We propose a mathematical model that allows us to determine the temperature field of a parallel-sided electrically conductive plate element subject to uniform non-stationary electromagnetic action. We formulate initial-boundary value problems to determine the parameters of the non-stationary electromagnetic field (NEMF) and the temperature. We develop a methodology to solve these initial-boundary value problems using the approximation of determining functions by cubic polynomials over thickness of the plate element. General solutions for the related Cauchy problems at uniform non-stationary electromagnetic action are obtained. Based on these solutions, the temporal variation of Joule’s heat and temperature in the plate element, subject to short-term induction heating by an NEMF in the mode of impulse modulating signal (MIMS), is analyzed. Temperature dependencies on the different values of electromagnetic field stress and on the different time duration were obtained. The choice of the carrier frequency of electromagnetic field oscillations is explained for the frequencies mostly used in industrial devices for inductive heating.

A mathematical model for determining the temperature field of a bimetallic plate with plane-parallel boundaries during short-term induction heating by a non-stationary electromagnetic field is proposed. Initial boundary value problems for determining the parameters of a non-stationary electromagnetic field and temperature are formulated. The temperature and the component of the magnetic field intensity vector that is tangential to the plate base were selected as defining functions. We used an approximation of the defining functions in each layer of the plate with quadratic polynomials by the thickness coordinate and Laplace transform of the integral over time. General solutions to the formulated problems under uniform non-stationary electromagnetic action were obtained. Based on them, the temperature during short-term induction heating by a non-stationary electromagnetic field was numerically analyzed depending on its amplitude-frequency parameters and duration.

A machine learning model for correcting errors in Ukrainian texts has been developed. It was established that the neural network has the ability to correct simple sentences written in Ukrainian; however, the development of a full-fledged system requires the use of spell-checking using dictionaries and the checking of rules, both simple and those based on the result of parsing dependencies or other features. In order to save computing resources, a pre-trained BERT (Bidirectional Encoder Representations from Transformer) type neural network was used. Such neural networks have half as many parameters as other pre-trained models and show satisfactory results in correcting grammatical and stylistic errors. Among the ready-made neural network models, the pre-trained neural network model mT5 (a multilingual variant of T5 or Text-to-Text Transfer Transformer) showed the best performance according to the BLEU (bilingual evaluation understudy) and METEOR (metric for evaluation of translation with explicit ordering) metrics.

Transition processes in a steel conductive strip are analyzed during its induction heating under a quasi-steady electromagnetic field. In particular, the temperature field in the strip is studied. A method of solving corresponding initial boundary problems in a two-dimensional mathematical model for differential equations of electrodynamics and heat conduction is developed. The Joule heat and the temperature are determined with a high level of accuracy. The defining functions are the temperature and component of the magnetic field intensity vector tangent to the bases and end planes of the strip. To find them, we use cubic approximation of the defining functions’ distribution along the thickness coordinate. The original two-dimensional initial boundary value problems for the defining functions are reduced to one-dimensional initial boundary value problems on their integral characteristics. General solutions for these problems are obtained using the finite integral transformation by the transverse variable and the Laplace transform of the integral by time. Integral characteristics’ expressions are represented as convolutions for functions that describe homogeneous solutions of one-dimensional initial boundary value problems and limiting values of defining functions on the bases and end planes of the strip. The change of temperature under a varying regime in the dimensionless Fourier time and temperature distribution over the strip cross-section in a steady state depending on the parameters of induction heating and the Biot number are numerically analyzed. Varying and constant temperature regimes of the strip under conditions of the near-surface and continuous induction heating are studied.

We present a combined ML/NLP (Machine Learning, Natural Language Processing) pipeline for protecting cloud-based APIs (Application Programming Interfaces), which works both at the level of individual HTTP (Hypertext Transfer Protocol) requests and at the access log file reading mode, linking explicitly technical anomalies with business risks. The system processes each event/access log through parallel numerical and textual branches: a set of anomaly detectors trained on traffic engineering characteristics and a hybrid NLP stack that combines rules, TF-IDF (Term Frequency-Inverse Document Frequency), and character-level models trained on enriched security datasets. Their results are integrated using a risk-aware policy that takes into account endpoint type, data sensitivity, exposure, and authentication status, and creates a discrete risk level with human-readable explanations and recommended SOC (Security Operations Center) actions. We implement this design as a containerized microservice pipeline (input, preprocessing, ML, NLP, merging, alerting, and retraining services), orchestrated using Docker Compose and instrumented using OpenSearch Dashboards. Experiments with OWASP-like (Open Worldwide Application Security Project) attack scenarios show a high detection rate for injections, SSRF (Server-Side Request Forgery), Data Exposure, and Business Logic Abuse, while the processing time for each request remains within real-time limits even in sequential testing mode. Thus, the pipeline bridges the gap between ML/NLP research for security and practical API protection channels that can evolve over time through feedback and retraining.