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A periodic signal is one that exactly repeats itself on a regular basis.
The proof of these estimates almost exactly repeats the proof of estimates (36).
Instead of freezing like water into a regular, repeating, wire-frame pattern of identical clusters of atoms, quasicrystals have a not-quite-regular structure that never exactly repeats.
In other words, a TW is a solution for which the forcing signal f exactly repeats at every site, modulo an appropriate time shift: the phase at any given site s and time t mimics the phase at the previous site and time (t-alpha) (see Fig. 3, left panel).
Every leap, every stain on the table cloth, the trajectory of every slice of strawberry tart thrown from one end of the table to the other, exactly repeats what happened the time before and anticipates what will happen next time.
The idea of the 12 late lessons is to make the most of past experience to help anticipate future surprises while recognizing that history never exactly repeats itself.
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Echoing Mark Twain, Kunstler sometimes says that history doesn't exactly repeat itself, but it rhymes.
She seems never to have exactly repeated a composition, even when she yielded to popular clamor for yet another go at "The Old Oaken Bucket" or some such chestnut motif.
Crucial facts in narrative, therefore, are incised in the memory by skillful repetition; instructions given in a speech are exactly repeated when the singer reports the complying action; answers follow the form of the questions that elicited them.
As phonographs spread throughout the world, they had a surprising effect: folk tunes, which had always been malleable, changing with each performer and in each performance, were transformed by the advent of recording into fixed songs that could be endlessly and exactly repeated.
In a circa-1922 self-portrait painthat that is not in the show, de Chirico poses with a sculptural bust of himself a conceit amplified by the German Julius Bissier, in 1928, with a portrait of an artist whose features are exactly repeated in the clay head that he has made.
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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