Sentence examples for suppose additionally from inspiring English sources

Second, we suppose additionally that A ℓ (L 2 ⊆ H 1. Then, the H -stability (78) yields that A ℓ ∈ L 2 (H 1 ; H 1 are uniformly continuous operators. For v ∈ H 1, the sequence (A ℓ v ) ℓ is hence bounded in H 1 and thus admits a weakly convergent subsequence A ℓ k v → w weakly in H 1 as k → ∞.

Suppose additionally that (4.8).

Suppose, additionally, that x 0, y 0 ∈ X are comparable.

Let G be an n-dimensional oriented, connected, simply connected, nilpotent Lie group and Λ a uniform lattice in G. Let {a1,..., a n } be a set of generators of Λ and write b i = log a i, then {b1,..., b n } is a basis for the Lie algebra g corresponding to G. Suppose additionally that the basis {b1,..., b n } is positively oriented.

From now on we additionally suppose that (X) is paracompact.

Additionally suppose that x and y are decreasing and satisfy conditions (1.7), (1.8).

In order to prove our main results, we additionally suppose the following assumptions: (2.1).

Additionally suppose that (minmathbb{N}), (x_{i},y_{i}in [ a,b ] ) and (w_{i}inmathbb{R}) for (iin{1,2,ldots,m}).

Remark 2.3 If, in the above remark, we additionally suppose that x ∗, y ∗ ∈ Fix ( T ) ⇒ ( x ∗, y ∗ ) ∈ E ( G ), then Fix ( T ) = S Fix ( T ) = { x ∗ }.

Additionally suppose that (mathbf{x}, mathbf{y}in[ a,b]^{m}) are two decreasing m-tuples and (mathbf{w}inmathbb{R}^{m}) which satisfy conditions (1.4), (1.5).

If we additionally suppose that f is a harmonic mapping, then there exists a holomorphic function (g:mathbb {H}to mathbb {C}) such that (f z)= operatorname {Re}g z) +icy).