Englishfor English speakers
extremal
adjective
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(mathematics) Relating to extrema (maximal or minimal)
extremal
noun
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(mathematics) Any solution to a variety of equations in the calculus of variations
basis
Noun
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The basis of something, is the main ideas or parts that it is built on.
On the basis of the information available, we have decided to cancel the project.
There is no basis for believing that he was killed.
Her experiences in Cambodia formed the basis for her first book.
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If something happens on a regular/daily/weekly etc. basis, it happens regularly, daily, etc.
The problems are now happening on a very regular basis.
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If we are on a first-name basis, we use first names when speaking to each other.
Josie Parkinson and I are on a first-name basis. I call her "Josie" when I see her.