A classical result of Conway and Pless is that a natural projection of the xed code of an automorphism of odd prime order of a self-dual binary linear code is self-dual [13]. In this paper we prove that the same holds for involutions under some (quite strong) conditions on the codes. In order to prove it, we introduce a new family of binary codes: the semi self-dual codes. A binary self-orthogo...

The quantum diffusion of a particle in an initially localized state on a cyclic lattice with N sites is studied. Diffusion and reconstruction time are calculated. Strong differences are found for even or odd number of sites and the limit N--> infinity is studied. The predictions of the model could be tested with microtechnology and nanotechnology devices.

It is an old problem in graph theory to test whether a graph contains a chordless cycle of length greater than three (hole) with a specific parity (even, odd). Studying the structure of graphs without odd holes has obvious implications for Berge’s strong perfect graph conjecture that states that a graph G is perfect if and only if neither G nor its complement contain an odd hole. Markossian, Ga...

The Text Encoding Initiative is using literate schema design, as instantiated in the completely redesigned ODD system, for production of the next edition of the TEI Guidelines. Key new aspects of the system include support of multiple schema languages; facilities for interoperability with other ontologies and vocabularies; and facilities for user customization and modularization (including a ne...

We use q-difference equations to compute a two-variable q-hypergeometric generating function for overpartitions where the difference between two successive parts may be odd only if the larger part is overlined. This generating function specializes in one case to a modular form, and in another to a mixed mock modular form. We also establish a two-variable generating function for the same overpar...

The power system monitoring problem asks for as few as possible measurement devices to be put in an electric power system. The problem has a graph theory model involving power dominating sets in graphs. The power domination number γP (G) of G is the minimum cardinality of a power dominating set. Dorfling and Henning [2] determined the power domination number of the Cartesian product of paths. I...

We discuss a strong relationship between Majorana fermions and odd-frequency Cooper pairs which appear at a disordered normal nano wire attached to a topologically nontrivial superconducting one. The zero-bias differential conductance in a normal / superconducting nano wire junctions is quantized at 2e/h irrespective of degree of disorder, length of disordered segment, and random realization of...