As in case (1), these

isomorphisms give (1.5) [mathematical expression not reproducible]

Moreover, the correspondence [mu] [right arrow] [F.sup.[mu]] given by (20) for [mu] [member of] M is an algebra isometric

isomorphism between M and [S.sub.[alpha],[beta];[phi]], so that [S.sub.[alpha],[beta];[phi]] is a Banach algebra.

[[mu].sub.0](f) and [[mu].sub.1](f) also induce

isomorphisms (see [8]):

A function f: [V.sub.1] [left arrow] [V.sub.2] is called

Isomorphism if

For a sup-algebra A we have the following

isomorphisms and order-embeddings of posets:

Scott (2001) deepens the understanding of

isomorphisms through the recovering of the philosophical and sociological bases of the institution construct.

This is why we think, as we mentioned above, that Sellars's explicit talk of

isomorphisms and projections as the basis of picturing is overshooting the mark when it comes to avoiding linguistic idealism.

Claude Bernard Lyon, France) and Rossi (Max Planck Institute for Mathematics, Bonn, Germany) offer a self-contained proof of the Duflo

isomorphism and its complex geometric analogues in the unified frameworks, and give in particularly a unifying explanation for why the series j(x) and its inverse appear.

(7.) Shea, Nicholas (2012), "Millikan's

Isomorphism Requirement," in Justine Kingsbury, Dan Ryder, and Kenneth Williford (eds.), Millikan and Her Critics.

In this section, we defined homomorphism and

isomorphism of SU-algebras, then we show some consequences of the relations between quotient SU-algebras and

isomorphisms.

This provides (up to

isomorphism) a unique ancestor for each connected cubic graph that has reducible triangles.

Their topics include quantum polynomials,

isomorphisms and derivations of algebras, semigroup properties of cooperations on finite sets, continuous co-algebra endomorphisms of some complete ultra-metric Hopf algebras, irreducible sub-algebras of matrix Weyl algebras, the length of conjugacy classes and P-nilpotence of finite groups, a symbolic calculus on defect revisions of axiomatic systems, and conformal field theory and modular functor.

The relation between the almost Lie structures of higher order and the vector bundles constructed in [18] are related by some

isomorphisms which depend on the almost Lie structures, in the case of order one and two; the general case is still a mystery for us.

3)and 4): first, we have the following

isomorphisms:

In my opinion, it is a decisive step, as it established the basic cross-level

isomorphisms that led to an integrated view of life's organization in the most general sense.