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

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2. Problem statement and terminology

The present article studies the model of personality criminal behavior, which is achieved by solving the task of determining the function of the personal's danger. The mathematical formalization of the problem boils down to the fact that on the left side of the equation is written some unknown function of the danger of the personality D, which depends on personality traits and social determinants over a certain period of time. And on the right-hand side of the equation, there is the probability of committing a crime p during the same period. The proposed model is reduced to the Fredholm integral equation of the first kind, Grigolyuk and Tolkachev (1987), Kantor (1990), Emelyanov (2023) (1) where �(х) and �(х,�) are known functions; �(�) - unknown function. The variable х , accepts, as well as � all values from the interval ( a, b ). The function �(х,�) is called the kernel of an integral equation and, for example, in shell theory, has a simple physical meaning. This is a Green's function that determines the deflection of the shell at point x from the force acting at point Kantor (1990), Emelyanov (2023). Thus, if the rule is given �(х) and the kernel �(х,�) of the integral equation is constructed, then after the solution of equation (1), the desired function of the personal's danger is determined. To model personality criminal behavior, the functions of quantitative significance were used, Emel’yanov and Dumanskaya (2022). This is the function of the personality Cc (Characteristic of Criminal) - a negative characteristic of the personality traits, which determines the likelihood of recidivism. This function depends on time t and is determined by a set of significance obtained by observing the person's life. The quantitative meaning of this function can vary within 0≤С � (�)≤1. The function � � (�) ( Social determinants) is determined by negative social processes in society and increasing the likelihood of recidivism. This function also has a quantitative meaning within 0≤� � (�)≤1 . The usage of the С � (�) and � � (�) function, which varies from zero to one, is similar to the damage function in materials mechanics, which is used in the study of damaged material, Kachanov (1958), Rabotnov (1991). The influence of different types of damage on the deformation process characteristics is known to be carried out with the scalar function ω - the measure of damage. Value of ω varying with value ω=0 for intact material , ω=1 for completely destroyed material . To model personality criminal behavior, the function � ( Personality dangerousness ) is used. This function determines the danger of the person, that is the tendency to commit a crime. This function also depends on time t and is determined by solving the problem of modeling person's behavior process, such as before and at the time of the crime. Since the personality of criminal can differ in suggestibility or susceptibility to social processes, the coefficient s (Suggestibility) is used. This coefficient is determined by the psychophysiological characteristics of the personality and has a quantitative value within 0≤�≤1 . At the same time, it is fixed that at case s =0 the personality is not susceptible, and at case s =1 it is highly susceptible to various social processes in society. Thus, it is believed that any person at any moment of time is under the influence of personal characteristics and a number of negative social processes in society. Taking into account the different susceptibility of the individual, the negative "burden" on a person can be represented as the sum of the influences on the person � � (�)+�� � (�) at every moment of time. 3. Solving equation and accepted hypotheses. In criminological research, there is a concept of the risk of committing a crime R (Risk assessment). The risk is known as a quantitative measure of danger or the frequency of the danger's appearance, the probability of the occurrence of one event when another occurs. Hence, risk, like a probability, can be estimated by a dimensionless quantity 0≤�≤1 . Obviously, the risk of committing a crime R is proportional to the multiplication of the function of personal criminal behavior and the function of negative "burden" on the person ( ) ( , ) ( ) K x D d p х b a     