This study explores the role of intercultural communicative competence (ICC) and STEM education in building the soft infrastructure necessary for economic development within Kazakhstan’s transforming education system. The authors conducted an interdisciplinary analysis, emphasizing the cognitive and communicative aspects of foreign language education in secondary schools, proposing a model for integrating ICC through the use of information and analytical technologies. The research focuses on personalized education, teacher competencies, and student engagement, with experimental methods applied in a Karaganda-based school. The study aims to identify mechanisms and principles that enhance ICC development, contributing to Kazakhstan’s modernization efforts in fostering globally competitive graduates prepared for the demands of the international arena. This research lays the foundation for further practical experimentation in profiled schools, aligning education with national development goals.

Usually in the study of limit problems, will encounter more complex problems, in this paper, we discuss how to use the concept of equivalent infinitesimal better limit operation. At the same time, in the process of research, we re-explore the proof of Taylor's formula, and find that some functions have a similar expansion form to Taylor's formula, that is, 'fractional expansion'. It is also found that after the linear combination of Taylor expansion and fractional expansion, the obtained expansion is more accurate, which helps us to have a better understanding of the approximation of function expansion.

This paper presents the state of displacement of a multilayered composite laminate subjected to transverse static load with varying balance, symmetric and anti-symmetric angle-ply and cross-ply staking sequences. Higher-order shear deformation theory (HSDT) is considered in the finite element formulation of nine-noded isoparametric element with seven degrees of freedom at each node. The finite element formulation is transformed into computer codes. A convergence study is carried out first to obtain the optimal mesh size for minimizing the computational time. The maximum deflection at the center of plate for both fixed and simply supported edges is verified with reported literature and a good conformity is found. An attempt has been made to observe the minimum value of maximum deflection in the laminate for attaining the maximum strength of laminate with a suitable combination of stacking sequences with a constant volume of material.

The Western capitalist system is an important part of the economy and society of the contemporary world, and it has played a huge role in the past few centuries. Nonetheless, with the continuous development of globalization, technological revolution and social change, the Western capitalist system is also facing a series of difficulties and new changes. This paper aims to explore the dilemma facing the Western capitalist system today, and to analyze and discuss the new changes.