science, a function f ( n ) {\displaystyle f(n)} is said to exhibit quasi-polynomial growth when it has an upper bound of the form f ( n ) = 2 O ( ( log ⁡...

produces a function with quasi-polynomial growth, and algorithms with this as their time complexity are said to take quasi-polynomial time. All polylogarithmic...

theorem on groups of polynomial growth, first proved by Mikhail Gromov, characterizes finitely generated groups of polynomial growth, as those groups which...

require superpolynomial time. Quasi-polynomial time algorithms are algorithms whose running time exhibits quasi-polynomial growth, a type of behavior that...

say that G has a polynomial growth rate. The infimum k 0 {\displaystyle k_{0}} of such k's is called the order of polynomial growth. According to Gromov's...

details. Two metric spaces are quasi-isometric if there exists a quasi-isometry between them. The property of being quasi-isometric behaves like an equivalence...

ecology, etc. Rational curves are subdivided according to the degree of the polynomial. Line Plane curves of degree 2 are known as conics or conic sections and...

properties of polynomials". Illinois Journal of Mathematics. 7 (4): 681–701. doi:10.1215/ijm/1255645104. Zbl 0117.04003. Néron, André (1965). "Quasi-fonctions...

turn that various properties of growth, such as polynomial growth, the degree of polynomial growth, and exponential growth, are isomorphism invariants of...

functions precisely corresponds to the generating functions that enumerate quasi-polynomial sequences of the form f n = p 1 ( n ) ρ 1 n + ⋯ + p ℓ ( n ) ρ ℓ n ...

quadratic growth at infinity. From this, elementary complex analysis can be used to show that g {\displaystyle g} must actually be a quadratic polynomial. Thus...

an algebraic integer. It has minimal polynomial x 2 − x − 1. {\displaystyle x^{2}-x-1.} This quadratic polynomial has two roots, φ {\displaystyle \varphi...

integer programs with few variables in time polynomial in the number of constraints. Eugene M. Luks for a polynomial time graph isomorphism algorithm for graphs...

identity of the complexity classes formed by taking "polynomial time" and "non-deterministic polynomial time" as least upper bounds. Simulating an NP-algorithm...

interpolation Padua points — set of points in R2 with unique polynomial interpolant and minimal growth of Lebesgue constant Hermite interpolation Birkhoff interpolation...

the length of that relation (see pp. 79–80 in ). The growth type of the Dehn function is a quasi-isometry invariant of a finitely presented group. The...

{\displaystyle P=0} . To avoid the solution of a transcendental function, a polynomial Taylor expansion to the second-order in P {\displaystyle P} is used for...

others. Theorems which use quasi-isometry invariants to prove algebraic results about groups, for example: Gromov's polynomial growth theorem; Stallings' ends...

(unemployment) as a function of the independent variable (GDP growth) is given in polynomial least squares. Econometric theory uses statistical theory and...

"Jump PDA's, deterministic context-free languages, principal AFDLs and polynomial time recognition (Extended Abstract)," Proceedings of the fifth annual...

{\displaystyle \mathbb {P} ^{n}} of some finite family of homogeneous polynomials that generate a prime ideal, the defining ideal of the variety. A projective...

randomized polynomial time algorithm, but not by a deterministic one: see Dyer, Martin; Frieze, Alan; Kannan, Ravi (January 1991). "A Random Polynomial-time...

bundle on projective space whose global sections are the homogeneous polynomials of degree 1 (that is, linear functions) in variables x 0 , … , x n {\displaystyle...

Polynomial regression, Muthukrishnan". Maths behind Polynomial regression. Retrieved 30 Jan 2024. "Mathematics of Polynomial Regression". Polynomial Regression...

dispersion Quasi-birth–death process Quasi-experiment Quasi-experimental design – see Design of quasi-experiments Quasi-likelihood Quasi-maximum likelihood...

deviate somewhat from Zipf's law. Such empirical distributions are said to be quasi-Zipfian. In 1913, the German physicist Felix Auerbach observed an inverse...

equations Sine-Gordon equation Sturm–Liouville theory of orthogonal polynomials and separable partial differential equations Universal differential equation...

are: the Lorenz attractor population growth (i.e. logistic map) parameter plane of complex quadratic polynomials with Mandelbrot set. In quantum mechanics...

differential geometry. They can also be defined as implicit equations, often polynomial equations (which spawned algebraic geometry). Analytic geometry also makes...

Dries and Alex Wilkie's treatment of Gromov's theorem on groups of polynomial growth. Nonstandard analysis was used by Larry Manevitz and Shmuel Weinberger...