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Processing of the Residuals of Numbers in Real and Complex Numerical Domains

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Data-Centric Business and Applications

Part of the book series: Lecture Notes on Data Engineering and Communications Technologies ((LNDECT,volume 48))

Abstract

The chapter discusses the procedures for the formation and use of real residuals of real numbers on a real module, as well as complex and real residues of an integer complex number on a complex module. The chapter focuses on the processing of complex and real residuals of an integer complex number by a complex module. This procedure is based on using the results of the first fundamental Gauss theorem. The chapter of the proposed procedure provides examples of determining deductions in a complex numerical domain. On the basis of the considered procedure, an algorithm was developed for determining the real deduction of an integral complex number using a complex module in accordance with which the device was synthesized for its technical implementation. The device received a patent of Ukraine for the invention, which confirms the novelty and practical value of research results. The results obtained in the chapter are advisable to be used when implementing tasks and algorithms in real and complex numerical domains. In particular, the use of real numbers for cryptographic applications was considered.

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Author information

Authors and Affiliations

  1. V. N. Karazin Kharkiv National University, Svobody Sq., 4, Kharkiv, 61022, Ukraine

    Victor Krasnobayev, Alexandr Kuznetsov & Tetiana Kuznetsova

  2. Poltava National Technical Yuri Kondratyuk University, Poltava, Ukraine

    Alina Yanko

  3. Abai Kazakh National Pedagogical University, Dostyk Ave., 13, Almaty, 050010, Republic of Kazakhstan

    Bakhytzhan Akhmetov

Authors
  1. Victor Krasnobayev
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  2. Alexandr Kuznetsov
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  3. Alina Yanko
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  4. Bakhytzhan Akhmetov
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  5. Tetiana Kuznetsova
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Corresponding author

Correspondence to Alexandr Kuznetsov .

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Editors and Affiliations

  1. V.V. Popovskyy department of Infocommunication Engineering, Faculty of Infocommunication, Kharkiv National University of Radio Electronics, Kharkiv, Ukraine

    Tamara Radivilova

  2. V.V. Popovskyy department of Infocommunication Engineering, Faculty of Infocommunication, Kharkiv National University of Radio Electronics, Kharkiv, Ukraine

    Dmytro Ageyev

  3. Department of e-Business, Faculty of Business, Economics and Statistics, University of Vienna, Vienna, Austria

    Natalia Kryvinska

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Krasnobayev, V., Kuznetsov, A., Yanko, A., Akhmetov, B., Kuznetsova, T. (2021). Processing of the Residuals of Numbers in Real and Complex Numerical Domains. In: Radivilova, T., Ageyev, D., Kryvinska, N. (eds) Data-Centric Business and Applications. Lecture Notes on Data Engineering and Communications Technologies, vol 48. Springer, Cham. https://doi.org/10.1007/978-3-030-43070-2_24

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