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The Isoperimetric Inequality on Natural Subsets
(2017-05-24)
The isoperimetric problem is an exercise of classical geometry posing the following question. If a closed Jordan region on the plane has area A, what is the smallest perimeter that the gure can attain? This question was ...
Necessary Conditions on Electric Potential for the Formation of Spectral Touching Points
(2017-12-01)
In recent years special attention has been given to graphene as building material and as an energy storage medium. The main property that make graphene uniquely suited to both of these concerns is that it possesses mass-less ...
A Probabilistic Proof of the Vitali Covering Lemma
(2017-05-23)
The Vitali Covering Lemma states that, given a finite collection of balls in R^d, there exists a disjoint subcollection that fills at least 3^{−d} of the measure of the union of the original collection. We present classical ...