Abel's Equation and Regular Growth: Variations on a Theme by Abel

Abel's Equation and Regular Growth: Variations on a Theme by Abel

Variations on a Theme by James Stirling

Variations on a theme.

A ring satisfying x = x is necessarily commutative. We consider a variety of weaker forms of this condition and show that many but not all of them imply commutativity. We also present a variety of elementary proofs of the fact that x = x implies commutativity.

Three Variations on a Theme by Collatz

The Collatz problem is reformulated in three ways as a non-arithmetic problem in first-order logic.

Variations on a theme by Huffman

Abstruct-In honor of the twenty-fifth amdversary of Huffman coding, four new results about Huffman codes are presented. 'Ibe ffrst result shows that a binary prefix condition code is a Huffmau code iff the intermediate and terminal nodes id the code tree can be listed by nonin-creasing probabiuty so that each node in the fist is adjacent to its sibling. The second result upper bounds the redund...