The phrase "auxiliary function for" is correct and usable in written English.
It can be used when describing a secondary or supportive role that a function serves in a particular context, often in technical or academic writing.
Example: "The auxiliary function for the main algorithm helps to optimize performance during data processing."
Alternatives: "supporting role for" or "secondary function for".
where, q ∈ [0,1] is an embedding parameter, H q) is a nonzero auxiliary function for q ≠ 0 and H 0) = 0.
The following function (20) is an auxiliary function for L (S ).
Our work describes an auxiliary function for viral autophagy suppression in disrupting host antiproliferative defenses.
L emma 3.5 If Z is an auxiliary function for function L(h), then L(h) is non-increasing under the update (Lee and Seung, 2000 ).
D efinition 3.4 Given a function L (h ) of any parameter h, a function Z (h, h ∼ ) is an auxiliary function for L (h ) if the conditions (18) Z (h, h ∼ ) ≥ L (h ) and Z (h, h ) = L (h ), are satisfied for any given h, h ∼ (Lee and Seung, 2000 ).
As in [ 13], given any current estimate b k ), a function Q(b | b k )) is an auxiliary function for J (b) if conditions (11) J (b (k ) ) = Q (b (k ) | b (k ) ) a n d J (b ) ≤ Q (b | b (k ) ) for all b, are satisfied.
After the operation, P is skipped from g using the auxiliary function Skip for optimization purposes (line 29).
(2) If an auxiliary unit to an electric powerplant consumes fuel only for the auxiliary functions of unit ignition, startup, testing, flame stabilization, and other control uses, its use of minimum amounts of natural gas or petroleum is not prohibited by FUA.
By introducing a piecewise continuous auxiliary function, some sufficient conditions for globally exponential lag synchronization are established by virtue of piecewise analytic method.
It is known that V ∈ R H q implies V ∈ R H q + ε for some ε > 0. Therefore, under the assumption V ∈ R H q 0, we may conclude q 0 > d / 2. We introduce the auxiliary function ρ defined as, for x ∈ R d, ρ ( x ) = 1 m ( x, V ) = sup r > 0 { r : 1 r d − 2 ∫ B ( x, r ) V ( y ) d y ≤ 1 }.
This paper is organized as follows: The proofs of Theorem 1.1 and a Sturmian comparison principle to the anisotropic elliptic equation are given in Section 2; Section 3 is devoted to the proof of Theorem 1.3 in which a key ingredient is to choose a suitable auxiliary function (see (3.3) below) for the anisotropic case.
