On unified theory for continuities

On Unified Theory for Continuities

Grand Unified Theory on Interval −

We investigate a construction of five-dimensional (5D) grand unified theories (GUTs) on an interval, which we call iGUTs. We analyze supersymmetric SO(10) iGUT as an example, where the gauge multiplet is spread over the 5D bulk. The SO(10) is directly reduced to the standard model gauge symmetry through the interval boundary conditions. Notice that this rank reduction is impossible in case of G...

On a Four Dimensional Unified Field Theory

The Gravitational, Electromagnetic, Weak & the Strong force are here brought together under a single roof via an extension of Reimann geometry to a new geometry (coined Reimann-Hilbert Space); that unlike Reimann geometry, preserves both the length and the angle of a vector under parallel transport. The affine connection of this new geometry – the Reimann-Hilbert Space, is a tensor and this lea...

On the buckling analysis of functionally graded sandwich beams using a unified beam theory

In this paper, a unified beam theory is developed and applied to study the buckling response of two types of functionally graded sandwich beams. In the first type (Type A), the sandwich beam has a hardcore whereas in the second type (Type B), the sandwich beam has a softcore. In both the type of beams, face sheets are made up of functionally graded material. The material properties of face shee...

Four Continuities on the Real Line

The two most commonly used topologies on R are the ordinary topology and the density topology. The ordinary topology is, of course, more widely known, and has the open intervals as its basic sets. The density topology, on the other hand, appears naturally in deeper studies of the structure of measurable sets. Its open sets are all measurable sets S ⊂ R which have the property that if x ∈ S, the...