Sentence examples for denoting by from inspiring English sources

Denoting by |M| the number of elements of a subset M⊂Ω we show that |⋃g∈GF g)|⩽4supg∈G|F g)|.

Denoting by (27).

Denoting by,, we say that.

and denoting by we have (2.26).

Denoting by, it is easy to see that (2.25).

Denoting by and the solutions of (4.11) and (4.13), respectively.

Precisely, denoting by (f_Omega ) a non trivial eigenfunction, that is a nontrivial solution to Eq. (6.30).

On the other hand, denoting by the integer part function, we have (4.13).

Denoting by the -neighborhood of and letting, then it follows that (4.10).

Denoting by the operator which acts from to in the following way: (215).

Denoting by the right-hand side of the last inequality, we obtain that (3.14).