Sentence examples for expansion useful from inspiring English sources

Moreover, we derive from our expression an asymptotic expansion useful for evaluating Legendre functions of the first and second kinds of large orders, as well as the derivative of the nonoscillatory phase function.

This expansion is useful when orthogonal Latin hypercube designs do not exist.

(5) Poleward expansion is useful as a working definition of substorm onset because the AIB is not regularly monitored and can be gradual.

The proposed method for the lattices of lightweight, robust stiffness, strength and tailorable thermal expansion is useful in the engineering applications.

Analytic results reveal that laminated layers having high elastic modulus and a small coefficient of thermal expansion are useful in moderating EIC warping.

This gives a simpler expression for the Taylor expansion, A useful expression derived from this is, (A.2) Note that the terms containing (1−2φ) disappear when φ = 1/2 (equal number of cases and controls), meaning that these approximations are particularly good in that case e.g.g

The following elementary power series expansions are useful in our investigation.

Expansions are useful, and if the game gets big enough, you may want to try to get it a business going, and some marketing.

Sometimes tissue expansion can be useful for reconstruction using local flap but the discomfort for the patient is very high and this technique cannot be dedicated to elderly patients [ 12, 13].

Therein lies the most compelling reason to reform the General Mining Law of 1872, a relic of the boisterous era of westward expansion that, while useful in its day, is an environmental disaster now.

This section will be devoted to a useful expansion of the gradient of J near infinity.