Sentence examples for space of order from inspiring English sources

If is in the Euclidean Lipschitz space of order for, then so is.

For an and a domain, we denote by the Sobolev space of order equipped with the usual Sobolev norm.

We denote by (H^{alpha}(0,T)) the fractional Sobolev space of order α on ((0,T)).

end{aligned} For each (sigmainmathbb{R}) we shall denote by (H^{sigma}(Omega)) the usual Sobolev space of order σ.

Also, in [1], it is shown that is bounded on the Euclidean Lipschitz space of order for, and bounded on.

Let L s, p ( Ω ; E ), − ∞ < s < ∞, denote the E-valued Liouville space of order s such that L 0, p ( Ω ; E ) = L p ( Ω ; E ).

In fact, the example of complex numbers is essentially the same (i.e., it is isomorphic) to the vector space of ordered pairs of real numbers mentioned above: if we think of the complex number as representing the ordered pair in the complex plane then we see that the rules for sum and scalar product correspond exactly to those in the earlier example.

This computational complexity limits not only the throughput of reconstructing metabolic models, but potentially their reproducibility: as the full solution space of ordered reaction removals is extremely large, the 1000 permutations sampled by MBA necessarily represent only a tiny fraction of all possibilities.

Those measures are associated with the Sobolev spaces of order s (s>1/2) of the free loops in the Lie algebra.

We can easily check, using Lemma 4.4 of [6], that each uniformly lipschitzian mapping F, with F 0) = 0, acts in inhomogeneous Orlicz-Sobolev spaces of order 1: W1,xL M (Q) and W 0 1, x L M ( Q ).

The energy functional is defined on Sobolev spaces of order −1, so the subdifferential mathematically formulates the energyʼs gradient which formally involves 4th order spacial derivatives of the surfaceʼs height.