Physical world and mathematics

Fourier transform

The Fourier transform, also called Fourier transformation, is a mathematical operation that converts a function of time or space into a function of frequency, named for Joseph Fourier and central to signal processing and differential equations.

Fourier transform holography

Fourier transform holography (FTH) is a lensless imaging technique that reconstructs an object from a hologram with a reference wave by a single Fourier transform.

Fourier transform infrared spectroscopy imaging

Fourier transform infrared (FTIR) spectroscopy imaging is a label-free chemical imaging technique that maps the spatial distribution of chemical components in a sample without stains.

Fourier transform microwave spectroscopy

Fourier transform microwave spectroscopy measures rotational transition frequencies of polar molecules in a pulsed supersonic jet; rotational constants yield molecular geometries, and chirped-pulse variants cover 10 GHz or more in a single shot.

Fourier-transform infrared spectroscopy

Fourier-transform infrared spectroscopy (FTIR or FT-IR) is an analytical technique that measures how molecules absorb infrared radiation, used to identify substances in diagnostics, food inspection, and environmental monitoring.

Fourier-transform ion cyclotron resonance mass spectrometry

Fourier-transform ion cyclotron resonance mass spectrometry (FT-ICR MS) traps ions in a magnetic field and measures their masses with the highest resolution of any mass analyzer.

Fourier-transform mass spectrometry

Fourier-transform mass spectrometry (FTMS) is a class of mass spectrometry in which trapped ions are excited into coherent motion, and a Fourier transform of the recorded signal yields a mass spectrum with very high resolution.

Fourier-transform near-infrared spectroscopy

Fourier-transform near-infrared (FT-NIR) spectroscopy is an analytical technique using a Michelson interferometer to record near-infrared absorption spectra, used for composition analysis, quality control, and process monitoring.

Fourier-transform spectroscopy

Fourier-transform spectroscopy (FTS) measures a spectrum by recording light intensity versus path difference in a Michelson interferometer and computing the interferogram's Fourier transform.

Fourier–Mukai transform

The Fourier–Mukai transform is a functor between the derived categories of coherent sheaves on smooth projective varieties that is an exact equivalence, introduced by Shigeru Mukai in 1981.

Fourier's law of heat conduction

Fourier's law of heat conduction, formulated by Joseph Fourier in 1822, states that heat flows in proportion to the temperature gradient, with thermal conductivity as the proportionality constant.

Fourth-order gravity

Fourth-order gravity, also known as quadratic or higher-derivative gravity, is a class of modified gravity theories whose field equations contain derivatives of the metric up to fourth order.

Fourth, fifth, and sixth derivatives of position

The fourth, fifth, and sixth derivatives of position, called snap (jounce), crackle, and pop, extend the sequence of velocity, acceleration, and jerk; they appear in ride comfort studies and quadrotor trajectory planning.

Fowler–Nordheim tunneling

Fowler–Nordheim tunneling is quantum-mechanical tunneling of electrons through a triangular potential barrier created by a strong electric field, derived by Fowler and Nordheim in 1928.

FR-4

FR-4, also called Flame Retardant 4, is a NEMA grade of flame-retardant woven-glass epoxy laminate rated UL 94 V-0 that serves as the base material of most printed circuit boards.

Fractal

A fractal is a geometric object whose structure repeats across scales, so magnifying a part reveals detail resembling the whole; the term was coined by Benoît Mandelbrot in 1975.

Fractal analysis

Fractal analysis is a family of mathematical and statistical methods that quantify self-similar, scale-invariant structure in images, point sets, and time series, used in physics, biomedical imaging, and machine learning.

Fractal cosmology

Fractal cosmology is a family of proposals in physical cosmology that the galaxy distribution, or spacetime itself, is fractal; SDSS and WiggleZ surveys find homogeneity beyond roughly 70–100 megaparsecs.

Fractal dimension

The fractal dimension measures how an object's size grows as measurement scale shrinks, taking non-integer values for irregular sets; Mandelbrot estimated Britain's coastline at 1.25 in 1967.

Oct 22, 2026

Fractal topological insulators

Fractal topological insulators are topological phases of matter defined on fractal lattices, such as the Sierpiński carpet and gasket, which lack translational symmetry and occupy a fractional dimension.

Fraction

A fraction is a number written a over b, representing a parts of a whole divided into b equal parts, with a the numerator and b the denominator.

Fractional Brownian motion

Fractional Brownian motion is a centered Gaussian stochastic process, defined by Mandelbrot and Van Ness in 1968, that generalizes Brownian motion with correlated increments governed by a Hurst parameter.

Fractional calculus

Fractional calculus is the branch of mathematical analysis that extends differentiation and integration to arbitrary, non-integer order, with more than fifteen competing definitions, including Riemann–Liouville and Caputo.

Fractional Chern insulator

A fractional Chern insulator is a fractionally filled topological band in a crystal whose interactions produce fractional quantized Hall conductance and anyonic excitations without a magnetic field.

Fractional crystallization

Fractional crystallization is a stagewise chemical separation method that crystallizes mixture components in sequence using solid–liquid equilibria, reaching purities above 99% and historically used to separate rare-earth salts.

Fractional differential equation

A fractional differential equation is a differential equation in which the derivative is taken to a non-integer order, making it a tool for modeling systems with memory.

Fractional diffusion equation

A fractional diffusion equation is a partial differential equation that replaces an integer-order derivative with a fractional one to model anomalous diffusion in porous media, finance, biology, and hydrology.

Fractional distillation

Fractional distillation is a separation technique that boils a mixture of miscible liquids and repeatedly condenses and revaporizes the vapors in a fractionating column, enriching the distillate in the lower-boiling component.

Fractional factorial design

A fractional factorial design is a designed experiment running only a selected fraction of a full factorial's treatment combinations, trading estimable effects for large run savings in industrial screening.