Physical world and mathematics

Dual carbon goals

The dual carbon goals (双碳目标) are China's climate commitments, announced by Xi Jinping in 2020, to peak carbon emissions before 2030 and reach carbon neutrality before 2060.

Dual dynamic programming (DDP), also called stochastic dual dynamic programming (SDDP), is an algorithm for multistage stochastic optimization that approximates future costs with Benders cuts, developed for Brazilian hydrothermal power planning.

Dual graph

The dual graph, or planar dual, of a planar graph has one vertex for each face and one edge for each pair of faces sharing an edge.

Dual map

The dual map, also called the transpose, is the linear map between dual spaces that a linear map induces, running in the opposite direction; its matrix is the transpose.

Dual matroid

The dual matroid of a matroid M is the matroid M on the same ground set whose bases are the complements of M's bases, introduced by Hassler Whitney in 1935.

Dual module

The dual module of a module M is Hom_R(M, R), the module of linear maps from M to the ring R, generalizing dual vector spaces.

Dual number

A dual number is an expression of the form a + εb, where ε is nonzero with ε² = 0, introduced by Clifford in 1873 and used in automatic differentiation.

Dual pair of topological vector spaces

A dual pair of topological vector spaces is two vector spaces over the same field with a non-degenerate bilinear form and topologies built from that pairing.

Dual photoredox–cobaloxime catalysis

Dual photoredox–cobaloxime catalysis is a two-catalyst strategy in organic synthesis, merged in 2015, that pairs a visible-light photoredox catalyst with a cobaloxime, a vitamin B12 mimic.

Dual polarization interferometry

Dual polarization interferometry (DPI) is a label-free optical biosensing technique that measures the thickness, density, and mass of molecular layers adsorbing at a solid–liquid interface in real time.

Dual polyhedron

A dual polyhedron is a polyhedron paired with another so that the faces of one occupy the positions of the vertices of the other, exchanged by reciprocation.

Dual quasar

A dual quasar is a pair of quasars powered by two different supermassive black holes, shining simultaneously in a single merging galaxy system, typically separated by kiloparsecs.

Dual quaternion

A dual quaternion is an eight-component number, formed from two quaternions and the nilpotent dual unit ε, that represents a rigid-body pose, combining rotation and translation compactly.

Dual representation

The dual representation, or contragredient representation, is the representation a group or Lie algebra induces on the dual space of its representation space, preserving the natural pairing.

Dual space

The dual space of a vector space V is the vector space V of all linear functionals on V, that is, linear maps from V to its scalar field.

Dual Z-scheme heterojunction

A dual Z-scheme heterojunction is a ternary photocatalyst architecture in which two Z-scheme charge-transfer pathways connect three semiconductors, so weak carriers recombine while strongly reductive and oxidative carriers are retained.

Dual-atom catalysts

Dual-atom catalysts are heterogeneous catalysts in which two metal atoms anchored on a support, usually nitrogen-doped carbon, act together as the catalytic site, extending single-atom catalysts.

Dual-comb spectroscopy

Dual-comb spectroscopy is an optical technique that measures a sample's absorption and phase spectrum across a broad bandwidth by interfering two frequency combs whose repetition rates differ slightly.

Dual-cycle hydrocarbon pool mechanism

The dual-cycle hydrocarbon pool mechanism describes how acid zeolite catalysts convert methanol into hydrocarbons through two interlinked cycles, one based on olefins and one on aromatics.

Dual-porosity model

The dual-porosity model is a mathematical representation of a fractured porous medium treating rock as two overlapping continua, fractures and porous matrix, introduced by Barenblatt and colleagues in 1960.

Dual-rail qubit

A dual-rail erasure qubit is a quantum bit encoded in one photon shared between two modes, so photon loss becomes a detectable erasure that improves error correction.

Dualite

Dualite is a rare yellow zircono-titanosilicate mineral of the eudialyte group, approved by the International Mineralogical Association in 2005 and found at Mount Alluaiv, Russia.

Dualizing sheaf

The dualizing sheaf is a coherent sheaf on a Noetherian scheme representing duality on coherent sheaves, generalizing the canonical bundle to singular spaces and underlying Serre and Grothendieck duality.

Dubnium

Dubnium, formerly known as unnilpentium, is a synthetic chemical element with symbol Db and atomic number 105, first reported in 1967 and named after Dubna, Russia.

Duck test

The duck test is an abductive heuristic that identifies something from converging familiar signs: if it looks, swims, and quacks like a duck, it probably is one.

Duct (flow)

A duct, also called a heating or air duct, is a closed conduit with a noncircular cross-section used to carry fluids, most commonly air in HVAC systems.

Ductility

Ductility is the ability of a solid material to deform permanently under tensile stress before it fractures, measured as percent elongation or reduction in area; mild steel and copper are ductile.