Sentence examples for the functional that from inspiring English sources

From the density of in, we deduce that the previous equality is fulfilled for all and, in consequence, is a critical point of the functional, that is, is a solution of (1.10).

Observe that, in a Hilbert space, (1.4) is reduced to The generalized projection  :   →  is a map that assigns to an arbitrary point, the minimum point of the functional that is, where is the solution to the minimization problem.

Following Alber [22], the generalized projection from onto is a map that assigns to an arbitrary point the minimum point of the functional ; that is,, where is the solution to the minimization problem.

The generalized projection is a mapping that assigns to an arbitrary point the minimum point of the functional, that is, =, where is the solution to the minimization problem: (1.6).

Observe that, in a Hilbert space, (2.2) reduces to, The generalized projection is a map that assigns to an arbitrary point the minimum point of the functional that is, where is the solution to the minimization problem (2.3).

Observe that, in a Hilbert space, (2.3) reduces to for all The generalized projection is a mapping that assigns to an arbitrary point the minimum point of the functional that is, where is the solution to the minimization problem: (2.4).

We study the identities that lead to symmetry results, the functionals that can be considered and the function spaces that can be used.

The functionals that satisfy these conditions approximately are constructed using discrete and continuous inequalities.

For example, Ambrosio and Tortorelli [23] show how to approximate the M-S functional, in the sense of gamma convergence, with a class of the functionals that are much more tractable numerically and can be subsequently minimized via gradient descent.

Another consequence of this inequality is that the linear functional that evaluates a function f at a point of D is actually continuous on L2,h(D).

The information functional that has been used [28] is based on determining the so-called j-spheres of a graph.