Sentence examples for exists flat from inspiring English sources

Definition 2.7: The continuous-time system dx/dt = f x,u), with f: ℜn×ℜm→ℜn, is differentially flat if there exists (flat) outputs z∈ℜm such that z = H x), x = F1 z, dz/dt, …, drz/dtr), and u = F2 z, dz/dt, …, drz/dtr) for some integer r and maps H, F1, F2.

Definition 2.8: The discrete-time system x + = f x,u) is difference flat (with memory k) if there exists (flat) outputs z∈ℜm such that z = H x), x t) = F1 z(t), z(t + 1), …, z(t + k − 1)), and u(t) = F2 z(t), z(t + 1), …, z(t + k − 1)) for some maps H, F1, F2. Background on flat systems may be found in[13].

Furthermore, our analysis of the band structures and density of states in hybrid double-layer architectures demonstrate that there exists a flat band and band dispersion near the Fermi level of graphene/CNT junctions, a feature not present in the graphene/BNNT junction due to the intrinsic wide band gap of BNNT.

These visionary artefacts have only ever existed as flat designs on paper.

Because there exist many flat surfaces where on architecture and there is a certain geometry relationship called homorgraphy, between two images, we can exploit this characteristic to locate the best fitted image patches for image inpainting.

But to pretend those deals don't exist is flat dishonesty.

On the tangent bundle ({T} G) there exists a canonical flat connection (nabla ).

E. distachya community is mainly distributed on dunes from the base to mid-dune and S. terrae-albae exists at the flat slope; both habitats are commonly covered by biological soil crusts (BSCs).

Recall that a Lie algebra L over R is called a form of g ⊗ k R (or simply a form of g ) if there exists a faithfully flat and finitely presented R –algebra R ~ such that L ⊗ R R ~ ≃ ( g ⊗ k R ) ⊗ R R ~ ≃ g ⊗ k R ~, (2.1 where all the above are isomorphisms of Lie algebras over R ~.

Therefore, whether a small swapped "domain" exists in a flat region of an A·D profile must be further analyzed (see Figure S4c for an example).

Further inward is the corneoscleral meshwork which exists as several flat sheets of trabeculae that are irregularly perforated [ 4, 14].