Sentence examples for means defined from inspiring English sources

are the de la Vallée Poussin means defined as.

We begin with the form of hyperbolic functions of Stolarsky means defined by (1.1) to introduce the two-parameter sine functions.

where { μ n } n = 1 ∞ is a sequence of left strong regular invariant means defined on an appropriate invariant subspace of l ∞ ( S ).

The monotonicities and log-convexities of S h p, q ( b, a ) and of C h p, q ( b, a ) in parameters p and q are clearly the same as those of S h ( p, q, t ) and of C h ( p, q, t ), which are in turn equivalent to those of Stolarsky means defined by (1.1) and of Gini means defined by (1.2), respectively.

In this paper, we also introduce a class of bivariate means defined as an integral of functions, where the underlying function is just continuous and increasing on ((0,infty)), which is not restrictive and so gives much more possibilities to define new means and new mean-inequalities.

In the same way, the Gini means defined by (1.2) can be expressed in hyperbolic functions by letting t = ln b / a : G p, q ( a, b ) = a b C h ( p, q, t ), where C h ( p, q, t ) = { ( cosh p t cosh q t ) 1 / ( p − q ), p ≠ q, e t tanh p t, p = q ≠ 0, 1, p = q = 0. (4.1).

To define the climate movement as a peace movement means defining the wars it seeks to end.

That means defining what apps they can access, as well as a full child lock when required.

5) Set specific writing goals and sub-goals Making your writing goals specific means defining the content, verb and word length for the section.

The shadow foreign minister said Trump was likely to be unorthodox as president, which means "defining an independent foreign policy within an alliance framework is now a more complex task".

This more or less means defining the space (H^1(X)) whenever X is a metric measure space (MMS).