Sentence examples for the previous formulae from inspiring English sources

Using the previous formulae, we can calculate that in we have ; in particular, the closed unit ball is noncompact.

In order to relate it to the previous formulae for group cohomology, we should preliminary observe that the group algebra ({mathbb {Z}}[G]) can be thought of as the subalgebra of the space of functions ( a: G rightarrow {mathbb {Z}}) generated by the characteristic functions of elements of G (so that (g in {mathbb {Z}}[G]) is the function such that (g(x) = 1 ) for (x=g), else (g(x) = 0, xne g ).

In the previous formulae, the number of trials is represented by the denominator of the point estimate equation, whilst the number of events (or successes) is given by the numerator.

The previous formula — which I also tried — is grittier and tougher on skin.

(b) Simulated and experimental (retrieved from the measurements with the previous formula) antenna gain, defined as G=DηT.

Based on the results, an addition to the previous formula for critical velocity estimate is proposed.

The previous formula remains valid for.

Informally, the following natural language sentences could be thought of as interpretations of the previous formulas.

This indeed holds by the previous formula since T∧τ=T.

The overall reliability of the network is as described by the previous formula.

Thus, we have enhanced the previous formula to accommodate this situation.