Sentence examples for closure of functions from inspiring English sources

Exact(1)

We will first study the action of the differential operator L L u = Δ u − a ( x ) u (3.2). on the class W 2, 0 2 , which may be defined as the closure of functions in C 2 that vanish on ∂G, where a ( x ) is for the bounded measurable functions defined in Ω.

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Four years later, just after the accident on Three Mile Island, a referendum was held in which two-thirds of voters agreed that nuclear power should be phased out gradually; the rest favoured doing so more quickly.Even at the time, nobody thought this non-binding vote required the early closure of functioning plants; in fact, six plants came on stream after it.

Denote by (C_{0}(mathbb{R}^{N})) ((Ngeq1)) the closure of continuous functions in (mathbb{R}^{N}) with compact support.

It is known that if is -periodic, then it has a Fourier expansion with and : is the closure of such functions with respect to the norm (2.1).

Consider the semilinear wave equations in dimension 3 with a defocusing and superconformal power-type nonlinearity and with data lying in the Hs×Hs−1 (s<1) closure of smooth functions that are compactly supported inside a ball with fixed radius.

The space (mathcal{AP}) of almost periodic functions is the closure of quasi-periodic functions in (L^{p}_{mathrm{loc}}).

The space (mathcal{AP}) of almost periodic functions is the closure of quasi-periodic functions in the space (L^{p}_{mathrm{loc}}) of f, where (|f|^{p}) is locally Lebesgue integrable on (mathbb{R}) for (pge1).

Note that the generalized theory also works for terminal conditions which are merely Borel measurable and do not need to be in the closure of uniformly continuous functions as required in Soner et al. (2012).

Indeed, introduce the space Vμas the closure of the set of functions in v ∈ C∞ (ℝ2 ∩ {ξ2 > 0}) which are 1-periodic with respect to ξ1, vanishing on Tμand with finite ∫ B | ∇ v | 2 d ξ.

The loss-of-function, dorsal closure phenotype associated with pkn is relatively mild (~10% of embryos with the phenotype) and may reflect functional redundancy with components of the Jun-terminal kinase (JNK) pathway, which is also required for dorsal closure in Drosophila.

As in [23], we introduce the function space (X^{1,2}(R^{n})), which is defined as the closure of (C_{0}^{infty}) functions with respect to the energy norm (|u|_{X^{1,2}}:=int |nabla u(x)|^{2},dx), that is, X^{1,2}bigl(mathbb{R}^{n}bigr)=bigl{ uin L^{frac{2n}{n-2}}bigl(mathbb{R}^{nablar) : nabla uin bigl(L^{2}bigl(mathbb{R}^{n}bigr bigr)^{n}bigr}.

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