Sentence examples for and its norm from inspiring English sources

where is the inner product in, and its norm will be denoted by.

In this subsection, let,, and be three arbitrary finite-dimensional real spaces with a scalar product and its norm.

and its norm is given by y D E C 2 = ∑ n = 1 N u n H r σ n 2 (7).

Using its time derivative v and the velocity aberration vector α is given as: and its norm |α| is equal to α.

For any real (r>0), we define the space (H_{chi^{(alpha,beta)},A}^{r}(Lambda)) and its norm by space interpolation as in [14].

The bilinear form (b_{delta}(cdot,cdot)) is continuous on (Y_{delta}times M_{delta}), and its norm is independent of δ.

And, though she acknowledged that the code did not technically apply to the justices, she noted: "They have publicly stated they follow it, and its norms are ones they should follow".

Many of them seem bound and determined to make their case that their imaginary made-up countries really do exist and deserve to be considered part of the international system, even if they have to trash the international system and its norms and agreements to do it.

The father was giving voice to the Egyptian bourgeoisie's discipline and anxieties, to its desire to keep its world and its norms intact.

Yet since his election, Mr. Trump's foes have defined themselves in opposition to a president they see as a unique threat to a well-oiled democracy and its norms.

One of the most frequently used tools for proving the existence of positive solutions to the integral equations and boundary value problems is the Krasnoselskii theorem on cone expansion and compression and its norm-type version due to Guo and Lakshmikantham [20].