Sentence examples for chosen coordinates from inspiring English sources

The position of a straight line (of infinite extent) in space may be specified by assigning four suitably chosen coordinates.

Assume also that γ 0 is tangent of finite order at x 0. Then there is a half neighborhood V of x 0 on ∂ M visible from y 0. The latter is not always true if γ 0 is tangent to ∂ M of infinite order at x 0. Choose local boundary normal coordinates near x 0 and y 0, and let g 0 be the Euclidean metric in each of them w.r.t. to the so chosen coordinates.

Note that we always assume a properly chosen coordinate system of (mathbb{C}); see (5).

The results of computing a shock reflection are found to strongly depend on the chosen coordinate system, Lagrangian or Eulerian.

It its original form, general covariance was understood "passively"; that is, as a freedom to describe structures in spacetime by means of arbitrarily chosen coordinate systems.

If the surface Σ is a channel, the correlation b 12 = 0 is valid for the chosen coordinate u and v.

In this case, a distribution of the magnetization along the axis OY has the Bloch form: sinθ = ch−1 y/Δ), where θ is the polar angle in the chosen coordinate system.

If (lambda_{1}<0), then steady state equations of (1) admit a solution (see [1]), psi= sqrt{-lambda_{1} / gamma_{2}}e^{i phi}, qquad u=0,quad phiin[0, 2pi). Equation (1) is invariant when we apply an orthogonal transformation, so (phi=0) in a properly chosen coordinate system of (mathbb{C}). Note that we always assume this coordinate system in this paper.

The geometry of the chosen coordinate system is illustrated in Figure 1, in which it is assumed that the airborne platform flies along positive y-direction at a speed of υ P. The platform is assumed to locate over the x y plane with a height of h.

A three-dimensional Gaussian mask was placed at the position of the chosen coordinate and residue scores summed with scores from other residues if they were close in three dimensions (within the expanse of the mask).

Ultra-small resin blocks (50 µm) were fine trimmed and serial sections (85 nm thickness) taken at areas corresponding to previously chosen coordinate positions, before post-staining in Reynold's lead citrate and uranyl acetate (5% in 50% ethanol) for 10 and 5 min, respectively.