Sentence examples for term we get from inspiring English sources

end{aligned} (12) Employing (12) in (10) and utilizing Fubini's theorem in the obtained term, we get (9).

After reducing the first term, we get that λ ( n + 1 ) λ ( n ) + Δ λ ( n ) + ∑ i = 1 m P i ( n ) ∏ j = n − k i ( n ) n − 1 1 λ ( j ) + 1 = 0, and we conclude that the sequence { λ ( n ) } satisfies the Riccati-type equation (4), and the first part of the proof is complete.

Suppose the dependent variable of the enterprise's competitive advantage (CA) is a linear function of multiple independent variables of X1, X2, ……Xn and the error term, we get the multiple linear regression model as follows: mathrm{CA}=upbeta 0+upbeta 1 mathrm{X}1+upbeta 2 mathrm{X}2+upbeta 3 mathrm{X}3+upbeta 4 mathrm{X}4+varepsilon.

By computing the right-hand term, we get begin{aligned} int_{Omega}frac{vert x-x_{0}vert ^{2}}{8lambda}biglvert f(x bigrvert ^{2}e^{-frac{vert x-x _{0}vert ^{2}}{4lambda}},dx leq&2lambda int_{Omega}biglvert nabla f(x bigrvert ^{2}e ^{-frac{vert x-x_{0}vert ^{2}}{4lambda}},dx &+frac{d}{2} int_{Omega}biglvert f(x bigrvert ^{2}e^{-frac {vert x-x_{0}vert ^{2}}{4 lambda}},dx.

Short term, we got it covered pretty much: gotta take out the recycling, check Techmeme, oh look, Mubarek quit after all, answer email, rinse, repeat.

Using again the positivity of the terms, we get (1.6).

Substituting the perturbation series expansions in (2.15) and then equating the constant terms and and terms, we get (2.21).

end{aligned} (11) Putting (11) in (10) and executing Fubini's theorem in the obtained terms, we get (9).

Substituting the above inequality into the right-hand side of (30) and arranging terms, we get the assertion (28) immediately.

Now, using the property of k-gamma function given in relation (8) and rearranging the terms, we get the required proof.

Expanding T 4 in a Taylor series about T ∞ and neglecting higher order terms, we get T 4 ≅ 4 T ∞ T − 3 T ∞ 4. (9).