The phrase "assumed locally" is correct and usable in written English.
It can be used in contexts where a certain assumption is made within a specific local context or environment.
Example: "In this study, we assumed locally that the environmental conditions would remain constant throughout the experiment."
Alternatives: "presumed in the local context" or "taken for granted locally".
We attempt to explain the ρ-dependence of Rp based on a non-uniform electrode model which assumes locally variable polarization resistances in combination with the interfacial electrolyte resistance.
At the tables are expensive bottles of alcohol and I assume (locally) famous people.
Sorghum map positions for our Miscanthus markers were then inferred by linear interpolation using flanking markers from the sorghum map, assuming locally constant recombination rates.
We also assumed that, locally, σ has a low value of about 30 MPa due to the existence of high pore pressure at a depth near 30 km; we did this by setting the local value of κ to about 0.1 (Ariyoshi et al. 2007), as shown in Figure 2.
Each neuron i in population α is described by a state vector noted as X t i, N in R d and has an intrinsic dynamics governed by a drift function f α : R × R d ↦ R d and a diffusion matrix g α : R × R d ↦ R d × m assumed uniformly locally Lipschitz continuous with respect to the second variable.
Without any loss of the generality, we can assume that locally begin{aligned} g^{j1}=updelta _{j1}.
The MAPMRP preserves edges and hotspots more than the smoothing prior but also assumes a locally monotonic image [13].
This method assumes that locally (over a distance of approximately the diameter of the spheres) the PSF is homogeneous and that there is no notable difference between axial and transaxial resolution.
First of all we note that in view of the short time existence result in the Riemannian setting we can assume that locally (u_epsilon ) are smooth both in time and space.
