Sentence examples for e continuously from inspiring English sources

We shall consider rearrangement invariant quasi-Banach spaces E, continuously embedded in L 1 ( R n ) + L ∞ ( R n ), such that the quasi-norm ∥ f ∥ E in E is generated by a quasi-norm ρ E, defined on M + with values in [ 0, ∞ ], in the sense that ∥ f ∥ E = ρ E ( f ∗ ).

E continuously embedded into (L^{p}(mathbb{R}^{N})) for (pin[2,2_{alpha}^]), and compactly embedded into (L_{mathrm{loc}}^{p}(mathbb{R}^{N})) for (pin[2,2_{alpha}^)). In order to prove Theorem 1, we need the following lemma whose proof is analogous to that of Lemma 1.21 in [17] (see also [18]).

Note that E is continuously embedded in L p ( R, R N ) for all p ∈ [ 2, + ∞ ].

Let e be continuously differentiable, and (nabla e(x)) be nonsingular at (x^) which satisfies (e(x^)=0).

Since E is continuously embedded in (H^{1}(mathbb{R},mathbb{R}^{N})), (u(t to0) as (|t|toinfty).

Evidently, E is continuously embedded into l q ( Z, R N ) for 2 ≤ q ≤ + ∞, i.e., there exists γ q > 0 such that ∥ u ∥ q ≤ γ q ∥ u ∥, ∀ u ∈ E. (2.2).

Evidently, E is continuously embedded into (L^{p}(mathbb{R}^{N})) for (2leq pleq2^) under the condition (V), that is, there exists (S_{p}>0) such that |u|_{p}leq S_{p}|u|, quad forall u in E, pin bigl[2,2^bigr].

A (quasi- Banach space A is said to be an intermediate space between (E_{0}) and (E_{1}) if E is continuously embedded between (E_{0}cap E_{1}) and (E_{0}+E_{1}).

E is continuously embedded into L p ( R N ) for p ∈ [ 2, 2 α ∗ ] and compactly embedded into L loc p ( R N ) for p ∈ [ 2, 2 α ∗ ). E is compactly embedded into L p ( R N ) for p ∈ [ 2, 2 α ∗ ) with 2 α ∗ = 2 N N − 2 α.

While Beagle, MaCH and Minimac provide allele dosage data (i. e. continuously distributed values ranging from 0 to 2), findhap.

Cyclin E increased continuously to a maximum between 14 and 18 h, decreasing thereafter.