Specifically, if G is a compact Lie group acting on Hausdorff space M with orbit space [M.sup.*], then Fix(H, M) will denote the fixed point set of the (closed) subgroup H [subset] G, the image of this set in the orbit space will be denoted by ImFix(H, [M.sup.*]), and IsType(H, [M.sup.*]) will denote the set of all orbits whose isotropy
subgroups lie in the conjugacy class of H (the terminology is meant to suggest the phrase isotropy
The familiar Lorentz transformations are finally recovered in Section 5 essentially by further appeal to spatial isotropy
, and without the assumption of reciprocity.
In terms of isotropy
(Figure 10(b)), it is worthy to note that the main texture directions are the same as those described for the shot blasting (Figure 4(b)).
We may reckon that FAIR-CBM energy range may not provide us with a proper platform to study the energy dependence of anisotropy, but it may be suitable for studying the issues related to the isotropy
(c) In the remaining cases [sup.1[[A.sub.n] or [sup.1][E.sub.6], there are infinite global fields k and almost simple k-groups G of the corresponding type, for which the local global principle for isotropy
does not hold.
We ask whether the plasma has similar isotropy
, but for ultra-weak magnetic field at specific condition.
19, the X-ray diffraction patterns taken in all the three directions exhibit isotropy
in (001) planes indicating random orientation of the clay particles.
k is the bending rigidity, H is the mean curvature, [K.sub.A] is the nematic elastic constant (elastic isotropy
approximation), [n.sup.y] represent the components of the director field and g is the metric tensor.
These conditions of homogeneity and isotropy
are the primary testable consequences of the cosmological principle, which states that the properties of the universe, viewed on a sufficiently large scale, are the same for all observers.
The experiments reported here address this preconception by investigating the turbulence properties including the evolution of r.m.s fluid velocity, integral length scales, isotropy
, and frequency spectrum; in particular the impermeable surface induced inhomogeneity for flow [Re.sub.l] < 150.
By studying shear-free models, we avail ourselves with a rather simpler avenue where we only need to provide solutions to the generalised condition of pressure isotropy
containing two metric functions.
Because hollow glass beads (HGB) possess the characters of low density, isotropy
and so on, they were broadly used to fabricate syntactic foams [19-23].