Physical world and mathematics

Directed C–H trifluoromethylation

Directed C–H trifluoromethylation is the site-selective replacement of a carbon–hydrogen bond with a trifluoromethyl group, where a directing group positions a metal catalyst, such as palladium, at a chosen site.

Sep 29, 2026

Directed content analysis

Directed content analysis is a deductive qualitative research method that applies theory-derived coding categories to text to validate or extend the theory, one of three content analysis approaches.

Directed evolution of enzymes for the Diels–Alder reaction

Directed evolution of enzymes for the Diels–Alder reaction iteratively mutagenizes and screens proteins to create biocatalysts for the [4+2] cycloaddition of a diene and dienophile to a cyclohexene product.

Directed graph

A directed graph, or digraph, is a graph whose edges are ordered pairs of vertices, drawn as arrows followed in one direction, modeling one-way streets, social networks, and dependencies.

Directed ortho metalation

Directed ortho metalation, also called ortho-lithiation, is an organic chemistry strategy in which a directing substituent guides strong bases to metalate the ortho position of aromatic rings regioselectively.

Directed percolation

Directed percolation is a nonequilibrium stochastic process in which activity spreads along a preferred direction, usually time, and it defines the principal universality class of continuous transitions into absorbing states.

Directed percolation transition in turbulence

The directed percolation transition in turbulence describes the onset of turbulence in shear flows as a non-equilibrium phase transition in the directed percolation class, proposed by Y. Pomeau in 1986.

Direction (geometry)

Direction, also called spatial direction or the direction of a line, is which way a line, ray, or displacement points, independent of position and often of length.

Direction cosines

Direction cosines are the cosines of the angles a directed line or vector in 3D space makes with the positive coordinate axes, equal to the components of the unit vector along it.

Directional dark matter detectors

A directional dark matter detector reconstructs the direction of nuclear recoils from galactic dark matter, typically using a low-pressure gaseous time projection chamber that images recoil tracks.

Directional derivative

The directional derivative of a multivariable function is its rate of change at a point along a chosen direction, generalizing the ordinary derivative of single-variable calculus.

Directional dichroism

Directional dichroism, also called nonreciprocal directional dichroism or the optical diode effect, is a difference in absorption of counter-propagating light, seen from microwave to X-ray.

Directional drilling

Directional drilling, also called slant drilling, is the practice of drilling a well at an angle to reach oil or gas reservoirs from a surface location away from the target.

Directional thermal emission from metasurfaces

Directional thermal emission from metasurfaces is the control of thermal radiation angles using two-dimensional subwavelength nanostructure arrays, applied in infrared sensing, radiative cooling, and thermophotovoltaics.

Dirham (درهم)

The dirham (درهم) is a silver coin and weight of the Islamic world from the 7th century, now the currency of the UAE and Morocco.

Dirhodium carbene C–H insertion

Dirhodium carbene C–H insertion is a C–H functionalization reaction in which a carbene generated from a diazo compound and bound to a dirhodium catalyst inserts into a C–H bond.

Dirhodium-catalyzed enantioselective C–H amination

A reaction in which a chiral dirhodium(II) catalyst converts an organic molecule's carbon–hydrogen bond into a carbon–nitrogen bond, creating a stereocenter with preference for one enantiomer.

Dirichlet algebra

A Dirichlet algebra is a uniform algebra of continuous functions on a compact space whose real parts are dense in all real continuous functions, defined by Gleason in 1958.

Dirichlet boundary condition

The Dirichlet boundary condition, also known as the first-type or fixed boundary condition, requires a partial differential equation's solution to equal given values on the domain's boundary.

Dirichlet character

A Dirichlet character modulo q is a completely multiplicative, periodic function vanishing on integers not coprime to q, central to Dirichlet's 1837 theorem on primes in arithmetic progressions.

Dirichlet conditions

The Dirichlet conditions are sufficient conditions on a periodic function, including absolute integrability over one period, guaranteeing pointwise convergence of its Fourier series, first proved by Dirichlet in 1829.

Dirichlet convolution

Dirichlet convolution is a binary operation on arithmetic functions, combining two functions by summing f(d)g(n/d) over divisor pairs of n, named after the German mathematician Dirichlet.

Dirichlet distribution

The Dirichlet distribution is a continuous multivariate probability distribution over vectors of proportions summing to one, generalizing the beta distribution and serving as the conjugate prior to the multinomial distribution.

Dirichlet divisor problem

The Dirichlet divisor problem in number theory seeks the smallest exponent bounding the error term in the asymptotic formula for the summatory divisor function, conjectured to be 1/4.

Dirichlet eta function

The Dirichlet eta function, also called the alternating zeta function, is defined by the series 1 − 2−s + 3−s − ⋯, convergent for Re(s) > 0.

Dirichlet form

A Dirichlet form is a closed, symmetric, Markovian quadratic form on an L²-space, introduced by Beurling and Deny, linking potential theory to symmetric Markov processes.

Dirichlet integral

The Dirichlet integral is the improper integral of sin x over x from 0 to infinity, equal to π/2, named after Peter Gustav Lejeune Dirichlet.

Dirichlet L-function

A Dirichlet L-function (Dirichlet L-series) is a meromorphic function L(s, χ) defined by a Dirichlet character, introduced in 1837 to prove Dirichlet's theorem on primes in arithmetic progressions.

Dirichlet problem

The Dirichlet problem is the potential-theory problem of finding a function harmonic in a domain, satisfying the Laplace equation, that takes prescribed values on the domain's boundary.