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Wyniki wyszukiwania dla: arihmetic

  • ACTA ARITHMETICA

    Czasopisma

    ISSN: 0065-1036 , eISSN: 1730-6264

  • Relativity of arithmetic as a fundamental symmetry of physics

    Arithmetic operations can be defined in various ways, even if one assumes commutativity and associativity of addition and multiplication, and distributivity of multiplication with respect to addition. In consequence, whenever one encounters ‘plus’ or ‘times’ one has certain freedom of interpreting this operation. This leads to some freedom in definitions of derivatives, integrals and, thus, practically all equations occurring in...

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  • Simple Fractal Calculus from Fractal Arithmetic

    Publikacja

    - REPORTS ON MATHEMATICAL PHYSICS - Rok 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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  • Information Processing and Fechner’s Problem as a Choice of Arithmetic

    Publikacja

    - Rok 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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  • If Gravity is Geometry, is Dark Energy just Arithmetic?

    Arithmetic operations (addition, subtraction, multiplication, division), as well as the calculus they imply, are non-unique. The examples of four-dimensional spaces, R^4 and (−L/2,L/2)^4, are considered where different types of arithmetic and calculus coexist simultaneously. In all the examples there exists a non-Diophantine arithmetic that makes the space globally Minkowskian, and thus the laws of physics are formulated in terms...

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