Sentence examples for minimizing the functional from inspiring English sources

Figuring out the function f minimizing the functional E(f), requires complex processing operations.

In order to obtain the exciton eigenfunctions, and the corresponding energies (E), we adopt a variational scheme[13] which consists minimizing the functional E=〈Ψ|H|Ψ〉 by using the trial wave function, Ψ, as[1] Ψ n e, n h ( r → e, r → h ) = N n e, n h Υ n e, n h × ( ρ e, ρ h, z e, z h ) e − α n e, n h ρ − β n e, n h ( z e − z h ) 2, (2).

To understand why observe that minimizing the functional above is equivalent to finding a minimizer (f_j) of the functional begin{aligned} frac{1}{2}int _{Omega }|nabla f|^2,dx-int _{Omega }f,dx+|alpha ({f>0} -alpha (Omega _j)| + Lambda big ||{f>0} -alphag | end{aligned} (6.41)amOmegall functions with a support of finite measure.

By minimizing the functional the identification parameters are obtained.

By minimizing the functional with membrane triangular elements, a series of intermediate configurations are obtained, consequently the forming path of sheet is described.

Compared with the existing literature which solved the problem by the B-spline finite element method, the essence of the proposed variational-difference numerical method lies in minimizing the functional directly by finite difference method and/or numerical quadratures rather than in approximating the solution of the corresponding Euler Lagrange equation to the functional.

The calculus of variations can be used to find the function F z) that minimizes the functional J(F) defined as follows: J ( F ) = ∫ Z I z, F ( z ), ∂F ( z ) ∂ z 1, ∂F ( z ) ∂ z 2, …, ∂F ( z ) ∂ z L d z, (6).

In other words, quite different (g ( t )) functions can minimize the functional (1.5).

We take (alpha > 0) as a regularization parameter and minimize the functional (7.4) using the minimizing sequence by (6.14) for (beta = 0.2).

Fixing ϕ, we minimize the functional E ϕ, h 1, h 2) with respect to the functions h 1 x) and h 2 x).

A partition < V1, V2> that minimizes the functional c(V) over all partitions of V is called the minimal partition (of V).