Sentence examples for implies for each from inspiring English sources

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.

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).

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

Assume that is a set-valued mapping satisfying the following conditions: for each, ; for each, implies that ; for each, is -convex on ; for each, is weakly lower semicontinuous on ; for each, the set is closed, here stands for the closed line segment joining and.

is a set-valued mapping satisfying the following assumptions: for each,,, ; for each,,, implies that ; for each,,, is -convex on ; for each, and, for any sequences, and with, and, there exists a sequence with such that.

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).

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 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.

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