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Before constructing a self-similar solution of the system of equations (1), let us
consider some cases of diffusion, for example:
2
,
1
,
0
3
i
p
m
i
-the state of slow
diffusion,
2
,
1
,
0
3
i
p
m
i
-the critical state(the asymptotic is summed up depending on
its solutions),
2
,
1
,
0
3
i
p
m
i
is called the state of fast diffusion. An asymptotic solution
is usually understood as a solution of a system of nonlinear equations that can satisfy
certain conditions.
(1) the equation represents a number of physical processes [1]: the reaction
diffusion process in a nonlinear environment, the heat dissipation process in a nonlinear
environment, the filtration of liquid and gas in a nonlinear environment, they represent
the existence of the law of polypore and other nonlinear displacements [1-3].
(1) the Cauchy problem and boundary value problems for the equation were
observed by many authors in one-dimensional and multi-dimensional cases [2-3].
(1) in the processes represented by the equation, the phenomenon of finite
distribution of temperature occurs [3]. In the presence of an absorption coefficient,
the phenomenon of the “rear” front can occur, that is, the left front can stop after a
certain time and move along the medium [4].
We can translate the system of equations (1) into a system of radial-symmetric
equations so that we can find a solution to a self-similar or an approximately self-similar.
To do this, we first introduce the notation as
x
r
, so that we can translate the system of
equations (1) into a radial-symmetric system:
k
r
q
l
p
m
N
n
k
k
r
q
l
p
m
N
n
k
r
v
u
t
r
v
r
v
v
r
div
t
v
r
r
v
u
t
r
u
r
u
u
r
div
t
u
r
1
1
2
1
1
1
2
1
1
2
1
1
(3)
After performing the substitution (3), to find a self-similar solution of the system
of equations (1) and the solution of the approximately self-similar, we use the following
method:
r
t
z
t
v
r
t
v
r
t
t
u
r
t
u
,
,
,
,
(4)
Now we calculate the initial part of the system of equations (1), as required, as
follows:
2
1
2
1
2
1
2
2
1
2
1
1
2
1
0
0
2
0
0
1
1
1
1
1
1
1
2
1
2
2
1
1
q
r
r
q
q
q
q
r
r
q
r
r
d
T
A
t
v
d
T
A
t
u
v
u
t
dt
v
d
v
u
t
dt
u
d
t
t
r
q
r
q
After performing the calculations, the system of equations (3) takes the following
form:
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z
z
v
u
t
z
z
z
z
z
v
u
t
r
q
l
p
m
r
q
l
p
m
s
s
r
q
r
l
p
m
q
l
p
m
s
s
2
2
2
2
2
1
1
1
1
1
1
1
3
2
1
1
1
3
2
1
1
1
(5)
From the system of equations (4)-(5) (1)-(2) there are important considerations
on the question: if
2
,
1
;
4
i
l
p
m
i
t
l
p
m
t
l
p
m
d
v
d
u
t
0
4
0
4
2
1
or if
2
,
1
;
4
i
l
p
m
i
is equal to
t
T
t
.
We form a system of equations of a new form:
0
0
2
2
2
2
2
2
1
1
1
1
1
1
3
2
1
1
1
3
2
1
1
1
g
g
f
v
u
t
p
d
dg
d
dg
g
d
d
f
g
f
v
u
t
p
d
df
d
df
f
d
d
r
q
l
p
m
r
q
l
p
m
s
s
r
q
r
l
p
m
q
l
p
m
s
s
(6)
To find a solution to this system of equations (6), we introduce another repeating
self-similar pattern:
4
3
2
1
2
1
a
B
g
a
A
f
where
2
,
1
;
0
i
a
i
,
4
,
1
;
0
i
i
is equal.
Combining all the calculated equalities, we get the integral self-similar solution
we are looking for:
4
3
2
1
1
1
2
1
1
2
1
2
1
1
1
2
1
2
0
0
1
1
1
1
0
0
1
1
1
2
,
,
a
B
d
T
A
x
t
v
a
A
d
T
x
t
u
t
r
q
A
t
q
r
r
q
r
r
r
A
References:
1. Angar Jungel.
Cross-Diffusion systems with entropy structure
. arXiv:
1710.01623v1 [math.AP] 4 Oct 2017. Proceedings of EQUADIFF, (2017).
Galaktionov V.A., Kurdyumov S.P., Mikhailov A.P. and Samarsky A.A.
On
comparison of solutions of parabolic equations
. DAN an SSSR. Vol. 248, No.3,
586–589 (1979).
3. Kurdyumov S.P., Zmitrenko N.V.
N-and S-modes of compression of the
final plasma mass and features of modes with sharpening.
PMTF, No.1, 3–23 (1977)
4. Mamatov A.U.
Modeling the effect of the two-fold nonlinear heat
dissipation equation on biological population with ambient density.
Scientific
Journal of Samarkand University(2020)
«Yangi O‘zbekistonda islohotlarni amalga oshirishda zamonaviy axborot-kommunikatsiya
texnologiyalaridan foydalanish» mavzusida Xalqaro ilmiy-amaliy konferentsiya
Andijon
27-29 oktabr 2021 yil
502
INDUSTRIAL ROBOTS AND THEIR ROLE IN INDUSTRY
Kh.Kh.Nosirov, M.M.Arabboev, Sh.A.Begmatov, Sh.A.Rakhimov,
Sh.A.Bobomurodov
Tashkent university of information technologies named after Muhammad al-
Khwarizmi, Tashkent, Uzbekistan
ICT refers to any digital technology that aids individuals, companies, and
organizations in their use of information. It encompasses all electrical gadgets that
work with digital information. As a result, information and communications
technology (ICT) is concerned with the storage, retrieval, and transfer of digital data.
This subject covers a thorough examination of the influence of information and
communication technology on various areas of development and progress. The list
of industrial robots analyzed in this article is as follows: Cylindrical Robots;
Cartesian Robots; Delta Robots, SCARA robots; Articulated robots; Polar robots.
Cylindrical Robots
Cylindrical robots feature at least one rotary joint at the base and one prismatic
joint that connects the links. They can slide vertically and horizontally because to its
pivoting shaft and extended arm. They provide both linear and rotational movement
around the vertical axis [1]. The effector’s small form enables the robot to access
confined areas without losing speed.
Figure 1. Cylindrical Robots
Cylindrical robots are most commonly employed in basic applications
requiring rotational actions, such as pick-and-place. Advantages: The operation and
installation are straightforward. Minimal assembly is required. Robots can reach 360
degrees from the ground. It takes up little floor area and can carry large weights [2].
Cartesian Robots
Cartesian robots, which have a rectangular configuration, are also known as
rectilinear or gantry robots. These industrial robots provide linear motion by sliding
along three perpendicular axes (X, Y, and Z) [3]. They can handle large weights due
to their strong construction and design. They may also be utilized for picking and
placing, loading and unloading, material handling, and even high precision
activities. Gantry systems are used by the majority of 3D printers [4]. Advantages:
Provides excellent precision while being easy to use. Offline programming is simple
and extremely flexible. Capable of carrying big weights. Relatively low-cost.
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