Physical world and mathematics

Intraplate deformation

Intraplate deformation is tectonic deformation, including faulting, folding, and earthquakes, that occurs within a lithospheric plate's interior, often hundreds to thousands of kilometers from any active plate boundary.

Intravascular brachytherapy

Intravascular brachytherapy (IVBT) is a catheter-based procedure delivering radiation inside an artery or bypass graft to prevent restenosis after angioplasty; first used in 1996, it treats recurrent in-stent restenosis.

Oct 22, 2026

Intrinsic bond orbitals

Intrinsic bond orbitals (IBOs) are localized quantum-chemical orbitals representing occupied space as recognizable bonds, lone pairs, and core orbitals, introduced by Gerald Knizia in 2013.

Intrinsic reaction coordinate

The intrinsic reaction coordinate (IRC) is a minimum-energy reaction path on a potential energy surface, connecting reactants to products through the transition state, proposed by Kenichi Fukui in 1970.

Intrinsic semiconductor

An intrinsic semiconductor, also known as an undoped or I-type semiconductor, is a crystal with no intentional impurity doping, where thermally excited electrons and holes are equal in number (n = p = ni).

Introduction to Automata Theory, Languages, and Computation

Introduction to Automata Theory, Languages, and Computation, nicknamed the Cinderella Book, is a standard textbook on formal languages, automata, and computability by John E. Hopcroft and Jeffrey D. Ullman.

Intuitionism

Intuitionism, also called mathematical intuitionism, is a philosophy of mathematics founded by the Dutch mathematician L. E. J. Brouwer in 1907, treating mathematics as a creation of the mind.

Intuitionistic logic

Intuitionistic logic, also called constructivist logic, is a logic without the law of excluded middle, abstracted by L. E. J. Brouwer's intuitionistic mathematics and formalized by Arend Heyting in 1930.

Inundation model

An inundation model is a computational model that simulates how floodwater spreads over land, predicting water depth and flooded extent from river, coastal, or rainfall events.

Invariant interval

The invariant interval is the quantity Δs² formed from the space and time separations of two events, the same in every inertial reference frame and central to special relativity.

Invariant mass

Invariant mass, also called rest mass or proper mass, is the mass of a particle or system that all inertial observers agree on; for systems it includes internal energy.

Invariant measure

An invariant measure, also called a stationary measure, is a measure left unchanged by a transformation, flow, or Markov kernel, central to ergodic theory and Markov chains.

Invariant subspace

An invariant subspace is a subspace of a vector space that a linear operator maps into itself, the concept underlying eigenvectors, the Jordan canonical form, and a famous open problem.

Invariant theory

Invariant theory is the branch of mathematics that studies polynomial functions left unchanged by a group action, classically begun in Arthur Cayley's 1845 paper and central to Hilbert's finiteness theorem.

Invasive weed optimization

Invasive weed optimization, also known as the invasive weed optimization algorithm, is a population-based metaheuristic for numerical optimization introduced by Mehrabian and Lucas in 2006.

Oct 22, 2026

Inverse catalysts (oxide-on-metal)

An inverse catalyst (oxide-on-metal) is a heterogeneous catalyst in which oxide covers a metal surface or nanoparticles instead of the usual metal-on-oxide geometry, giving active metal-oxide interface sites.

Inverse Compton scattering

Inverse Compton scattering (ICS) transfers energy from high-energy electrons to low-energy photons, raising them to X-ray or gamma-ray energies; it is the reverse of the ordinary Compton effect.

Inverse distance weighting

Inverse distance weighting, also known as Shepard's method, is a spatial interpolation method proposed by Donald Shepard in 1968 that weights nearby measured values by inverse distance.

Inverse eigenvalue problem

The inverse eigenvalue problem asks whether a matrix with prescribed eigenvalues exists within a given structural class, such as symmetric or nonnegative matrices, and how to construct it.

Inverse electron-demand Diels–Alder reaction

The inverse electron-demand Diels–Alder reaction (IEDDA) is a cycloaddition of an electron-poor diene such as a tetrazine with an electron-rich dienophile, used in synthesis and bioorthogonal labeling.

Inverse function

An inverse function is a function that reverses another function, sending each output back to its input. It exists only when the function is bijective.

Inverse function theorem

The inverse function theorem of calculus states that a continuously differentiable map between open sets is locally invertible, with a differentiable inverse, wherever its derivative is invertible.

Inverse Galois problem

The inverse Galois problem asks whether every finite group occurs as the Galois group of a finite Galois extension of the rational numbers; it remains open in general.

Inverse gas chromatography

Inverse gas chromatography (IGC) is a chromatographic technique in which volatile probes of known properties measure the surface and bulk properties of a packed material.

Inverse Gaussian distribution

The inverse Gaussian distribution, also called the Wald distribution, is a continuous probability distribution on positive numbers, arising as the first passage time of Brownian motion.

Inverse hyperbolic functions

The inverse hyperbolic functions, also known as the area hyperbolic functions, are the six inverses of the hyperbolic functions, written arcsinh, arccosh, arctanh, and the reciprocals.

Inverse iteration

Inverse iteration is an eigenvalue algorithm that finds the eigenvector whose eigenvalue lies nearest a chosen shift, working by the power method applied to the inverse shifted matrix.

Inverse limit

The inverse limit, also called the projective limit, is a mathematical construction that assembles objects connected by backward-pointing maps into a single object of compatible choices, used across algebra, topology, and number theory.

Inverse photoemission spectroscopy

Inverse photoemission spectroscopy (IPES), formerly bremsstrahlung isochromat spectroscopy, probes unoccupied electronic states above the Fermi level: electrons of known energy strike a sample, and emitted photons are detected.