Sentence examples for symmetric coordinates from inspiring English sources

The main ingredient is the passage from the Cartesian coordinates to the radially symmetric coordinates.

Specifically, skull shape was quantified by all non-zero variance components of a Principal Component Analysis (PCA) on the covariance matrix of the symmetric coordinates.

Allometric effects were assessed by running independent regressions of the symmetric coordinates onto loge centroid size for different sets of individuals grouped according to the ecosystem in which they were collected (ecosystems definitions followed [ 45]; Additional file 5).

Since the results were consistent (i.e., neither the main effect of sex, nor the interaction term in the MANCOVA were significant [ 43], Wilks' λ = 0.08, F260/453.83 = 0.98, p = 0.15), we used the residuals of a regression of the symmetric coordinates onto loge-transformed sized, pooling all individuals together, as a size-corrected shape component.

Using axis-symmetric properties, many three dimensional problems can be solved efficiently using two dimensional axis-symmetric coordinates.

The numerical algorithm is based on a finite difference discretization and uniform grid in the axis-symmetric coordinates.

The code is in 2D axi-symmetric coordinates, allowing quasi 3D simulations during the initial stages of streamer formation.

In this paper, the immersed interface method (IIM) in axis-symmetric coordinates is developed for elliptic interface problems that have a discontinuous coefficient, solution or flux.

Other challenges include deriving the jump relations in axis-symmetric coordinates, designing the numerical algorithm when the interface is close to the pole (r = 0); computing interface quantities such as the normal and tangential directions, surface derivatives, curvature information, etc.

The model is formulated in an axi-symmetric coordinate system and incorporates with various sub-models to describe the behavior of the composite cylinder under extreme thermo-mechanical loadings.

It should be stressed at this stage that if we assume the usual Schwarzschild spacetime characterized in symmetric spherical coordinates by the metric d s static 2 = - e 2 m r d t 2 + e 2 n r d r 2 + r 2 d θ 2 + sin 2 θd ϕ 2 Open image in new windowthen the metric is time-independent, and from Equation 14, it follows that γ is constant.