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Form the matrix E 1 E 2 − 1 and express it as the sum of a polynomial term − V 12 and strictly proper remainder.
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The estimated population of Timucua speakers was 13,000 in 1650, with 8,000 speaking Timucua proper and the remainder speaking various sister tongues.
Japan is divided into 47 prefectures, 43 of which are ken (prefectures proper); of the remainder, Tokyo is a to (metropolitan prefecture), Hokkaido is a dō (district), and Ōsaka and Kyōto are fu (urban prefectures).
It should be noted that although there are five physically separate stations in the examination proper, for the remainder of this paper the term 'station' will be used rather more conveniently to refer to each of the seven separate assessments made of a candidate, rather than to the five twenty-minute sessions within which those seven assessments are made.
This was a meta-analysis of 10 trials containing a mixture of published and unpublished data, two of which are reported in this update and the remainder inaccessible to proper scrutiny, so that we are now obliged to disregard them.
Proper feng shui dictates its placement in the remainder bin.
The purpose of wastewater treatment is generally to remove, from the wastewater, enough solids to permit the remainder to be discharged to receiving water without interfering with its best or proper usage.
Finally, the first morphologically distinct cell type of the fetal lineage is the epiblast, which constitutes the remainder of the late ICM and gives rise to amnion, extraembryonic mesoderm, and embryo proper [1].
For example, one may consider the idea that whenever something has a proper part, it has more than one i.e., that there is always some mereological difference (a "remainder") between a whole and its proper parts.
However, proper design and analysis of stability studies requires specific statistical expertise, and much of the material presented in the remainder of this chapter is technically quite complex and oriented to meet the needs and interests of professional statisticians.
According to this principle, every proper part must be "supplemented" by another, disjoint part, and it is this last qualification that captures the notion of a remainder.
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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