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\title{Age, Size, Dynamics of Energy, Matter, and Masses of Black Holes in the Model of Accelerated Expansion of the Universe, based on the Idea of a Hypothetical 4-dimensional Inverted Substance}
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\date{\small \em Received: 1 January 1970 Accepted: 1 January 1970 Published: 1 January 1970}

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{{\textit{CrossRef DOI of original article:}} \underline{}}
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\section[{\textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore  ABSTRACT}]{\textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore \textunderscore  ABSTRACT}\par
The consequences of the previously proposed model of accelerated expansion of the Universe based on the idea of a hypothetical 4-dimensional substance with an inverse population of energy levels are considered. Based on the data on the time and redshift of the beginning of recombination and the last scattering, taking into account the dependence of the redshift on time obtained in this model, the age of the Universe was found, which turned out to be ?230 billion years. The dimensions of the Universe, which is a 4-dimensional spherical layer with a radius of 2400 Gpc, are determined. The dynamics of black hole mass growth is found to coincide with the observed data on the growth of black hole masses in elliptical galaxies, where there is no gas, the accretion of which could explain the growth of their masses. The dynamics of the masses of black holes in the considered model is compared with the dynamics of the masses in the model based on the standard model. It is shown that the dynamics of the growth of the energy of baryonic and dark matter coincides in form with the dynamics of the growth of the masses of black holes. The rate of matter formation is compared with the rate of star formation. It is concluded that currently dark matter is practically not formed, and it was formed at the most rapid temps at a redshift of more than two.  
\section[{?????????}]{?????????} 
\section[{I. ???Ð?"????}]{I. ???Ð?"????}\par
? ?????? \hyperref[b0]{[1]} ?? ?????? ????????????? ? ?????????????? 4-?????? ?????????? ? ????????? ????????????? ?????????????? ??????? ???? ?????????? ?????? ??????????? ?????????? ?????????, ??????? ? ??????? ????????? ????????? ????????? ?????? ??? ?????????? ???? Ia \hyperref[b1]{[2]}, ???????? \hyperref[b2]{[3]} ? ?????????? ?????-????????? \hyperref[b3]{[4]}. ??? ????? ????????? ????????? ?????? ???????? ??????, ???????????? ?? ??????????? ?????????, ?????????? ?? ????????? ??????, ?????????? ?? ?????? ???????? ?????????? \hyperref[b4]{[5,}\hyperref[b5]{6]}.\par
??? ? ? \hyperref[b6]{[7]}\hyperref[b7]{[8]}\hyperref[b8]{[9]}\hyperref[b9]{[10]}   
\section[{II. ??????? ????????? ? ??Ð?"??? ????? ?????Ð?"??Ð?"? ?????????}]{II. ??????? ????????? ? ??Ð?"??? ????? ?????Ð?"??Ð?"? ?????????}\par
??????????? ???????? ???????? ?? ??????? ??????????????? ????????? ?? ????????? ? ??????????????? ?????? ??????????? ???????? \hyperref[b0]{(1)} ??? x = (t -t e )/t 0 ; H 0 -???????? ??????; t -????????? ?????? ???????; t e -?????? ???????, ? ??????? ?????????? ????????? ?????????; t 0 -?????? ???????, ????? ?????? 4-?????? ??????????? ????, ?? ???? ???? ?????????; R 0 -?????? 4-??????? ???????????? ???? ? ?????? ??? ????????????? t 0 ; T 0 = ct 0 . ??? ?????????, ???????? ? ??????? ?????????? ? \hyperref[b0]{[1]} ?? ????????? ?????????? ???????????? ? ??????????? ?????? ??? ?????????? Ia, ???????? ? ?????-?????????: H 0 = 67.7 ??/?/???; t 0 = 27.7 ???? ???; H 0 t 0 = 1.92; R 0 = 2.24 Ð?"??; T 0 = 8.5 Ð?"??; H 0 t 0 T 0 /(2?R 0 ) = ?/4, ??? ? = 4.64 \hyperref[b0]{[1]}. ?????? ??????? t e ??? ??????, ??????? ??????????? ? ??????? ?? ?????????? ???????. ???????? ?????????? ? ???????????? ???????? ??????? ????? ?????????? ?????? ?.\par
??? ????????, ? ?????? ???????? ?????? \hyperref[b15]{[16]} ?????????????? ????? ???????? ????? ????? ????????????? 4-??????? ???????????? ???? ????????? ???????????? ??????????? ? ???????? ?? ????????? ???????????? ????? ?????????????? ????????-?????-????????? ??????, ????? ??????? ? ???????. ??????? ????????? ???????? ????? ??????, ??? ????? ??????????? ?????, ???? ?????????????, ????? ????? ??????????? ? ??????????? ?? ??????? ? ?????????. ?????? ??????????????? ? ????????? ???????, ????????? ??? ?????????? ???????? ?????????? ?????? ? ??????????? ?? ???.\par
?? ???? ?????????? ????????? ?????? ????????. ? ?????-?? ?????? ?????? ??????????? ? ????????? ???, ?????????? ?????????? ? ?????????? ???????????? ?? ??? ???????, ??????????? ??, ??? ?????????? ?????????? ?????????? \hyperref[b18]{[19]}. ????? ???????, ??????????? ??????? ?????????? ????????? ???????????? ?? ????? ???????? ?????????????? ??????????????????? ?????? ? ????????? ???? ??????????? ?????? -?????? ???????? ? ?????.\par
??????? ???????, ? ??????? ???????????? ?????????? ?????????, ???????? ???????????? ?????????? ????????? \hyperref[b15]{[16]}. ??? ???????? ??? ?? ???? ?????? ? ????? ???? ???????????? ? ???? ????? ??????? R f . ?????? ??????????? ?????????? ????????? ????????? ???????? ??????????. ??????????? ?????????? ????????? ???????????? ??? ??????????? ?????? ????? 3000 ? ? ????????? ???????? ????????? 380000 ??? \hyperref[b19]{[20]}. ??????? ???????? ??? ??????????? ?????????? ????????? ?????????? z f ? 1090 \hyperref[b20]{[21]}. ?? ?? ??????? ?????????? ????????? ???? ????? ????????? ?????????????? ?????? ? ????????? ?? ??? ????? ????????????. ?????? ????? ???????????? ????????????? 200000 ??? ?? t 0 ? z r = 1400 \hyperref[b21]{[22]}. ????????? ???? ???????? ?????? ?????????? ? ??????????? ??????????????? ??????. ? ??????????????? ?????? ??????????? ???????? ?????????? ? ???????????? ???????? ??????? ? ?? ???????? ????????, ?????????? ?? ??????????? ? ??????????? ?????? ? ??????????? ???????? (1), ???. 1. ?????, ??? ??? ?????????????? ?????????, ??????????? ? ???????, ???????????  ? ? ? ? 0 0 0 0 0 0 exp ln 1 1 2? H t T x z x H t x x x R ? ? ? ? ? ? ? ? ? ? ? ? ? ? London Journal of 
\section[{??????? ?????????}]{??????? ?????????}\par
???? ??????? ?????????, ????? ???????? ???????? ? ?? ????????. ??????? ? ??????? ??? ??????? 4-??????? ???????????? ?????????????? ? [1], t -t 0 = T, ??????? ?????? ????????? R = R(t 0 + T) ? 2.4?10 3\par
Ð?"??, ??? ???????? ? ???? ?????? ????????? ? \hyperref[b0]{[1]} ?????? ?????????? ????????? ????????? ?????????, ?????? ???? ?? ????? ???????? ??????????? ??? ?? ????? ??????? ???????? UDFj-39546284 ? GN-z11 ?? ????? ??????? ?????????. ??? ???????? ? \hyperref[b0]{[1]} ?????????? ?? ???? ???????? ?????????? ???????? D g ? 80 Ð?"??. Ð?"?? ?????????? ?????? ?????????? ??????????? ? 3-?????? ????? ? ????? ???????????? ????? Ð?"???????? ?? ??????????? ??????????? ? ????? ???????????? ??????????? ?????????, ??????? ??????? ?? ?????????? D g . ???? ????? ????????????? ?? ?????? 3-?????? ????? ? ???? Ð?"???????? ? ? ??????? ????????? ? = D g /R. ?????????? ??????????? ? ????? ?????????? ?? ????????? ????????? ? = R(1/cos? -1) ? R? 2 /2. ?????????? ???? ?, ???????? ?/R ? (D g /R) 2 /2 ? 0,55?10 -3 << ? k , ??? ? k = 0.04 -???????? ?????????, ????????? ? \hyperref[b17]{[18]}. ????? ???????, ?????????? ?? 3-?????? ????? ?? ?????????? ?? ????? ??????? ???????? ???????? ? 73 ???? ?????? ???????? ?????????, ??? ???? ?? ????? ???????? ?? ??????????? ????? ???????? ??????????????? ????????????? ???????. ????? ????? ???? ???????? ???????? ????????? ?? ??????????? ???????? ?????????? ?????????? ????????? ????????? ?? ????? Ð?"???????? ?? D g > R(2? k ) 1/2  ? 680 Ð?"??.\par
? ??????????????? ?????? ????? ?????? ??????? ????? ???????? ?????????, ?? ???? ????? ???????? 3-?????? ????? L e = 2?R, ??????? ?????????? ? 1.5?10 4  Ð?"??. ???????? ????????? R f /(L e /2) ? 0.74 ?????, ??? ?????????? ????????? ???????? ?? ???????, ??????? ?????? ????????? 4-??????? ????. ????? ???????, ????? ??????? ?????, ??? ? ??????????????? ?????? ??????? ????? ????????? ????????? ??? ??????????? ?????????.\par
????? ????? ???????? ?? ?????? ?????????, V ??? ??????? ???????????????? 3-?????? ????? S 3 :V = S 3 = (4/3)? 2 R 3 ? 1.7?10 11 Ð?"?? 3 . ? ???????????? ? ????????? ? [1] ????????? ????????? ( ) 0 0 0 0 0 0 0 exp ln 1 1 d 2 2 1 x H t ct H t D x ct x x x p p ì ü ï ï ï ï = - + + í ý ï ï ï ï î þ ò ( ) 2 0 0 0 0 0 0 exp ln 1 1 d 2 2 1 H t ct H t x D x ct x x x R x p p ì ü ae ö ¢ ï ï ï ï ÷ ç é ù ¢ ¢ ¢ = - + + ÷ í ý ç ê ú ÷ ë û ÷ ç ï ï ¢ è + ø ï ï î þ . ¢ ¢ ¢ ? ? ? ? 0 2 3 0 0 0 0 0 exp ln 1 1 d 5.6 10 4 2? 1 f t f f H t x D t T x x x x ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? T R T Ð?"??. ? ? 0 0 0 0 0 exp ln 1 4 t t t t R t R t t ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?\par
, London Journal of Research in Science: Natural and Formal ??????? ? 4-?????? ???? ? ?? ????????? ??? ????????? ???????????????? ???????? ?????? ??????? ?????????. 
\section[{IV. Ð?"??????? ?????? ????Ð?"?? ?????????}]{IV. Ð?"??????? ?????? ????Ð?"?? ?????????}\par
???? ??????? ????????? ????? ?????? ?????????? ?? ??????? ??? ???????? ????????? ??????? ?????? 4-??????? ????, ? ???????? ????????? 4-?????? ??????????? ???? ?, ??????????????, ?? ??????? ??? ??????????? ????????? ??????? ??????? ?? ??????? ??????????? 4-??????? ???????????? ????. ?????????? ? ?????????? ? \hyperref[b0]{[1]} ????????? ? ? (t) = ? ? (t 0 )(t/t 0 ) ? ???????? t = T + t 0 , ???????? ? ? (T)/? ? (t 0 ) = (1 + T/t 0 ) ? ? 3?10 4  . ?? ??????? ?? ??? ??????????? ????????? ??????? ??????? ?? ????????? ? E (t), ??? ??? ? ?????? ?????? ? E (t) = const/? ? (t) \hyperref[b0]{[1]}. ????????? ????????? ??????? ??????? ?? ????????? ? ????????? ?????? ?????????????? ?????? ??????????? ????????? ? ?????????? 5.2?10 -6  Ð?"??/?? 3 \hyperref[b22]{[23]}, ?? ? ?????? ??????????? ????????? ? E (t 0 ) = ? E (T)(1 + T/t 0 ) ? ? 0.16 Ð?"??/?? 3  .\par
?????? ??????? ????????? ?????? 4-??????? ????? ?????? ????, ??? ? ? (t 0 )(R 0 ) 4 = ?(t 0 ), ? ? (t) = ? ? (t 0 )(t/t 0 ) ? , ? ????????? R(t)/R 0 ????? ???? ???????????? ? ???? (2)\par
?????? ??????? ?????? 4-??????? ???? ?????????? ??? ?(t) = ?(t 0 )exp[?(t -t 0 ) ? ?????? ???????????? ? ???????? ? \hyperref[b0]{[1]} ?????????? d?/dt = ??, ??? ? = 5.31×10 -18  ? -1 -???????????? ? [1] ??????????? ???????? ? ???????? ????????? ? ??????? ?????????????? ??????? 4-?????? ?????????????? ?????????? ?? ???????????.\par
?????? ??????? ??????? ?? ????????? ???????? ? ???????????? ? ???????? ???E(t 0 ) = ? E (t 0 )V(t 0 ) = (4/3)? 2 (R 0 ) 3 ? E (t 0 ) -?????? ??????? ????????? ? ?????? ?? ???????????. ? ?????? (2), ? ????, ??? ? E (t) = ? E (t 0 )(t/t 0 ) -? , ????????\textbf{(3)}\par
Ð?"????? ??????????? E(t)/E(t 0 ) ??????????? ?? ???. 2. ?????, ??? ??????? ?????? ??????? ????????? ?????? ???????? ? 9 ???, ? ????? ???????? ????? ? ????? ?????????? ???????, ?????? ???????? ?????????, ????????????? ? 4?10 4  ??? ?? ????????? ? ???????? ????????? ? ?????? ?? ???????????. ????? ???????, ???????? ? ??????, ??? ????? ????? ??? ??????, ??? ? ?????? ??????? ??????? ?? ?????????. ????? ???????? ??????????? ????? ???????? ??????? ? ?? ???????? ????????????? ?????????? ??? ???????? ????????? ??????? ?? ?????????, ??????? ?????????? ?????????????????? (3) ?? ???????: . ?? ????????? ??????? ?? ???. 2 ? ?? ??????? (4) ?????, ??? ??? t = t 0 ??????????? ????????????. ?????? ?????????? ???????, ????????????? ?? ??????? ??????? ??????????? ????????? t -t 0 = 4t 0 /3 ? 37 ???? ??? ??????????? ?????????? ? ????, ? ????? ????????? ?????????? ? ??? t -t 0 ? ? ????????? ? ???????? 3?/4t 0 . ??????? ? ??????? ? 37 ???? ??? ?????? ???????? ????????? ??????.( ) ( ) ( ) ( ) ( ) ( ) ( ) 4 4 4 0 0 0 0 t R t t t V t t R t R r r r r X X X X é ù ê ú X = = ê ú ë û . ? ? 4 0 0 0 0 0 exp 1 4 R t t t t t t t R ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ( ) ( ) ( ) ( ) ( ) ( ) ( ) 3 E E 0 E 0 0 t R t E t t t E t t R r r r é ù ê ú = = ê ú ë û V ( ) ( ) 7 4 0 0 0 0 0 3 exp 1 4 E t t t t t t t E t b b ae ö ae ö - - ÷ ÷ ç ç ÷ ÷ = + ç ç ÷ ÷ ç ç ÷ ÷ ç ç è ø è ø London Journal of 
\section[{???. 2:}]{???. 2:}\par
????????? ?????? ??????? ????????? ?? ??????? ? ??????? ?? ???????????. ???????????? ????????? ?????? ????????????? ???????? ????????? 228 ???? ???, ????????????? ?? ??????????????? ??????. 
\section[{V. Ð?"??????? ???? ?????? Ð?"??}]{V. Ð?"??????? ???? ?????? Ð?"??}\par
????????? ?????????? ?????? ??????? ???????????? ?? ???, ??? ????? ???????, ??????????? ?? ????????? ?? 4-??????? ????, ??????????? ??????? ?????? (?Ð?") \hyperref[b23]{[24]}. ????? ??????? ????????? ? 4-?????? ???? ?????? ??????????????? \hyperref[b0]{[1]}. ??? ??? «?????????????» ?????????? ??????? 4-??????? ???????????? ???? ??????? ?????? ??-?? ?????? ?????????? ??????? ????????? ? 4-?????? ????, ?? ??????? ?????????? ??????? ?Ð?" ??????????? ??? ????????? ??????????? ??? ? 4-?????? ??????????? ????, ????????????? «??????????????» ?????????? ??????? 4-??????? ???????????? ???? ???????? ????????? ?????????????? 4-?????? ??????????. ?? ???? ????????????????? ????? ????? ??????? ????????? ? 4-?????? ???? ??????? «?????????????» ????????????? ? ???????? ???????? ???????????? ?????? ???????? ??? ???????? ??????? ? ?Ð?".\par
( )0 0 0 d 7 3 d 4 1 E E t t t t t b é ù ê ú = - ê ú + - ê ú ë û\par
. ; ? -???? ??????? E (+) ? ?????? ??????????? ????????? ? ?????? ??????? E: E (+)  (t 0 ) = ?E(t 0 ); 0 ? ?? 1, ? + ? = 1. ????????? ? ???????? (1), ? ??????? x = ?/t 0 , ???????? ??????????????? ??????????? ??????? ????? G ??????? ??????? ?? ???????? ????????, ?????? ??????? ??????????? ?? ???. 3b. ?????, ??? ??????? ????? ????????? ???????????? ??????? ? ??????????? ?Ð?" ????? ?? ?????. ??? ??????? ? ?????????? ???? ???????????? ???????, ??? ????????????? ??????? \hyperref[b26]{[27]}.London\par
??????? dE (+)  /dt ????? ??? ? ??????? E(t) ??????????? ??? t -t 0 = 4t 0 /3 ? 37 ???? ??? ?? ??????????? ?????????. ????????? ??????? (1), ???????, ??? ????? ??????? ??????? ????????????? z = (4/3)H 0 t 0 exp(?/3)/(7/3) (1+?/4) ? 1.93. ??? ???????? \hyperref[b27]{[28]}, ??? ????? ???????? z ??????????? ???????? ???????? ?????????????????. ? ????? ? ???? ?????????? ??????? ???????????????? ??????? [dE (+)  /dt] -1 , ? ??????? ???????? t -t 0 ???????? ?? ?:. (\textbf{6})\par
? ???????????? ? ???????? (1) ???????? ??????????????? ??????????? M FR ?? z. Ð?"????? ???? ??????????? ????????? ?? ???. 4 ???????? ??????. ???????? ??????? (6) ?????????? ?? ??????? ??????? dE (+) /dt, ?? ???? ?? ???????? z = 1.93, ? ????????? ????????????? ???????? ? ???????? ??? z = 0 ?????????? (7/3) 7?/4 exp(-?) ? 9.4, ??? ????????? ? ???????????????? ???? ???????? ????????????????? \hyperref[b27]{[28]}.\par
?? ?????? ?????? \hyperref[b28]{[29]} ???? ??????????? ????? ??? z = 1.125 ?? ??????? ???? ? 4 ???? ????????? ??????????? ???????? ??? z = 0.375. ?? ?????? ????? \hyperref[b27]{[28,}\hyperref[b29]{30]} ???????? ????????????????? ??? z = 2.75 ? ??? ???? ????????? ??????????? ????????, ?? ? ?????? ???? ????, ??? ??? z = 1. ??? ? ??? ???? ??????????? ???????? ????????????????? ????????? ? z = 4. ??????????? ?? ???? ?????? ?????? ??????????? ???????? ????????????????? ?? ???????? ???????? ????????? ?? ???. 4 ????????? ??????. ????? ?? ????????? ???????? ????????????????? ??????????? ????????? ?? ????????? ???????????? ???????, ? ?????????????? ??????????? ???? ??. ???????? ?? z =1.3 ?? z = Z ?????????? ? 90\% ?? ????? ????????? ?? z ?? z = 0 ?? z = Z, ??? ??????????? ?????? 50\%, ??? ??? ????????????????? \hyperref[b27]{[28]}. London Journal of Research in Science: Natural and Formal ???. 4: ??????????? ???????? ???????????? ??????? ?? ???????? ???????? (???????? ??????) ? ???????? ????????????????? (????????? ??????). ????? ??????????? ? ???????????? ? ??????? ????? \hyperref[b27]{[28]}\hyperref[b28]{[29]}\hyperref[b29]{[30]}.\par
???? ?????????, ??? ?????? ??????? (6) ????????? ???????? ???????????? ???????, ?? ????? ????????????, ??? ??????????????? ??????? ????????????? ???????? ???????????? ?? ?????? ????????? ???????, ?? 10\% ????? ??????? ??????? ??????, ?? ? ???????? ???????????? ???????? ?????? ???????. ??? ????????????? ??????? ??????????????, ??????? ??????? ?? ????? ?????? ??????. 
\section[{VII. ?????Ð?"???? ???????????}]{VII. ?????Ð?"???? ???????????}\par
??? ?????????? ? \hyperref[b0]{[1]} ????????? ? ??? ??????? ????????? ? 270 ???? ??? ? ???????????? ? ?????? ?????? ? ?????? 230 ???? ??? ??????????? ? ??????? ??????????, ? ??????? ??????????, ??? ???????? ??????????????? ????? ? ???? ????? ???????? ?????????? ?? ????????? ?? ??? ????? ?? ?????, ??., ????????, \hyperref[b30]{[31]}. ? \hyperref[b31]{[32]} ?????????, ??? ?? ????????? ???? ?????? ???????? ??????, ??? ?? ?????? ????? ?????????? ???-???? ? ???????? ????????? ??? ??????? ?????????. ????? ???? ????????????? ????? ? ???, ??? ?????????? ????????? ???, ????????????????? ? ?????????????? ?????????? ????? ? ????????, ???? ????????? ??? ??????????? ? ?????? ????????????? ?????????. ??????????????? ?????? ?? ???? ?????? ??????????? ? ????? ??????????????. ?????????? ? ??? ??????? ????????? ?230 ???? ??? ???? ????? ??? ? 16 ??? ?????? ???????? ? ??????????? ?????????? ?????? ? 14 ???? ???, ?? ???????.\par
?????? ? \hyperref[b0]{[1]} ??????? ?????????, ????????? ?? ??????? ?/D g = D g /(2R) ? 0.1? k , ???? ??? R ???????? ?10 4  Ð?"??, ? ??? ???????? ????????? 270 ???? ???. ???? ???????? ?? ??????? ?/R ? (D g /R) 2  /2 ? 0.1? k , ?? ???????? R ? 900 Ð?"??, ? ??????? ????????? ??? ????? ???????? R ?????????? ? 200 ???? ???. ????? ???????, ?????????? ?? ?????? ?????? ? ?????????? ????????? ? ?????? ? ????????? ???????????? ?????? ????????? R ? 2,4?10 3  Ð?"?? ???????? ????? ?????????? 900 ? 10 4  Ð?"??, ??????????? ?? ?????? ?????? ? ???????? ???????????? ?????????, ? ??????? ????????? T = 230 ???? ??? -????? ?????????? 200 ? 270 ???? ???, ??? ??????????? ????????????? ????????? ? ?????? ?????? ???????? R ? T. ????????? R/R 0 ? 1000,  ????????? ??????? (6) ?? ????????? ????????????????? ???????? ? ?????????????, ??? ???????? ????????????????? ? ???????? ???????????? ??????? ??????? ??????????????? ???????? ??????? ??????? ?? ????????? ?? ??????? ???????, ??????????? ?Ð?". ????? ???????, ????? ????????????, ??? ??????????????? ??????? (6) ????????????? ???????? ???????????? ?? ?????? ????????? ???????, ?? 10\% ??????? ??????? ??????, ?? ? ???????? ?????? ???????. ??, ??? ??? z ? 1.9 ?????????????? ??????? (6) ????????? ? ???????????????? ???????? ?????????????????, ? ???????? ?? ??? ? ????????? ???????? 1.3 ? z ? Z ??????????? ????????? ??????????????? ???????? ?? ???????? ????????????????? ??????? ? ???, ??? ? ????? ?????? ????? ???????????? ????????? ? ???????? ?????? ??????? ??? ????? ?????????? ?? ????????? ?? ?????????????????? ? ??????, ??????? ? ????????? 0 < z < 1.9. ?????????? ???????? ???????????? ???????? ?????? ??????? ? ???????? ???????????? ????????? ??????? ??????? ?? ????? ?????? ?????? ? ??????? ?????????? ????????????. 
\section[{VIII. ??????????}]{VIII. ??????????}\par
? ?????? ?????? ??????????????? ????????? ?? ???????????? ????? ? \hyperref[b0]{[1]} ?????? ??????????? ?????????? ?????????, ?????????? ?? ????????????? ? ?????????????? 4-?????? ?????????? ? ????????? ????????????? ?????????????? ???????. ?? ?????? ?????? ? ??????? ? ??????? ???????? ?????? ???????????? ? ?????????? ????????? ? ?????????? ? \hyperref[b0]{[1]} ??????????? ???????? ???????? ?? ???????? ?????????? ??????? ??????? ? ??????? ???????, ? ??????? ??????????? ??????? ?????????, ?????? ??????? ?????????, ??????? ???????? ?????? ?230 ???? ???. ??? ??????????? ? ???????? ?? ???????????? ???????? ???????? ??????????????? ????? \hyperref[b30]{[31]} ? ? ???????? ???????? ?????????, ??????????? ? \hyperref[b0]{[1]} ?? ?????? ???????? ?????????.\par
????????? ?????? 4-??????? ????, ? ???????? ????????? ???? ? ????????, ?? ???? ?????? ?????????, R ? 2.4?10 3  Ð?"??, ? ????? ????? ???????? ????? ???? L e = 2?R, ??????? ?????????? ? 1.5?10 4  Ð?"??. ????????, ??? ????????? ???????? R ??????????? ? ???????? ?? ?????? ???????? London Journal of Research in Science: Natural and Formal\par
?????????. ?????? ????? ????? ????????? V ??? ??????? ???????????????? 3-?????? ?????: V ? 1,9?10 10 Ð?"?? 3 .\par
????????? ?????? ????? ?????????? ????????? R f , ??????? ???????? ?????? ? 5,6?10 3  Ð?"??. ?? ????????? R f ? L e ?????? ?????, ??? ? ??????????????? ?????? ??????? ????? ????????? ????????? ??? ??????????? ?????????. ? ?????????????, ??? ? ????????? ????? ????????? ??????? ?? ????????? ????? ??????????? ??????? ????????? ??????? ??? ????????????? ?????????, ??????? ?????????? 0.16 Ð?"??/?? 3  . ???????????????? ???????? ?????? ??????? ?????????. ????????, ??? ? ?????? ?????? ?????? ??????? ????????? ???????? ?? ???????. ? ??????? ?????? 37 ???? ??? ????? ????????????? ????????? ?? ?????? ??????? ?????? ???????? ? 10 ???, ? ????? ???????? ????? ? ? ?????????? ??????? ??????? ??????????? ???????? ? 10 4  ??? ?? ????????? ? ???????? ????????? ? ?????? ?? ???????????. ????? ???????, ?????? ?????, ??? ????? ????? ??? ??????, ??? ? ?????? ??????? ?? ?????????. ?? ?????? ??????? ???????? ????????? ??????? ?? ????????? ? ????????? ? ??????? ?????????? ?? ?????? ???? ?????? ??? ? ????????????? ?????????? ?????? ?????, ??? ?????? ??????? ?? ????????? ??????????? ?? ??????????? ??????? ??????, ? ?????? ?????????? ???????????? ??? ? ??????? 4-?????? ???? ??? ????????? «?????????????» ?????????? ??????? ????? ???? ???????? ????????? ? 4-?????? ????, ???????????? ? ???????? ??????????????? ????????? ? ??????? ?????????????? ??????? ?????????????? 4-?????? ?????????? ?? ???????????. ????????, ??? ???????? ????? ???? ?????? ???, ??????????? ??????????? ? ????????? ?????? ?????????, ?? ??????? ?? ?????? ?????? ????. ?????????? ???????? ??????????, ??? ????? ?????? ??? ? ????????? 0 ? z ? 1.2 ?????????? ????? ? 7 ???, ? ? ????????? 0 ? z ? 2 -? 20 ???. ??? ?????? ????????? ? ???????????? ?????????? ?????? ??? ? ????????????? ?????????? \hyperref[b24]{[25,}\hyperref[b25]{26]}, ??? ? ??????? ?????????? ?????? ??? ?? ???????? ???????? ??? ?????????? ?? ????.\par
????????? ???????? ?Ð?", ????????????? ? ?????? ??????, ? ???????????? ???????????? ???????? ?Ð?", ?????????? ? ?????? ???????, ??????????, ??? ? ????????? ?????????? ???????? z ??????? ?????????? ?????????????????? ??????????. ??? ? ??????????????????? ?????? \hyperref[b33]{[34]}, ??????????? ?? ??????????? ??????????????? ??????, ??? ???? ??????????????? ?????, ?????? 2,96 ??????? ?????????????????? ?????????? ? ????????? ???????? 1 ? z ? 4.5. ??? ?????? ?? ??????? ?????????? ????????? ?????????? ???????? ?? ?????? \hyperref[b33]{[34]} ?????? ?????????? ?? ??????????? ???????? ?? ???????? ????????? ??????. Ð?"?? ????????? ???? ????? ??????????? ????????? ????????? ????? ???? ?Ð?" ?????????? ?????????? ?????????? ????????, ????????? ?? ??? ?? z ? 4.5.\par
????????, ??? ???????? ????? ??????? ????????? ? ?????? ??????? ?? ????? ????????? ? ????????? ????? ???? ?????? ???. ????????? ????????? ???????? ???????????? ??????? ?? ????????? ?????????????????. ?????? ?????, ??? ? ????????? ????? ?????? ??????? ??????????? ?? ??????????, ? ???????? ???????? ??????? ??? ?????????????? ??? ??????? ???????? ?????? ????. 
\section[{???????? ?????????}]{???????? ?????????}\par
????? ??????????? ?????????? ????????? ?????????, ????????? ? ??????????? ?????? ??????. London Journal of Research in Science: Natural and Formal\begin{figure}[htbp]
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\begin{longtable}{P{0.85\textwidth}}
???????????? ???????? ???? ?Ð?", ??????????? ? ?????? [33], ? ????? ????????????,\\
???????????, ????????, ? [27], ??????????, ??? ? ????? ??????, ????????? ????? ?Ð?" ??\\
??????? ??????? ?? ?????? ?Ð?". ????????????, ??????????? ? ?????? ??????, ???????? ?\\
??????????, ??? ???????? ???? ?Ð?" ?? ??????? ?? ?????? ?Ð?", ? ??????? ? ????????????? ??\\
???????? ? ????????? ???? ?? ??? ?????? ?? ???????? ??????? ????????? ? 4-?????? ???? ?\\
???????? ?????????? ?????????. ? ????????? ???????? 0 ? z ? 10 ???????? ???? ?Ð?"\\
??????????? ?? ??????? ?? ???? ???????, ??????????? ? ??? ??? ???????? ?????????.\end{longtable} \par
 
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 			\label{foot_0}\footnote{\label{foot_0} © 2023 Great ] Britain Journals Press} 			\label{foot_1}\footnote{\label{foot_1} © 2023 Great ] Britain Journals Press} 			\label{foot_2}\footnote{\label{foot_2} © 2023 Great ] Britain Journals Press} 		 		\backmatter  			  				\begin{bibitemlist}{1}
\bibitem[ London Journal of Research in Science: Natural and Formal]{b34}\label{b34} 	 		\textit{},  	 	 		\textit{London Journal of Research in Science: Natural and Formal}  		 	 
\bibitem[????????? and ????????? ()]{b18}\label{b18} 	 		\textit{},  		 			? ? ????????? 		,  		 			????????? 		.  		1987.  	 	 (?????, ????? (?.: ?????) 
\bibitem[ ??????? ?????????? ???????????? (?.: ??????? ?????????? ???????????? ()]{b20}\label{b20} 	 		\textit{},  	 	 		\textit{??????? ?????????? ???????????? (?.: ??????? ?????????? ????????????}  		2004.  	 
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\end{bibitemlist}
 			 		 	 
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