Since the square root is a strictly concave function, it follows from Jensen's inequality that the square root of the sample variance is an underestimate.
2.
Let U ( x ) be an increasing, strictly concave function, called the utility, which measures how much benefit a user obtains by transmitting at rate x.
3.
Near a local maximum in the interior of the domain of a function, the function must be concave; as a partial converse, if the derivative of a strictly concave function is zero at some point, then that point is a local maximum.
4.
Since the log function is a strictly concave function, if there is more than one equilibrium allocation then the utility derived by each buyer in both allocations must be the same ( a decrease in the utility of a buyer cannot be compensated by an increase in the utility of another buyer ).
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