Advances in Sciences and Humanities

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Volume 1, Issue 1, August 2015

  • Invariants of the Hilbert Transform for 23-Hilbert Problem

    Mazurkin Peter Matveevich

    Issue: Volume 1, Issue 1, August 2015
    Pages: 1-12
    Received: 20 July 2015
    Accepted: 31 July 2015
    Published: 1 August 2015
    DOI: 10.11648/j.ash.20150101.11
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    Abstract: Process of identification of steady laws in the form of asymmetric wavelet signals is stated. Thus the wave equations with variables amplitude and the period of fluctuation are designed from the generalized invariant and its fragments. This invariant according to Hilbert is reasonable as the biotechnical law generalizing almost all known laws of di... Show More
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  • Riemann’s Hypothesis and Critical Line of Prime Numbers

    Mazurkin Peter Matveevich

    Issue: Volume 1, Issue 1, August 2015
    Pages: 13-29
    Received: 20 July 2015
    Accepted: 31 July 2015
    Published: 1 August 2015
    DOI: 10.11648/j.ash.20150101.12
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    Abstract: The binary numeral system is applied to the proof of a hypothesis of Riemann to a number of prime numbers. On the ends of blocks of a step matrix of binary decomposition of prime numbers are located a reference point. Because of them there is a jump of a increment of a prime number. The critical line and formula for its description is shown, interp... Show More
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