Exact(57)
If, then the value of for all u becomes expanded.
If, then the value of for all u becomes contracted.
where = min, that means the minimum value of for which.
where is the -curve corresponding to the maximum value of for a fixed (or, equivalently, to the maximum value of for a fixed ).
The objective here is to estimate the value of for the situation of neglected interference.
We then use bisection on to find the value of for which (34).
The value of for is obtained by interchanging and in (4.43).
The value of for a given is determined by the mapping function according to (2).
Similar(3)
The premises of William G. Tierney's argument about the value of for-profit colleges to the greater economy are sound, but his conclusion -- that for-profits are essential to economic growth -- is debatable.
What is not discussed in Professor Tierney's analysis or by many on either side of the public debate about the value of for-profit higher education is who most often pays for that expensive proposition.
"Education officials knowingly allowed that process to be tainted by the undisclosed role of short-sellers, seeking to use the regulatory arena to manipulate the financial markets and drive down the share value of for-profit education companies, all for their own personal gain," declares a letter CREW sent Wednesday to Education Secretary Arne Duncan.
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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