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Cosa (chi) è smoothness - definizione

FUNCTION HAVING DERIVATIVES OF ANY ORDER

Smooth function; Infinitely often differentiable function; Smooth map; Infinitely differentiable function; Smooth mapping; Smooth functions; Differentiability class; Differentiabillity class; Geometric continuity; Geometrical continuity; C-infinity function; C-infty function; C-k function; C^k function; C infinity; Parametric continuity; C^n; Smoothing Function; Infinitely differentiable; Geometrical Continuity; C0 continuity; C1 continuity; C2 continuity; Ck space; Cinfty function; Ck function; C∞ function; Differentiability classes; Tangential continuity; Tangent continuity; G⁰; G¹; G²; Gⁿ; Smooth approximation; C-infinity; C^k; Smoothness (mathematics); C1 function; Regularity (smoothness)

$<math>(1-\varepsilon^2) x^2 -2px+y^2=0 , \ p>0 \ , \varepsilon\ge 0</math><br /> pencil of conic sections with ''G''<sup>2</sup>-contact: p fix, <math>\varepsilon</math> variable <br /> (<math>\varepsilon=0</math>: circle,<math>\varepsilon=0.8</math>: ellipse, <math>\varepsilon=1</math>: parabola, <math>\varepsilon=1.2</math>: hyperbola)$
$The function <math>f:\R\to\R</math> with <math>f(x)=x^2\sin\left(\tfrac 1x\right)</math> for <math>x\neq 0</math> and <math>f(0)=0</math> is differentiable. However, this function is not continuously differentiable.$

Smoothness

·noun Quality or state of being smooth.

Smoothness (probability theory)

IN PROBABILITY THEORY, MEASURE OF A DENSITY FUNCTION

Supersmooth; Ordinary smooth

In probability theory and statistics, smoothness of a density function is a measure which determines how many times the density function can be differentiated, or equivalently the limiting behavior of distribution’s characteristic function.

https://en.wikipedia.org/wiki/Smoothness_(probability_theory)

Navier–Stokes existence and smoothness

MILLENNIUM PRIZE PROBLEM

Navier-Stokes existence and smoothness; Navier–Stokes existence and smoothness problem; Navier-Stokes existence and smoothness problem

The Navier–Stokes existence and smoothness problem concerns the mathematical properties of solutions to the Navier–Stokes equations, a system of partial differential equations that describe the motion of a fluid in space. Solutions to the Navier–Stokes equations are used in many practical applications.

https://en.wikipedia.org/wiki/Navier–Stokes_existence_and_smoothness

Wikipedia

Smoothness

In mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives it has over some domain, called differentiability class. At the very minimum, a function could be considered smooth if it is differentiable everywhere (hence continuous). At the other end, it might also possess derivatives of all orders in its domain, in which case it is said to be infinitely differentiable and referred to as a C-infinity function (or $C^{\infty }$ function).

https://en.wikipedia.org/wiki/Smoothness

Esempi dal corpus di testo per smoothness

1. Pregnant at 41 and her skin a miracle of smoothness.

2. His eyes widen on takeoff; he smiles at the smoothness.

3. In fact, motion smoothness is better than in the movies.

4. But the speed and smoothness of the evacuation have come as an added bonus.

5. Kekalos cooked it in the manner of risotto, achieving a comparable smoothness and richness.