Sentence examples for by taking p from inspiring English sources

Indeed, by taking p = − λ in Eqs.

Hence Theorem 1.2 ii) follows from Theorem 3.2 by taking p = θ.

Proof The proof is similar to the proof of the previous lemma, by taking p = 0. □.

The same bound is achieved for ψ 18 ( t ), also by taking p = 1 and q = 1 2 log r.

(a) Impact of ω ϕ and (b) impact of M. By taking P p  = 14 dB, λ = 1, i.e., P S  = P R, in Figure 6, we present the outage probability versus the transmit power P s.

One of these RLS derivatives is the affine projection (AP) algorithm [38] that speeds up convergence when compared to its simpler gradient counterpart by taking P past regression directions into account.

Further, the influence of surface coverage on the electrocatalytic properties of the polymerized films was studied by taking p-4β-CoIITAPc and p-4α-CoIITAPc films as examples.

This newly obtained formula results in the fact that by taking p-norm, ∥ A x ∥ p ≤ ∥ A ˜ y ∥ p + | l | ∥ ( a n ) ∥ p < ∞.

If the supremum is obtained at the point C, by taking t p = (a p, b p ), b p = b r, a p = ε, with ε sufficiently small, the desired strict inequality follows immediately.

If the supremum is obtained at the point E, the conclusion follows by taking t p = (a p, b p ), b p = b r - ε, a p = 3ε/2, with ε sufficiently small.

which is a special case of ( E, p ) by taking f ( x, p ) = f 1 ( x ), g ( x, p ) = g 1 ( x ) and p ↦ e p defined as the identity operator on P = E 0 ( R ).