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SCIENTIFIC STUDY AND MATHEMATICAL STATISTICAL ANALYSIS
OF PROCESSES OF RADICALIZATION OF MILITARY PERSONNEL.
Makhmudov Nemadulla Akhmatovich
cand. physical. -mat. science., Professor of the Academy of the Armed Forces of
the RU, Republic of Uzbekistan, Tashkent.
https://doi.org/10.5281/zenodo.12798391
Key words:
Radicalism, radicalization, respondent, frequency, empirical
function, regression equation, correlation binding, correlation coefficient,
student distribution
Abstract.
The article appreciates the processes of radicalism among
military personnel and students of the military system, mathematical analysis
and scientific reasoning through a survey.
Noncommissioned officers (50) and cadets (50) were selected as
respondents in order to scientifically investigate the processes of radicalization
of military personnel.
The aim of the survey is to develop recommendations and scientifically
based proposals to solve the problem of radicalization of military personnel,
primarily the development of empirical theoretical formulas based on
mathematical-statistical laws between the upper and lower ranks, with at least
two parameters Similar, based on the laws of correlation between groups, is to
develop regression equations in order, as a result, to diagnose with great
accuracy the phenomena of radicalism that may appear in the current and future
military.In today's conditions of globalization and the existence of conflict
situations and conflicts at the international or regional level, the issue of
combating destructive ideologies such as extremism, radicalism and terrorism is
one of the current issues on the agenda. This is because most of the people who
come under the influence of extremist and radical ideas are young people and
their number is increasing. “Radicalism” – (Latin “vein”, “root”, “core”) means a
sharp, uncompromising realization of a goal, the striving to radically change the
existing situation in one or another work. Radicalism is a process that consists of
the desire to fundamentally and uncompromisingly change the existing social,
political and cultural situation of a particular person or group.Psychologists say
that young people act on the basis of inexperience and emotions, i.e. H. changes
in their mental state due to external influences; rapid depression and
intolerance to emotional shocks; to be completely removed from the attention of
loved ones; A number of factors, such as extreme curiosity and inability to fully
analyze information, and gullibility can promote the process of
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radicalization. Among the reasons why young people get involved in various
currents, it is also necessary to highlight moral and spiritual factors, such as
their knowledge, including their desire to acquire everything at once and
everything (wealth, fame, career, etc.), in scientific terms Maximalism. It should
be noted that different directions and measures are taken to counter threats in
countries around the world. In particular, our government has organized
corresponding activities in Uzbekistan. In this regard, it can be noted that this
was determined by the adoption of high-level documents aimed at preventing
the spread of radical and extremist ideas among the population, especially
among young people.
In particular, the 82nd goal of the State Program for the Implementation of
the Development Strategy of New Uzbekistan for 2022-2026 in the “Year of
Attention to the People and Quality Education”, approved by the Decree of the
Resident of the Republic of Uzbekistan dated February 28.02.2023 “Effective
Mechanisms to combat extremism and terrorism” were named. Within the
framework of this direction, the task is to organize activities to form strong and
stable immunity in the fight against extremism in the young generation
was transferred to the relevant authorities. As a practical expression of
this, under the motto "Enlightenment against Ignorance", to ensure the stability
of the social and spiritual environment, strengthen interreligious and
international harmony, fight against the ideas of terrorism and extremism,
representatives of The Committee on Religious Affairs of the Republic of
Uzbekistan, professors-teachers of the International Islamic Academy of
Uzbekistan, Imam Vukhoryu of our country, Imam Termizi and Imam Moturidi,
international scientific and research centers, are engaged in events for spiritual
and educational promotion. Propaganda activities are organized by
representatives of state and public organizations of the republic, town hall
meetings, state and non-state higher and secondary educational institutions.
As part of these events, the practice of holding discussions among students
from more than 100 universities on preventing the spread of ideas alien to
Islam, subversive views and various ideologies that deny universal human
values was introduced. At the same time, the processes of giving students
explanations about the importance of virtue principles such as love for the
country, respect for parents and teachers showed their positive state.
In addition, normative legal documents aimed at combating radicalism and
extremism have been adopted in our country, and the implementation of these
legal documents has contributed to the more effective functioning of existing
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mechanisms in this direction. In particular, new requirements for measures to
prevent extremism were introduced in our country on July 30, 2018 with the
adoption of the Law of the Republic of Uzbekistan “On Combating Extremism”.
This law expanded the definitions of extremist activities, extremist groups and
organizations, and the consequences of financing these activities.
On July 1, 2021, the National Strategy of Uzbekistan to combat extremism
and terrorism for the period 2021-2026, adopted on the basis of the Decree of
the President of the Republic of Uzbekistan, was approved. The adoption of the
national strategy can be interpreted as a historic event. The reason is that this
document defined the specific directions for combating destructive evils in the
conditions of the new Uzbekistan. Existing experience in combating extremism
and terrorism in the strategy and in the region
The specific aspect of extremist and terrorist activities as well as national,
social and religious situations were studied in Markaziu Osiuo and the situation
in combating these threats in their countries was comparatively analyzed. The
priorities of the national strategy were defined as follows:
- to promote the ideas of patriotism, traditional values and tolerance in
order to prevent the spread of the ideology of extremism and terrorism;
- Preventing the spread of extremist ideas among minors and young people;
- Protecting women's rights and strengthening their role in the fight against
extremism and terrorism;
- Protection of citizens staying abroad for a long time from the influence of
extremism and terrorist ideas;
- Fight against the use of the global information network Internet for
extremist and terrorist purposes;
- Ensuring the participation of civil society institutions and mass media in
the fight against extremism and terrorism;
- Improve measures to prosecute and prosecute extremist and terrorist
activities and their financing;
- Improving the normative legal framework in the field of combating
extremism and terrorism;
- international and regional cooperation.
Each of the tasks and directions defined in the strategy shows that the goal
is to comprehensively protect the population of our country, especially our
future generation, from radical views. In addition, through the initiative of the
leader of our country, within the framework of the framework program,
thousands of convicts were amnestied, citizens were removed from various lists,
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and more than 500 women and small children were brought to our country from
conflict zones. The “More” speeches emphasize the value of man and his freedom
is once again shown to be the highest value of society. It can be said that this
served to increase the trust of some people in society towards their country and
to create goodwill towards the state policies of the time, which was embodied in
people's minds as goodness.
German nationalism, which was initially founded to support the cultural
unity of Germans, became radicalized after some time and became extremist,
racist, anti-Semitic, anti-democratic, full of hatred for the environment, "racial
hygiene" - purifying the nation from "racial aliens" and " defective” elements
morphed into the idea of totalitarianism – National Socialism, which includes
tyranny and other negative vices. If we give an example of radicalization, a
person's concern for his nation and his homeland, his desire for his development
and freedom is a good feeling that can be an award for every person he is.
However, if someone sets moral standards aside for the sake of such a pursuit,
then he has left this circle - in the process of radicalization, he is exposed to
extremism and other serious vices.
As President Shavkat Mirziyoev explained
“We will not allow any kind of radicalization in our society, no poisoning of
the minds of our youth with destructive foreign ideas, no misuse of religion for
political purposes, no replacement of enlightenment with ignorance” [1]
“So that our young people become independent thinkers, have high
intellectual and spiritual potential and become people who are not inferior to
their peers in any field of the world, we mobilize all the forces and capabilities of
our state and society to be happy “we deliver” [2]
Results and analysis
We present the results of scientific research (observation) in the form of a
table. There are basically one hundred survey questions and each question is
worth
1
point
or
1
percent.
First
of
all
𝑥
1
– patriotism 24,
𝑥
2
– humanitarianism 14,
𝑥
3
– faith 17,
𝑥
4
– trust 18,
𝑥
5
– will 10,
𝑥
6
- pride 15,
𝑥
7
- compromise 8,
𝑥
8
– compassion consists of 4 questions, and each number out of a hundred is
proportional to this percentage.
For example, 14 questions are given 14%. The appearance of this diagram is
presented in the form of a histogram or graph, and we perform a mathematical
statistical analysis.
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We present the results of our scientific research (based on a survey)
conducted in order to protect military personnel and cadets from the influence
of radicalism under the Ministry of Defense of the Republic of Uzbekistan.
The results of questionnaires about the attitudes of sergeants and cadets to
the processes of radicalism.
Table 1.1
N
Respondents
𝑥
1
𝑥
2
𝑥
3
𝑥
4
𝑥
5
𝑥
6
𝑥
7
𝑥
8
To
tal
score%
1
Sergeants
20
12
5
14
9
13
7
2
82
2
Cadets
18
13
6
14
9
14
3
3
80
3
Volume
of
conducted
surveys
(frequency)
7
4
7
8
4
4
10
6
𝑛 = 50
4
Classical
probability
0.14
0.08 0.14 0.16 0.08
0.08
0.20
0.12
𝑝 = 1
We compare the parameters of the cadets and the sergeants who are their
leaders.
Х
𝑖
- variants of the obtained scientific research,
𝑛
𝑖
– frequency of the
observed or studied object. Based on the results of table 1.1, we draw up the
empirical function of the respondents. Empirical distribution function (sampling
distribution function) is each
𝑥
for the value
𝑋
,
𝐹
∗
(𝑥) =
𝑛
𝑥
𝑛
is said to be likely.
Here
𝑛
𝑥
-
𝑥
is smaller than,
𝑥 ≤ 𝑥
1
at
𝐹
∗
(𝑥) = 0
,
𝑥
𝑛
–
even if it is the biggest
option.
In short, the empirical function of the sample distribution serves to estimate
the theoretical function of the population distribution.
𝑋
𝑛
we place the options in
ascending order
Table 1.2 shows the responses of the sergeants to the survey questions
1.2 - table
№
options
(consequence)
𝑋
𝑖
2
5
7
9
12
13
14
20
1
.
Frequency
(repetition of an
event)
𝑛
𝑖
6
7
10
4
4
4
8
7
2
.
...
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The size of the tests
𝑛
𝑖
= 𝑛
1
+ 𝑛
2
+ 𝑛
3
+ 𝑛
4
+ 𝑛
5
+ 𝑛
6
+ 𝑛
7
+ 𝑛
8
= 50
The smallest option is equal to 2, so
𝑥 < 2
at
𝐹
∗
(𝑥) = 0
,
𝑥 ≤ 5
value,
𝑥
1
= 2
; 6 repeated times
2 < 𝑥 ≤ 5
dа
𝐹
∗
(𝑥) =
6
50
= 0,12
𝑥 ≤ 7
values, including
𝑥
1
= 2
;
𝑥
2
= 5
; qiymаtlаr 6+7=13times is observed,
then
5 < 𝑥 ≤ 7
dа
𝐹
∗
(𝑥) =
13
50
= 0,26
𝑥 ≤ 9
values, including
𝑥
1
= 2
;
𝑥
2
= 5
;
𝑥
3
= 7
; values, 6+7+10=23 times is
observed, then
7 < 𝑥 ≤ 9
dа
𝐹
∗
(𝑥) =
23
50
= 0,46
𝑥 ≤ 12
values, including
𝑥
1
= 2
;
𝑥
2
= 5
;
𝑥
3
= 7
;
𝑥
4
= 9
values,
6+7+10+4=27 times is observed, then
9 < 𝑥 ≤ 12
da
𝐹
∗
(𝑥) =
27
50
= 0,54
𝑥 ≤ 13
values, including
𝑥
1
= 2
;
𝑥
2
= 5
;
𝑥
3
= 7
;
𝑥
4
= 9
;
𝑥
5
= 12
; qiymаtlаr
6+7+10+4+4=31 times is observed, then
12 < 𝑥 ≤ 13
da
𝐹
∗
(𝑥) =
31
50
= 0,62
𝑥 ≤ 14
values, including
𝑥
1
= 2
;
𝑥
2
= 5
;
𝑥
3
= 7
;
𝑥
4
= 9
;
𝑥
5
= 12
;
𝑥
6
= 13
values, 6+7+10+4+4+4=35times is observed, then
13 < 𝑥 ≤ 14
da
𝐹
∗
(𝑥) =
35
50
= 0,70
𝑥 ≤ 20
values, including
𝑥
1
= 2
;
𝑥
2
= 5
;
𝑥
3
= 7
;
𝑥
4
= 9
;
𝑥
5
= 12
;
𝑥
6
= 13
;
𝑥
7
= 14
values, 6+7+10+4+4+4+8=43 times is observed, then
14 < 𝑥 ≤ 20
,
𝐹
∗
(𝑥) =
43
50
= 0,86
𝑥 > 20
dа
𝐹
∗
(𝑥) = 1
As a result of scientific research, the calculated theoretical empirical
distribution function is expressed as follows:
𝐹
∗
(𝑥) =
{
𝑥 < 2 𝑑а 0
2 < 𝑥 ≤ 5 𝑑а 0.12
5 < 𝑥 ≤ 7 𝑑а 0.26
7 < 𝑥 ≤ 9 𝑑а 0.46
9 < 𝑥 ≤ 12 𝑑а 0.54
12 < 𝑥 ≤ 13 𝑑а 0.62
13 < 𝑥 ≤ 14 𝑑а 0.70
14 < 𝑥 ≤ 20 𝑑а 0.86
𝑥 > 20 𝑑а 1
(1.1)
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𝐹
∗
(𝑥)
1
0.5
1
4
3
2
0
5
7
6
8
10
9
11
13
12
14
15
17
16
18
19
21
20
22
We construct the empirical function we are looking for:
Figure 1.1
Figure 1.1 depicts the graph of the empirical distribution function
(theoretical analysis) of the scientific results of military sergeants based on
questionnaires
As a result of scientific research - Sergeants - and cadets - received
according to the results of the survey, both groups of respondents took part, and
the correlation of the answers to 100 questions of eight types that are important
for the military and the regression we construct equations (lines).
𝑀(𝑋) ≈ 𝑥 = ∑
/𝑛
𝑛
𝑖=1
;
𝑀(𝑌) = ∑
/𝑛
𝑦
𝑖=1
≈ 𝑦
;
(1.2)
σ
𝑥
2
=
∑
𝑋
𝑖
2
𝑛
𝑖=1
𝑛
− 𝑥
2
,
σ
𝑦
2
=
∑
𝑌
𝑖
2
𝑛
𝑖=1
𝑛
− 𝑦
2
;
𝐶
𝑥𝑦
=
∑
𝑋
𝑖
𝑌
𝑖
𝑛
𝑖=1
𝑛
− 𝑥 𝑦
Here you can find the correlation coefficient using the following formula:
𝑟
𝑥𝑦
=
𝐶
𝑥𝑦
σ
𝑥
σ
𝑦
We find the straight line of regression of Y on X from the data presented in
Table 1.3
1.3.table
№
𝑋
𝑖
Serjan
tlar
𝑌
𝑖
Kursa
ntlar
𝑋
𝑖
2
𝑌
𝑖
2
𝑥
𝑖
𝑦
𝑖
I
zоh
1.
20
18
400
324
360
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2.
12
13
144
169
156
3.
5
6
25
36
30
4.
14
14
196
196
196
5.
9
9
81
81
81
6.
13
14
169
196
182
7.
7
3
49
9
21
8.
2
3
4
9
6
n
=5
0
∑ = 82
𝑋
𝑖
∑ = 80
𝑌
𝑖
∑ = 1068
𝑋
𝑖
2
∑ = 1020
𝑌
𝑖
2
∑
= 1032
𝑋
𝑖
𝑌
𝑖
From the table we get the following:
∑
𝑥
𝑖
= 82
8
𝑖=1
;
∑
𝑦
𝑖
= 80
8
𝑖=1
;
∑
𝑥
𝑖
2
= 1068
8
𝑖=1
;
∑
𝑦
𝑖
2
= 1020
8
𝑖=1
;
∑
𝑥
𝑖
𝑦
𝑖
= 1032
8
𝑖=1
(1.3)
𝑥̅ =
∑
𝑋
𝑖
8
𝑖=1
𝑛
=
82
50
= 1.64
;
𝑦̅ =
∑
𝑌
𝑖
8
𝑖=1
𝑛
=
80
50
= 1.60
;
↑ σ
𝑥
2
=
∑
𝑋
𝑖
𝑛
𝑖=1
2
𝑛
− 𝑥̅
2
=
1068
50
− 2.68 = 18.67
;
σ
𝑥
= 4.32
;
σ
𝑦
2
=
∑
𝑌
𝑖
2
𝑛
𝑖=1
𝑛
− 𝑦̅
2
=
1020
50
− 2.56 = 17.84
;
σ
𝑦
= 4.22
;
𝐶
𝑥𝑦
=
∑
𝑋
𝑖
𝑌
𝑖
𝑛
𝑖=1
𝑛
− 𝑥 𝑦 =
1032
50
− 1.64 ∙ 1.60 = 20.64 − 2.62 = 18.02
If the multiplication
|𝑟
𝑥𝑦
| ∙ √𝑛 − 1 ≥ 3
if there is a correlation between the
values of X and Y (X-officers and Y-cadets) taken at random, it will be sufficiently
probable. That is, it shows that there is a possible linear relationship between
them. If a linear approximation is established between X and Y,
𝑦̅
𝑥
from x to
the linear regression formula is written as follows.
The linear regression equation is as follows
𝑦̅
𝑥
− 𝑦̅ = 𝑟
𝑥𝑦
∙
𝜎
𝑦
𝜎
𝑥
(𝑥 − 𝑥̅)
(1.4)
If we put the obtained results into the formula (1.4) and calculate,
𝑦̅
𝑥
− 1,60 = 0,99 ∙
4,22
4,32
(𝑥 − 1,64)
;
𝑦̅
𝑥
− 1,60 = 0,96 ∙ (𝑥 − 1,64) = 0,96𝑥 −
1,57
;
𝑦̅
𝑥
= 0,96𝑥 + 1,60 − 1,57 = 0,96𝑥 + 0,03
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𝑦̅
𝑥
= 0,96𝑥 + 0,03
as well as
𝑥̅
𝑦
− 𝑥̅ = 𝑟
𝑥𝑦
∙
𝜎
𝑥
𝜎
𝑦
(𝑦 − 𝑦̅)
(1.5)
𝑥̅
𝑦
− 1,64 = 0,99 ∙
4,32
4,22
(𝑦 − 1,60)
;
𝑥̅
𝑦
− 1,64 = 1,01(𝑦 − 1,60) = 1,01𝑦 −
1,62
;
𝑥̅
𝑦
= 1,01𝑦 + 0,02
A correlation table representing the ratio of to and
Table 1.4
№
𝑋
𝑖
Serge
ants
𝑌
𝑖
Stude
nts
𝑦̅
𝑥
𝑥̅
𝑦
𝑦̅
𝑥
− 𝑥̅
𝑦
1
20
18
19,32
18,20
1,11
2
12
13
11,60
13,15
-1,56
3
5
6
4,84
6,08
-1,24
4
14
14
13,53
14,16
-0,64
5
9
9
8,70
9,11
-0,41
6
13
14
12,56
14,16
-1,60
7
7
3
6,77
3,05
3,72
8
2
3
1,95
3,05
-1,11
Based on the data presented in the correlation table 1.4 below, we
construct the equations of the regression straight lines of .
𝑌
𝑥
ഥ
1
4
3
2
0
5
7
6
8
10
9
11
13
12
14 15
17
16
18 19
21
20
22 23
х
х
х
х
х
х
х
х
4
2
6
8
10
12
14
16
18
20
22
24
26
4
2
6
8
10
12
14
16
18
20
22
24
26
𝑥
𝑖
ഥ
𝑋
𝑦
̅̅̅̅
𝑦
𝑖
ഥ
x -
𝑦
𝑥
̅̅̅ = 0,96𝑥 + 0,03
y -
𝑥
𝑦
̅̅̅ = 1,01𝑦 + 0,02
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Figure 1.2
Figure 1.2 shows the regression equations representing the attitudes of
sergeants and cadets to the process of radicalization
In order to evaluate the real value of the conducted scientific research, the
real value is unknown, with equal (same) accurac
𝑛 = 50
let it be the results of
the trial conducted once. The results of separate studies
𝑥
1
, 𝑥
2
, 𝑥
3
, … 𝑥
𝑛
as a
random variable. These quantities are arbitrary, have the same mathematical
expectation (the true value of the sought (measured) quantity), the same
𝜎
2
(𝑥
1
)
dhave ispersils and are normally distributed (experiments confirm this
assumption). The actual value of the scientific research (quantity being
measured) is equal to its mathematical expectation. Therefore, the problem is
the mathematical expectation
𝜎
–mean square deviation,
𝑥̅
– arithmetic mean
value and mathematical expectation
𝛾 = 0,95
based on the double inequality
with reliability values, it is given in intermediate evaluation. Thus, using the
Student's distribution, it is unknown
𝑎
parameter
𝛾
(0.95, 0.99, 0.999) which
determines with reliability
𝑥̅ − 𝑡
𝛾
∙
𝜎
√𝑛
< 𝑎 < 𝑥̅ + 𝑡
𝛾
∙
𝜎
√𝑛
(1.6)
we find the confidence interval (interval). First of all, we will consider the
mathematical statistical analysis of the reliability of the composition of the
sergeants, the validity of the scientific research conducted on the basis of
questionnaires, the accuracy of the assessment;
From table 1.3
𝑥̅ = 82, 𝜎
𝑥
= 4.32
va
[𝑥]
app 3
𝑡
𝛾
= 𝑡(𝛾; 𝑛)
𝑛 = 50
;
𝑡
𝛾
(0,95; 50) = 2,009
[3]
(1.6) using the formula
82 − 2,009 ∙
4,32
√50
< 𝑎
𝑎𝑠
< 82 + 2,009 ∙
4,32
√50
82 − 8,67 ∙
1
7,07
< 𝑎
𝑎𝑠
< 82 + 8,67 ∙
1
7,07
82 − 1,23 < 𝑎
𝑎𝑠
< 82 + 1,23
80,77 < 𝑎
𝑎𝑠
< 83,23
The conclusions are that the processes of radicalism were mathematically
analyzed in the section of military personnel (in today's era of globalization). On
the eight most basic subjects, sergeants and cadets were rated with 0.95 (95%)
accuracy and 0.05 (5%) deviation. Table 1.4 shows that the patriotism of
sergeants and cadets-
𝑥
1
, trust -
𝑥
4
, the will -
𝑥
5
and pride-
𝑥
6
the answers to the
relevant questions are almost the same, from which it can be concluded that
DEVELOPMENT OF PEDAGOGICAL TECHNOLOGIES IN
MODERN SCIENCES
International scientific-online conference
55
their outlook on such questions is the same. It is noteworthy that humanitarian
pride and indomitable will had the same answer, so the regression line
𝑀(13; 14)
at the point
𝑦
𝑥
̅̅̅
and
𝑥
𝑦
̅̅̅
(
𝑦
𝑥
̅̅̅
-trust of sergeants to cadets, and the
relationship of cadets to sergeants) shows that it is the closest (see Figure 1.2). It
should be noted that the interim assessment obtained by sergeants and cadets
based on the theoretical results of our scientific work on the processes of
radicalism
80,77 < 𝑎
𝑎𝑠
< 83,23
.
Today, it is considered a high result, the practical proof of this is that
institutions belonging to the Ministry of Defense of the Republic of Uzbekistan
record record results in the world Olympiads, as a clear fact, professional
training took place at the Chirchik Oliy Tank Command Engineering Educational
Institution. the international science olympiad among the cadets can be cited as
an example.
It is not without benefit to carry out such a questionnaire suddenly, during
work processes or during military service recruitment. As a proposal, we believe
that it is possible to eliminate or reduce the tendency of young people to this
process, if questions adapted to the processes of radicalism are created in
mathematics lessons in militarized lyceums and schools. For example, we can
use it in classes of grouping, substitution, combinatorics elements.
References:
1. O‘zbekiston Respublikasi Prezidenti Shavkat Mirziyoyevning Oliy Majlis va
O‘zbekiston xalqiga murojaatnomasi. www.prezident.uz
2. O‘zbekiston Respublikasi Prezidenti Shavkat Mirziyoyev “ERKIN VA
FAROVON, DEMOKRATIK O‘ZBEKISTON DAVLATINI BIRGALIKDA BARPO
ETAMIZ” Toshkent-“O‘zbekiston”-2016.
3. Gmurman V E. “Ehtimollar nazariyasi va matematik statistika” O‘qituvchi T-
1988.
4. Rasulov A. S, Raimova G.M, Sarimsakova X. K “Ehtimollar nazariyasi va
matematik statistika” Toshkent-2006
