The following proposition is our substitute for the use of Banach limits in convergence proofs of modified Halpern iterations.
A proof-of-concept modified ELISA using the selected ssDNA MRE had a reported sensitive target detection at 200 nM in human serum [ 154].
A proof-of-concept modified ELISA using ssDNA as the toxin capturing element was developed and able to detect toxin B at 50 nM concentration in human fecal matter [ 111].
Since the proof of this modified version differs from the one in [19] only slightly in technical details, we omit it here.
As a crucial result we have to inspect the proof of a modified inf sup condition, in particular, the dependence of the stability constant with respect to the Reynolds number (cf. appendix).
In the next section we recall some concepts and facts associated to Carnot Carathéodory spaces and give the proof of the modified A-harmonic approximation lemma for vector fields.
They have been used for proof-of-principle studies such as taking photographs with films made of modified bacteria, but not yet for serious applications.
Then either i ( B n, f, p ) = 0 or i ( B n, f, p ) = i ( S n − 1, ϕ, p ). Proof The following proof is a modified version of Theorem 5.1 in [1].
As a proof-of-concept, we use modified MPI libraries and unmodified MPI programs to evaluate the proposal.
In a proof-of-concept-experiment, we modified and validated conditions of mRNA preparation from whole blood samples for NGS applications.
We caution, however, that genetic proof of sfl as modifying the phenotype in this population will require additional studies.
