Sentence examples for coordinates as follows from inspiring English sources

As in [8], we define a log-convex function on the coordinates as follows: a function will be called coordinated log-convex on if the partial mappings, and,, are log-convex for all and.

We may write the solutions of (1.1) in polar coordinates as follows: x ( t ) = r ( t ) ( cos φ ( t ), sin φ ( t ) ). (2.1).

Thus, we introduce the new stretching coordinates as follows: xi = varepsilon (x - U_{0} t),quad tau = varepsilon^{3} t, (15).

Using the moment tensor for the isotropic source in Equation 7, we obtain the radial displacement due to the isotropic source in spherical coordinates as follows: u r = M 0 Iso 4 π ( λ + 2 μ ) r 2. (2.).

The basis of the paper relies on the local and cylindrical coordinates as follows [5, 6]: R = R 0 + r cos θ + δ sin θ Open image in new window (1).

When the local coordinate system is selected in this manner, we can move back and forth between global and local coordinates as follows: Figure 10 Local coordinates systems that move with the bee.

The injection coordinates were as follows (in mm): 2.85 posterior of bregma, 3.2 lateral of the midline, and 5.05 deep from the pia.

The injection coordinates were as follows (in mm): 2.85 posterior of bregma, 3.2 lateral of the midline, and 5.05 deep from the pia for VPM and 3.25 posterior, 2.1 lateral, and 5.2 deep for POm.

To identify the background deformation, we processed the daily coordinates (F3 solution) as follows.

Alice then incrementally sends the remaining aligned coordinates of T as follows.

The variance parameter of the th cluster and th coordinate is then estimated as follows [27]: (6).