Karlygash Nurtazina

The notion of “randomness” in the mathematical theory of composites has typically been used abstractly within measure theory, making practical applications difficult. In contrast, engineering sciences often discuss randomness too loosely, lacking a theoretical foundation. This paper aims to bridge the gap between theory and applications, focusing on the effective properties of two-dimensional conducting composites with non-overlapping circular inclusions. It is shown that there is no universal minimum number of inclusions per cell in simulations of random composites. Even minor changes to Random Sequential Addition algorithms lead to different formulas for the effective constants. Application of the analytical representative volume element (aRVE) theory methodologically and practically addresses the diversity issue of random composites based on homogenization principles. In particular, it examines how the spatial arrangement of inclusions impacts the overall composite properties. The proposed method can be applied to a large number of inclusions and to symbolically given geometric and physical parameters relevant to optimal design problems. The method leverages structural sums and enables a more refined classification of different classes of composites, which was unattainable using previous approaches. The obtained results demonstrate a diversity of apparently similar composites. This paper outlines the investigation strategy and provides a detailed description of each step.

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 ITMiNV 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.