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- W393854396 abstract "A scale-invariant model of statistical mechanics is applied to examine the physical foundation of nonstandard analysis and to identify the nature and the range (Oβ, Oβ-1) of nonstandard numbers and to establish the existence of infinitesimals (Oβ>L∞β-2>Xβ>Oβ-2). An invariant logarithmic definition of coordinate is presented and the concept of measureless or dimensionless numbers (L′∞β, λβ, Oβ)= (L∞β, 1β, Oβ) is described. Also, a scale-invariant definition of fractal dimension is introduced that suggest exceedingly large values 107 of fractal dimension. A scale invariant form of the wave equation is derived that applies to electromagnetic waves that propagate at the speed of light vt=c and gravitational waves that propagate at superluminal speeds vg≥2×1010c." @default.
- W393854396 created "2016-06-24" @default.
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- W393854396 date "2007-03-22" @default.
- W393854396 modified "2023-09-23" @default.
- W393854396 title "Implications of a scale invariant model of statistical mechanics to nonstandard analysis and the wave equation" @default.
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