Sentence examples for boundary s from inspiring English sources

Since G ≠ ∅, let { x n } n = 1 ∞ ⊆ G be an arbitrary convergent sequence with boundary s ∈ Ω, i.e., lim n → ∞ ρ ( x n, s ) = 0. Then we have lim n → ∞ μ ( M x n Δ M s ) = 0, and there exists n 0 integer such that for each n ≥ n 0 the inequality μ ( M x n Δ M s ) < μ ( M z ) 2 holds.

Second, let (Omegasubset R^{n}) be a bounded open domain with smooth boundary S, (overline{Omega}=Omegacup S).

end{aligned} (1.12) Open image in new window Fig. 1 (S_0) is part of the boundary (S, S_0cap partial D_tne emptyset ) for (forall t).

According to the properties of the function F with respect to the heat flow, (V y, s)=u_{x} 0, y, s)) at the boundary S.

By introducing an artificial boundary S enclosing the scatterer, the original unbounded domain Ω is decomposed into a bounded computational domain Ω− and an exterior unbounded domain Ω+.

The well-posedness of the problem without initial condition is dealt with in Sections 3 and 4. Let Ω be a bounded domain in R n ( n ≥ 2 ) with boundary S = ∂ Ω.

A considerably greater number of genes involved in cellular proliferation and cell cycle transition through the G1/S boundary, S-phase progression, and the G2/M transition, were significantly down-regulated in expression, and common to both cell lines.

At 5 dpf pea3 can be seen in a few cells near somite boundaries (S, arrowhead).

We define quantization boundaries q s = infA s.

Then ℛ contains the vertices defining the boundary of [ s, t].

We call a map r : V → V{u} defined by r u) = v and r(x) = x for x ∈ V{u}, a retraction if: (i) u and v do not belong to the boundary ∂ S ⊂ K ≤ n of some simplex S ∉ K ≤ n, (ii) the complex K ≤ n ′ defined on vertices V{u} with simplices S ∈ K ≤ n, such that u ∉ S or S = S'{u} ∪ {v} for some S ′ ∈ K ≤ n and S' ∋ u, is a subcomplex of K ≤ n.