It should be emphasized that in the framework of this model, motion of the massive particles [P.sub.0], [P.sub.1], [P.sub.2] is given and is determined by the corresponding solutions of the three-body problem, namely, by the Lagrange triangular solutions or by the Euler collinear solutions (see [17]).

Different from Figure 2(b), when Figure 3(b) is expressed in polar coordinates, the collinear point ([x.sub.a], [y.sub.a]) and point ([[rho].sub.0], [[theta].sub.0]) mapped to the parameter space in the original image intersect at the point ([[rho].sub.0], [[theta].sub.0]) [21].

In such regions, covering several cells of the crystal lattice (10 / 15), the arrangement of the collinear magnetic moments is described in the spin density wave representation.

Obvious choices are not admissible, however: The noninteracting Kohn-Sham system of spin-density-functional theory is ruled out because, for collinear magnetic systems, the effective potential contains an explicit spin-dependent exchange-correlation field that forces the breaking of the spin symmetry [15], which arises spontaneously even without magnetic fields in the real physical system due to the Coulomb interaction.

In this paper, the SIF of two unequal collinear cracks is first derived using the Kachanov method, and then the formulation of determining the SIF of two winged interacting cracks is developed.

Suryanarayana, "Effect of [sup.87]Sr hyperfine structure on the isotope selective excitation of 89Sr and [sup.90]Sr isotopes in collinear resonance ionization spectroscopy," Journal of Physics B: Atomic, Molecular and Optical Physics, vol.

The middle of the box color matches the type: Collinear: with linear comparison; Translocation: translocation comparison; Inversion: inverted comparison; and Tran + Inver: translocation and inverted comparison.

Multilateration is infeasible when three references are collinear, and it is feasible when three references are not collinear [21].

For cultivation and weeding, Matt uses a standard garden rake, a variety of hoes (wheel, stirrup, collinear, and others), and a propane flame weeder.

For d = 2, it is a (2n - 4) dimensional manifold (where [P.sub.n-2](C) minus collinear and minus collisions is its double cover).

(1) These variables are used because other socioeconomic attributes (e.g., income) were found to be collinear to and therefore well explained by these two main factors across national groups.

Vectors are parallel (collinear) if their vector product is zero:

Then P, Q, R are collinear if and only if P + Q + R = O [member of] [(Z/3Z).sup.[direct sum]2].