Zig-zag-matrix algebras and solvable quasi-Hermitian quantum models

The zig-zag product

The expander constructions based on algebraic methods can give expanders that are both explicit (i.e. we can quickly construct the graph, or even obtain neighborhood information without constructing the entire graph, and Ramanujan, meaning that the spectral gap is essentially as large as possible. It also follows from this spectral bound that the edge expansion of Ramanujan graphs is essentiall...

On quasi-exactly solvable matrix models

An efficient procedure for constructing quasi-exactly solvable matrix models is suggested. It is based on the fact that the representation spaces of representations of the algebra sl(2,R) within the class of first-order matrix differential operators contain finite dimensional invariant subspaces. The Lie-algebraic approach to constructing quasi-exactly solvable one-dimensional stationary Schröd...

Zig-zag Path to Understanding

OUT understanding of the fundamental physical limits of information handling has developed along a very convoluted path. Most of the initially plausible physical conjectures have turned out to be wrong. A participant’s personal view of these events is not a disciplined contribution to the history of science. I do, however, last my own mistakes along with those of others.

Reverse mathematics and Isbell's zig-zag theorem

ZIG-ZAG PVD – A Nontraditional Approach

Communication has to be secure in order to be kept private. The latest developments in the field of digital communication have made secret communication possible. Image hiding is a method in which a secret image is hidden in a cover image thereby forming a hybrid or stego image. In this paper, data hiding is performed by taking difference value of three and two neighbouring pixels by adapting Z...