Let X(U) be a Lorentzian surface in anti-de Sitter space, the lightcone Gauss indicatrix
is constant if and only if there exists a unique lightlike hyperplane HP(n, -1) in [R.sup.n + 1.sub.2], such that the M = X(U) is a part of [H.sup.n.sub.1] [intersection] HP(n, -1), where n = [L.sup.[+ or -]] (u).
The recorded species of Foraminifera are as follows: Alveolina indicatrix
Tissot's ellipse of distortion (indicatrix
) and [??] function
Moreover, we give some new characterizations of the Mannheim partner curves by considering the spherical indicatrix
of some Frenet vectors of the curves.
Scientists mostly from post-socialist countries describe their experiments or review the literature regarding such matters as paraxial light beams with angular momentum, quasi-ballistic light scattering on particulate media, a novel single-shot technique of micro-nano patterning in single-step through selective laser ablation, optical design techniques in developing current eye models, optical waves in a medium with a rotating optical indicatrix
, and a geometrical-optics analogue of an astigmatic elliptic Gaussian beam.
To better imagine optical relationships, the model of the indicatrix
has proven very useful.
(For all p [member of] P, [e.sub.p] denotes the indicatrix
row-vector of state p) and two matrices [R.sub.r] and [S.sub.r] and are defined for the block (i, j) with 0 [less than or equal to] i, j [less than or equal to] r - 1 by:
It is applicable for any Finsler space  for which in any point of the main space [x.sup.1], [x.sup.2] ..., [x.sup.n] the indicatrix
volume [([V.sub.ind]([x.sup.1], [x.sup.2], ..., [x.sub.n])).sub.ev] can be defined, provided the tangent space is Euclidean.
Kittler  further developed a sky luminance model for the clear sky by expressing the relative sky luminance as a product of two functions, namely, indicatrix
and gradation functions.
This curve is called the tangent spherical image or tangent indicatrix
of the curve [beta] in [E.sup.4.sub.1].
(2) The following statement about dispersion is given: "Dispersion follows in the format r [greater than] v or r [less than] v in accordance with whether the indices are greater for red or violet light, but the notation may also refer to dispersion of the optic axis or orientation of the indicatrix
." This is wrong; a statement such as "dispersion r [greater than] v, strong" refers only to the dispersion of the optic axes not the indices of refraction.
This enables one to explain that the nonlinear effects in the polarizability are linked with a "nonspherical optical indicatrix
surface on microstructures distribution of the crystalline phase" .