Sentence examples for Under the relations from inspiring English sources

The region (pi _g (L_i,L_j,L_k)) is classified into eight geometrical patterns (Fig. 3a) under the relations of variables (h_{mathrm{ref}}^i, h_{mathrm{ref}}^j) and (h_{mathrm{ref}}^k) (see Table 2).

end{aligned} (10)The region (pi _{{mathrm{grp}},g} (L_i,L_j,L_{mathrm{grp}})), which is represented by Eqs. 9 and 10, is classified into four geometrical patterns (Fig. 3b) under the relations of the variables (h_{mathrm{ref}}^i, h_{mathrm{ref}}^j) and (h_{mathrm{ref}}^{mathrm{grp}}) (see Table 2).

Another way to define them is that they are equivalence classes of edges under the relation \((u,v) \sim (v,u)\).

The interpretability hierarchy is the collection of all theories (satisfying our three simplifying assumptions) ordered under the relation ≤.

One very general way to investigate the space of possible mathematical systems is under the relation of interpretability.

If she does so, then she indirectly ascribes the property of being hungry to Bill, under the relation of being a man uniquely seen.

Note that in the previous theorem (the parts (ii), (iii), (iv)) it is proved that the logical entropy and conditional logical entropy are invariant under the relation ≈.

The seismic moment M 0 (Nm) is calculated from the moment magnitude M w under the relation derived by Hanks and Kanamori (1979): log {M}_0=1.5{M}_W+9.1 (1).

The equivalence class of all theories mutually interpretable with T is called the interpretability degree of T. The interpretability hierarchy is the collection of all theories ordered under the relation ≤.

1. Probably the best all-purpose understanding of what logics are would take them as equivalence classes of proof systems under the relation of having mutually interderivable rules, though even this ignores issues about translational equivalence across differing languages.

Let us define a world as a maximal fact under the relation of fact-containment: x is a world iff for every fact y, if x ≤ y, then x = y.