This study examines a novel use of the Jacobi elliptic function expansion method to solve the Shynaray-IIA equation, a significant nonlinear partial differential equation that arises in optical fiber, plasma physics, surface symmetry geometry, and many other mathematical physics domains. This kind of solution has never been attained in research prior to this study. Numerous properties of a particular class of solutions, called the Jacobi elliptic functions, make them useful for the analytical solution of a wide range of nonlinear problems. Using this powerful method, we derive a set of exact solutions for the Shynaray-IIA equation, shedding light on its complex dynamics and behaviour. The proposed method is shown to be highly effective in obtaining exact solutions in terms of Jacobi elliptic functions, such as dark, bright, periodic, dark-bright, dark-periodic, bright periodic, singular, and other various types of solitons. Furthermore, a detailed analysis is conducted on the convergence and accuracy of the obtained solutions. The outcomes of this study extend the applicability of the Jacobi elliptic function approach to a novel class of non-linear models and provide valuable insights into the dynamics of Shynaray-IIA equation. This study advances the creation of efficient mathematical instruments for resolving intricate nonlinear phenomena across a range of scientific fields.

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We investigate a unified dark-energy scenario based on the combined effects of Barrow entropy corrections and the QCD ghost mechanism, referred to as the BH--QCDGDE model. The dark-energy density is constructed in a generalized holographic form that incorporates both Barrow-deformed entropy corrections and low-energy QCD vacuum effects within a single framework. The cosmological dynamics are analyzed in a spatially flat Friedmann--Lemaître--Robertson--Walker background. The model exhibits a smooth transition from a decelerated matter-dominated era to a late-time accelerated phase without crossing the phantom divide, indicating a viable background evolution. An equivalent scalar-field description of the effective dark-energy sector is reconstructed and shown to admit a quintessence-like behavior. The thermodynamic viability is examined by testing the generalized second law at the apparent horizon, which is found to be satisfied throughout the parameter space. The classical stability of the model is further investigated through the squared speed of sound, revealing the role of model parameters in shaping stable cosmological regimes. Overall, the BH--QCDGDE framework provides a consistent and physically viable description of late-time cosmic acceleration.

In the context of modern educational realities, characterized by strict criteria for assessing students' knowledge, high academic workload, reduced hours of study, as well as outdated and insufficient equipment, the problem of improving the quality of education is becoming particularly acute. In this regard, the training of specialists within the framework of the credit education system highlights the need to develop new conceptual approaches to the organization of educational and methodological activities and the active introduction of modern information and communication technologies into the educational process. This implies the widespread use of information technology and personal computers for modelling a variety of physical phenomena, both in the framework of training and in the implementation of ongoing knowledge control. This paper demonstrates that the use of modern applied software packages in the educational process can significantly transform the methodology of studying certain sections of the physics course, providing visual visualization of the results of solving problems using these applied tools. For a clearer demonstration of physical phenomena, this article presents modelling of complex systems described by second-order differential equations using the MathCad software environment. Using the odesolve function built into Mathcad, a graph of the addition of two harmonic oscillations was obtained. The method of solving differential equations presented in this paper can be used to model various other physical processes considered in the physics course. The main purpose of this work is to master the methods of modelling non-stationary physical processes in the Mathcad environment using the odesolve function, using the example of oscillatory movements. In addition, the article highlights the importance of using physical models in the educational process. This allows not only to visualize complex processes, but also contributes to a deeper understanding of the principles underlying physical phenomena.

Целью данного исследования является оценка эффективности использования искусственного интеллекта (ИИ) в педагогических стратегиях преподавания русского языка как иностранного. Анализируются четыре ключевых компонента, в том числе информационно-поисковая система, электронная информационно-образовательная среда, цифровой учебно-методический комплекс и цифровые инструменты управления образовательным процессом. С лингвометодической точки зрения подчеркивается систематическое взаимодействие этих компонентов и их влияние на развитие коммуникативных и информационных навыков в процессе обучения. Особое внимание уделяется интеграции нейротехнологий, таких как нейронные сети, для персонализации обучения, синхронного перевода, распознавания речи и оценки компетенций студентов. Результаты исследования позволяют сделать выводы о применимости и эффективности использования ИИ в образовательном процессе по иностранному языку, определяя перспективные направления дальнейших исследований.