PSI - Issue 65

Dumanskaya E.I. et al. / Procedia Structural Integrity 65 (2024) 75–82 Dumanskaya E.I., Emelyanov I.G. / Structural Integrity Procedia 00 (2024) 000–000

77 3

D t

C t sS d c 

( )) t

kR t

( ) ( ( ) 

( ),



(2)

where k is the proportionality factor. The implication of equation (2) is that the risk of committing a crime will be greater in a person who has a greater function of personality dangerousness � and has greater negative personal characteristics. Let's consider the ultimate scenario of the crime. If a crime has committed, the probability of committing it is therefore one

1.  p

(3)

Let us assume that the set of personal characteristics and the set of negative social processes have the maximum possible significance, therefore,

(4)

[ ( ) C t

sS d

( )] 2.  t



c

Normalize equation (4) by dividing it by 2

( )] 2 1. 1    (5) Taking into account equations (2) and (5), we get that the proportionality coefficient k = 2, and the function of a person's danger � at the time of a crime under the most unfavorable external conditions and the maximum set of negative personal characteristics is equal to one ( ) 1.  D t (6) Under more favorable external conditions, (� � +�� � )<1 the function of personality dangerousness at the time of the crime will be greater than one �(�)>1. Since the process of committing a crime is a non-stationary process that depends on time and on many preceding events the probability of committing a crime will depend on the accumulated negative " burden " on a person over a certain period of time. Probably, it is appropriate and correct to define this period as the time of the person's life under study from birth to the crime � � . Let us introduce a hypothesis that the risk of crime over a certain period of time is equal to the density of the probability of committing a crime �(�) . Thus, the mathematical model of the function of personality criminal behavior can be represented as [ ( ) t C t sS d c 

T L

( ) 2 [( ( ) 1  

D t

C t sS d c 

( ) f t t dt  ( )]

(7)

0 

Since we consider the behavior of a person who committed a crime, the integral of the probability density of committing a crime is equal to

( )  f t dt L T

1. (8) Equation (7) is an integral equation that contains the desired function of the personality dangerousness � under the sign of the integral, Kantor (1990), Emelyanov (2023). And if the rule of the probability density distribution is known, then equation (7) is analogous to the Fredholm integral equation of the first kind (1). Since it is not possible to determine the kernel of integral equation (7) analytically from any social regularities, this equation can only be solved by numerical methods. In mechanics, when solving problems that are described by 0 