Sentence examples for indeed utilizing from inspiring English sources

Indeed, utilizing Proposition 2.8, we have, for each, (3.52).

Indeed, utilizing (3.8), we deduce from algorithm (3.2) that (3.23).

Indeed, utilizing (2.8) and (2.9) and simplifying these inequalities, we have (2.19).

Indeed, utilizing the arguments similar to those of Step 5 in the proof of Theorem 3.1, we can obtain the desired conclusion.

Indeed, utilizing 0.1 M NaOH resulted in a high RFI but almost equal to the fluorescence intensity achieved upon utilizing 0.2 M borate buffer with pH 7.0.

Indeed, utilizing ICT and particular the use of interactive facilities of Maple in teaching and learning which will provide a new challenge to both mathematics educators as well as students.

These computer simulations also confirmed that tensegrity principles are indeed utilized at the level of individual molecules, multi-molecular assemblages, and whole living cells.

If Max i m i s − m i s − 1 ≤ ε or s >T, then stop; else s = s + 1 and go to step 2. For the two-phase image segmentation, Chan and Vese [12] indeed utilized an alternating optimization to solve the following minimization problem: Min c 1, c 2, ϕ F CV c 1, c 2, ϕ = ∫ Ω I x, y − c 1 2 H ε ϕ x, y dxdy + ∫ Ω I x, y − c 2 2 1 − H ε ϕ x, y dxdy + v ∫ Ω δ ε ϕ x, y ∇ ϕ x, y dxdy (13).

However, it is likely that it, indeed, utilizes AS, given that the rat Sert gene has two alternative promoters and its transcripts are alternatively spliced in a tissue-specific manner [66].

The presence of roots within microsites showed that nutrients of these spots were indeed utilized by plants.

However if, as the evidence suggests, some bacterial pathogens do indeed utilize unique means of targeting such a critical host enzyme, the findings would have wide reaching repercussions outside bacterial infection (Kim et al., 2007; Srikanth et al., 2010).