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17. Functions for the interval [690; 700] for 110 elements

      Graph 18. Functions for the interval [790; 800] for 110 elements

      Graph 19. Functions for the interval [890; 900] for 110 elements

      Schedule 20. Functions for the interval [990; 1000] for 110 elements

      As a result of the analysis, it was possible to clearly see the change in the patterns of graphs for a variety of intervals when testing the Collatz hypothesis, each of which has its own importance, finding its application in a variety of fields. And today we can hope to find in the future the possibility of solving this problem in the face of proof of this hypothesis, or its refutation.

      Used literature

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      2. Stuart Ian. The greatest mathematical problems. – M.: Alpina non-fiction, 2015. – 460 p. – ISBN 978-5-91671-318-3.

      3. Jeff Lagarias. The 3x+1 problem and its generalization // American Mathematical Monthly. – 1985. – Vol. 92 – P. 3—23.

      4. Alfutova, N. B. Algebra and number theory. Collection of problems for mathematical schools / N. B. Alfutova, A.V. Ustinova. – M.: ICNMO, 2018. – 336 p.

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      6. Arnold, V. I. the Theory of numbers by I. V. Arnold. – M.: Lenand, 2019. – 288 c.

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      9. Boss, V. Lectures on Mathematics vol.14: Theory of numbers / V. Boss. – M.: CD Librocom, 2010. – 216 p.

      10. Boss, V. Lectures on mathematics: Theory of numbers / V. Boss. – M.: Lenand, 2017. – 224 p.

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      12. Bukhstab, A. A. Number theory: A textbook / A. A. Bukhstab. – St. Petersburg: Lan, 2015. – 384 p.

      13. Weil, G. Algebraic theory of numbers / G. Weil. – M.: URSS, 2011. – 224 p.

      14. Gankel, G. The theory of complex numerical systems, mainly ordinary imaginary numbers and Hamilton quaternions together with their geometric interpretation. Trans. from German / G. Gankel. – M.: Lenand, 2015. – 264 p.

      15. Gankel, G. The theory of complex numerical systems, mainly ordinary imaginary numbers and Hamilton quaternions together with their geometric interpretation / G. Gankel. – M.: Lenand, 2015. – 264 p.

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      17. Zolotarev, E. I. Theory of integral complex numbers with an application to integral calculus / E. I. Zolotarev. – M.: Lenand, 2016. – 216 p.

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      ABOUT MODERN RESEARCH IN THE FIELD OF IMPROVING THE TECHNOLOGY OF ELECTRONIC TUNNELING

      Aliyev Ibratjon Xatamovich

      3rd year student of the Faculty of Mathematics and Computer Science of Fergana State University

      Ferghana State University, Ferghana, Uzbekistan

      Annotation. This article discusses the theoretical foundations and mathematical apparatus of a new method of transmitting information at high speeds, in contrast to the classical electromagnetic method, the method of using quantum entanglement and other similar recognized methods. The technological improvement of information transmission methods today really deserves attention, since they become a sufficient reason for a new revision of new achievements in this field. One of such technologies, currently developing mainly in a theoretical way, is the method of using the electronic tunnel effect. Now becoming more and more relevant.

      Keywords: quantum tunneling effect, electrons, information transfer, theoretical foundations, physical and mathematical apparatus.

      Аннотация. В настоящей статьи рассматриваются теоретические основы и математический аппарат нового метода передачи информации на больших скоростях, в отличие от классического электромагнитного метода, метода использования квантовой запутанности и прочих подобных признанных методом. Технологическое совершенствования методов передачи информации сегодня действительно заслуживает внимания, поскольку становятся достаточной причиной для нового пересмотра новых достижений в настоящей области. Одной из таких технологий, ныне развивающаяся в основном в теоретическом ключе является метод использования электронного туннельного эффекта. Ныне становящийся

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