Sentence examples for exists a section from inspiring English sources

Then for any section (s in H^0(X_0, K_{X_o} otimes L)) there exists a section (H^0 X, K_X^{otimes m} otimes L)) such that begin{aligned} S|_{X_o} = s otimes (dpi )^{otimes m}.

Then for any section (s in H^0(X_0, K_{X_o} otimes L)) such that begin{aligned} int _{X_o} frac{|s|^2 e^{-varphi }}{omega ^{m-1}} < +infty, end{aligned}there exists a section (H^0 X, K_X^{otimes m} otimes L)) such that begin{aligned} S|_{X_o} = s otimes (dpi )^{otimes m}.

Then for any section (f in H^0(Z,H)) satisfying begin{aligned} int _Z frac{|f|^2e^{-psi }}{|dT|_{omega }^2e^{-lambda }}dA_{omega } <+infty end{aligned}there exists a section (Fin H^0 X,H)) such that begin{aligned} F|_Z=f quad text {and} quad int _X |F|^2e^{-psi } dV_{omega } le frac{24pi }{delta }int _Z frac{|f|^2e^{-psi }}{|dT|_{omega }^2e^{-lambda }}dA_{omega }. end{aligned}.

But in most cases there exists an intermediate section of the replication neighbourhood scale at which system extinction occurs.

Both indicate a relation that there exists a certain weaving section length threshold under which the travel time variability strongly increases.

If a fractal transformation h = π G ∘ τ F : A F → A G is a homeomorphism, then there exists a shift invariant section τ G of π G such that the following diagram commutes: A F → h A G τ F ↘ ↙ τ G Ω Conversely, if there exists sections τ F and τ G and a homeomorphism h such that the above diagram commutes, then h = π G ∘ τ F and h − 1 = π F ∘ τ G.

The complementary vector bundle S ( T M ) ⊥ of S ( T M ) is called screen transversal bundle and it has rank 2. Since Rad T M is a lightlike subbundle of S ( T M ) ⊥, there exists a unique local section N of S ( T M ) ⊥ such that g ˜ ( N, N ) = 0, g ˜ ( N, ξ ) = 1.

In the framework of this section, there exists a unique such that (3.19).

If heterogeneity of staining intensity existed in a section, the staining intensity was scored based on that which was predominantly observed.

Although these two features are presented in separate sections, there actually exists a tight relation and interaction between them.

Nevertheless, as we will see in this section, there exists an open and everywhere dense set in the space of all nonexpansive self-mappings of any closed and convex (not necessarily bounded) set in a Banach space (endowed with the natural metric of uniform convergence on bounded subsets) such that all its elements have approximate fixed points.