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References
:
1.
.,
. Influenza hemagglutinin drives viral
entry via two sequential intramembrane mechanisms//
2020 Mar 18. pii: 201914188. doi: 10.1073/pnas.1914188117. [Epub
ahead of print]
2.
Faravonova T.E., Olenina L.V., Kuzmina T.I., Sobolev B.N., Kuraeva T.E.,
Kolesanova E.F., Archakov A.I. Identification of glycosaminoglycan-binding
sites within hepatitis C virus envelope glycoprotein E2//Journal of Viral
Hepatitis. â 2005. â V. 12. â6. - P. 584-593.
3.
Wang T., Palese P. Universal epitopes of influenza virus
hemagglutinins// Nature structural & molecular biology. â 2009. â N2. â C.1-
2.
4.
4.Khamidov D.Kh., Lim A.V., Salikhov R.S. et al. Immunoaffinity
fractionation of neutralizing antibodies against nerve growth factor//
Chemistry of natural compounds. â 1991. â N6. â P.828-832 [in Russian].
5.
Salikhov R.S. et al. Determination of unique peptide fragments in
nerve growth factors// Molecular biology. â 1994. â Vol.28, N 1. â P. 201-
203 [in Russian].
Navruzov Dilshod Primqulovich, PHD I year of study in the laboratory
"Mechanics of fluid and gas" Institute MISS them. Urazboeva AN zUz
,Tashkent ,Uzbekistan
APPLICATION OF FINITE DIFFERENCE METHODS FOR SOLVING THE TWO-
DIMENSIONAL EQUATION OF HEAT CONDUCTIVITY.
Navruzov D
Abstract: A comparison is made of finite-difference schemes with the
exact solution of a parabolic partial differential equation. A stability analysis
has also been carried out. To solve the parabolic equation, one-step and two-
step finite-difference methods are used.
Keywords: two-step method, nonlinear equations, implicit scheme, heat
equation, finite difference scheme, parabolic.
Introduction: In this article, various finite-difference schemes have
been studied in detail, with the help of which it is possible to solve the
simplest model equations of heat conduction. We restrict ourselves to
considering the diffusion equation. Difference schemes with a first order of
accuracy are considered. For the numerical solution of the heat equation, the
Scientific research results in pandemic conditions (COVID-19)
99
Kranko-Nicholson method and implicit methods of variable directions are
used [1].
The two-dimensional heat equation is a parabolic partial differential
equation that describes the process of heat propagation or diffusion [1-2].
)
(
2
2
2
2
y
U
x
U
t
U
ï¶
ï¶
ï«
ï¶
ï¶
ï½
ï¶
ï¶
ï¡
(1)
This equation is the simplest model equation for parabolic equations.
heat propagation rate.
Consider the problem of temperature distribution in a pipe. In this case,
equation (1) takes the following form
)
(
2
2
2
2
y
T
x
T
t
T
ï¶
ï¶
ï«
ï¶
ï¶
ï½
ï¶
ï¶
ï¡
(2)
We now turn to the study of finite-difference schemes for solving the
two-dimensional heat equation.
Numerical method
Application of model methods for solving
)
(
2
2
2
2
y
U
x
U
t
U
ï¶
ï¶
ï«
ï¶
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ï¡
the heat
equation.
1.
The Kranko-Nicholson method for the two-dimensional heat
equation.
ï·
ï·
ï¸
ï¶
ï§
ï§
ï¨
ï¦
ï«
ï¶
ï«
ï¶
ï½
ï
ï
ï«
ï«
)
)(
(
2
,
1
,
2
2
,
1
,
n
j
i
n
j
i
y
x
n
j
i
n
j
i
T
T
t
T
T
ï¡
(3)
To shorten the notation, two-dimensional central-difference operators
are introduced here
2
x
ï¶
n
j
i
T
,
and
2
Ñ
ï¶
n
j
i
T
,
defined by the relations
2
,
2
2
,
1
,
,
1
,
2
)
(
)
(
2
Ñ
T
Ñ
T
T
T
T
n
j
i
x
n
j
i
n
j
i
n
j
i
n
j
i
x
ï
ï¶
ï½
ï
ï«
ï
ï½
ï¶
ï
ï«
(4)
2
,
2
2
1
,
,
1
,
,
2
)
(
)
(
2
y
T
y
T
T
T
T
n
j
i
y
n
j
i
n
j
i
n
j
i
n
j
i
y
ï
ï¶
ï½
ï
ï«
ï
ï½
ï¶
ï
ï«
2.
Th
e implicit method of variable directions.
Scientific research results in pandemic conditions (COVID-19)
100
Step 1
ï·
ï·
ï¸
ï¶
ï§
ï§
ï¨
ï¦
ï¶
ï«
ï¶
ï½
ï
ï
ï«
ï«
)
(
2
/
,
2
2
/
1
,
2
,
2
/
1
,
n
j
i
Ñ
n
j
i
x
n
j
i
n
j
i
T
T
t
T
T
ï¡
(5)
Step 2
ï·
ï·
ï¸
ï¶
ï§
ï§
ï¨
ï¦
ï¶
ï«
ï¶
ï½
ï
ï
ï«
ï«
ï«
ï«
)
(
2
/
1
,
2
2
/
1
,
2
2
/
1
,
1
,
n
j
i
Ñ
n
j
i
x
n
j
i
n
j
i
T
T
t
T
T
ï¡
2
x
ï¶
2
/
1
,
ï«
n
j
i
T
,
2
Ñ
ï¶
n
j
i
T
,
and
2
Ñ
ï¶
1
,
ï«
n
j
i
T
defined by the relations
2
2
/
1
,
2
2
2
/
1
,
1
2
/
1
,
2
/
1
,
1
2
/
1
,
2
)
(
)
(
2
Ñ
T
Ñ
T
T
T
T
n
j
i
x
n
j
i
n
j
i
n
j
i
n
j
i
x
ï
ï¶
ï½
ï
ï«
ï
ï½
ï¶
ï«
ï«
ï
ï«
ï«
ï«
ï«
2
,
2
2
1
,
,
1
,
,
2
)
(
)
(
2
y
T
y
T
T
T
T
n
j
i
y
n
j
i
n
j
i
n
j
i
n
j
i
y
ï
ï¶
ï½
ï
ï«
ï
ï½
ï¶
ï
ï«
(6)
2
1
,
2
2
1
1
,
1
,
1
1
,
1
,
2
)
(
)
(
2
y
T
y
T
T
T
T
n
j
i
y
n
j
i
n
j
i
n
j
i
n
j
i
y
ï
ï¶
ï½
ï
ï«
ï
ï½
ï¶
ï«
ï«
ï
ï«
ï«
ï«
ï«
Calculation results.
Here are some specific examples illustrating the briefly described
models above. The results of calculations are comparable to those of
calculations [1].
In Fig. 1. The results of the temperature distribution by the Cranco-
Nicholson method are derived.
1.
Cranco-Nicholson Method.
Scientific research results in pandemic conditions (COVID-19)
101
Fig. 1.
2. The implicit method of variable directions.
Fig. 2.
Scientific research results in pandemic conditions (COVID-19)
102
Conclusion: The calculation results are compared. It is shown that these
finite-difference schemes give very close calculated results for the exact
solution of the parabolic equation.
References:
1. Anderson D, Computational hydromechanics and heat transfer //
Moscow "Mir" 1990, 382 p.
2. Spalart P. R., Allmaras S.R. A One-Equation Turbulence Model for
Aerodynamic Flows. AIAA-92-0439.
3.A. Faysman, Professional programming in Turbo Pascal. 1992.
4. Shur M., Strelets M., Zaikov L., Gulyaev A., Kozlov V., Secundov A.
Comparative numerical testing of one and two leveling turbulence models
for flows with separation and addition, "AIAA Paper 95-0863, January 1995
year
5. Shur M., Strelets M., Zaikov L., Gulyaev A., Kozlov V., Secundov A.
Comparative numerical testing of one and two leveling
models of turbulence for flows with separation and accession, "AIAA
Paper 95-0863, January 1995
6. L. G. Loytsyansky, Mechanics of liquid and gas, M .: Nauka, 1970. 904
s .; L. G. Loitsyansky, Fluid and Gas Mechanics, Moscow, Nauka, 1970, 904
pp. (In Russian)
7. Vladimirov V.S. Equations of mathematical physics. - M .: Nauka,
1988.512 s
Bahodir Ibragimov, assistant of the Department of Obstetrics and
Gynecology, Samarkand State Medical Institute, Uzbekistan
THE RELATIONSHIP OF METABOLIC DISORDERS WITH POLYCYSTIC
OVARIAN SYNDROME IN YOUNG WOMEN
B. Ibragimov
Annotation. The article presents some pathogenetic mechanisms of the
development of metabolic disorders in young women with polycystic ovary
syndrome. In recent years, polycystic ovary syndrome is considered as part
of metabolic disorders [1]. Metabolic disorders are manifested by disorders
of carbohydrate and lipid metabolism, abdominal obesity, hypertension,
followed by the development of type 2 diabetes mellitus and cardiovascular
diseases.
Keywords: metabolic disorders, polycystic ovary syndrome, insulin
resistance, hyperinsulinemia, dyslipidemia