Sentence examples for required smoothness from inspiring English sources

b The required smoothness of higher derivatives is related to the order of the used collocation method.

This structure represents mechatronic system and consists from the set of on-off valves and computer control device that operates the valves and reaches the optimum motion control of the object with required smoothness.

aNote that u 0, min ( T ) = u 0, max ( T ) = v ( T ) = 0. bThe required smoothness of higher derivatives is related to the order of the used collocation method.

Simplicity and robustness compared with closest point projection is emphasized, in particular no longer required smoothness conditions on the shape of the boundary.

This is a substantial decrease in required smoothness of the star-like domain, especially for low dimensions.

The required smoothness of the distance function h is essential for the performance of the Newton method.

Optimization algorithms that require smoothness can fail on such problems.

These two theorems do not require smoothness of operators and the abstract two-dimensional bifurcation theorem can be regarded as an extension of the well-known Crandall Rabinowitz bifurcation theorem, and therefore are of interest for their own sake.

For (d=2), we require smoothness of (F_{12}), (g^{jk}) and V marginally larger than (mathscr {C}^2) to recover the same remainder estimate as in the smooth case, but there is a twist: unless the smoothness is (mathscr {C}^3), a correction term needs to be included.

Daily activities require smoothness and efficiency, with coordinated actions of all parts of the body, for example, coordinated movement of the head, arms, and feet during walking and hopping [ 9– 11].

Observe that these assumptions do not require any smoothness beyond (mathscr {C}^1).