Sentence examples for order continuously from inspiring English sources

Then, we prove the existence of smooth kernels with second order continuously derivative for the forward and inverse transformations in the backstepping feedback control law design.

For ensuring that x ( t ) in Eq. (5) makes sense, σ has to be at least first order continuously differentiable, i.e., σ ∈ C 1 [ 0, π ].

The functions (f_{j}(x)) ((j in I cup J)) are all first order continuously differentiable, and there exists an index (l_{x} in I x)) for each (x in X) such that the gradient vectors ({ nabla f_{i}(x) - nabla f_{l_{x}}(x), i in I x backslash { l_{x}};nabla f_{j}(x),j in J x)}) are linearly independent.

When the intron length was sorted by order continuously, short introns showed a lower divergence than the long introns between human and chimpanzee, and this trend was also present in the comparison of introns between the two rice lines (Additional file 1, Fig. S4A).

If (d^{m} f cdot)) is continuous at (x_{0}) then f is said to be mth-order continuously Fréchet differentiable at (x_{0}).

Virtually all modern financial markets match orders continuously – that is, as orders arrive to the exchange.

Theorem 2.1 Suppose that f : J → R is second-order continuously differentiable.

For the simplicity of our proof in Theorem 3.1, f ( t, x ) is a first-order continuously differentiable function satisfying Lipschitz condition.

Furthermore, a refined SS-TVD flux-limiter, referred to henceforth as TCDF (Third-order Continuously Differentiable Function), is proposed for steady-state calculations based on the review.

Fourth, the main technical novelty is the construction of three new nth-order continuously differentiable switching functions, which are used to design the desired controller.

Thirdly, the main technical novelty is to construct three new nth-order continuously differentiable switching functions such that multiswitching-based adaptive neural backstepping controllers are designed successfully.