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Using the second boundary condition and the formula (2.18) for, we have (2.20).
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Similar results were obtained when defining the HMR boundaries using the second unmethylated CG (Additional file 2: Figures S3c, S4e-h), although this approach yielded a less periodic nucleosome signal outside of the HMR boundaries (Additional file 2: Figure S5c).
Branch reconstructions that span different seasons were performed by sampling the state (here the location) within the first season's boundaries using the initial migration matrix, and by continuing the stochastic mapping forward using the second matrix.
To verify these conditions, we characterize the stability boundaries using the first two vibration modes and compare them to damping contours obtained by long-time integration of the full nonlinear equations of motion.
However, when HMR boundaries are set using the first unmethylated CG, we find a striking pattern in both cell types with nucleosomes enriched at the boundaries with a periodic array of nucleosomes propagating into the methylated region.
It is shown that the accuracy for the approximate value of the first derivatives can be improved up to (O(h^{5}vert ln hvert )) for the same boundary functions by using the fifth-order formulae on some faces of the parallelepiped.
We use the first-order slip boundary conditions at the walls and consistent pressure boundary conditions at both ends of the long microchannel.
The same thing would happen at the second boundary.
That's only the second boundary from eight Botha overs.
Similarly, for the second boundary condition, (2.16).
(b) Boundary optimization : We use the second order differences of control points, i.e., b α − 2 b α + 1 + b α + 2. We choose this method in order to maintain cylinders/cones and to minimize the curvature along the boundary.
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