Sentence examples for Upon differentiating from inspiring English sources

Upon differentiating Eq. (62) with respect to z one can obtain the temperature gradient within the film as, begin{aligned} T_z=frac{R^2}{2} M_z+N_z.

Upon differentiating contour interpolation from a higher-order contour representational ability ("contour abstraction") and upon accommodating seemingly inconsistent experimental results, it is argued that interpolation is modular to the extent that the initiating conditions for interpolation are strong.

Upon differentiating with respect to time we obtain begin{array}{l}{C}_{ijkl}^{(1)}{overset{varepsilon}}_{kl}+{C}_{ijkl}^{(2)}left({overset{varepsilon}}_{kl}N+{varepsilon}_{kl}overset{N}right -{C}_{ijkl}^{(2)}{varepsiloN}right -{C}_{ijkl ={overset{C}}_{ijkl}{varepsilon}_{kl}+{C}_{ijkl}{overset{varepsilon}}_{kl}-{varepsilon}_{kl}{overset{C}}_{ijkl}end{array} (28).

Thus, upon differentiating both sides of Eq. (2.5), if we make use of Eqs.

Converse to the GRA, ROP, and MIC families, many members of the parasite surface antigen gene family (SRS) were upregulated (44.8%) upon differentiating into the first of the enteric stages as a merozoite.

Mcl-1L is a very short-lived protein (t1/2=2 4 h), belonging to a group of immediate response genes upregulated in immature cells upon exposure to differentiating agents and antiapoptotic cytokines.

In addition, macrophages differentiating upon stimulation with macrophage colony-stimulating factor express indoleamine 2,3-dioygenase and inhibit T cell proliferation in vitro by depleting the important amino acid tryptophan from co-cultures in response to T cell activation [ 86].

MRI atrophy, at least as a global measure, cannot be relied upon to differentiate a neurodegenerative versus vascular etiology.

The fate of stem cells in the SVZ remains unclear; some may migrate into the olfactory bulb (OB) via the rostral migratory stream (RMS) and differentiate, where upon they differentiate into local interneurons.

Scientists, clinicians and politicians often are called upon to differentiate between the effectiveness and the efficacy of a prevention or intervention.

Moreover, when intravenous contrast cannot be administered, for instance in patients with end-stage renal disease, and heterogeneity between T1 and T2 is very important, and one MRI sequence alone cannot be relied upon to differentiate between benign and malignant tumors.