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Search results for: ARYTMETYKA NIEDIOFANTEJSKA

Search results for: ARYTMETYKA NIEDIOFANTEJSKA

  • Information Processing and Fechner’s Problem as a Choice of Arithmetic

    Publication

    - Year 2017

    Fechner’s law and its modern generalizations can be regarded as manifestations of alternative forms of arithmetic, coexisting at stimulus and sensation levels. The world of sensations may be thus described by a generalization of the standard mathematical calculus.

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  • Simple Fractal Calculus from Fractal Arithmetic

    Publication

    - REPORTS ON MATHEMATICAL PHYSICS - Year 2018

    Non-Newtonian calculus that starts with elementary non-Diophantine arithmetic operations of a Burgin type is applicable to all fractals whose cardinality is continuum. The resulting definitions of derivatives and integrals are simpler from what one finds in the more traditional literature of the subject, and they often work in the cases where the standard methods fail. As an illustration, we perform a Fourier transform of a real-valued...

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  • Imitating Quantum Probabilities: Beyond Bell’s Theorem and Tsirelson Bounds

    Publication

    Local hidden-variable model of singlet-state correlations discussed in M. Czachor, Acta Phys. Polon. A 139, 70, is shown to be a particular case of an infinite hierarchy of local hidden-variable models based on an infinite hierarchy of calculi. Violation of Bell-type inequalities can be interpreted as a `confusion of languages' problem, a result of mixing different but neighboring levels of the hierarchy. Mixing of non-neighboring...

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