Sentence examples for imply for each from inspiring English sources

The properties (i - iv) i - ivfor each α ∈ ( 0, 1 Open imply in new window, the α Open image in new window-level set, X α = { x ∈ R n : X ( x ) ≥ α } = X ― α, X ― α Open image in new window (7). is a non-empty compact convex subset ofor n Opeachmage in new window.

Let us consider the equilibrium-like function which satisfies the following conditions with respect to the multivalued mapping : for each fixed, is an upper semicontinuous function from to, that is, and imply ; for each fixed, is a concave function; for each fixed, is a convex function.

The Young inequality and (B1) imply (for each δ > 0 ) that Homogeneity (B0) with α = h (T ℓ + 1, k ) / h (T ℓ, k ) and h ^ (T ) = h (T ℓ, k ), and the contraction  (8.19) yield The second term on the right-hand side of  (8.33) is similarly estimated by use of monotonicity  (8.20) instead of  (8.19).

"Proponents" implies "for"; make it "proponents of".

Note that for each implies for each.

any -nondecreasing sequence with implies for each ; any -nonincreasing sequence with implies for each ; there exists a -function such that for any, with, (226).

This implies for each switching time interval, the dwell time has a lower bound.

Thus (4.12) must hold, implying for each i and (mathcal{Q}), lim_{trightarrowinfty} h_{i} bigl(x t bigr)=0, qquad lim _{trightarrow infty} h^{mathcal{Q}}bigl(x t bigr)=0quad mbox{a.s.} (4.27).

Then according to ( i ̃ ) ( i i ̃ ) and the connectivity of C 1 +, we obtain C 1 +, k ∩ λ × C 1 [ 0, 1 ] ≠ ∅, ∀ λ ∈ 1 2, 2, k = 1, 2, …, N, which implies for each λ ∈ ( 1 2, 2 ), (1.1) has N positive solutions: u k, k = 1, 2, …, N, and u k ∈ C 1 +, k ⊂ C 1 +, k = 1, 2, …, N. In this section, an example is given to illustrate the application of our main result (Theorem 3.1).

Colors represented the number of proteins implied for each tRNA for each strain.

Firstly, there appears to be an asymptote as k B → ∞, implying for each background k A there is a minimum λ necessary for equal fitness strategies.