Sentence examples for sum is reduced from inspiring English sources

By Lemma 7 we can assume that the sum is reduced.

Let (Omega '=Omega {setminus }Omega _{max}.) Then (a=sum nolimits _{iin Omega '} a_i) and this sum is reduced.

The resulting sum is reduced by following similar procedures to the ones mentioned in the first item.

For an arbitrary nonzero converging sum (a=sum nolimits _{iin Omega } a_i,, a_iin L(Gamma ),) there exists a nonempty subset (Omega 'subset Omega ) such that (a=sum nolimits _{iin Omega '} a_i) and this sum is reduced.

Finally, in the case where this sum is reduced to one element, which is the case for non-characteristic points, we use modulation theory coupled with a nonlinear argument to show the exponential convergence (in the self-similar time variable) of the various parameters and conclude the proof.

Rewriting each summand (p q^*, (p,q) in mathcal {P'} (p_0,q_0),) as a linear combination of basic elements from (B gamma )) and using Lemmas 5, 6 we get (a'=sum beta _{p,q}pq^*,) where (beta _{p,q}in F,,, l(p)=l q), s(p)=s q)=v, pq^* in B gamma )) for each summand and the sum is reduced.

This sum was reduced on appeal to £40,000 – but McDonald's never enforced payment.

The lawsuit, filed in New York State Supreme Court, originally sought $25 million in damages on the grounds of defamation and gender discrimination; it was later narrowed to gender discrimination and the sum was reduced to $13 million.

The footballer was awarded damages of £80,00, but that sum was reduced on appeal to £1 and Grobbelaar was ordered to pay NGN's legal costs, which totalled several hundred thousand pounds.

The sum power and infeasibility ratio is lower compared to Figure 7, since the sum interference is reduced in the system.

By forcing one receiver to decode all streams, the sum DoF is reduced to unity4.