The phrase "auxiliary relation" is correct and usable in written English.
It can be used in contexts related to linguistics, mathematics, or systems theory where a secondary or supportive relationship is being described.
Example: "In the study of syntax, the auxiliary relation between verbs and their subjects is crucial for understanding sentence structure."
Alternatives: "supporting relationship" or "secondary connection".
In the following, \(P\) is an auxiliary relation symbol of arity 0, that is, a propositional letter.
If \ \phi_0\), \ \phi_1\), …, \ \phi_k\) are formulas and \(P_1\), …, \(P_k\) are (new) auxiliary relation variables, the following is a formula.
A valuation \ v\) in this structure is a mapping from individual variables to members of \ \bD\) and from auxiliary relation symbols to partial relations on \ \bD\).
A process p is well-formed if ({{mathrm{wf}}(p)}) holds, and ({{mathrm{wf}}(p)}) holds if the auxiliary relation (with the same name, with abuse of notation) ({{mathrm{wf}}(p, emptyset )}) holds; the auxiliary relation ({{mathrm{wf}}(p, I }), where the second parameter is a set of constants, is defined as the least relation induced by the axioms and rules of Table 7.
Well, take \ v\) to be a valuation assigning to each auxiliary relation symbol \(P_i\) the corresponding partial relation \ \bP_i\) (this is how 'before' values for our partial relation symbols come in), and assigning to the variables in \ \bx_i\) the corresponding members of \ \bd\).
We also have an auxiliary relation for n′: 3 To simplify these three-dimensional (3D) equations, we note that the net flow occurs along the direction of the axis of the macroscopic porous affinity region and that this region is homogeneous and anisotropic.
Secondly and for the purpose of benchmarking, the main practical approaches identified for the application of Exergy Cost Theory are presented and formalized, including the fundamental aspects related to the definition of auxiliary relations and the reallocation of the exergy cost of the residues.
Maxwell's equations give rise to the following two auxiliary relations [4].
The advective velocity u in these equations is determined from θ by a stream function φ via the auxiliary relations u = u 1, u 2 = - ∂ φ ∂ x 2, ∂ φ ∂ x 1, (1.2). and the relationship (1.1 2.
The semigroup S(M) is defined by the relations from the union R of all (R_kappa ) (which is finite since we have only a finite number of commands) and usually some auxiliary relations Q which are in a sense "independent" of R but make the semigroup "smaller".
A number of auxiliary relations were needed, these were determined based on the F-rule [18] and are listed in Table 3. Further, it was assumed that the specific unit cost of exergy for the vapour stream and liquid stream exiting the separator were equal: (c_{2}=c_{9}) and that no cost was affiliated with the inlet condition of the sink and source: (c_{12}=c_{15}) = 0 €/s.
