The phrase "and furthermore assuming" is not standard in written English and may be considered awkward.
It can be used when introducing an additional assumption in a discussion or argument, but it is better to simplify the expression.
Example: "We can conclude that the project will succeed, and furthermore assuming we have the necessary resources."
Alternatives: "and additionally assuming" or "and also assuming".
Assume that (1.2) holds,, and Furthermore, assume that there exist positive rd-continuous -differentiable functions and such that, for all sufficiently large for (2.18).
Assume that (1.2) holds, and Furthermore, assume that there exists such that and Then an eventually positive solution of (1.1) satisfies eventually (2.5) or.
Assume, i = 1,2, where f i ∈ ℘+, i = 1, 2,, where ε > 0 is a constant, and furthermore, assume, is the solution of the following difference equation (33).
Assume, i = 1, 2, where f i ∈ ℘+, i = 1, 2,, and furthermore, assume, is the solution of the following difference equation (42).
Let and suppose (2.3) holds and furthermore assume that there exists a satisfying conditions (i) and (iii) of Theorem 3.1 and.
Suppose (2.3) holds and furthermore assume that there exists a function such that (i) there exist -functions such that for any, (31) .
Assume that (1.3) holds,,, and Furthermore, assume that there exist positive rd-continuous -differentiable functions, and such that, for all sufficiently large for one has that (2.33) and (2.35) hold.
Assume that (1.3) holds, and Furthermore, assume that there exist positive rd-continuous -differentiable functions, and such that then for all sufficiently large for one has that (2.18) holds, and (2.35).
Under the conditions of Lemma 2.2, and furthermore assume a(m, n) ≥ 0. If for (m, n) ∈ Ω, u(m, n) satisfies the following inequality u ( m, n ) ≤ a ( m, n ) + ∑ s = m + 1 ∞ ∑ t = n + 1 ∞ b ( s, t, m, n ) u ( s, t ), (13).
We also assume that the axes of the lobules are parallel to the surface and furthermore assume that the surface cuts the lobules in such a way that the areas of the outermost lobules (now pentagonal prisms) are the same as those of the interior hexagonal lobules, as shown in Fig. 1b.
