Sentence examples for by using the identities from inspiring English sources

Thieves are increasingly obtaining fraudulent tax refunds by using the identities of lawful taxpayers, according to a government watchdog report released Wednesday.

Similarly, by using the identities (2.7).

The statements directly follow by using the identities (3.1), (3.3) and (3.4).

Now we state the main generalization of the majorization inequality by using the identities just obtained.

He also pleaded guilty to state charges of larceny and credit card fraud, partly for avoiding paying creditors by using the identity of a man who died in 1994.

Then by using the identity.

By using the identity the chain of inequalities (1.2) gives (3.3).

Notice that in this case the inequality holds; then the results can easily be obtained by using the identity (3.1).

The other two partial derivatives in (21) can be found by using the identity ∂ x H =(∂ x) H. Thus, (20) can be solved by using (24) and (25).

In this case, the CCDF of can be obtained by substituting in (A.4) and by using the identity of the Marcum- function, as follows (Appendix D): (24).

After solving (4), the solution (phi (t)) of (1) can be obtained by using the identity phi(t)=x t)+psi(t).