Bulletin of L.N. Gumilyov Eurasian National University. Mathematics, computer science, mechanics series

Machine learning algorithms in SIEM systems for enhanced detection and management of security events

A.M. Nurusheva — 2024-09-30

As cyber threats become increasingly sophisticated, traditional Security Information and Event Management (SIEM) systems face challenges in effectively identifying and responding to these dangers. This research presents the development of a SIEM system integrated with machine learning (ML) to enhance threat detection, anomaly identification, and automated incident response. The integration of ML allows the SIEM system to go beyond conventional rule-based approaches, enabling the detection of previously unknown threats by learning from historical data. The system employs advanced algorithms to analyze large-scale log data and network traffic, providing real-time insights and reducing false positives. Key features of this SIEM include anomaly detection, predictive analytics, and adaptive thresholds, which allow it to adjust dynamically based on contextual data. By adapting to new and evolving cyber threats, the system provides a more resilient and proactive defense against potential attacks. The results indicate that integrating machine learning into SIEM systems can offer organizations a more effective, scalable, and adaptive security solution, ensuring the protection of critical infrastructure and data in a rapidly changing digital landscape.

Kernel of triangular derivation of the ring of polynomial of rank 3

Shynar Abutalipova — 2024-09-30

Let $k[x_1,x_2,x_3]$ be an algebra of polynomials in variables $x_1,x_2,x_3$ over an arbitrary field $k$ of characteristic $0$ In this paper we consider triangular derivations of the form $D=\alpha x_2^l x_3^m \partial_1+\beta x_3^n \partial_2+\gamma \partial_3,$ where $\alpha ,\beta ,\gamma \in k$, of the algebra $k[x_1,x_2,x_3].$ It is well known that triangular derivations of the algebra $k[x_1,x_2,x_3]$ are locally nilpotent. The algorithm of A. van den Essen for computing the kernel of locally nilpotent derivation of the polynomial algebra $k[x_1,x_2,\ldots,x_n]$ in variables $x_1,x_2,\ldots,x_n$ over a field $k$ of characteristic $0$ uses the map of J. Dixmier. M. Mayanishi’s theorem states that the kernel of locally nilpotent derivation of the algebra of polynomials in three variables over the field of characteristic 0 is the algebra of polynomials in two variables. In this paper, a completely new algorithm for computing the kernel of triangular derivation of the algebra of polynomials of rank 3 over a field of characteristic 0 is constructed.

Kazakh mathematical justice in school education is equal conditions for all in teaching textbooks and teachers

Nurlan Temirgaliyev — 2024-09-30

Equity in school mathematics education ideally means providing students with the opportunity to realize their potential through the provision of public responsibility for the means to achieve "Mathematical Maturity" in full and in detail. To gain an understanding of the nuances of this concept, it is enough to delve into just one topic of elementary school mathematics curriculum. Select an arbitrarily unit segment, build two segments with lengths of ordinary fractions with different denominators and make sure that it is impossible to compare them in length in numerical terms. Then, appreciate the remarkable ability of Mathematics, to provide a solution to what would otherwise appear to be an insoluble problem.

In the educational process, it is essential to differentiate between the state and the student. The first provides the opportunity to obtain knowledge, but is not to answer for the second. However, there must be moral and material motivation to obtain high-quality knowledge. In his teachings, wise Abay cautioned that the word from the educated though demanding, can illuminate the path to understanding. He urged to perceive the light and mystery that surrounds us. With his words "Aitshy-aytshyp zhalynar, Uqqysh zhansyp shabynar. Uqpay zhatyp zhalyǵar, uıqyly-oıaý boıkúıez", which translates as ‘mindless boredom, drowsiness’, he emphasised the importance of remaining alert and awake to the world around us. In the absence of boredom, sleepiness", as in the case of personal transformation of the individual and the principle of "you can lead a horse to water, but you cannot make it drink".

The concept of "Justice" is a multifaceted topic in the International Educational Space. It is the universal division between "Global North" and the "Global South", where the former has a stronger economy, infrastructure and technology, while the latter is characterized by less diverse economy, by poverty and inequality and a history of colonization by the countries of the Global North. These studies adopt from various points of views: sociological, economic, pedagogical, legal and political, as well as various professional approaches such as "Fair education from the standpoint of textbook quality" or "Development and implementation of programs that take into account the needs of different groups of students", "Evaluation of the effectiveness of pedagogical strategies aimed at eliminating educational inequality", and "The role of technology in providing access to education", etc.

This article is a presents a methodically structured National Program of the Republic of Kazakhstan, based on many years of experience and previously developed ideas, the result will be noticeable in a few years.

Every hour of delay makes one math lesson in all classes and for each student unschoolable, and damages the State in man-hours in the number of all students: "I, Nurlan Temirgaliyev, as a direct specialist, demand to declare a "State of emergency for the current state of mathematics and computer science of the Republic of Kazakhstan!" dated 04/13/2015 and, earlier, since 1974; "Save the future of a capable boy Imanbek" dated 01/31/2019; "Galiya Taugynbayeva alone can conduct an indisputable examination of all approved by the Ministry of Education and Science of the Republic of Kazakhstan in 13 calendar days textbooks on school mathematics" dated 07/12/2020; "The education and Science system of 30-year-old independent Kazakhstan turns a Kazakh, even if with the rudiments of Ramanujan's thinking, into a Mathematical Mowgli" dated 11/14/2021; "The academic year ended 2023-2024 for 5 million teachers and students was non-educational in all School mathematics, in Higher education in all specialties based on Mathematics, and this is in the presence of the National ITMandSC Program for elevation in Mathematics, Computer Science and AI-ML to World leading positions, which cannot be ordered with execution even for 10 annual budgets of the Republic of Kazakhstan" from 1.07.2024;Admission to teaching "First, complete theoretical training in the subject, only then the methodology, including understanding the accessibility or inaccessibility to assimilation by students and not the other way around" on the example of just one problematic topic "Comparison of ordinary fractions with different denominators of "Elementary school". To adopt in the form of a Law "Those who have made demonstrative scientific and methodological mistakes in textbooks and scientific publications, official reviews are included in the "Blacklist of a specialized institution" with lifelong excommunication from the sphere of activity of this department, there will be no losses from this, only recovery will occur, , never learned at the time never learned, cannot teach without knowledge itself" from 10/30/2024, numerous of the same earlier and later dates.

Study of the positional cross-section of acoustic wave scattering for a system of sound-permeable spheres

Эльвира Насибуллаева — 2024-09-30

In the frame of solving the acoustic scattering problem on a system consisting of many sound-permeable spheres, one of the main characteristics of the scattering phenomenon, namely, the positional scattering cross-section, is investigated. This characteristic allows one to analyze the intensity of a scattered wave in a fixed direction. The formula for this characteristic is transformed in the case of many scatterers, taking into account the interaction between the spheres in the system. This formula is applicable to any number of spheres in the system and their arbitrary distribution in 3D space. Two types of external pressure are considered --- a plane wave and a spherical wave from a monopole radiation source. The numerical algorithm is verified with the data of other numerical studies; qualitative agreement between the results is obtained. Numerical parametric analysis for a system consisting of two sound-permeable spheres showed that in the case when the density of the medium inside the spheres is much less than the surrounding medium, the system has the best scattering properties; backscattering in a system with spheres of the same radius is higher than in a system with spherical particles of different sizes; for a plane wave, an increase in the wave radius leads to a decrease in the value of the backscattering cross-section function, while for a monopole radiation source, an increase in the wave radius leads to an increase in this value. For a system containing a 121~drop of water in air, it was found that an increase in the distance between the centers of the spheres leads to an increase in the scattering properties of this layer in the opposite direction.