Sentence examples for exists a component from inspiring English sources

Then there exists a component in which joins with, and (1.8).

There exists a component F α ( u ) of F ( u ) such that m ⊂ F α ( u ).

There exists a component, say (H_{i_{0}}) ((i_{0}in{ 1,2,ldots, p})) that has a pendant vertex.

If there exists a component function (f_{i}:[0,T]timesmathbb{R}^{3}timesmathbb{R}^{3}rightarrow mathbb{R}) such that (f_{i}) is always positive or negative on its domain, then equation (1.1) with periodic boundary condition or Neumann boundary condition has no solution.

Then there exists a component T in ∑ which joins to , and Proj R T = [ ρ ∗, + ∞ ). for some ρ ∗ > 0. Moreover, there exists μ ∗ ≥ ρ ∗ > 0 such that (1.1) has at least two positive solutions for μ ∈ . Here T joins to such that lim ( μ, u ) ∈ T, ∥ u ∥ ≤ 1 μ → ∞ ∥ u ∥ = 0, lim ( μ, u ) ∈ T, ∥ u ∥ > 1 μ → ∞ ∥ u ∥ = ∞.

More precisely, there exists a component Σ 0 of positive solutions of (1.1), (1.2) which meets [ λ ˜ 1 ( a 0 ), λ ˜ 1 ( a 0 ) ] × { 0 }, where λ ˜ 1 ( a 0 ), λ ˜ 1 ( a 0 ) will be defined in Section  4; (iii) If (H 4) and (H 5) also hold, then there is a number λ ∗ > 0 such that problem (1.1), (1.2) admits no positive solution with λ > λ ∗.

Because of the maximal connectedness of (mathscr{D}^), there does not exist a component (mathscr{D}^{ast}) of (overline{mathcal{U}}capmathscr {S}^) such that (mathscr{D}^{ast}cap D^neqemptyset), (D^{ast }cap partialmathcal{U}capmathscr{S}^)neqemptyset).

There are 6 connected components and, among them, there exists a giant component (the largest connected components) consisting of 3,435 proteins (99.57% of the total number of proteins) and 7,251 interactions (98.43% of the total number of interactions).

Let S and S ′ be two minimal separators of a graph G. Then S and S ′ are parallel if and only if there exists a full component C S of G − S and a connected component C S ′ of G − S ′ such that C S ⊆ C S ′.

If (G=langle phi _1,phi _2,ldots,phi _nrangle) where each (phi _i in mathcal {E}_k) for every (1 le i le n) and let (Omega _G) be a Fatou component of G. Then for any (phi in G) there exists a Fatou component of G, say (Omega _{phi }) such that (phi (Omega _G) subset bar{Omega }_{phi }) and begin{aligned} partial Omega _Gsubset bigcup _{i=1}^n phi _i^{-1}(partial Omega _{phi _i}).

In particular, Theorem 5.3 in [7] gives an example of a polynomial semigroup (G=langle phi _1,phi _2, ldots rangle) in (mathbb C), such that there exists a Fatou component, (say (mathcal {B}), which is conformally equivalent to a disc), that is wandering, but returns to the same component infinitely often.