Sentence examples for formulae above from inspiring English sources

By using mathematical induction, we now suppose the formulae above also hold for n ≥ 0. Then ( I n + 1 ) : ∥ x n + 1 − x 0 ∥ ≤ ∥ x n + 1 − y n ∥ + ∥ y n − x 0 ∥ ≤ t n + 1 − s n + s n = t n + 1.

The concrete formulae above are consequences of a more general mathematical duality called Pontryagin duality.

In this context we rewrite the chemical formulae above by adjoining E designing the lone pair (LP) and M* formulating the LP-bearing element: ClF{E3}, M*2OE2{E3}2 (M* = F, Cl, Br), M*F3E2 (M* = Cl, Br, I) and XeF4E2.

In this approach, the weighting of the subindices within the formulae above was stated with (frac{1}{3}).

From the formulae above, we can see that any positions in the Voronoi cell are closer to its Voronoi sites.

If written out more formally in classical predicate logic, using a suitable formalism for representing time and action such as the situation calculus (McCarthy & Hayes 1969), the two formulae above only license the conclusion that Position A, Garden) holds.

Estimated (using allometric formulae) above-ground dry tree woody biomass.

Using the approximation formulas above, difference schemes (2) and (3) are constructed.

The formulas above could then be used to create (varDelta ^{i}).

Let's use this technique to alter the circumference formula above, C=2πr.

One way of exploring them is to construct modal systems in which the formulas listed above are theorems.