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Physical world and mathematics

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Exergy efficiency

Exergy efficiency, also called second-law efficiency, is the ratio of useful exergy a system delivers to the exergy supplied, weighing energy by quality as well as quantity.

Exiobase

Exiobase is a global environmentally extended multi-regional input-output database linking economic relationships among countries with environmental pressures such as emissions, water, land, materials, and employment, built through EU-funded projects.

Existence

Existence is the property of actually being, as opposed to being merely imagined or possible. Analytic philosophy studies it through logic, quantifiers, and ontological commitment.

Existential quantification

Existential quantification, or the existential quantifier, is the logical operation written ∃ asserting a formula holds for at least one value of a variable, one of the two standard quantifiers of first-order logic.

Existentially closed model

An existentially closed model, also called an existentially complete model, is a model of a theory that already solves every existential condition solvable in an extension.

Exit pupil

The exit pupil, also called the Ramsden disc, is the circle of light a telescope or binocular delivers to the eye, its size equaling aperture divided by magnification.

Exogeny

Exogeny, also called exogeneity, refers to external drivers as opposed to internal ones, distinguishing surface processes from Earth's interior forces, environmental toxins from genetic causes, and outside variables from those within a model.

Exoplanet

An exoplanet, or extrasolar planet, is a planet orbiting a star other than the Sun. Over 6,000 have been confirmed since the first discovery around a Sun-like star in 1995.

Exoplanet atmosphere

An exoplanet atmosphere is the envelope of gas around a planet orbiting a star other than the Sun, studied by the fingerprints its molecules leave on starlight.

Exoplanet atmospheric chemistry

Exoplanet atmospheric chemistry is the study of chemical composition in atmospheres of planets orbiting other stars, inferred from spectroscopy and models, with detections of water, methane, and carbon dioxide.

Exoplanet biosignature false-positive framework (abiotic O2)

The exoplanet biosignature false-positive framework for abiotic O2 distinguishes life-produced atmospheric oxygen from oxygen made without life, chiefly on planets orbiting M dwarf stars, using observational tests.

Exoplanet magnetic field

An exoplanet magnetic field is the global magnetic field generated inside a planet orbiting a star other than the Sun, first directly detected via radio bursts from Beta Pictoris b in the mid-2020s.

Exoplanet phase curve

An exoplanet phase curve is the measurement of a star-planet system's total brightness as the planet orbits, letting astronomers infer an exoplanet's atmosphere, clouds, winds, and heat distribution without imaging it.

Exopolymeric substances

Exopolymeric substances (EPS) are organic polymers, mostly polysaccharides and proteins, excreted by microbes such as bacteria and phytoplankton, binding marine snow aggregates and driving biofilm fouling.

Exosphere

The exosphere, also known as the exoatmosphere, is the outermost layer of a planet's atmosphere, where atoms travel without colliding and the fastest escape into space.

Exothermic process

An exothermic process is a chemical or physical change that releases energy to its surroundings as heat, with a negative enthalpy change, as in combustion, freezing, and condensation.

Exothermic reaction

An exothermic reaction is a chemical reaction that releases heat to its surroundings because its enthalpy change is negative; combustion is the most familiar example.

Exotic matter

Exotic matter is matter with negative energy density in general relativity, the substance needed to hold traversable wormholes open and sustain warp bubbles, with the Casimir effect its established source.

Exotic R4

An exotic R4 is a smooth manifold homeomorphic to ordinary Euclidean four-space but not diffeomorphic to it; dimension four is the only one with such structures, and uncountably many exist.

Exotic sphere

An exotic sphere is a smooth manifold that is topologically a sphere but has a different smooth structure, first discovered by John Milnor in dimension 7 in 1956.

Exotic star

An exotic star is a hypothetical compact star composed of matter other than ordinary nuclear matter, including strange stars, quark stars, boson stars, and electroweak stars.

Expander graph

An expander graph is a sparse but highly connected graph, usually studied as constant-degree families, with applications in network design, error-correcting codes, and proof systems.

Expansion of the universe

The expansion of the universe is the increase over time of distances between gravitationally unbound galaxies, at the Hubble rate of about 67 to 74 kilometers per second per megaparsec, and accelerating since 1998.

Expectation propagation

Expectation propagation (EP) is a deterministic approximate Bayesian inference algorithm, introduced by Minka in 2001, that approximates an intractable posterior by iteratively matching moments of local site approximations.

Expectation value (quantum mechanics)

The expectation value in quantum mechanics is the average measurement outcome of an observable, weighted by each result's probability; a single measurement returns an eigenvalue, not the average.

Expectation–maximization algorithm

The expectation–maximization (EM) algorithm, formalized by Dempster, Laird, and Rubin in 1977, is an iterative method for maximum likelihood estimation in statistical models with unobserved latent variables or incomplete data.

Expectation, moments and probability inequalities

Expectation, moments and probability inequalities is an area of probability theory in which expectation and moments measure random variables and inequalities such as Markov's and Chebyshev's bound their deviations.

Expected information gain

Expected information gain is a criterion in Bayesian experimental design measuring how much an experiment reduces uncertainty about unknown parameters; pioneered by Dennis Lindley in 1956.

Expected utility hypothesis

The expected utility hypothesis, also called expected utility theory, says a rational decision maker chooses among risky options by picking the act with the highest expected utility.

Expected value

The expected value, also called the mathematical expectation or mean, is the probability-weighted average of a random variable over repeated trials. Blaise Pascal introduced the concept in 1654.