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Quadratic formula
The quadratic formula, also called Sridharacharya's formula, is an algebraic formula giving the roots of any quadratic equation directly from its coefficients, derived by completing the square.
Quadratic function
A quadratic function, also called a quadratic trinomial or second-order polynomial, is a polynomial of degree two, written f(x) = ax² + bx + c, whose graph is a parabola.
Quadratic interpolation
Quadratic interpolation is a numerical analysis method that estimates intermediate function values by fitting the unique parabola through three known data points and evaluating it between them.
Quadratic programming
Quadratic programming (QP) optimizes a quadratic objective function subject to linear constraints. Convex QP is solvable reliably and arises in portfolio optimization, support vector machines, and model predictive control.
Quadratic reciprocity
Quadratic reciprocity is a number theory theorem relating the solvability of x² ≡ q (mod p) and x² ≡ p (mod q) for distinct odd primes.
Quadratic regression
Quadratic regression is a statistical method that fits a second-degree polynomial curve to data, estimating U-shaped or inverted-U relationships between one predictor and an outcome.
Quadratic residue
Quadratic residue, also called quadratic residuosity, describes an integer a for which x² ≡ a (mod m) is solvable; the concept underlies quadratic reciprocity and cryptosystems like Goldwasser–Micali.
Quadratic sieve
The quadratic sieve is a general-purpose integer factorization algorithm invented by Carl Pomerance in 1981, fastest known until 1996 and still used below roughly 100 digits.
Quadratic variation
Quadratic variation, also called the bracket or quadratic-variation process, measures a stochastic process's accumulated squared fluctuations; for Brownian motion it equals t, which produces the second-order term in Itô's formula.
Quadrature rule
A quadrature rule is a numerical method that approximates a definite integral of a function by a weighted sum of its values at selected points, or nodes.
Quadric
A quadric, also known as a quadric surface or quadric hypersurface, is a geometric set defined by a degree-two polynomial equation; ellipsoids, hyperboloids, cones, cylinders, and paraboloids are familiar quadric surfaces.
Quadricyclane
Quadricyclane is a highly strained tetracyclic hydrocarbon formed when norbornadiene absorbs light, first observed in 1961 and the most studied molecule for molecular solar thermal energy storage.
Quadrilateral
A quadrilateral is a polygon with four sides and four vertices, such as a square, rectangle, parallelogram, or trapezoid, with interior angles summing to 360°.
Quadrivium
The quadrivium is the group of four mathematical arts of the classical seven liberal arts: arithmetic, geometry, music, and astronomy. It followed the trivium in medieval university education.
Quadruple bond in C2
The quadruple bond in C2 is a proposed description of bonding in the dicarbon molecule, with a weak fourth bond added to one σ and two π bonds, proposed by Sason Shaik in 2012.
Quadrupolar order
Quadrupolar order is a type of electronic order in solids in which the electric quadrupole moments of ions align into a long-range pattern without magnetic order, studied chiefly in cubic Pr compounds.
Quadrupole
A quadrupole is the third term in the multipole expansion of an electric, magnetic, or gravitational field, arising when the monopole and dipole moments of a charge distribution vanish.
Quadrupole formula
The quadrupole formula, first derived by Einstein in 1916 and corrected in 1918, gives the energy radiated as gravitational waves by an isolated mass distribution.
Quadrupole interaction
The quadrupole interaction is an electrostatic interaction involving the quadrupole moment, the second-rank moment remaining after charge and dipole; it shapes the adsorption and phase behavior of molecules like CO₂.
Quadrupole magnet
A quadrupole magnet, or Q-magnet, is an accelerator magnet with four poles that focuses a charged-particle beam in one plane and defocuses it in the other.
Quadrupole mass spectrometry
Quadrupole mass spectrometry separates and detects ions by mass-to-charge ratio using oscillating radiofrequency and DC fields between four parallel rods, and anchors GC-MS, LC-MS/MS, and ICP-MS.
Quadrupole time-of-flight mass spectrometry
Quadrupole time-of-flight mass spectrometry (Q-TOF-MS, also written QTOF or QqTOF) is a tandem mass spectrometry technique that combines a quadrupole mass filter with a high-resolution time-of-flight analyzer.
Quadrupole topological insulator
A quadrupole topological insulator (QTI) is a two-dimensional higher-order topological insulator whose quantized bulk quadrupole moment appears as in-gap corner states rather than conducting edges.
Quadrupole triplet lens
A quadrupole triplet lens is a beam-focusing system of three quadrupole lenses with alternating polarities, used to focus charged-particle beams to micrometer-scale spots in nuclear microprobes.
Qualitative coding
Qualitative coding is a social science analysis method in which researchers assign short labels, called codes, to data segments and group them into categories and themes.
Qualitative comparative analysis
Qualitative comparative analysis (QCA) is a set-theoretic research method introduced by Charles Ragin in 1987 that compares cases to find conditions necessary or sufficient for an outcome.
Qualitative content analysis
Qualitative content analysis is a social science method for interpreting text data through systematic coding and identifying themes, heavily used in healthcare and public health research.
Qualitative document analysis
Qualitative document analysis is a systematic research method for reviewing and interpreting documentary evidence, such as reports, policies, and archival records, to answer specific research questions.
Qualitative meta-analysis
A qualitative meta-analysis, also called qualitative meta-synthesis, is a systematic synthesis that interprets findings from several qualitative studies to produce themes, translated concepts, or lines of argument.
Qualitative research
Qualitative research is a method of inquiry that analyzes open-ended data, such as interviews and documents, to understand reasons, opinions, and motivations rather than measure frequencies with numbers.