6 papers
Product of three octonions
Mikhail Kharinov
This paper is devoted to octonions that are the eight-dimensional hypercomplex numbers characterized by multiplicative non-associativity. The decomposition of the product of three…
Large Scale (~25 m^2) metal diffraction grating of submicron period as possible optoelectronic detector for short scalar gravitational waves
Valery A. Zhukov
A method of detecting of short scalar gravitational waves with a wavelength of ~ 0.5 micrometers is proposed, in contrast to LIGO Project, aimed at detecting of long quadrupole gra…
Morse index of a cyclic polygon
Gaiane Panina, Alena Zhukova
It is known that cyclic configurations of a planar polygonal linkage are critical points of the signed area function. In the paper, we announce an explicit formula of the Morse ind…
Flattening single-vertex origami: the non-expansive case
Gaiane Panina, Ileana Streinu
A single-vertex origami is a piece of paper with straight-line rays called creases emanating from a fold vertex placed in its interior or on its boundary. The Single-Vertex Origami…
Geometric information in eight dimensions vs. quantum information
Victor I. Tarkhanov, Michael M. Nesterov
Complementary idempotent paravectors and their ordered compositions, are used to represent multivector basis elements of geometric Clifford algebra for 3D Euclidean space as the st…
A new look at the Burnside-Schur theorem
Sergei Evdokimov, Ilia Ponomarenko
The famous Burnside-Schur theorem states that every primitive finite permutation group containing a regular cyclic subgroup is either 2-transitive or isomorphic to a subgroup of a…