Jalalabad State University

This is an example of a paper that will provide a numerical simulation study on analytical solutions for optimal control of solar heat supply systems (SHSS). It will develop and solve a mathematical model for the “solar collector - storage tank” subsystem using a finite element technique and standard k-epsilon turbulence closure, derive an optimal pump speed control law for maximizing heat delivery to the storage tank, through a collection of output heat functions demonstrated as quadratic with respect to flow rate G opt for each instantaneous solar insolation level J, continuously determine G opt through algorithm methodology based on microcontroller maximum heat exchange outlet temperature and non-volatile “J-G” maps in memory for rapid response to non-stationary irradiance conditions. The simulation results demonstrated that the proposed strategy can achieve a seasonal thermal efficiency increase of 11-22 percentage points compared to conventional ON/OFF differential temperature control while increasing the pressure drop only 10.3%. In addition, the thermal-enhancement of peak Nusselt number (18.9%) and Performance Evaluation Criterion (1.15) indicates that there is a net thermohydraulic benefit to implementing the proposed strategies. The results of the study quantitively identify tuning of controllers and sizing of heat exchangers in residential and commercial solar installations.

The article examines the essence of modular learning as one of the modern pedagogical technologies. The main principles, structure, and features of the organization of modular learning are revealed. Special attention is paid to the issues of individualization of the educational process, the development of students’ independence, and the improvement of learning effectiveness. The advantages and challenges of implementing the modular approach, as well as the conditions for its effective application, are analyzed. The role of the teacher in modular learning is highlighted, along with the possibilities of using this technology in various educational contexts, including distance and e-learning. The study concludes that modular learning is an effective and promising direction for the development of the modern education system.

Examines the asymptotic behavior of solutions to a system of singularly perturbed differential equations with logarithmic poles. The system under consideration possesses an equilibrium point whose stability is lost at a certain value of the slow variable. The main focus is on the phenomenon of solution delay after the loss of stability, in which the trajectory of the solution corresponding to the fast variables remains in the vicinity of the unstable equilibrium point for a finite time interval. For the analysis, the system is transformed into a complex form and reduced to a special type of integral equation. An appropriate domain is constructed in the complex plane, and the existence of a solution is proved using the methods of level curves and successive approximations. An asymptotic estimate of the solution on an interval, part of which corresponds to the unstable equilibrium, is obtained. The results clarify the influence of logarithmic poles on the system dynamics and describe the region in which the phenomenon of solution delay is observed.

The article will focus on the work of Professor Karatai Sartbayev, a scientist who has conducted research in Kyrgyz primary schools to enhance students' creative abilities. This research focuses on teaching students to express themselves through oral and written communication in the Kyrgyz language. Creative activities include performing grammatical analysis in a Kyrgyz language lesson, independent work with exercises, working with exercises, analyzing them, composing sentences, working with them verbally and factually, copying, and analyzing the material in the textbook verbally and in writing. The majority of the scientist's work focuses on teaching the above-mentioned grammatical rules and developing a reading and writing culture through the study of stylistic, spelling, and punctuation rules. The scientist emphasized the need for Kyrgyz primary schools to develop recommendations.

This article examines the application of digital tools such as Sanarip KAMPA, Google Classroom, and Quizizz in modular organic chemistry training. Examples of the practical use of digital resources in studying the topic "Hydrocarbons" are provided. It is demonstrated that the integration of digital platforms into the educational process promotes student independence, increases their learning motivation, and improves academic performance.