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It is obviously that for any ((x, y)in X^{2}), the functions (max{x, y}), (min{x, y}) are the upper and lower bounded of (x, y), respectively.
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Some lower bounds of E χ2) are obtained.
Furthermore, upper and lower bounds of the performance measures can be computed.
The obtained criterion depends on upper and lower bounds of delays.
And the general upper and lower bounds of the optimal COP have been obtained.
Some comparisons between simple random sampling and the lower bounds of U-type designs are given.
Explicit expressions are derived in this paper, for lower bounds of achievable bandwidth.
The lower bounds of the penalty parameter and convergence time are also estimated.
We further show a lower bound of 32 for a wider class of D-benevolent instances.
However we suppose that the upper and lower bounds of the uncertainties are known.
Moreover, we derive upper and lower bounds of the new measure.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com