Sentence examples for functional over the from inspiring English sources

Alternatively, the evolution equation for the level-set function also can be directly derived from the minimization problem for the energy functional over the level set functions via the gradient descent [3 7]: ∂ ϕ ∂ t = F δ ϵ ϕ, (3).

Since the class of sequences with the zero boundary conditions on both x 0 and x N + 1 is a subset of the class of sequences with zero boundary condition at 0, the nonnegativity (positivity) of the functional (1) over the class of functions which satisfy x 0 = 0 implies the nonnegativity (positivity) of this functional over the class of functions which satisfy x 0 = 0 = x N + 1.

This point of view has been exploited in the proof of Theorem 3.1 where the idea is precisely to view the perimeter of E as an integral functional over the sphere depending on the function u and then to write the second order Taylor expansion of that functional.

It is concluded that the TMJ prosthesis could remain stable and functional over the initial healing period.

The segmenting contour and the corresponding density are found as minimizers of a Mumford Shah like functional over the set of admissible contours and – for a fixed contour – over the space of piecewise constant densities which may be discontinuous across the contour.

The tool DAVID [ 24] was used for the calculation of the functional over-representation statistics of the different lists of significant genes obtained with Rank Prod analysis.

Clinical-pathologic correlation was made using functional over-representation analysis of the top 100 mutations associated with each variable.

Also in this case, as expected, the mean of the Minkowski functionals over the sections is oscillating more in direction Y than in direction X. Furthermore we note an increased local variability of the functionals in direction Y with respect to direction X.

In this section, we present a necessary and sufficient condition for nonnegativity and positivity of the functional (1) over the class of admissible functions, i.e. functions with zero left endpoint and free right endpoint.

Accordingly, detection of viral constituents alone does not allow identifying functional structures over the large background of non-functional complexes.

This process clearly implies the successful immobilization of functional groups over the Au nanospheres surface, which improves the stability of functional nanospheres.