Sentence examples for and therefore proceeding from inspiring English sources

then I and T have a common fixed point in B M ( p ), provided cl ( T ( D ) ) is compact and T is continuous on D. Proof Let x ∈ D. Then x ∈ B M ( p ), and therefore, proceeding as in the proof of Theorem 22, we have T x ∈ B M ( p ).

We noted that there was no significant increase in cell death in DMNQ-treated cells up to 6 h of exposure (data not shown) and therefore proceeded to score cell viability at later time points.

The first article of common ground I'd like to suggest to him is this: "We acknowledge that both atheistic and theistic beliefs can legitimately claim reasonable epistemic warrant and therefore proceed in debate on the basis of an attitude of mutual intellectual respect for each other's convictions".

She was reviewed by the obstetrician on call who discovered the history of hysteropexy and therefore proceeded to emergency caesarean section.

A subset of 36 cases (60%) presented with visual acuity of ≤hand movements (HM) (logMAR > 2.3), including 10 (16.7%) with HM (logMAR 2.3), and 26 (43.3%) who had VA of < HM (logMAR > 2.3) and therefore proceeded to vitrectomy.

We noted that pool 4 frequently induced responses and therefore proceeded to define the reactive constituent peptides (Figure 2A and D).

Of these 14 had a positive response to the ECT and therefore proceeded to the treatment part of the study.

One of the 66 patients had disease progression in the pelvic cavity during the neoadjuvant treatment and therefore proceeded to palliative surgery.

Fourteen patients had a positive ECT and therefore proceeded to optimized treatment, their baseline characteristics and lung function are shown in detail in Table  1 where the results are stratified according to the MCT outcome.

In the present case, we observed a good response to 3 days of intravenous methylprednisolone (80 mg/day) with subsequent oral methylprednisolone (36 mg/day), and therefore proceeded to taper the methylprednisolone dosage to a long-term maintenance dose (8 mg/day).

The progression, therefore, proceeding upward from atoms and energy, is toward fewer units, larger and more complex in pattern, at each successive level.