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A negative semi-cycle of a solution of (1.1) consists of a "string" of term, all less than, with and such that (1.4).
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A negative semicycle of the solution of (2.1) consists of a "string" of terms, all less than the equilibrium point, with and such that (4.2).
A positive semi-cycle of a solution of (1.1) consists of a "string" of terms, all greater than or equal to the equilibrium, with and such that (1.3).
A positive semicycle of the solution of (2.1) consists of a "string" of terms, all greater than or equal to the equilibrium point, with and such that (4.1).
A negative semicycle of a solution { x n } n = - 1 ∞ of Equation (1.1) consists of a string of terms {x r, x r+1,..., x m }, all less than the equilibrium x ̄, with r ≥ -1 and m ≤ ∞ such that e i t h e r r = - 1 o r r > - 1 a n d x r - 1 ≥ x ̄. and e i t h e r m = ∞ o r m < ∞ a n d x m + 1 ≥ x ̄.
A positive semicycle of a solution { x n } n = - 1 ∞ of Equation (1.1) consists of a string of terms {x r, x r+1,..., x m }, all greater than or equal to the equilibrium x ̄, with r ≥ -1 and m ≤ ∞ such that e i t h e r r = - 1 o r r > - 1 a n d x r - 1 < x ̄. and e i t h e r m = ∞ o r m < ∞ a n d x m + 1 < x ̄.
In fact, Googling a string of terms like "Obama--Pennsylvania--bitter--guns--religion--San Francisco" produces hundreds of articles from known media outlets and bloggers, all linking to one another in a circle, like an enormous tiger chasing its tail.
10 15 Based on the best-performing individual search terms, we developed various strings of search terms, termed search filters, which we used in combination with the Yale prognostic filter.
The review team sought to identify such a model by combining a sensitive string of search terms (e.g. model$ORR framework$ OR theoretical OR theory OR concept OR conceptual) with terms representing the health-related behaviour of interest.
He resigned two months later and was followed by a string of short-term leaders.
Most research worldwide is fuelled by a vast legion of enthusiastic, talented younger scientists – PhD students and postdocs who work on a string of short-term contracts.
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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