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