Development of a fuzzy GERT-model for investigating common software vulnerabilities

This paper has determined the relevance of the issue related to improving the accuracy of the results of mathematical modeling of the software security testing process. The fuzzy GERT-modeling methods have been analyzed. The necessity and possibility of improving the accuracy of the results of mathematical formalization of the process of studying software vulnerabilities under the conditions of fuzziness of input and intermediate data have been determined. To this end, based on the mathematical apparatus of fuzzy network modeling, a fuzzy GERT model has been built for investigating software vulnerabilities. A distinctive feature of this model is to take into consideration the probabilistic characteristics of transitions from state to state along with time characteristics. As part of the simulation, the following stages of the study were performed. To schematically describe the procedures for studying software vulnerabilities, a structural model of this process has been constructed. A "reference GERT model" has been developed for investigating software vulnerabilities. The process was described in the form of a standard GERT network. The algorithm of equivalent transformations of the GERT network has been improved, which differs from known ones by considering the capabilities of the extended range of typical structures of parallel branches between neighboring nodes. Analytical expressions are presented to calculate the average time spent in the branches and the probability of successful completion of studies in each node. The calculation of these probabilistic-temporal characteristics has been carried out in accordance with data on the simplified equivalent fuzzy GERT network for the process of investigating software vulnerabilities. Comparative studies were conducted to confirm the accuracy and reliability of the results obtained. The results of the experiment showed that in comparison with the reference model, the fuzziness of the input characteristic of the time of conducting studies of software vulnerabilities was reduced, which made it possible to improve the accuracy of the simulation results.

Algebraization Levels in the Study of Probability

The paper aims to analyze how the different degrees of mathematical formalization can be worked in the study of probability at non-university educational levels. The model of algebraization levels for mathematical practices based on the onto-semiotic approach is applied to identify the different objects and processes involved in the resolution of a selection of probabilistic problems. As a result, we describe the possible progression from arithmetic and proto-algebraic levels of mathematical activity to higher levels of algebraization and formalization in the study of probability. The method of analysis developed can help to establish connections between intuitive/informal and progressively more formal approaches in the study of mathematics.

Mathematical Modelling and Study of Stochastic Parameters of Computer Data Processing

The main goal of dispatching strategies is to minimize the total time for processing tasks at maximum performance of the computer system, which requires strict regulation of the workload of the processing units. To achieve this, it is necessary to conduct a preliminary study of the applied model for planning. The purpose of this article is to present an approach for automating the investigation and optimization of processes in a computer environment for task planning and processing. A stochastic input flow of incoming tasks for processing is considered and mathematical formalization of some probabilistic characteristics related to the complexity of its servicing has been made. On this basis, a software module by using program language APL2 has been developed to conduct experiments for analytical study and obtaining estimates of stochastic parameters of computer processing and dispatching. The proposed model is part of a generalized environment for program investigation of the computer processing organization and expands its field of application with additional research possibilities.

Alain Badiou

Alain Badiou (b. 1937) is a leading French philosopher and European intellectual. He is the former chair of philosophy and emeritus professor at the École Normale Supérieure, one of France’s most prestigious and well-known graduate schools. His thought and political commitments, which revolve around a renewed idea of communism, were shaped by the student uprisings in France in 1968. A playwright, novelist, mathematician, and political activist, he is the author of hundreds of publications, which include novels, plays, pamphlets, criticism, political writings, and works of philosophy. Much of his earlier work focuses on the implications and consequences of the uprisings, which he submits to philosophical analysis and mathematical formalization to develop a materialist theory of the subject. Badiou achieved international prominence, however, with the publication of Being and Event, in which he grounds the question of being in mathematics, specifically set theory. His use of mathematics as a way to address the main questions of ontology—combined with meditations on art, science, politics, and love— provides the backbone of his philosophy. Badiou’s project, then, can generally be understood as focused on developing a theory of being, truth, and the subject, though in hindsight it is the question of truth, or truths, that constitutes its trajectory. Like many contemporary philosophers, Badiou, rather than considering being in light of unity or the one, considers it in terms of difference and multiplicity, whose relational organization can be grasped via formal, mathematical operations. Ontology, however, mainly serves in Badiou’s thought as a vehicle for thinking the event, or what is not being qua being. An event ruptures being, introducing novelty to closed situations or worlds. Although such events are rare, they instigate the creation of subjects who, in fidelity to an event, construct unexpected, novel truths. Following on his reading of Plato, who remains a constant inspiration for his philosophy, Badiou claims that truths can be produced in four domains: art, science, politics, and love. Philosophy, in this sense, does not produce truths but, rather, thinks them and their interrelation. Art, science, politics, and love are thus the raw materials for thought or, as he refers to them, the conditions for philosophy. The following article provides an overview of the main features of Badiou’s philosophy, including main primary texts, general overviews, anthologies, and a discussion of secondary literature related to the four conditions of philosophy. The concluding section focuses on religion, as an area that has generated a lot of discussion, perhaps against Badiou’s intent.

Calculation Method Modification of Spare Parts Quan-tity to Restore Operability of Weapon Systems

The article proposes a methodical approach to calculating the number of spare parts for weapon systems (WS) combat damage elimination and operability restoration based on criteria of minimization of spare parts cost, meeting the requirements of the spare parts, tools, supplies and materials, as well as timeliness of damaged WSs repair. The main points of the methodological approach (mathematical formalization of the task, basic calculation ratios, stages and order of calculation of spare parts stocks) are represented with a simplified scheme of the calculation of spare parts to ensure WS combat damage elimination and operability restoration. Probability of sufficiency and developed mathematical model for its calculation are used as a sufficiency indicator of spare parts to ensure WS combat damage elimination and operability restoration.

The effect analysis of the diapause duration on the hatching parameters of the artificial semi-annual population of Lymantria dispar caterpillars

The paper investigates the existence of a relationship between the diapause duration and the temperature threshold of hatching, the variances in temperature and hatching time of the artificial six-month population of Lymantria dispar caterpillars. A half-year population gives two generations a year under artificial conditions. A comparative analysis of these parameters with similar parameters of the hybrid population of L. dispar, as well as studies by other authors, has been carried out. The Eigen quasispecies model was used for the mathematical formalization of the evolution process. The results of this work can be used to study the evolution of L. dispar.

Simulation of the growth of sucrose crystals in a sugar-containing solution

Crystallization is one of the most important steps in the technological flow of commodity sugar. By its nature, it develops in a fairly wide temperature range, conditions of varying concentration of the solution, its peptization and other mass-exchange process of formation and growth of sugar crystals in a sugar solution by diffusion transfer in it sucrose molecules. To this it is necessary to add such complicating physical and mathematical formalization phenomena, affecting crystallization, such as the shape of the crystal, purity, viscous properties and surface tension of the solution, the presence of non-sugars, etc. Therefore, among the factors that determine the whole process, the factors usually take place, keeping among them only priority and most important from the point of view of the study. The article, unlike known analogues, provides justification and quantitative analysis of the kinetics of the sucrose crystallization process, taking into account the features of the crystal shape and diffusion properties of the solution. From the point of view of classical diffusion theory, the phenomenon of crystallization is interpreted as molecular with infinite rate of perilation from the source of diffusion transfer in the solution of sucrose molecules, so that the concentration in the sugar-containing liquid system is also supposed to change instantly at each point. However, since in the real world this effect is not observed, in order to resolve this contradiction, introduce the concepts of the indignant and unperturbed, separated by the diffusion front of the concentration of the regions of these phase states. Using the kinematic characteristics of the front, determine the time of the crystallization process in general in both phases. This allows us to calculate the processing period of the solution with greater accuracy than the results obtained on the basis of classical theory.

Fractal mathematical over extended finite fields Fp[x]/(f(x))

In this paper, we have defined an algorithm for the construction of iterative operations, based on dimensional projections and correspondence between the properties of extended fields, with respect to modular reduction. For a field with product operations R(x) ⊗ D(x), over finite fields, GF[(pm)n−k]. With Gp[x]/(g(f(x)), whence the coefficient of the g(x) is replaced after a modular reduction operation, with characteristic p. Thus, the reduced coefficients of the generating polynomial of G contain embedded the modular reduction and thus simplify operations that contain basic finite fields. The algorithm describes the process of construction of the GF multiplier, it can start at any stage of LFSR; it is shift the sequence of operation, from this point on, thanks to the concurrent adaptation, to optimize the energy consumption of the GF iterative multiplier circuit, we can claim that this method is more efficient. From this, it was realized the mathematical formalization of the characteristics of the iterative operations on the extended finite fields has been developed, we are applying a algorithm several times over the coefficients in the smaller field and then in the extended field, concurrent form.

ANALYSIS AND COMPARATIVE RESEARCH OF THE MAIN APPROACHES TO THE MATHEMATICAL FORMALIZATION OF THE PENETRATION TESTING PROCESS

In dynamic models, threats (vulnerabilities) can be viewed as a flow of temporary events. If the intervals of realized cyber threats are recorded, then a continuous log-list of events related to software security can be formed. In some cases and models, only the number of realized cyber threats for an arbitrary time interval can be recorded. In this case, the software response to threats can be represented only at discrete points. In static models, the implementation of cyber threats is not related to time, but the dependence of the number of errors or the number of implemented test cases (models by error area) on the characteristics of the input data (models by data area) is taken into account. The article analyzes the methods of mathematical formalization of the software penetration testing process. This software testing method is one of many approaches to testing the security of computer systems. The article substantiates the importance of the processes of preliminary prototyping and mathematical formalization. The classification is carried out and the advantages and disadvantages of the main approaches of mathematical modeling are highlighted. The list and main characteristics of dynamic and static models are presented. One of the negative factors of formalization is indicated - the neglect of the factors of a priori uncertainty in the safety parameters in static models.

Estimate of Efficiency of Class and Learning Activities based on Criterion-Oriented Testing

The research featured the views of the teaching staff of a military engineering university about didactic testing and diagnostics. It included a survey of students' learning motivation based on the achievement goal theory. The military students proved to be oriented towards improving their skills and getting new knowledge in order to achieve professional and personal growth. The article introduces a criterion-oriented estimate of efficiency methods that can be used to assess class activities and communicative interaction between the teacher and the student. The modeling process was illustrated using the mathematical formalization method. The authors believe that criterion-oriented testing can help to verify teachers' achievements. The article justifies the need to develop new criterion-oriented methodologies for identifying teachers' performance and offers a detailed algorithm that can be used in future research and verification of professional achievements.