M. S. El Naschie, “On Two New Fuzzy Kahler Manifolds, Klein Modular Space and ’t Hooft’s Holographic Principles,” Chaos, Solitons & Fractals, Vol. 29, No. 4, 2006, pp. 876-881. doi:10.1016/j.chaos.2005.12.027

has been cited by the following article:

• TITLE: A Fractal Menger Sponge Space-Time Proposal to Reconcile Measurements and Theoretical Predictions of Cosmic Dark Energy

  AUTHORS: Mohamed S. El Naschie

  KEYWORDS: Menger Sponge Space; Revising Relativity; Dark Energy; Energy of the Quantum Particle; Energy of the Quantum Wave; Kähler Manifold as Space-Time; Modified Lorentz Transformation

  JOURNAL NAME: International Journal of Modern Nonlinear Theory and Application, Vol.2 No.2, June 13, 2013

  ABSTRACT: The 95.5 percent of discrepancy between theoretical prediction based on Einstein’s theory of relativity and the accurate cosmological measurement of WMAP and various supernova analyses is resolved classically using Newtonian mechanics in conjunction with a fractal Menger sponge space proposal. The new energy equation is thus based on the familiar kinetic energy of Newtonian mechanics scaled classically by a ratio relating our familiar three dimensional space homology to that of a Menger sponge. The remarkable final result is an energy equation identical to that of Einstein’s E=mc2 but divided by 22 so that our new equation reads as . Consequently the energy Lorentz-like reduction factor of percent is in astonishing agreement with cosmological measurements which put the hypothetical dark energy including dark matter at percent of the total theoretical value. In other words our analysis confirms the cosmological data putting the total value of measured ordinary matter and ordinary energy of the entire universe at 4.5 percent. Thus ordinary positive energy which can be measured using conventional methods is the energy of the quantum particle modeled by the Zero set in five dimensions. Dark energy on the other hand is the absolute value of the negative energy of the quantum Schrodinger wave modeled by the empty set also in five dimensions.