Integer Subsets with High Volume and Low Perimeter

We consider a certain variation of the 'isoperimetric problem' adopted for subsets of nonnegative integers. More specifically, we explore the sequence P(n) as described in OEIS A186053. We provide the first exact formulas for P(n) including multiple recursive relations involving auxiliary functions as well as concise and satisfying representations and even quasi-explicit formulas. We also discuss some of the intricate fractal-like symmetry of the sequence as well as the development of algorithms for computing P(n). We conclude with open questions for further research. Note this is a more developed, but more concise version of a previous arXiv paper arXiv:1107.2954 by the name "Sets with High Volume and Low Perimeter".Comment: 14 pages, 2 figures. Note this is a more developed, but more concise version of a previous arXiv paper arXiv:1107.2954 by the name "Sets with High Volume and Low Perimeter

Non-Profit Hospitals, Tax Exemption, and Community Benefits

Research Associate Heather Devlin explores the recent literature on non-profit hospitals, tax exemption, and community benefit laws and their implications for Georgia. (January 2009

Speed enhancement of complementary MOS devices

Speed required for Sisyphus experiment on Pioneer probe was attained at supply voltage well within component limitations by combining supply voltage higher than nominal with low reactance interconnections. Speed was found to be far in excess of typical. parameters suggested by manufacturers of MOS devices