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Notice that even in this case we have no defined frontiers as we transit from a 0 value (no consolidation) to a 1 value (one quadrant consolidation), or from 1 to 2, or 2 to 3, or 3 to 4. So, for example, in a small neighbourhood of the intermediate point 1.5 between 1 and 2 we would assign a greater than zero membership value to two functions.
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For a long time thereafter Kiev had little function except as a fortress and minor market on the vaguely defined frontier between Lithuania and the steppe Tatars, based in the Crimea.
The wars of Sumer also laid bare another imperative of monarchy the drive for empire, arising from the need to defend and define frontiers by extending them and the need to find new means to pay for troops and weapons, whether by the plunder of an enemy or by the conquest of new lands, or both.
Still firmly in place, however, are rigidly defined tax frontiers that mean that people living just a few yards from one another can pay vastly different levels of tax, particularly if they happen to be wealthy.
At the same time, Great Britain ceded the Los Islands (off French Guinea) to France, defined the frontier of Nigeria in France's favour, and agreed to French control of the upper Gambia valley, while France renounced its exclusive right to certain fisheries off Newfoundland.
Applying the defined Mass Frontier parameter settings, it is expected that MS n data are reported, where n > 2. This relatively high number of fragments illustrates the complexity and diversity of the fragmentation mechanisms.
The important second section of the exhibition, "Still-life or Trompe l'Oeil?" illustrates, primarily through examples from these northern schools, how problematic it can be to define the frontiers between sheer virtuoso mimesis and an intention to dupe the viewer.
After a period of warfare with Henry of Flanders, Latin emperor of Constantinople, Theodore signed a treaty (c. 1214) defining the frontiers between the Greek empire of Nicaea and the Latin empire of Constantinople.
In China, media content is largely controlled and these Internet companies are defining new frontiers of politically acceptable content (entertainment, sports, blogs).
Even though a group of remarkable experts could agree on the variables to be considered as indispensable to characterize the degree of injury, it is almost impossible to fully agree on those crisp numbers that must define the frontiers as discussed before.
Our capability to operate on the frontier - in fact to define that frontier - shapes the game in ways that redound to our advantage in the future".
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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