Sentence examples for from relation from inspiring English sources

If x ∗ is not a weakly efficient solution for problem (FP), then there exists x ∈ X ∘ such that f i ( x ) g i ( x ) < f i ( x ∗ ) g i ( x ∗ ) = v i ∗ for  i ∈ K. From relation (6) and α i 1 ( x, x ∗ ) > 0, we have ∑ i = 1 k y i ∗ A i ( x ) α i 1 ( x, x ∗ ) < ∑ i = 1 k y i ∗ A i ( x ∗ ) α i 1 ( x, x ∗ ), which contradicts (7).

Then there is a feasible solution x ∈ X ∘ such that f i ( x ) g i ( x ) < f i ( x ∗ ) g i ( x ∗ ) = v i ∗ for  i ∈ K. From the above inequality, we have f i ( x ) − v i ∗ g i ( x ) < f i ( x ∗ ) − v i ∗ g i ( x ∗ ) for  i ∈ K. From relation (6) and α i 1 ( x, x ∗ ) > 0, for i ∈ K, we obtain ∑ i = 1 k α i 1 ( x, x ∗ ) y i ∗ A i ( x ) < ∑ i = 1 k α i 1 ( x, x ∗ ) y i ∗ A i ( x ∗ ).

The contemporary Greek theologian, Christos Yannaras, has developed a rich and complex metaphysics of relation, stressing that Christian theology sees the human person as purely abstract if cut off from relation with God and others and the material world.

Setting from relation (3.27) we deduce that.

From relation (3.38) we have that.

end{gathered} The result follows from relation (5.5).

Recall that the following-from relation is a causal relation.

Recall that the modal transfer principle states that necessity transfers down the following-from relation.

Hence necessity will track the following-from relation because both are grounded in the same relations of conceptual involvement.

To see why, notice that the difference between [iii] and [iv] is not a function of the presence or absence of the following-from relation itself.

Of course, we need not and should not interpret Spinoza's following-from relation as the strict logical entailment of contemporary modal logic.