Sentence examples for property of the functional from inspiring English sources

In our case we have no longer the supperadditivity property of the functional (Vert cdot Vert _{ptext{-TV}, [a,b ]}^{p}) as the function of interval (see Remark 4), and hence the method of the proof of Theorem 3 will be different from those of related estimates in [15].

By Lemma 2.2 and the property of the functional ⟨·,·⟩ + α2 ⟨∇·, ∇·⟩, the conclusion holds.

By Lemma 2.2 and the property of the functional ⟨·, A·⟩ + α2⟨A·, A·⟩, the conclusion holds.

The next step is to consider the property of the functional I.

Detailed examination of the results indicates that the proximity of the catalytic residues to the centroid is a property of the functional unit, defined as the assembly of domains or chains that form the active site (in most cases the functional unit corresponds to a single whole polypeptide chain).

Let E be a smooth, strictly convex, and reflexive real Banach space and let C be a nonempty closed convex subset of E. Following Alber [8], the generalized projection Π C from E onto C is defined by Π C ( x ) = arg min y ∈ C ϕ ( y, x ), ∀ x ∈ E. The existence and uniqueness of Π C follows from the property of the functional ϕ ( x, y ) and strict monotonicity of the mapping J.

In this subsection, we will discuss the properties of the functional (I^_{varepsilon}).

At very high pressures, physical properties of the functional groups govern the adsorption of CO2.

In this section, we present some properties of the functional F, and we prove the existence of minimizer.

In this section, we present some properties of the functional F and prove the existence of a minimizer.

In this section, we first establish some properties of the functional I and then prove Theorem 1.1.