Scale relativity in Cantorian E(∞) space-time

The present note highlights some mathematical and formal connections between the theory of scale relativity and the Cantorian space-time approach to particle physics.     

Cantorian E(∞) space-time,de Broglie and the pair-breaking time of high-temperature superconductors

We show that the de Broglie time for Cooper pairs admits discontinuities for Cantorian sequences 1/3,1/5,1/7,…, and the pair-breaking time depends only on the phase of the pair wave function.     

On ARX(∞) approximation

Given data, u_j,y_j,j=1,…,n, with u_j an input sequence to a system while output is y_j, an approximation to the structure of the system generating y_j is to be obtained by regressing y_j on u_j−i,y_j−ii=1,…,p_n, where p_n increases with n. In this paper the rate of convergence of the coefficient matrices to their asymptotic values is discussed. The context is kept general so that, in particular, u_j is allowed to depend on y_i, i≤j, and no assumption of stationarity for the y_j or u_j sequences is made.     

On the 26-Dimensional Leech Lattice and E(∞) Nuclear Space

The aim of the present communication is to draw attention to a connection noticed recently between the KAM theorem, the signature of four manifolds and the dimensions of a nuclear spacetime, E ^(∞), relevant to quantum physics.     

A note on the differential forms of ε(∞) space

This short note intends to show how to carry over some of the most elementary concepts of differential geometry to fractal-like ε^(∞) spaces.     

On immersions ofn-dimensional Lobachevskií space in 2n-dimensional Euclidean space withn principal direction fields

In this article we prove that the principal direction fields are holonomic and use them to introduce curvilinear coordinates on an immersed region in terms of which the linear element of Lobachevskií space is written in the form where The fundamental system of equations is established for an immersion ofn-dimensional Lobachevskií space into 2n-dimensional Euclidean space withn principal direction fields for the functions _i and, and a way of constructing an arbitrary local analytic immersion is shown.Translated from Ukrainskií Geometricheskií Sbornik, No. 28, pp. 3–8, 1985.