Two site-specific recombinases are primarily involved in determining whether the bacteria are Phase-OFF or Phase-ON by influencing the position of a fimS invertible element
that contains the promoter for the structural gene, fimA.
Now since f is bounded below and bounded above on [OMEGA] it is an invertible element
o [H.sup.[infinity]]([OMEGA]) and so the operator [M.sub.[psi]] is invertible on H because M(H) = [H.sup.[infinity]]([OMEGA]).
Site I is present downstream of FimE gene while site II is present within invertible element
. IHF can introduce DNA bending and before recombination event is responsible for aligning inverted repeats present at the terminal sites of fim element.
This family consists of powers of the S-fixed central invertible element
If 2e is invertible element
in R with the inverse ([2e).sup.-1], then a finite n-symmetric set A [subset or equal to] R is of the above form or of the form
They also proved that if f is harmonious labeling of a graph G of size q, then so is af + b labeling, where a is an invertible element
of [Z.sub.q] and b is any element of [Z.sub.q].
If [E.sub.N](p) is not an invertible element
, then we assume that there exist positive scalars [[lambda].sub.i], with [SIGMA] [[lambda].sub.i] = 1, and unitaries [u.sub.i] [member of] M identified with [u.sub.i] [cross product] 1 such that
Then I contains an invertible element
of R, and so I = R = [M.sub.t](E) and c[[r.sub.1], [r.sub.2]].sup.m] [member of] Z(R), for all [r.sub.1], [r.sub.2] [member of] R.
To determine the orientation of the fimS invertible element
, previously described PCR techniques were used and products visualized with FOTO/Analyst PC Image Software [41, 45].
More generally, if B is a unital complex Banach algebra, A is a closed semisimple commutative subalgebra of B containing the unit of B and [x.sub.0] is an invertible element
of B with [parallel][x.sub.0][parallel] = [parallel][x.sup.-1.sub.0] [parallel] = 1 (for example unitary elements in C*-algebras satisfy these conditions), then for the complex normed space X = A[x.sub.0], the element [x.sub.0] [member of] X has the mentioned property.
Every graded connected bialgebra B is in fact a Hopf algebra --this means, by definition, that the identity map id : B [right arrow] B is an invertible element
in the convolution algebra L(B, B).
Where [PHI] : A([G.sub.1]) [right arrow] A([G.sub.2]) is a homomorphism and [tau] is an invertible element
in the Fourier-Stieltjes algebra of [G.sub.2].