Sentence examples for first term using from inspiring English sources

For the first term, using (5.7), the embedding property and η = ∥ L t ∥ < 1, the term can be estimated as ∥ L t k n u 0 − P L t k n u 0 ∥ ≤ M h θ ∥ u 0 ∥ 2. (5.38).

For the first term, using (5) we obtain for all (Tleqtau^{ast}) I_{1}leq C int_{0}^{T}e^{-varepsilon^{-4}w T-tau }biglVert psi(tau )bigrVert _{sigma},dtauleq Csup_{tauin[0,tau ^{-varepsilon^{-4}w T-tau }biglVert_{sigma} int _{0}^{-varepsilon^{-4}w T-tau }biglVerteq C varepsilon^{-varepsilon^{-4}w T-tau }biglVertnition of (tau^{ast}).

Hence, by the additivity of the expectation we get Now we can rewrite the first term using the independence property as follows: which is the expected accuracy of σ1 in the sequence s1.

You can factorize these by factorizing the first term, using each factor as the first term of each binomial factor, then finding two factors of c that can be used as the second terms of the binomial factors.

George W. Bush's tax-cut legislation in his first term used the reconciliation process, and, as a consequence, many of the tax cuts expired a decade later, under a deal between Obama and the Republicans.

The estimate of the first term used Hölder inequality and Sobolev's imbedding theorems.

The most important legacy Mr. Obama could have would be to spend his second term using executive orders, judicial appointments and the bully pulpit to return democracy to everyday Americans by demanding clean elections, uncorrupted by money.

Obama appeased them to an extent during his first term by using more stimulus money to preserve the jobs of hundreds of thousands of teachers during the recession.

During Obama's first term, he used the Antiquities Act sparingly, even timidly.

During the 2000 campaign and his first term, Bush used to make regular, if highly choreographed, trips into town.

But the Obama administration, in the president's first term alone, used it six times to go after leakers.