Sentence examples for Under the relation from inspiring English sources

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

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

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

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 ≈.

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.

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).

We recognise that misclassifications of individuals' socioeconomic circumstances can cause under- or overestimates of the relation between socioeconomic circumstances and admission type/procedure use.

The above two samples are imaged under four channels, and the relation between image contrast and the state of polarization are examined and analyzed.

In this paper, it is shown that it is an invariant under the equivalence relation among bent functions.