Екатерина Вавилова – All sciences. №1, 2023. International Scientific Journal (страница 8)

Therefore, the constant component of the total signal of the first radiation receiver 3 does not pass through the AC amplifier 4. That is, the amplitude of the variable component of the amplified signal is proportional only to the amplitude of the flux Fλ1mPI1.

The variable component of the amplified signal is detected by the first amplitude detector 5. The detected signal (see Figure 3.d) from the output of the first amplitude detector 5 is integrated by the first integrator 6 and fed to the first input of the signal ratio device 13.

In this case, the voltage supplied to the first input of the signal ratio receiving device 13, taking into account the above, can be described by the expression:

where k1=kPI1kU1kAD1kINT1 is the total transmission coefficient of blocks connected in series with the first radiation receiver 3, the first amplifier 4, the first amplitude detector 5 and the first integrator 6; kAD1 is the transmission coefficient of the first amplitude detector; kINT1 is the transmission coefficient of the first integrator.

When the output signal of the first amplifier 4 is exposed to the input of the control device of the collimated radiation source 12, an antiphase electrical signal is formed at its output. The latter is fed to the input of the collimated radiation source 11 and causes a pulsed flow of collimated radiation at its output.

The formed flow, by the source of collimated radiation 11, is induced to the area of the controlled object 1. In this case, the flow reaching the surface of the controlled object 1 in the case Ako ≤ Aki is defined as:

where Aki is the cross – sectional area of collimated radiation; τλ2mc is the transmittance of the atmosphere at wavelengths λ2m; Foλ2 is the initial flux of collimated radiation. In this case, the reflected flow from the surface of the controlled object 1 is defined as:

where uco is the reflection coefficient of the surface of the controlled object at wavelengths λ2.

In this case, the expression for the reflected modulated flux from the surface of the controlled object and reaching the sensitive area of the second radiation receiver 7 has the form:

where: DPI2 is the diameter of the entrance pupil of the second radiation receiver.

In addition, in the case of a partial coincidence of the radiation spectrum of the controlled object with the spectral sensitivity of the second radiation receiver 7, an unmodulated radiation flux from the controlled object at a wavelength of λ2m affects the sensitive area of the latter.

where: ελ2m is the spectral coefficient of thermal radiation of the controlled object at wavelengths λ2m;

Then the total radiation flux acting on the sensitive area of the second radiation receiver 7 has the form.

Therefore, the output voltage of the second radiation receiver is defined as:

or

where cFP2 is the transmission coefficient of the second radiation receiver.

The voltage corresponding to expression (18) from the output of the second radiation receiver 7 is amplified by the second amplifier 8, as a result of which an alternating electrical signal is formed at its output (see Fig.3. d) the amplitude of which is defined as:

where ky2 is the transmission coefficient of the second amplifier 8.

Since during the period the repetition of the modulation Uλ2mPI2 can be considered constant, i.e. (see Fig. 3.b)

Therefore, the constant component of the total signal of the second radiation receiver 7 does not pass through the AC amplifier 8. That is, the amplitude of the alternating component of the amplified signal is proportional only to the amplitude of the flux Fλ2mPI2.

The variable component of the amplified signal is detected by the second amplitude detector 9. The detected signal (see Figure 3. e) from the output of the second amplitude detector 9 is integrated by the second integrator 10 and fed to the second input of the signal ratio device 13.

In this case, the voltage supplied to the second input of the signal ratio receiving device 13, taking into account the above, can be defined as:

where k2=cFP2kU2kAD2kINT2 is the total transmission coefficient of the blocks connected in series of the second radiation receiver 7, the second amplifier 8, the second amplitude detector 9 and the second integrator 10; kAD2 is the transmission coefficient of the second amplitude detector; kINT2 is the transmission coefficient of the second integrator.

It is known that optical devices designed to measure temperature mainly use a transparent region of the atmosphere spectrum. Therefore, for a small distance between the object of control and the radiation receiver, it can be assumed that, τλ1mc=τλ2mc"1. Then, when using identical electronic blocks for the radiation fluxes Fλ1mPI1 and Fλ2mPI2, we have k1 = k2. Therefore, at the output of the signal ratio receiving device 13, in proportion to the temperature of the control object 1, a voltage ratio is formed:

or

Since solar parabolocylindrical concentrators have a reflection coefficient in the near and middle IR spectral region that is constant and is γλ2ko = 0.1.

Then the temperature in the local focal zone of solar parabolocylindrical concentrators is defined as:

Thus, it can be seen from the last expression that the temperature in the local focal zone of solar parabolocylindrical concentrators is proportional to the voltage ratio Uλ1m and Uλ2m, which is recorded by the recording device, where it is taken into account.

Literature

1. Ergashev S. F., Kuldashov O. H. Control of gas concentration in geothermal energy. NTZH FerPI, 2014.No.3. from 105-109.

2. Daliev S. H., Nasriddinov S. S., Kuldashov O. H. The use of LEDs (1.94 µm) to measure the moisture content of raw cotton. Proceedings of the International conference "Optical and photoelectric phenomena in semiconductor micro- and nanostructures". Fergana, 2020, pp.426—427.

3. Kuldashov O. H. Optoelectronic device for remote temperature control of raw cotton riots. International Conference "Geoinformation support of aerospace monitoring of hazardous natural processes". Irkutsk, NIU, 2010.

4. Bezylaznaya T. V., Bogdanovich M. V., Kabanov V. V., Kabanov D. M., Lebedok E. V., Paraschuk V. V., Ryabtsev A. G., Ryabtsev G. I., Shpak P. V., Shchemelev M. A., Andreev I. A., Kunitsyna E. V., Sherstnev V. V., Yakovlev Yu. P. Optoelectronic pairs of LEDs-photodiode based on the InAs/InAsSb/InAsSbP heterostructure for carbon dioxide detection. Physics and Technology of Semiconductors, 2015, volume 49, vol. 7. C1003—1006.

5. Jha S. et al.«Violet-blue LEDs based on p-GaN/n-ZnO nanorods and their stability // Nanotechnology. – 2011, doi: 10.1088/0957—4484/22/24/245202.

MATHEMATICAL SCIENCES

THE PARADOXES OF MATHEMATICS POPULAR IN MODERN SCIENCE

UDC 520.254

Aliyev Ibratjon Xatamovich

2nd year student of the Faculty of Mathematics and Computer Science of Fergana State University

Aripova Sayyora Boxodirovna

Teacher of secondary school No. 1 of the city of Ferghana

Annotation. There is a weak spot in the foundation of mathematics, because of which it is impossible to know everything for sure, there will always be true statements that cannot be proved, no one knows exactly what these statements are, but they are similar to the hypothesis of «twin numbers». So pairs of prime numbers, where one of them is larger than the other by 2, for example 11 and 13 or 17 and 19. If you go higher up the numerical line, prime numbers are becoming rarer, not to mention such pairs. But the hypothesis about prime numbers says that there are infinitely many of them. So far, no one has been able to prove or disprove this yet.

Keywords: mathematics, calculations, discrete mathematics, logic.

Аннотация. В фундаменте математики есть слабое место, из-за чего нельзя знать всё наверняка, всегда будут истинные утверждения, которые нельзя доказать, никто точно не знает, что это за утверждения, но они похожи на гипотезу о «числах близнецах». Так пары простых чисел, где одна из них больше другого на 2, например 11 и 13 или 17 и 19. Если идти выше по числовой прямой простые числа встречаются всё реже, не говоря уже о таких парах. Но гипотеза о простых числах гласит, что их бесконечно много. До сих пор никто ещё не смог это доказать или опровергнуть.

Ключевые слова: математика, расчёты, дискретная математика, логика.

But the amazing thing is that most likely no one will ever be able to do it. After all, it is well known that in any mathematical system where operations are defined, there will always be true statements that cannot be proved. The best example is the mathematical model of the game "Life", created by mathematician John Conway in 1970.

"Life" unfolds on an endless field of square cells, each of which is either "alive" or "dead", there are only 2 rules in the game: any dead cell with 3 neighbors comes to life and any living cell with less than 2 or more than 3 neighbors dies. So you can set the initial configuration of the location of points and the model creates the first, second, third and subsequent generations. Everything happens automatically, although the rules are simple, they generate quite complex behavior, where the following situations arise: