Sentence examples for by the auxiliary function from inspiring English sources

By the auxiliary function (4.11).

The boundary conditions are exactly satisfied by the auxiliary function Φ = A1sin (πx/l).

Using this approximation, we end up with a straight forward score update by the auxiliary function (18).

In the scalar case, an important role is played by the "auxiliary function" K u)≔(s u /f′ u))′, where f is the flux function and s is the source.

We define the generalized Baum-Welch algorithm by extending the auxiliary function in (5) to Q = ∑ Q ∑ F ∑ E Pr ( Q, F, E | O, λ ) ln Pr ( O, Q, F, E | λ ̄ ), (81).

The second part of (23) also follows by employing the auxiliary function g Λ, 1 : I → R, g Λ, 1 ( t ) = Λ t log t − Φ ( t ) ; and this completes the proof.

The second inequality in (19) follows by considering the auxiliary function ψ Δ, q ( x, y ) : I → R with ψ Δ, q ( x, y ) = Δ t q − Φ ′ ′ ( t ), and we omit the details.

Then, bandgap edges of the equivalent 1D structure are determined by the auxiliary functions of generalized scattering matrix (AFGSM) method.

The optimization can be found by iteratively maximizing the auxiliary function based on the Baum-Welch method, (4).

For any finite-net multi-CCS process p, the set of its sequential subterms sub(p) is defined by means of the auxiliary function (with the same name, with abuse of notation) sub p, emptyset )), whose second parameter is a set of already known constants, initially empty, described in Table 1.

(Names in sequences of a process) Let ns((p) subseteq mathcal {L} cup overline{mathcal {L}}) be the set of (free) names occurring in sequences of length two or more of p. Set ns(p) is defined by means of the auxiliary function (with the same name, with abuse of notation) ns((p, emptyset )), whose second parameter is a set of constants, where ns p, I) is defined in Table 6.