Sentence examples for connected boundaries from inspiring English sources

Throughout this paper we consider a domain (open connected set) Ω ⊂ ℝ n, n ≥ 2, of the form Ω = Ω 0 ⋃ j = 1 m Ω ̄ j, where Ω j (j = 0,..., m) are m + 1 bounded domains of ℝ n with connected boundaries Σ j ∈ C1, λ(λ ∈ (0, 1]) and such that Ω ̄ j ⊂ Ω 0 and Ω ̄ j ∩ Ω ̄ k = ∅, j, k = 1,..., m, j ≠ k.

The connected boundaries have been filled up and shown in Figure 3f representing the nucleus of the WBC. Figure 4 shows cytoplasm extraction result.

The implementations of several boundary conditions, including the connect boundary, absorbing boundary and periodic boundary are described, then some applications and important developments of this method are provided.

Given the collection of putative boundary points determined in the first three steps, the fourth step defines the RF+CAN boundary by connecting boundary points across the entire B-scan image.

The boundary properties can be estimated by comparing the characteristics of the components under the free condition and connected to boundary conditions.

By a similar way to prove (12), we can easily obtain the following version of Hopf's boundary point lemma, which is a generalization of [30, Lemma C.3]. (Hopf's boundary point lemma for elliptic Waldenfels operators) Let D be an open set (not necessarily bounded or connected) with boundary (partial D) being (C^2).

Some applications to systems of conservation laws are presented and connected with boundary and inventory control.

However, such flux patches are not necessarily connected to boundary heterogeneity.

The fluid and solid motions are connected by boundary conditions at the fluid-solid interface.

To generate the arbitrary number of patterns using definition, certain features are assumed for each 64-pixel pattern such that each is regular (i.e., bounded by straight lines), clustered (i.e., the pixels are connected), and boundary-adjoined.

The paper investigates a fixed point problem in the space ( W 1, ∞ ( [ a, b ] ; R n ) ) p + 1 which is connected to boundary value problems with state-dependent impulses of the form z ′ ( t ) = f ( t, z ( t ) ), a.e.