Sentence examples for by sets of functions from inspiring English sources

In this note, we establish some bounds on the supremum of certain empirical processes indexed by sets of functions with the same L2 norm.

In "Regularization by sets of functions of ε-approximation-type scale.

In such context, the simultaneous regularization by sets of functions of (varepsilon )-approximation-type scalsoand also by "known" sets works.

So one lesson we should learn from dilation is that imprecise belief is represented by sets of functions rather than by a set-valued function (see also, Joyce 2011; Topey 2012; Bradley and Steele 2014b).

Precisely, as we shall see, generally, the "reduction" of the complex dimensions to their real part requires the regularization by sets of functions of (varepsilon )-approximation-type scale, while the "reduction" to their imaginary part requires regularization with "known" sets, that is, sets for which we have some informations.

Finally, we denote by and the sets of functions which are absolutely continuous on and which have absolutely continuous first derivatives on, respectively.

Altogether, these observations suggest that mutualism and parasitism are two distinct host-relationships supported by significantly different sets of functions.

Moreover, let us by and denote the sets of functions being continuous on and having continuous first derivatives on, respectively.

The components of stress are also expressed in terms of complete sets of functions by using the expression for displacement.

We denote by the set of functions such that, (2.1).

Then, we denote by the set of functions which are (Lebesgue) integrable on.