Sentence examples for mapping of class from inspiring English sources

Theorem 4.12 Let T : E ∗ ∗ → 2 E ∗ be a bounded mapping of class ( S + ).

Then it is easy to see that T 1 is a mapping of class ( S + ).

Theorem 4.11 Let T : Ω ¯ → 2 E ∗ be a mapping of class ( S + ), where Ω ⊂ E ∗ ∗ is an open bounded subset.

Proposition 4.5 Let T : D ( T ) ⊆ E ∗ ∗ → 2 E ∗ be a mapping of class ( S + ) and S : E ∗ ∗ → E ∗ be a mapping with closed convex values.

Lemma 4.8 Under the condition of Lemma  4.7, there exists a finite dimensional subspace F 0 of E ∗ ∗ such that deg ( T F, Ω ∩ F, 0 ) does not depend on F. Now, let Ω ⊂ E ∗ ∗ be a nonempty open bounded subset and T : Ω ¯ → 2 E ∗ be a mapping of class ( S + ).

Let (F Rtimes R^{2}rightarrow R^{2}) be a mapping of class (C^{4}) of the form (F k, x, y)= y, G k,x,y))) which satisfies: (i) For every (kin R), there exists (tilde{z} k)) such that (F k, tilde{z} k),tilde{z} k))= tilde{z} k),tilde{z} k))).

We can observe the mapping of classes into components by using the matching keyword.

Then, we define the mapping of classes into modules, i.e., in this step, we specify the module that represents source code classes.

Theorem 10 Let R be a subset of R 2 with a nonempty interior, and let T = ( f, g ) : R → R be a map of class C p for some p ≥ 1. Suppose that T has a fixed point ( x ¯, y ¯ ) ∈ int R such that a : = f x ( x ¯, y ¯ ), b : = f y ( x ¯, y ¯ ), c : = g x ( x ¯, y ¯ ), d : = g y ( x ¯, y ¯ ).

The TF energy map of class c, denoted by Γ c,. is a table of real numbers specified by the triplet (j, k, l) as Γ c j, k, l : = ∑ i = 0 2 n o − 1 v j, k, l T x i ( c ) ∑ i = 0 2 n o − 1 x i ( c ) 2 (3).

Towards this end, let (u in {mathscr {A}}_{varphi}^{p}(mathbb{X})) be an admissible map of class (mathscr{C}^{1}) and pick (phiinmathscr{C}^{infty}_{0}(mathbb{X}^{n}, {mathbb {R}}^{n})) and, for (varepsiloninmathbb{R}) sufficiently small, set u_{varepsilon}= frac{u+varepsilonphi}{|u+varepsilonphi|}.