Smoothness

What gives this chocolate mousse its luscious smoothness?

In experiments in which Sorensen was blindfolded and wore earplugs, he was able to detect how strongly he was grasping the different objects he picked up, as well as their shape and smoothness.

Russian vodka is known for its smoothness and purity.

The admirable smoothness of the riding also reflected the greatest credit on those who, despite the difficulties caused by the shortage of men and materials, have succeeded in maintaining the track in such first-class order.

The ‘smoothness’ of distributions can be understood in various senses, this is why we used quotation marks before; further we will drop them. The smoothness can be understood as the differentiability of the distribution function, boundedness of some of its derivatives, the existence of the absolutely continuous component, the decrease of the characteristic function with a certain rate, the validity of the Cramér condition, the condition #92;sigma(#92;Phi)#92;rightarrow 0 as n#92;rightarrow#92;infty, etc.

With it,^([a pavement profile]) paving operations can be adjusted "on the fly" to maintain or improve smoothness.

Smoothness can vary from 0 (for a nondifferentiable function) to infinity (for a smooth function).

A central problem in approximation theory is to characterize the best approximation of a function by polynomials, or other classes of simple functions, in terms of the smoothness of the function. In this chapter, we study the characterization of the best approximation by polynomials on the sphere. In the classical setting of one variable, the smoothness of a function on #92;mathbbS¹ is described by the modulus of smoothness, defined by the forward difference.