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Fractal Mechanics Is Not Quantum but Original—Geometric
Published in Anirban Bandyopadhyay, Nanobrain, 2020
Lie group, conformal group of the sphere: Geometric language of PPM computing: The conformal group is the group of transformations from a space to itself that preserve all angles within the space. It is the group of transformations that preserve the conformal geometry of the space. Harry Bateman and Ebenezer Cunningham showed in 1908 that the electromagnetic equations are not only Lorentz invariant, but also scale and conformal invariant (Bateman, 1909). Putting co-ordinates together with sphere’s radius was Lie’s first work in 1871, The conformal group includes the Lorentz group and the Poincaré group as subgroups, but only the Poincaré group represents symmetries of all laws of nature including mechanics, whereas the Lorentz group is only related to certain areas such as electrodynamics. Due to this universality, the conformal feature has been used in constructing the geometric language for PPM computing. All basic geometries used as letters for operational language are encompassed inside a circle or sphere and ratios of contact coordinates are used. The preservation of conformational geometry enables a precise encoding of sensory data as a stream of nerve impulses. List of simple Lie groups Classical An Bn Cn Dn; Exceptional G2 F4 E6 E7 E8. This book does not endorse any unified theory starting from a single geometry because PPM metric described in Chapter 3 demands for several evolving vortexes each carrying a distinct PPM, and depending on its prime number origin, the evolution of symmetries change, redefine. Also, for a conscious machine, E8 does not suffice, we need a dodecanion with 11 imaginary and one real world, whose manifold geometries with 12 planes overlap to create a physical form of conscious thought.
Modified nonlocal boundary value problem method for an ill-posed problem for the biharmonic equation
Published in Inverse Problems in Science and Engineering, 2019
The theory for elliptic equations of order greater than two is much less well developed [2]. Such equations are common in physics and in engineering design, they naturally appear in many areas of mathematics too, including conformal geometry [3], identification of the population density [4] and non-linear elasticity [5,6]. The prototypical example of a higher order elliptic operator, well known from the theory of elasticity, is the bilaplacian a more general example is the polyharmonic operator The biharmonic equation arises in many engineering applications such as the deformation of thin plates, the motion of fluids, free boundary problems and non-linear elasticity see [7,8] and for historical details we refer to [9–13]. For a more elaborate history of the biharmonic problem and the relation with elasticity from an engineering point of view one may consult a survey of Meleshko [14].