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  • ACTA ARITHMETICA

    Journals

    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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  • FPGA realization of fir filter in residue arithmetic

    Publication

    - Year 2009

    w pracy zaprezentowano realizację fpga przepływowego filtru fir o stałych współczynnikach w arytmetyce resztowej z użyciem 8 5-bitowych modułów o łącznym zakresie liczbowym 37.07 bita. zastosowano formębezpośrednią fir. mnożenia wykonywane są przy użyciu odczytu z pamięci. sumowania w każdym z kanałów są realizowane przy zastosowaniu wielopoziomowej struktury sumatora opartego o 4-operandowe sumatory csa. w stopniu końcowym wykonywane...

  • 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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  • 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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