Jamolitdin Abdullayev – All sciences. №8, 2023. International Scientific Journal (страница 2)
Graph 6. Functions for the interval [40; 50] for 110 elements
The picture described for the situation from 40 to 50 retains its specific role model for the subsequent graph for numbers from 50 to 60, which can be traced during its analysis, however, in this case, the role of the upper and lower maximum functions, of course, are already other values, which also carry a sharper increasing However, this, along with other things, can be traced during the analysis of the maximum and average initial peaks, after which there was a small drop, and after the maximum – a sharper one, as can be seen, with a large coincidence for the peaks on Graph 7.
Graph 7. Functions for the interval [50; 60] for 110 elements
Thus, in the future, graphs are presented for the intervals from 60 to 70, where, surprisingly, a sharp increase in correlation can be observed again, when part of the functions goes down as a separate line, and one single one acts as the only upper correlating one (Graph. 8). In the future, the graph begins to change again for the interval from 70 to 80 and the state described in the early interval for the interval from 40 to 50, it will be possible to observe an increase in the number of peaks at the beginning to two classes, and in the center of three large maximum peaks, where you can observe a situation where the main plan describes the main yellow function, correlation with which it increases for the red function at the third peak and with a small second central right peak, from where it is possible to trace the similarity of the pictures, but with a noticeable shift in Graph 9.
Graph 8. Functions for the interval [60; 70] for 110 elements
Graph 9. Functions for the interval [70; 80] for 110 elements
The continuation of the study allows us to observe the similarity of the interval from 17 to 27, from 20 to 30, from 60 to 70 and from 80 to 90, without small distinguishing features, as can be seen in Graph 10. And the situation for the interval from 90 to 100 is one of the most beautiful images, because here almost every graph is not like another, although most of them retain their definite trend, as can be seen in Graph 11. After that, the interval from 190 to 200 takes a more ordered, beautifully shaped form, where most of the functions take their general, uniform form, however, with a different level of bias with a decrease in the degree of correlation for each of them (Graph. 12).
This difference begins to decrease when analyzing Graph 13 for numbers from 290 to 300, where you can pay attention to an already more clearly verified and rather beautiful picture. This aspect is already beginning to change, leading to an increase in the degree of differing properties between functions from 390 to 400, as can be seen in Graph 14. The subsequent increase in the degree of gaps leads to the continuation of such a trend, which is clearly seen in a cardinal difference with the formation of a real house in the range from 490 to 500, so that even when most functions have already reached the final form, some functions begin to continue to increase forming massive peak forms (Graph. 15).
The continuation of the growth of the boundaries leads to a further increase, so the initial shape of the graph begins with a sharp increase, then decreases, and then continues at maximum peaks, which has never been repeated before, given that the graphs decline further and then sharply increase again to two peaks (Graph. 16). Further, the situation with a small difference continues at the moment from 690 to 700, while having a sharp shift of large peaks, having an elongation in the initial difference and the range of the initial small class of peaks (Graph. 17). And it would seem that the correlation situation can be increased, however, according to the graphs for values from 790 to 800, from 890 to 900, from 990 to 100, they retain the form of a house (Graph 18—20).
Graph 10. Functions for the interval [80; 90] for 110 elements
Graph 11. Functions for the interval [90; 100] for 110 elements
Graph 12. Functions for the interval [190; 200] for 110 elements
Graph 13. Functions for the interval [290; 300] for 110 elements
Graph 14. Functions for the interval [390; 400] for 110 elements
Graph 15. Functions for the interval [490; 500] for 110 elements
Graph 16. Functions for the interval [590; 600] for 110 elements
Graph 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.
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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.