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Using the notion of asymptotically invariant sequences of means on l ∞, we obtain a mean convergence theorem for pointwise convergent sequences of hybrid mappings in Hilbert spaces.
Ritual is, for Rappaport (1999, p. 26) 'the performance of more or less invariant sequences of formal acts and utterances not entirely encoded by the performers'.
Then we identified invariant sequences longer than 10 codons and P < 0.01 as SCCSs.
Then the length and numbers of invariant sequences in the permuted alignment are counted.
Therefore, the rareness of invariant sequences differs depending on the conservation background in each alignment.
We used the length and averaged frequency of invariant sequences obtained from the permutation results as random expectation, and evaluated the probability of invariant sequences in the original alignment based on the expectation.
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All tRNA molecules carry the invariant sequence CCA at their 3′-terminus for amino acid attachment.
However, an interesting difference between the two time scale invariant transitions is an opposite order of the high and low-flux phase in the time-scale invariant sequence.
An augmented TDNN (ATDNN) which builds frequency and scale induction functionals into TDNN is then developed and proved to be a frequency and scale invariant sequence classifier.
Let { μ n } be an asymptotically left invariant sequence of means on X.
Let { μ n } be an asymptotically invariant sequence of means on l ∞.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com