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Longer titles found: Quadratic-linear algebra (view), Quadratic (collection) (view), Quadratic Fourier transform (view), Quadratic Frobenius test (view), Quadratic Gauss sum (view), Quadratic Jordan algebra (view), Quadratic Lie algebra (view), Quadratic algebra (view), Quadratic assignment problem (view), Quadratic bottleneck assignment problem (view), Quadratic classifier (view), Quadratic configuration interaction (view), Quadratic differential (view), Quadratic eigenvalue problem (view), Quadratic equation (view), Quadratic field (view), Quadratic form (view), Quadratic form (statistics) (view), Quadratic formula (view), Quadratic function (view), Quadratic growth (view), Quadratic integer (view), Quadratic integral (view), Quadratic integrate and fire (view), Quadratic irrational number (view), Quadratic knapsack problem (view), Quadratic mean diameter (view), Quadratic pair (view), Quadratic probing (view), Quadratic programming (view), Quadratic pseudo-Boolean optimization (view), Quadratic quadrilateral element (view), Quadratic reciprocity (view), Quadratic residue (view), Quadratic residue code (view), Quadratic residuosity problem (view), Quadratic set (view), Quadratic sieve (view), Quadratic transformation (view), Quadratic unconstrained binary optimization (view), Quadratic variation (view), Quadratic voting (view), Quadratically closed field (view), Quadratically constrained quadratic program (view), Quadratics (view), Definite quadratic form (view), U-quadratic distribution (view), Complex quadratic polynomial (view), Sequential quadratic programming (view), Isotropic quadratic form (view), Linear–quadratic–Gaussian control (view), Linear–quadratic regulator (view), Binary quadratic form (view), Solving quadratic equations with continued fractions (view), Ε-quadratic form (view), Rational quadratic covariance function (view), Ramanujan's ternary quadratic form (view), Proofs of quadratic reciprocity (view), Inverse quadratic interpolation (view), Somos' quadratic recurrence constant (view), Periodic points of complex quadratic mappings (view), Hasse invariant of a quadratic form (view), Genus of a quadratic form (view), Tensor product of quadratic forms (view), Sequential linear-quadratic programming (view), Universal quadratic form (view)

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S x {\displaystyle \mathrm {RMS} _{x}} . The RMS is also known as the quadratic mean (denoted M 2 {\displaystyle M_{2}} ), a special case of the generalized

general-purpose sorts run in linear time, but the change from quadratic to sub-quadratic is of great practical importance. An algorithm is said to be of

It is often useful to specify quadratic degrees of freedom. These are degrees of freedom that contribute in a quadratic function to the energy of the

require exponentially many steps, and Grover's algorithm provides at most a quadratic speedup over the classical solution for unstructured search, this suggests

extension is a trivial extension. Extensions of degree 2 and 3 are called quadratic extensions and cubic extensions, respectively. A finite extension is an

Online tools for linear Archived 2016-09-18 at the Wayback Machine, quadratic Archived 2016-09-18 at the Wayback Machine, cubic spline Archived 2016-08-20

_{i=1}^{N}\left(x_{i}-{\bar {x}}\right)^{2}}},} The error in this approximation decays quadratically (as ⁠1/N2⁠), and it is suited for all but the smallest samples or highest

+ ⋯ + a n n {\displaystyle A={\frac {a_{1}+a_{2}+\cdots +a_{n}}{n}}} Quadratic mean : Q = a 1 2 + a 2 2 + ⋯ + a n 2 n {\displaystyle Q={\sqrt {\frac

triangles (see affine texture mapping above). The NV1 hardware also allowed a quadratic interpolation mode to provide an even better approximation of perspective

effect is either linear (proportional to the applied electric field) or quadratic with a high accuracy. The Stark effect can be observed both for emission

In mathematics, a square-integrable function, also called a quadratically integrable function or L 2 {\displaystyle L^{2}} function or square-summable

the Λ-quadratic form (h, q) on M. A quadratic module over (R, Λ) is a triple (M, h, q) such that M is an R-module and (h, q) is a Λ-quadratic form. To

then there is a quadratic transformation of the hypergeometric function, connecting it to a different value of z related by a quadratic equation. The first

The tap code, sometimes called the knock code, is a way to encode text messages on a letter-by-letter basis in a very simple way. The message is transmitted

type. (Note: while the polynomial piece 2t is not quadratic, the result is still called a quadratic spline. This demonstrates that the degree of a spline

The Mahalanobis distance is a measure of the distance between a point P {\displaystyle P} and a distribution D {\displaystyle D} , introduced by P. C.

relies on first analyzing the internals of a cipher and deriving a set of quadratic simultaneous equations. These systems of equations are typically very

This is a list of articles about prime numbers. A prime number (or prime) is a natural number greater than 1 that has no positive divisors other than 1

In mathematics, in the area of abstract algebra known as Galois theory, the Galois group of a certain type of field extension is a specific group associated

A neume (/njuːm/; sometimes spelled neum) is the basic element of Western and some Eastern systems of musical notation prior to the invention of five-line

out for its use of quadratic texture mapping, a departure from the triangular primitives favored by competitors. The use of quadratics made it possible

is that of linear quadratic Gaussian control. Here the model is linear, the objective function is the expected value of a quadratic form, and the disturbances

The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary smooth potential can usually

problem (for imaginary quadratic fields), as usually understood, is to provide for each n ≥ 1 a complete list of imaginary quadratic fields Q ( d ) {\displaystyle

data sets, much like other quadratic (i.e., O(n2)) sorting algorithms More efficient in practice than most other simple quadratic algorithms such as selection

body dynamics in 1931. The most commonly-used Casimir invariant is the quadratic invariant. It is the simplest to define, and so is given first. However

create a quadratic Koch island or Minkowski island/[snow]flake: Islands Self-avoiding walk Vicsek fractal Quadratic Koch curve type 2 Quadratic Koch curve

the mathematical concept of envelope of a family of straight lines). Quadratic Bézier curve are obtained from strings based on two intersecting segments

from a quadratic form associated to a Seifert surface. If F is a Seifert surface of a knot, then the homology group H1(F, Z/2Z) has a quadratic form whose

environment, they may be approximated by Bézier curves. Commonly, eight quadratic segments or four cubic segments are used to approximate a circle. It is

r-th mean to X for r = 2, we say that Xn converges in mean square (or in quadratic mean) to X. Convergence in the r-th mean, for r ≥ 1, implies convergence

the algorithm checks for edges for all pairs of nodes, the runtime is quadratic. For applications where N {\displaystyle N} is big, this is not viable

numerical integration proposed by Thomas Simpson. It is based upon a quadratic interpolation and is the composite Simpson's 1/3 rule evaluated for n

and any μ {\displaystyle \mu } is called quadratic convergence and the sequence is said to converge quadratically. Convergence with q = 3 {\displaystyle

placement. Quadratic placement is an early analytical method that models interconnect length by a quadratic function and uses high-performance quadratic optimization

previous section is the linear quadratic (LQ) optimal control problem. The LQ problem is stated as follows. Minimize the quadratic continuous-time cost functional

of A is a direct sum of one-dimensional modules. Consider an imaginary quadratic field K = Q ( − d ) , d ∈ Z , d > 0 {\textstyle K=\mathbb {Q} \left({\sqrt

roofs approximating the yurt's round shape. Further expansion led to a quadratic shape in the design of the temples, with roofs in the shape of pole marquees

Squaric acid, also called quadratic acid because its four carbon atoms approximately form a square, is a diprotic organic acid with the chemical formula

the General Directorate of Foundations. The mosque is a single-dome, quadratic-plan building having stone masonry walls alternating with brick. There

chapter called "Logical Necessities in Mixed Equations", on the solution of quadratic equations, has survived. The manuscript gives exactly the same geometric

be one unique initial angle and path that will land on the terminus. A quadratic with two real roots, for example, will have exactly two angles that satisfy

the case of a cubic equation, this resolvent is sometimes called the quadratic resolvent; its roots appear explicitly in the formulas for the roots of

mind. QUAD relies on the iteration of a randomly chosen multivariate quadratic system S=(Q1, ..., Qm) of m=kn equations in n unknowns over a finite field

Hardy-Ramanujan-Hecke asymptotic formula for representation by positive definite quadratic forms. His other notable findings include the determination of the structure

contain any variables and therefore is constant. For example, in the quadratic polynomial, x 2 + 2 x + 3 ,   {\displaystyle x^{2}+2x+3,\ } The number

In theoretical computer science and cryptography, a trapdoor function is a function that is easy to compute in one direction, yet difficult to compute

components. Those effects are referred to as Voigt effect or quadratic Kerr effect. Quadratic magneto-optic Kerr effect (QMOKE) is found strong in Heusler

staircases flanking the narthex lead to women's and muezzin section. The quadratic-plan mosque was constructed in limestone ashlar. Its inside is plastered

hardness of the problem of finding solutions to a system of multivariate quadratic equations (the so-called MQ problem) since it uses private affine transformations

double-angle formula with supplementary-angle formula to get the nested quadratic polynomial below. cos ⁡ 2 m π 17 = 2 cos 2 ⁡ m π 17 − 1 {\displaystyle

three-story stone house with a high, split roof that lies around an almost quadratic yard. In two corners there are large, square towers. On both sides of

In a quantum computer, amplitude amplification can be used to obtain a quadratic speedup over several classical algorithms. The derivation presented here

algebraic geometry, an elliptic curve E over a field K has an associated quadratic twist, that is another elliptic curve which is isomorphic to E over an

needed for the following goal.) The design should be sufficient to fit a quadratic model, that is, one containing squared terms, products of two factors

constructible. n = 5: The field Q(ζ5) is not a quadratic extension of Q, but it is a quadratic extension of the quadratic extension Q(√5 ), so a regular 5-gon is

to polarisability and basicity. The Marcus equation is an example of a quadratic free-energy relationship (QFER).[citation needed] IUPAC has suggested

boundaries one element to the right. The time efficiency of selection sort is quadratic, so there are a number of sorting techniques which have better time complexity

the distribution of quadratic residues, and in particular in the classical question of finding an upper bound for the least quadratic non-residue modulo

connect the hidden neurons to output neurons. Thus, the error function is quadratic with respect to the parameter vector and can be differentiated easily

Mevlana. It is so one of the oldest buildings in Eskişehir. The almost-quadratic rectangular-plan mosque is constructed in rubble masonry. An octagonal

In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element

launched a new subject, and a new school, studying properties of iterated quadratic complex mappings. They made important mathematical contributions in this

connect the hidden neurons to output neurons. Thus, the error function is quadratic with respect to the parameter vector and can be differentiated easily

of 23 quadratic equations in 80 terms. The key schedule can be described by 1,120 equations in 768 variables using 3,328 linear and quadratic terms.

} describes the rotations. In the case of rigid bodies, the so-called quadratic velocity vector Q v {\displaystyle \mathbf {Q} _{v}} is used to describe

indeterminate equations, quadratic equations, simple equations, surds. The contents are: Introduction On Simple Equations On Quadratic Equations On Equations

n ) } {\displaystyle {\mathcal {O}}=\{{\mathcal {O}}(n)\}} is called quadratic if it has a free presentation such that E = O ( 2 ) {\displaystyle E={\mathcal

satisfaction—for instance the extent to which the environment is protected. → Quadratic utilities: The respective utilities of S and R can be specified by the

that varies by 0.02 magnitude over a period of 0.68674 days. The average quadratic field strength of the magnetic field is (254.7±57.2)×10−4 T. With an age

numbers, Pythagorean triples, Ramsey theory, Lucas-Bernoulli numbers, quadratic residues, higher-order recurrence sequences, nonlinear recurrence sequences

all items have to be packed to certain bins. The quadratic knapsack problem maximizes a quadratic objective function subject to binary and linear capacity

solution separates into a Kalman filter and a linear-quadratic regulator. This is known as linear-quadratic-Gaussian control. More generally, under suitable

Museum. The 6-room building with stoa facing the center is designed in quadratic form surrounding a large courtyard. It covers an area of 360 m2 (3,900 sq ft)

f at (0, 0) can be characterised by: Having a degenerate quadratic part, i.e. the quadratic terms in the Taylor series of f form a perfect square, say

Donaldson (1983) who proved Donaldson's theorem restricting the possible quadratic forms on the second cohomology group of a compact simply connected 4-manifold

"waveguide" is used to describe horns with low acoustic loading, such as conic, quadratic, oblate spheroidal or elliptic cylindrical horns. These are designed more

simple harmonic motion. In this approximation, the vibrational energy is a quadratic function (parabola) with respect to the atomic displacements and the first

3-space, ⁠ P 3 {\displaystyle \mathbb {P} ^{3}} ⁠. Because they satisfy a quadratic constraint, they establish a one-to-one correspondence between the 4-dimensional

if r {\displaystyle r} is a quadratic non-residue modulo p {\displaystyle p} (this is almost the definition of a quadratic non-residue). There are p −

Darcy's law is an equation that describes the flow of a fluid through a porous medium and through a Hele-Shaw cell. The law was formulated by Henry Darcy

of the form K = Q(√d), for a square-free integer d. K is called real quadratic if d > 0. K has class number 1 for the following values of d (sequence

Duursma zeta function of error-correcting codes Epstein zeta function of a quadratic form Goss zeta function of a function field Hasse–Weil zeta function of

Riemannian but rather a Lorentzian manifold). More precisely, looking at the quadratic form q ( x ) = x 1 2 + ⋯ + x n 2 − x n + 1 2 {\displaystyle q(x)=x_{1}^{2}+\cdots

noble gases. In this example, the key point is that the kinetic energy is quadratic in the velocity. The equipartition theorem shows that in thermal equilibrium

also known as the power mean or Hölder mean, is an abstraction of the quadratic, arithmetic, geometric, and harmonic means. It is defined for a set of

landscape. This hypothesis has been proven for a static model relying on a quadratic approximation. In 2025, Chen et.al. proposed a multi-agent evolution strategy

(respectively, quadratic, cubic, polynomial, exponential, etc.) function in n, the presentation is said to satisfy a linear (respectively, quadratic, cubic,

of the form K = Q(√d), for a square-free integer d. K is called real quadratic if d > 0. K has class number 1 for the following values of d (sequence

a Heegner point is a point on a modular curve that is the image of a quadratic imaginary point of the upper half-plane. They were defined by Bryan Birch

Bilinear time–frequency distributions, or quadratic time–frequency distributions, arise in a sub-field of signal analysis and signal processing called

G=\chi (M)} . In lower dimensions, it identically vanishes. Despite being quadratic in the Riemann tensor (and Ricci tensor), terms containing more than 2

Speaker of the ICM in 1962 at Stockholm. His main publications were on quadratic forms and algebraic groups. Approximation in algebraic groups Betke–Kneser

overlap here, in the sense that some classical groups arising from pseudo-quadratic spaces can be obtained from quadrangular algebras (which Weiss calls special)

of the rotor diameter, whereas in a radial flux the increase is only quadratic. Axial flux motors have a larger magnetic surface and overall surface

that the unit group has rank 1 exactly when the number field is a real quadratic field, a complex cubic field, or a totally imaginary quartic field. When

1 / r 3 ) {\displaystyle (\Delta E\sim 1/r^{3})} Quadratic Stark broadening occurs via the quadratic Stark effect, which results from the interaction

a good approximation to irrational numbers that are not quadratic by using either quadratic irrationals or simply rational numbers. It is named after

9938^{\text{Age}}\ } Another estimation tool to calculate GFR is the Mayo Quadratic formula. This formula was developed by Rule et al., in an attempt to better

field. If the polynomials have degree two, we talk about multivariate quadratics. Solving systems of multivariate polynomial equations is proven to be

In algebraic geometry, a line complex is a 3-fold given by the intersection of the Grassmannian G(2, 4) (embedded in projective space P5 by Plücker coordinates)

foundations of most common types of preferences — that are representable by quadratic or additive functions — laid down by Gérard Debreu enabled Andranik Tangian

Commons Math contains a Java implementation of the algorithm running in quadratic time. ELKI offers an implementation of DBSCAN as well as GDBSCAN and other

manipulations such as translation and dilation. For example, for the family of quadratic functions having the general form y = a x 2 + b x + c , {\displaystyle

_{j=1}^{n}(u_{i}v_{j}-u_{j}v_{i})^{2}\geq 0} or by considering the following quadratic polynomial in x {\displaystyle x} ( u 1 x + v 1 ) 2 + ⋯ + ( u n x + v

University of Padua where he dealt with Riemannian geometry and differential quadratic forms. He formed a research group in which Tullio Levi-Civita worked,

loess curve, particularly when each smoothed value is given by a weighted quadratic least squares regression over the span of values of the y-axis scattergram

eponymous book. The algorithm uses locally-quadratic models of the dynamics and cost functions, and displays quadratic convergence. It is closely related to

when it is pointing toward Earth, making the object appear to pulse. quadratic field strength A method of computing the mean strength of a varying stellar

in the theory of quadratic forms". J Math Sci. 57 (6): 3489. doi:10.1007/BF01100118. S2CID 122865942. Kaplansky, I. (1951). "Quadratic forms". J. Math

1960s. Quadratic plane vector fields with four limit cycles are known. An example of numerical visualization of four limit cycles in a quadratic plane

useful in response surface methodology, for building a second order (quadratic) model for the response variable without needing to use a complete three-level

mathematical foundations of most common types of utility functions — quadratic and additive — laid down by Gérard Debreu enabled Andranik Tangian to

geometric algebra naturally accommodates any number of dimensions and any quadratic form such as in relativity. Examples of geometric algebras applied in

period of 39 minutes. A magnetic field has been detected with an averaged quadratic field of (194.5±230.7)×10−4 T. The star has a moderate rate of rotation

Quadratic magnetic rotation (also known as QMR or QMR effect) is a type of magneto-optic effect, discovered in the mid 1980s by a team of Ukrainian physicists

Gauss's lemma (number theory), condition under which an integer is a quadratic residue Gauss's lemma (Riemannian geometry), theorem in manifold theory

⁡ 13 {\displaystyle \log _{3}13} 2.3347 3D quadratic Koch surface (type 1) Extension in 3D of the quadratic Koch curve (type 1). The illustration shows

in the star's photosphere. A magnetic field has been detected with a quadratic field strength of (764.7±311.3)×10−4 T. The star is radiating 113 times

_{b}(r_{i})} is strictly proper for all b > 1 {\displaystyle b>1} . The quadratic scoring rule is a strictly proper scoring rule Q ( r , i ) = 2 r i − r

iron, titanium, and magnesium on the surface of the star. The averaged quadratic field strength of the surface magnetic field is (859.1±712.3)×10−4 T.

independently from E. M. L. Beale. In 1962 he developed for the convex quadratic linear programming case a new simplex method using an original complementary

in the star's photosphere. A magnetic field has been detected with a quadratic field strength of (764.7±311.3)×10−4 T. The star is radiating 113 times

Lagrangian describing such a field A {\displaystyle A} contains an algebraic quadratic term and an arbitrary linear term, while it contains no kinetic terms

analogous Stiefel–Whitney classes for vector bundles with a non-degenerate quadratic form, taking values in etale cohomology groups or in Milnor K-theory.

attempts to generalise the results known on the class numbers of imaginary quadratic fields, to a more general sequence of number fields K 1 , K 2 , … .  

corresponding classical equations of motion, provided the Hamiltonian is at most quadratic in the coordinates and momenta. Otherwise, the evolution equations still

}R^{\alpha \beta \mu \nu }-4R_{\mu \nu }R^{\mu \nu }} is precisely the quadratic Gauss–Bonnet term, which is the dimensionally extended version of the

polynomials) are called linear curves, third-order curves are called quadratic curves, and fourth-order curves are called cubic curves. The number of

combination of these is taken as the latent variable) and the quadratic is for the quadratic form in the latent variables ν {\displaystyle {\boldsymbol {\nu

relevant to numerical analysis because it shows that (outside the region of quadratic convergence) the Newton method can be very sensitive to its choice of

lifespan. It is a chemically peculiar magnetic B star, showing an averaged quadratic field strength of (167.2±140.4)×10−3 T. Helium-weak, it displays an underabundance

Gödel asked whether a certain NP-complete problem could be solved in quadratic or linear time. The Gödel Prize has been awarded since 1993. The prize

mathematics, Scholz's reciprocity law is a reciprocity law for quadratic residue symbols of real quadratic number fields discovered by Theodor Schönemann (1839)

The Kerr effect, also called the quadratic electro-optic (QEO) effect, is a change in the refractive index of a material in response to an applied electric

solved using three different versions of adaptive FEM: linear elements, quadratic elements, and hp-FEM. Fichera problem: singular gradient. Fichera problem:

\displaystyle f(x)=A_{0}x_{1}^{2}+2A_{1}x_{1}x_{2}+A_{2}x_{2}^{2}} is a binary quadratic form with an invariant given by the discriminant Δ = A 0 A 2 − A 1 2

Bonn. His doctoral thesis Quadratische Formen und Galois-Cohomologie (Quadratic Forms and Galois Cohomology) was supervised by Friedrich Hirzebruch. Scharlau

-L.; Parimala, R., Invent. Math. 101, no. 1, 81–99. MR1055712 1982: "Quadratic spaces over polynomial extensions of regular rings of dimension 2", Mathematische