Commutative Hypercomplex Numbers and the Geometry of Two Sets

The main task of the theory of phenomenologically symmetric geometries of two sets is the classification of such geometries. In this paper, by complexing with associative hypercomplex numbers, functions of a pair of points of new geometries are found by the functions of a pair of points of some well- known phenomenologically symmetric geometries of two sets (FS GDM). The equations of the groups of motions of these geometries are also found. The phenomenological symmetry of these geometries is established, that is, functional relationships are found between the functions of a pair of points for a certain finite number of arbitrary points. In particular, the s + 1-component functions of a pair of points of the same ranks are determined by single-component functions of a pair of points of the FS of GDM ranks (n,n) and (n + 1,n). Finite equations of motion group and equation expressing their phenomenological symmetry are found

Absolute Motion Determined from Michelson-Type Experiments in Optical Media

The symmetry of vacuum is characterized by the Lorentz group with the parameter c. Physical space inside the homogeneous optical medium should be described by the Lorentz group with the parameter c/n, where n is the refractive index of the medium. Violation of a one-parameter phenomenological symmetry in the discrete medium, such as gas, creates the opportunity for the experimental detecting of the motion of the optical medium relative to luminiferous aether.

FLAVOR-SPIN SYMMETRY AND THE TENSOR CHARGE

Exploiting an approximate phenomenological symmetry of the JPC = 1+- light axial vector mesons and using pole dominance, we calculate the flavor contributions to the nucleon tensor charge. The result depends on the decay constants of the axial vector mesons and their couplings to the nucleons.