Physical world and mathematics

Multiple-try Metropolis

Multiple-try Metropolis (MTM) is a Markov chain Monte Carlo algorithm introduced by Liu, Liang, and Wong in 2000, drawing several candidate states each step and selecting among them by weight.

Multiplication

Multiplication is one of the four basic arithmetic operations, producing a product that represents repeated addition of one number a number of times equal to another.

Multiplication algorithm

A multiplication algorithm is a procedure for computing the product of two numbers or polynomials, from schoolbook long multiplication up to Karatsuba's and FFT-based methods approaching O(n log n).

The multiplication sign (×), also called the times sign, is a mathematical symbol for multiplication shaped as a diagonal cross, introduced by William Oughtred in 1631 and standard in elementary arithmetic.

Multiplication table

A multiplication table, also known as a times table, is a table showing the products of pairs of numbers, typically up to 10 or 12.

Multiplicative function

A multiplicative function is an arithmetic function on the positive integers with f(ab) = f(a)f(b) whenever gcd(a, b) = 1; examples include Euler's totient and the Möbius function.

Multiplicative group of integers modulo n

The multiplicative group of integers modulo n, also written Z n, is the finite abelian group of residue classes coprime to n, with order given by Euler's totient function.

Multiplicative inverse

A multiplicative inverse of a, written a⁻¹, is an element that multiplies a to give 1; for ordinary nonzero numbers it is the reciprocal, 1/a, and zero has none.

Multiplicative noise

Multiplicative noise is random forcing whose amplitude depends on the state of the system it perturbs, unlike additive noise, which has a constant amplitude. It appears in stochastic differential and partial differential equations.

Multiplicative order

The multiplicative order of an integer a modulo n is the smallest positive k with a^k ≡ 1 (mod n); it always divides Euler's totient φ(n).

Multipole expansion

The multipole expansion is a series representation of the potential or field of a localized charge or current source, valid outside the source region, with monopole, dipole, quadrupole, and higher terms.

Multipole radiation

Multipole radiation is electromagnetic or gravitational radiation whose angular structure is described by a multipole expansion, ordered by l, that begins with the lowest moment conservation laws allow.

Multiproxy analysis

Multiproxy analysis is a paleoclimate method that combines independent proxies, such as tree rings, pollen, and isotopes, to reconstruct past temperature as a single curve with quantified uncertainty.

Multireference configuration interaction

Multireference configuration interaction (MRCI) is a quantum chemistry method that expands the wavefunction over multiple reference configurations with single and double excitations, used for bond breaking, transition metals, and excited states.

Multiresolution analysis

Multiresolution analysis (MRA) is a framework in wavelet and harmonic analysis that decomposes a signal into coarse approximations plus detail components at successively finer scales.

Multiscale geographically weighted regression

Multiscale geographically weighted regression (MGWR) is a spatial statistics method, introduced by A. Stewart Fotheringham and colleagues in 2017, that extends geographically weighted regression by giving each predictor variable its own spatial bandwidth.

Multiset

A multiset, also called a bag, is a mathematical collection in which elements may appear more than once, each carrying a multiplicity, unlike an ordinary set where repeats collapse.

Multislice method

The multislice method is a numerical technique in electron microscopy that simulates electron scattering by dividing a specimen into thin slices, introduced by Cowley and Moodie in 1957.

Multispectral optoacoustic tomography

Multispectral optoacoustic tomography (MSOT) is an imaging method that illuminates tissue with multiple laser wavelengths and detects ultrasound, separating hemoglobin, oxygenation, and contrast agents by their absorption spectra.

Multistage sampling

Multistage sampling is a survey design that first selects clusters, then subsamples units within them, reducing framing costs; it underlies surveys such as the CPS and NHANES.

Multistate analysis

Multistate analysis is a statistical method for modeling how individuals move stochastically among a finite set of states over time, estimating transition rates and state probabilities.

Multistate model

A multistate model is a statistical model for continuous-time stochastic processes in which individuals move among a finite number of states, used in survival analysis and medical statistics.

Multitaper

The multitaper method is a nonparametric spectral estimation technique that reduces variance by averaging periodograms from orthogonal Slepian tapers, reported by D. J. Thomson in 1982.

Multivariable calculus

Multivariable calculus, also called multivariate calculus, is the branch of calculus extending differentiation and integration to functions of several variables and vector fields, culminating in Green's, Stokes', and Gauss' theorems.

Multivariate adaptive regression splines

Multivariate adaptive regression splines (MARS) is a nonparametric regression method introduced by Jerome H. Friedman in 1991, which fits a response with spline basis functions whose knots are chosen automatically from the data.

Multivariate analysis of variance

Multivariate analysis of variance (MANOVA) is a statistical procedure extending ANOVA to two or more correlated dependent variables, tested simultaneously using statistics such as Wilks' Lambda.

Multivariate calibration

Multivariate calibration is a chemometric method that builds a mathematical model relating many spectral signals to an analyte's concentration, so new samples can be quantified.

Multivariate curve resolution

Multivariate curve resolution (MCR) is a chemometric method that decomposes overlapping spectroscopy, chromatography, and imaging data into pure spectra and concentration profiles without prior separation.

Multivariate empirical mode decomposition

Multivariate empirical mode decomposition (MEMD) is a signal-processing method that decomposes multichannel, non-stationary data into scale-aligned intrinsic mode functions, introduced by Rehman and Mandic in 2009.