gold extracted by humans.

Orogeny

Orogeny is the process by which mountain belts form, typically when tectonic plates collide or converge, folding and thickening the crust; examples include the Alps, Himalayas, and Appalachians.

Orographic lift

Orographic lift is the forced upward movement of air over rising terrain such as a mountain, cooling it and producing clouds and precipitation on the windward side.

Orowan strengthening

Orowan strengthening is a precipitation and dispersion hardening mechanism, described by Egon Orowan in 1948, in which dislocations bow between non-shearable particles and bypass them, leaving loops that raise the alloy's strength.

Orpiment

Orpiment, also known as King's yellow or Auripigment, is a yellow arsenic sulfide mineral found in hydrothermal veins and hot springs, long used as a golden-yellow artist's pigment until abandoned for its toxicity.

Orrery

An orrery is a mechanical model of the solar system showing the positions and motions of the planets, named for Charles Boyle, the 4th Earl of Orrery.

Orthocarbonate esters

Orthocarbonate esters are organic compounds of general formula C(OR)₄, the stable tetraesters of hypothetical orthocarbonic acid C(OH)₄, with tetramethyl and tetraethyl orthocarbonate the best known.

Orthocarbonic acid

Orthocarbonic acid, also called methanetetrol, is the hypothetical compound C(OH)₄, first detected in the gas phase in 2025 in laboratory simulations of interstellar ice chemistry.

Orthocenter

The orthocenter of a triangle is the point where its three altitudes meet, lying inside an acute triangle, outside an obtuse one, and at the right-angle vertex itself.

Orthoclase

Orthoclase, also called orthoclase feldspar, is a rock-forming potassium feldspar mineral with the formula KAlSi₃O₈, common in granite and named in 1823 for its right-angle cleavage.

Orthoester

An orthoester is a compound bearing three alkoxy groups on one carbon atom, formally the ester of a hypothetical ortho acid RC(OH)₃, and hydrolyzing irreversibly to esters in acid.

Orthogonal array

An orthogonal array, introduced by C. R. Rao in the 1940s, is a table of symbols in which every chosen set of columns contains all combinations equally often.

Orthogonal array design

Orthogonal array design is a design of experiments method using orthogonal arrays to estimate all main effects uncorrelatedly from relatively few test runs, widely used in industrial quality engineering.

Orthogonal collocation

Orthogonal collocation is a numerical method for solving differential equations by expanding the solution in orthogonal polynomials and forcing the equation to hold at their roots, introduced by Villadsen and Stewart in 1967.

Orthogonal complement

The orthogonal complement of a subset U of an inner product space is the set of all vectors whose inner product with every vector of U is zero.

Orthogonal coordinates

Orthogonal coordinates are a coordinate system in which coordinate lines or surfaces intersect at right angles, a common case of curvilinear coordinates including Cartesian, cylindrical, and spherical systems.

Orthogonal experimental design

Orthogonal experimental design is a design-of-experiments method that arranges factor levels in orthogonal arrays, estimating each factor's effects independently with far fewer runs than a full factorial experiment.

Orthogonal group

The orthogonal group, or general orthogonal group, is the classical group of linear transformations preserving a non-singular quadratic form; O(n) consists of the real orthogonal matrices preserving distances in n-dimensional Euclidean space.

Orthogonal iteration

Orthogonal iteration, also called subspace iteration or simultaneous iteration, is a numerical linear algebra algorithm that generalizes the power method to compute bases for eigenspaces.

Orthogonal matching pursuit

Orthogonal matching pursuit (OMP) is a greedy algorithm for sparse approximation, introduced by Mallat and Zhang in 1993, which recovers sparse signals from fewer measurements than the signal dimension.

Orthogonal matrix

An orthogonal matrix, also called an orthonormal matrix, is a real square matrix whose transpose equals its inverse; it preserves lengths and angles, representing a rotation, a reflection, or both.

Orthogonal partial least squares

Orthogonal partial least squares (O-PLS) is a multivariate regression method that separates variation correlated with a response from uncorrelated variation, introduced by Trygg and Wold in 2002.

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.

Orthogonal protecting groups and deprotection strategy

Orthogonal protecting groups are masking groups on one molecule, each removable selectively under conditions that leave all the others intact, a concept defined by Barany and Merrifield in 1977.

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 map projection

The orthographic map projection, also called the orthographic projection in cartography, is an azimuthal perspective projection that shows one hemisphere as a globe appears from space.

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.