Sentence examples for attain their values from inspiring English sources

We will consider the case where the integrand and integrator attain their values in Banach spaces.

(2) Unfortunately, this result is no more valid for functions attaining their values in more general metric spaces.

Now we will obtain an improved version of the Loéve-Young inequality for integrals driven by irregular signals attaining their values in Banach spaces.

The first aim of this paper is a generalisation of the results of [1] and [2] to the functions attaining their values not only in (mathbb{R}) but in more general spaces.

We prove an inequality of the Loéve-Young type for the Riemann-Stieltjes integrals driven by irregular signals attaining their values in Banach spaces, and, as a result, we derive a new theorem on the existence of the Riemann-Stieltjes integrals driven by such signals.

There is a corresponding increase in the kinetic stresses, which attain their maximum values at the hopper exit.

It is of interest to note that for a given initial porosity, the radial stress and the pressure attain their maximum values at r = 0 (at center).

These two terms may not attain their best values for the same transceivers in some MIMO IC system model, due to the contradiction between them.

Floor rotations attain their maximum values for the structures where the walls are in farthest positions from the centers of mass.

At the upstream flow, a third zone is observed (Figure 7c), where the temperature and void fraction attain their maximum values causing probably a partial dry regions near the channels' outlet.

See Appendix 1. □. Suppose that problem (Pε) is feasible, then, strong duality holds true for problem (Pε) and its dual problem (Dε), and they can both attain their optimal values.