[en] The fractal dimension analysis of the Weyl-Dirac type object shows that the wave and the corpuscle are two-dimensional projections of a higher-dimensional string in a Cantorian fractal space-time (Cantorian fractal string)

[en] In the frame of hydrodynamic formulation of scale relativity theory for a coherent quantum fluid, one shows that some parameters of high-temperature superconductors (critical field, critical current, pair breaking time, fluxoid, state density, gap energy, etc.) come from the non-differentiability of the quantum space-time. Then, the vortex streets (responsible for superconductivity by means of the in-phase lattice oscillations mechanism) and the anyons (responsible for superconductivity by means of the composite fermions mechanism) may be considered as two-dimensional projections of a higher-dimensional fractal string, which implies the existence of just one mechanism inducing type II superconductivity

[en] We prove that the fractal space-time interpretation of Nelson's stochastic quantum mechanics may be put into a one-to-one correspondence to the hydrodynamic model of quantum mechanics. Some implications of this correspondence are analyzed: Navier-Stokes type equations, uncertainty relation and type II superconductivity by means of a higher-dimensional fractal string. The two-dimensional (2D) projections of the higher fractal string corresponds to the anyons and 1D projections to the Cooper pair. The Cantorian-fractal structures occur, either by assimilating the Cooper pair with a two coupled oscillators (a simple mechanical model for ε^(∞) theory), or by El Naschie's filling factor ν≡phi³=0.23606 (Cantorian-fractal quantum Hall effect)

[en] Using a lagrangian formalism of invariantive mechanics the deviation of the light in a gravitational field is studied; the result is in full agreement with the theory of General Relativity. (author)

[en] The influence of the electric quadrupole moment on a test charge is studied by using the elliptic functions in nonrelativistic approximation. (author)

[en] A generalisation of Ernst's principle for the stationary gravitational field based of the Matzner and Misner's principle for the construction of the Lagrangian is proposed

[en] In the weak-field approximation, some implications of duality in the Weyl-Dirac (WD) theory, using the Gregorash-Papini-Wood approach, are investigated. Any particle is in a permanent interaction with the 'subquantic level' (Madelung's fluid) and, as a result of this interaction, the particle acquires the proper fluctuation curvature and the proper fluctuation energy, respectively. By fixing the fluctuations scale, the quantum fluid orders either by means of bright cnoidal oscillation modes inducing causality, or by means of dark cnoidal oscillation modes inducing acausality, and non-linear effects, respectively. The periodic mode is associated with the undulatory characteristic, and the solitonic one with the corpuscular one. By not fixing the fluctuations scale and keeping the symmetry, the quantum fluid orders like a two-dimensional (2D) lattice of vortices, so that the duality needs coherence. In the compatibility between quantum hydrodynamics in the Madelung's representation and the wave mechanics, the self-gravitational field of the Weyl-Dirac type physical object is generated. El Naschie's space-time implies, by means of transfinite heterotic string theory, the masses of nucleons, and, by the gravitational fractional quantum Hall effect, the dispersion of the wave-packet on the particle. The analysis of the fractal dimension of the physical object described by the WD theory shows that the waves, and corpuscle, respectively are 2D projections of a higher dimensional special string in El Naschie's space-time (El Naschie's string)

[en] We study the influence of the anisotropy of electrical properties on the propagation of the plane waves in a plasma with high temperatures, when the radiative processes are taken into account. Two cases of particular interest are considered in more detail. These are the cases when the waves propagation vector is directed along the magnetic field or is orthogonal to it. (author)

[en] One builds the vacuum metrics of the stationary electromagnetic field through the complex potential model. There are thus emphasized both a variational principle, independent on the Ricci tensor, and some internal symmetries of the vacuum solutions. One shows that similar results may be obtained using the Barbiliant's group. By analytical continuation of a Barbilian transformation the link between the fixed points of the modular groups of the vacuum and the golden mean PHI=(1/(1+PHI))=(√5-1)/2 of ε^(∞) space-time is established. Finally, a Cantorian fractal axiomatic model of the space-time is presented. The model is explained using a set of coupled equations which may describe the self organizing processes at the solid-liquid, plasma-plasma, and superconductor-superconductor interfaces

[en] A frame is characterized by a hermitic operator with independent of direction eigenvalues. For a particular type of frames (El Naschie's frame), the hermitic operator eigenvalues may be put in correspondence with a Cantor set. This is the situation when the used coordinates, could be some values directly measurable for instance, via the mass spectrum of high energy particle physics. By using the Cayleyene metric associated to the hermitic operator and to Ernst's equations, the generalized hyperbolic stationary metrics is obtained. When imposing on the metrics the conform Minkowskian character, we obtain both the inertial nature of the Universe expansion and, by the gravitational coupling constant, the correspondence with ε^(∞) space-time. The quantum mechanics in the form of a Schroedinger type equation with complex eigenvalues appears in the process of frames synchronization