Sentence examples for indeed utilized from inspiring English sources

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).

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

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.

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

Step 4. lim n → ∞ ∥ S y n − y n ∥ = 0. Indeed, utilizing the arguments similar to those of Step 4 in the proof of Theorem 3.1, we can obtain the desired conclusion.

Step 6. lim n → ∞ ∥ x n − x ¯ ∥ = 0. Indeed, utilizing the arguments similar to those of Step 6 in the proof of Theorem 3.1, we can obtain the desired conclusion.