Since its inception, ideas Ehlers introduced in the context of his frame theory have found important applications in the study of both the Newtonian limit of general relativity and of the Post-Newtonian expansion, where Newtonian gravity is complemented by terms of ever higher order in 1/c^2 in order to accommodate relativistic effects.
For example, the classic Tandem Affinity Purification or TAP tag is a small specific polypeptidic sequence that is introduced in-frame into the C-terminus of a desired protein (bait).
Parallel to discrete Hilbert space frames, the theory of atomic decompositions, p-frames and framings have been introduced in the literature to address this problem.
Considering the well-defined power functions, we can introduce fractional operators in the frame of the time scales theory (see [6, 15] and [12, 18]) following the continuous paradigm (see, e.g., [1, 2]).
These constructs also each contain an artificially introduced in-frame ATG codon at, or upstream or downstream of the GGC1274-1276 position.
Furthermore, a short DNA fragment encoding biotinylated domain (BSP) was introduced in frame at the 3' of the P65-β-Fos cassette for biotinylation of Mamu-DR molecules to assemble tetramer (Fig. 2a).
To facilitate the production of HA-tagged NHP PARs, a ClaI restriction site was introduced, in frame, upstream of the HA-tag sequence in the pcDNA3-huPAR2HA (pcDNA3/huPAR-2ClaHA) by PCR-based mutagenesis using complementary primers C11 C12, in association with primers C3 C13 (Table S1) as previously described [42].
egfp was introduced in frame upstream of the zebrafish smad2 coding sequence.
To preserve the codon frame, we corrected any frame-shifting indels introduced in the alignment step by normalizing the alignments relative to the human RefSeq transcript coding sequences.
An explicit iterative process to approximate fixed point of a nonexpansive mapping (T : C rightarrow C) was introduced in 1967 by Halpern [16] in the frame of Hilbert spaces: uin C, x_{0} in C, quad x_{n+1}= alpha_{n} u + 1-alpha_{n} Tx_{n}, quad n geq 0, (1.3) where ({alpha_{n}} subset[0,1]).
On the other hand, one explicit iterative process was first introduced, in 1967, by Halpern [13] in the frame of Hilbert spaces: u ∈ C, x 0 ∈ C, x n + 1 = α n u + ( 1 − α n ) T x n, n ≥ 0, (1.2).
