Local linearity now implies that the "other" endpoint of [J.sub.2] corresponds to an orbit with

isotropy subgroup (conjugate to) [A.sub.4] and is an interior point of [J.sub.3], the "other" endpoint of [J.sub.3] corresponds to an orbit with

isotropy subgroup (conjugate to) [D.sub.6] and is an interior point of [J.sub.2], and the "other" endpoint of [J.sub.5] corresponds to an orbit with

isotropy subgroup (conjugate to) [D.sub.10] and is an interior point of [J.sub.2].

(It is akin to the task of specifying what is meant by spatial

isotropy without being able to appeal to the notion of 3-tensors).

Isotropy remains relatively constant until [xi]/[l.sub.0] [approximately equal to] 1.2, before suppression or amplification of

isotropy at [xi]/[l.sub.0] [approximately equal to] 0.3.

Equations (4b)and (fc), together with the transformation u = [r.sup.2], give the pressure

isotropy condition

The underlying requirement of structural

isotropy can be expected violated however inside the ITZ, so the method should be applied to bulk cement only.

Linearity primarily varies with field strength and much less with frequency while

isotropy depends largely on symmetry.

Unfortunately most modeling software assumes

isotropy, which may result in over or underestimation of the heat removal.

Stretching of rubber causes orientation of rubber molecules, but as the orientation is in the direction of stretching, the assumption of

isotropy can be said to remain valid.

The

isotropy of the HiTcSP3 is a significant asset in thermal expansion matching, in eliminating thermal fatigue of the materials, and in quickly transferring the heat to other sources such as fans or external water-cooling systems.

A fundamental concern worth mentioning is that all the Friedmann models are based on the assumption that the universe has the same density at all places (homogeneity) and the same expansion rate in all directions (

isotropy).

We'll prove that if the generic

isotropy subgroup [H.sup.1.sub.0] of D is connected semi-simple, then I'([phi]) is absolutely convergent for every [phi][Epsilon] S(XA), and this convergence is invariant under castling transforms, which means that if two irreducible regular prehomogeneous vector spaces (G,X) and [Mathematical Expressions Omitted] are castling transforms of each other and [Mathematical Expressions Omitted] for (G,X) is absolutely convergent for every [phi][Epsilon] S([X.sub.A]), so is [Mathematical Expressions Omitted] for [Mathematical Expressions Omitted].

Yield strength and Lankford coefficient have been shown to have little correlation with specimen orientation; therefore planar

isotropy can be assumed for the chosen material.