Models of optimum multidimensional signals in the solid systems
Keywords:vector IRB-space, rotating symmetry, basis vector, development of torus surface, optimum vector code, vector data, dimensionality, multidimensional control system, vector information technology
AbstractModels of optimum multidimensional discrete signals using novel design based on the “perfect” vector combinatorial configurations, namely the concept of Ideal Ring Bundles (IRB)s for development of new directions in fundamental and applied research in vector information technologies presented. IRB means an n-stage cyclic sequence of semi-measured terms, e.g. integers for which the set of all circular sums enumerates row of natural numbers by fixed times. Development of vector multidimensional models and techniques, based on the remarkable geometric properties of rotational symmetry-asymmetry relationships allows configure optimum multidimensional control systems for reproduce the maximum number of combinatorial varieties in the systems with a limited number of basis vectors. The modular vector sums of connected basis vectors of an IRB-space enumerate the set of t-coordinates specified with respect to t-dimensional cyclic frame reference exactly R-times. The remarkable technical merits of IRB–space, which properties hold for the same set of the IRB-monolithic vector code in varieties permutations of its terms is demonstrated, and method for design of two- or multidimensional vector signals coded based on the optimum binary monolithic code is presented. Proposed vector models of optimum multidimensional discrete signals provide, essentially, a new approach to generalize them to great class of optimized problems in radio-telecommunications, navigation and vector information technology. Moreover, the optimization embedded in the underlying combinatorial models. The favourable qualities of the Optimum Multidimensional Ring code provides breakthrough opportunities to apply them to numerous branches of science and advanced technology, with direct applications to vector data telecommunications, vector encoded design, and optimal vector information technology.
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