Geometry of multidimensional universes

Maximal Fermi charts and geometry of inflationary universes

A proof is given that the maximal Fermi coordinate chart for any comoving observer in a broad class of Robertson-Walker spacetimes consists of all events within the cosmological event horizon, if there is one, or is otherwise global. Exact formulas for the metric coefficients in Fermi coordinates are derived. Sharp universal upper bounds for the proper radii of leaves of the foliation by Fermi ...

Complex geometry and vacua: Counting universes in string theory

Newtonian Normal Shift in Multidimensional Riemannian Geometry

Explicit description for arbitrary Newtonian dynamical system admitting the normal shift in Riemannian manifold of the dimension n > 3 is found. On the base of this result the kinematics of normal shift of hypersurfaces along trajectories of such system is studied.

Smooth Infinitesimal Analysis Based Model of Multidimensional Geometry

In this work a new approach to multidimensional geometry based on smooth infinitesimal analysis (SIA) is proposed. An embedded surface in this multidimensional geometry will look different for the external and internal observers: from the outside it will look like a composition of infinitesimal segments, while from the inside like a set of points equipped by a metric. The geometry is elastic. E...

Consumption universes based supermarket layout through association rule mining and multidimensional scaling

The success of retail business is influenced by its fast response and its ability in understanding consumers’ behaviors. Analysis of transaction data is the key for taking advantage of these new opportunities, which enables supermarkets to understand and predict customer behavior, has become a crucial technique for effective decision-making and strategy formation. We propose a methodological fr...