Sentence examples for using this proposition from inspiring English sources

The results obtained using this proposition are shown in Table 7.

Using this proposition, we can get that the continuum limit transforms of lattice Eqs.

Using this proposition, we can show that problem (3.2) admits a smallest positive solution (widehat {u}_{v}in D_) on ([0,eta]).

So, the result follows by using this equality and Proposition 10. □.

Using this equality and Proposition 14, one can state the following result.

Using this notation, we have therefore: Proposition 1 ∑ r < M α k j ( t − r ) ⪯ P d ( t − M τ k j ) e − t − M τ k j, (12).

Let us use this very example to illustrate Proposition 4.1.

Proposition 2.2 can be easily shown by using the Proposition 2.1 (see [6]).

For forming propositions we use this type structure: thus R a1,…,an) is a proposition if R is of type (A1,…,An) and ai is of type Ai for i = 1,…,n.

A case study is used to illustrate this proposition.

By using [9, Proposition  2.5], the following proposition is proved.