What constitutes learning in the 21st century is the capacity for e-learning. Integral components of e-education are training content management systems. Existing content generators more transform content than create original content. Creating a methodology and technology for generating original content is important and relevant. In order to form adequate methods for generating content, primarily for mathematical and related disciplines, the problem of generating a triangle, together with its many attributes, is considered as the simplest object of elementary mathematics. We create a simulation model that describes the properties of the object and apply modified methods of optimization and corresponding algorithms to it. The current algorithmic layout demonstrates the performance of the developed system. It generates triangles in any configurations matching the given parameters and demonstrates their properties.

As the main problem of the research, the possibility of creating a universal educational platform that combines the possibilities of an online generation of educational content with the interface of the training process itself was considered. The methodology of the educational platform has been developed, in which the mass generation of content is carried out at random, based on simulation models of educational objects. A matrix interface is used, which allows performing custom operations by entering a sequence of typical operators. The system forms a reference base of operators, replenishing it from user solutions, which makes it possible to train and improve the system in order to provide methodological support to student users. An active demo layout of an educational content generator was created and tested, using the example of a specific problem from school mathematics. All methodological options function in the layout. There are three interface options: administrative, training and control. It was concluded that the approach based on the simulation of educational objects makes it possible to create a unified algorithmic platform that combines the functions of content generation with educational training. The system contains a unique option to teach yourself based on its interaction with students.

The influence of the automation of content creation on the development trends of e-education based on artificial intelligence is considered. Widely used content generators do not actually create new content but modify the finished content accumulated in the databases. The concept of generating primary content is based on the use of simulation models of the studied objects. The methodology for generating the content initial-generation demonstrates the possibility of incorporating AI-based content management sys- tems into e-education.

This article is devoted to overcoming the contradiction between the problem of maximizing the extraction of wind energy as the goal of optimizing wind turbines, and the use of traditional methods based on criteria for the aerodynamic quality of the blades. A modified technique is considered in which the optimization criterion is the directly extracted flow power. It is based on pulse theory methods that use specific power as an optimization criterion. A comparative analysis of the energy efficiency of different types of turbines is carried out, and the effects of blade inversion are considered. A method for calculating multi-rotor turbines based on the concept of uniform power distribution is presented. The compatibility of proprietary and traditional methods is considered by comparing the results of numerical experiments with calculated and experimental data from sources. Optimization computational algorithms generate data from numerical experiments and determine optimal parameter configurations for the turbines under consideration. It is shown that orthogonal Darrieus turbines in high-speed mode provide energy efficiency comparable to collinear turbines, and multi-rotor turbines with power uniformly distributed over the working section are not inferior in energy efficiency to basic turbines, with linear blade velocities halved.

Configurable intelligent design is formalized here as the selection of a consistent configuration from interdependent alternatives under constraints of budget, quality, risk, and compatibility. It is examined not as a universal solver but as a class of domain-specific systems, each defined for a task family with explicitly formalizable variables, hard constraints, and objectives. Locally correct predictions for individual components do not guarantee a globally feasible solution. This study compares direct neural-network inference, the exact HIM-D solver, and a procedural hybrid whose network candidate is checked by an independent verifier, with an exact search invoked whenever a constraint is violated. A reproducible synthetic corpus of 24,000 problems across educational, engineering, and commercial scenarios was assessed for feasibility, optimality, robustness to distribution shift, repeatability, and latency. Pure neural-network models were feasible in only 17.40% and 19.12% of cases and degraded sharply out of distribution, whereas the hybrid maintained 100.00% feasibility and 83.08% joint optimality. A staged ablation identifies pairwise incompatibility density as the dominant source of that degradation, and constraint-aware correction alone raises feasibility without reaching a guarantee. The results therefore support separating probabilistic candidate generation from independent formal verification within a bounded class of specialized configuration problems, not a universal solver.