Sentence examples for imposing the growth from inspiring English sources

Imposing the growth condition on || · ||α,βin (2.1) a new space of test functions has emerged as follows.

Imposing the growth condition on ∥ ⋅ ∥ α, β in (2.1), we get a new space of test functions as follows.

Imposing the growth condition on ∥ ⋅ ∥ α, β in (2.1) Sato and Kawai introduced the new space of test functions for the Fourier hyperfunctions as follows.

Imposing the growth condition on ||·|| α,β in (2.1) a new space of test functions has emerged as follows: Definition 2.2[22].

In particular, we impose the growth condition A ( x, ξ ) ⋅ ξ ≈ ∣ ξ ∣ p. then Equation (1.1) simplifies to the p-harmonic equation d * ( ∣ d u ∣ p - 2 d u ) = 0.

Namely, we impose the growth condition of Wintner-Nagumo type | f ( t, x, y ) | ≤ ψ ( | y | ) ( l ( t ) + c ( t ) | y | ( p − 1 ) / p ).

In this section, by constructing upper and lower solutions and with the maximum principle Lemma 2.9, we impose the growth conditions on which allow us to establish necessary and sufficient condition for the existence of (1.1 - 1.2 1.1 - 1.2

We begin by imposing the linear growth condition on both drift and diffusion coefficients of SDE (2.1): | f ( x ) | 2 ∨ | g ( x ) | 2 ≤ κ | x | 2 + a, ∀ x ∈ R n, (3.10).

Our main result shows the existence of two constant sign solutions and a sign changing solution in the case where we do not impose the subcritical growth condition to the nonlinear term not including derivatives of the unknown function.

Results without this correction (excluding those with zero payments) and results for annual growth (imposing the logarithm to be zero) lead to similar conclusions and are available on request.

While few mainstream economists have predicted that the UK will suffer a double-dip recession, the Treasury is under pressure to show it can maintain growth while imposing the toughest curbs on public spending in 40 years.