Banjo Drum Physics - theoretical preliminaries

The interaction of a drum's head with its enclosed air is presented in the simplest possible form appropriate to the questions and issues that arise in understanding the timbre of the banjo. The inherent air-head impedance mismatch allows treating the head as driver of the air and the air's effect, in turn, as back reaction. Any particular question can then be addressed with a calculation in simple wave mechanics. The analysis confirms and quantifies the notion that internal air resonances enhance the response of the head at its and their frequencies. However, the details of just how are fairly complicated.Comment: 31 pages, 13 numbered figures + 2 on page

On algorithmic equivalence of instruction sequences for computing bit string functions

Every partial function from bit strings of a given length to bit strings of a possibly different given length can be computed by a finite instruction sequence that contains only instructions to set and get the content of Boolean registers, forward jump instructions, and a termination instruction. We look for an equivalence relation on instruction sequences of this kind that captures to a reasonable degree the intuitive notion that two instruction sequences express the same algorithm.Comment: 27 pages, the preliminaries have textual overlaps with the preliminaries in arXiv:1308.0219 [cs.PL], arXiv:1312.1529 [cs.PL], and arXiv:1312.1812 [cs.PL]; 27 pages, three paragraphs about Milner's algorithmic equivalence hypothesis added to concluding remarks; 26 pages, several minor improvements of the presentation mad

A Hoare-like logic of asserted single-pass instruction sequences

We present a formal system for proving the partial correctness of a single-pass instruction sequence as considered in program algebra by decomposition into proofs of the partial correctness of segments of the single-pass instruction sequence concerned. The system is similar to Hoare logics, but takes into account that, by the presence of jump instructions, segments of single-pass instruction sequences may have multiple entry points and multiple exit points. It is intended to support a sound general understanding of the issues with Hoare-like logics for low-level programming languages.Comment: 22 pages, the preliminaries have textual overlaps with the preliminaries in arXiv:1402.4950 [cs.LO] and earlier papers; introduction and conclusions rewritten, explanatory remarks added; introduction partly rewritten; 24 pages, clarifying examples adde

Preliminaries

Abstract not applicable