Sentence examples for the sphere defined from inspiring English sources

Moreover, let J ∗ SPH p ( n − 1 ) = J SPH p ( n − 1 ) ( 1, ϕ ) be the restriction of the Jacobian of SPH p ( n − 1 ) to the sphere defined by r=1.

The normalization factor Z in line 5 is defined as so that c → gets assigned to the 'center of mass' of points falling within the sphere defined by the kernel function.

Using an auxiliary function, that is the solution of a wave equation on the sphere defining the outer boundary of the numerical grid, the absorbing boundary condition is simply written as a perturbation of the usual Sommerfeld radiation boundary condition.

Due to symmetry, the centre of the sphere defining the boundary of the bubble is located along the axis of symmetry (i.e. r = 0) displaced below the origin a distance Z 0. The contact angle can be found done using the bubble height at the origin, h 0, and the height at any other location on the sphere, h(r).

The intersection of a projection direction with the sphere defines a point on its surface that denotes the projection orientation.

The political space must be protected from the private sphere, defined as the domain of necessity and inequality, where the material reproduction of the polis is secured.

The centre of projection of the perspective camera model is analogous to the effective pupil of the camera, therefore a virtual caustic is applied onto the virtual sphere defined in Section 3. Assuming that the spherical mirror's centre coincides with the optical axis, the caustic surface is rotationally symmetrical about the optical axis and is therefore reduced to a curve in ρ-z plane.

Thus, in terms of the variables (beta_{1},ldots, beta_{m}), our problem is to minimize ({J_{m}}(beta_{1},ldots{2},beta_{m}ta_{m})) on the surface (sigma_{m}) of the m dimensional sphere defined in (5.8).

Let S n denote the n-dimensional sphere defined by S n = { x = ( x 1, …, x n + 1 ) ∈ R n + 1 : ( x | x ) = 1 }, with metric d S n ( x, y ) = arccos ( x | y ), x, y ∈ S n.

The intersection of the plane of the Earth's Equator with the celestial sphere defines the celestial equator.

If the incident illumination field on the scatterer is in direction k⃗0 and the scattered field is measured in direction of k⃗, the first-order Born approximation states that the 3D CTF is given by the cap of an Ewald sphere defined for (11) K →   =   k →   −   k → 0, as schematically shown in Fig. 1(b) for DHM [ 21].