A [W.sub.J]- submolecule of M is a [W.sub.J]-molecule (i.e.
The proof will proceed by induction on n, so the preliminary results will start with an [A.sub.n] molecule whose [A.sub.n-1] submolecules are Kazhdan-Lusztig.
The first of these results states that if two such [A.sub.n-1] molecules are connected by a simple edge, then the connecting [A.sub.n-2] submolecules are isomorphic and there is a "cabling" of edges (possibly arcs) of weight 1 between these [A.sub.n-2] molecules:
Lemma 4.1 Let M be an [A.sub.n] molecule whose [A.sub.n-1] submolecules are Kazhdan-Lusztig.
The second preliminary result shows that if, out of three [A.sub.n-1] submolecules, two pairs (satisfying some conditions) are connected by simple edges, then the third pair is also connected by a simple edge:
The conditions will later be removed to show that any pair of [A.sub.n-1] submolecules of an [A.sub.n] molecule is connected by a simple edge.
Lemma 4.2 Let M be an [A.sub.n]-molecule whose [A.sub.n-1] submolecules are Kazhdan-Lusztig.
It remains to show that it satisfies the axiom (6), namely that any two [A.sub.n-1] submolecules are connected by a simple edge.
In our previous work (18, 30, 39, 41) we applied the lattice theory to blends of a thermotropic liquid crystalline polymer and flexible chain polymers such as PET, PEEK, PAr, and P0 and reported the polymerpolymer interaction parameter ([[chi].sub.12]) and equilibrium degree of disorder (y/[x.sub.1]) of the blend at melting processing tempe rature, where [x.sub.1] is the axis ratio of each of the m, the number of freely rotating joint in submolecule
[x.sub.1], rods comprising the molecules, and y denotes disorientation.