International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

This paper presents AMNI-AS, a compact method and Python package for surface integration on non-parametrized geometries known only through point-cloud samples. The method extends a corrected minterpy_levelsets [9] workflow: first, a global polynomial level-set function ϕ_h reconstructs the surface as Γ_h={x∈R^3:ϕ_h (x)=0}; [6] second, nodal values of the integrand are extended by regression; third, a closest-point projection and a regularized coarea formula [4], [5], produce a mesh-free quadrature rule. The theoretical core is the identity ∫_(Γ_h)▒  fdS=∫_Ω▒  f(x)δ(ϕ_h (x))‖∇ϕ_h (x)‖dx, implemented with a compact smooth delta and data-driven evaluation f ˜_h (Π_h (x)). The prototype package AMNI-AS, contains adapters to minterpy_levelsets, an SVD fallback level-set fit, RBF/nearest integrand regression [3], [15], [16], [17], projection, and quadrature routines. Numerical checks on the unit sphere show relative errors near 〖10〗^(-5) for area and polynomial integrands on a moderate grid. The method is intended as a short, reproducible bridge from global polynomial level-set reconstruction to integration tasks on data-defined surfaces.

This paper presents a refined modification of the classical Newton–Raphson method for solving nonlinear equations. The proposed method integrates a dual strategy: the replacement of the analytic derivative with a central finite-difference approximation and the implementation of a dynamic adaptive mechanism for step-size regulation. Through rigorous mathematical analysis, we demonstrate that the new approach ensures reliable convergence even when initial guesses are far from the true root. The adaptive step-size improvement is based on monitoring the relative error of the derivative and dynamically optimizing the accuracy of the approximation. The article provides a comprehensive convergence analysis, a geometric interpretation of the proposed approach, and practical implementations with significant implications for problems in which the classical method tends to fail.

The paper examines the role of visual signs, interface hierarchy, and emotional engagement mechanisms in mobile application design. Icons, pictograms, maps, menus, landmark distribution, and achievement screens are analyzed as components of an integrated visual-interactive system. These elements do not merely transmit information; they guide attention, reduce cognitive load, support orientation, and influence the user’s subjective experience. The study is based on theoretical foundations from semiotics, cognitive psychology, visual search research, human-computer interaction, and gamification. The paper outlines principles for designing mobile interfaces that are understandable, accessible, navigationally coherent, and emotionally engaging.

Contemporary manufacturing environments are characterized by continuous variability in product types, production volumes, data availability, network performance, and computational resource allocation. Conventional digital twin architectures, designed for static operating conditions, are fundamentally inadequate to address such dynamic contexts. This paper presents the Adaptive Digital Twin Framework (ADTF) — a novel architecture enabling digital twins to autonomously reconfigure their internal operating modes in response to evolving manufacturing conditions. The proposed framework integrates physics-based modeling, machine-learning inference, and hybrid paradigms within a unified self-adaptive system. Additionally, ADTF incorporates dynamic computation offloading across edge, fog, and cloud layers, as well as explicit economic viability constraints. A Python-based simulation environment was developed to validate the framework across three representative industrial scenarios: a transition from serial to customized production, progressive degradation of computational resources, and escalating financial constraints. In all cases, ADTF demonstrated measurably superior performance compared to static digital twin systems, maintaining operational continuity, model fidelity, and cost efficiency. The results establish ADTF as a foundational contribution toward intelligent, self-managing digital twins aligned with the principles of Industry 4.0 and Industry 5.0.

This paper investigates the efficacy of generative artificial intelligence in automating the creation of technical documentation for non-destructive testing (NDT). The research focuses on a comparative performance analysis between a specialized AI agent, built on the Gemini 3.1 Flash platform, and certified human NDT Level 2 experts. A comparative cross-sectional study was conducted using three distinct industrial forging products. Both the AI agent and two human experts were tasked with generating Visual Testing (VT) work instructions based on a 14-point framework derived from the STN EN 13018 and ISO 9712 standards. The outputs were evaluated by a blind-reviewing Level 3 expert using a modified HEAT (Expertise, Accuracy, Trust) rubric, focusing on regulatory compliance, technical precision, and readability. he results demonstrate that the AI agent achieved a 98.4% reduction in generation time, averaging 54.5 seconds per instruction compared to 57.3 minutes for human experts. While the AI agent consistently outperformed humans in text clarity and structural consistency (scoring 5.0 in usability), it exhibited “conservative technical hallucinations,” such as prescribing unnecessary magnification tools and incorrect defect-coding standards (ISO 6520-1 instead of CSN 421240). Furthermore, cloud-based API instabilities (HTTP 503 errors) were identified as a critical reliability risk for real-time industrial deployment. The study concludes that while AI agents are highly effective as rapid drafting tools, they cannot currently replace certified personnel due to lack of situational engineering judgment and legal accountability. A “Human-in-the-loop” model remains mandatory, where a certified Level 2 or 3 professional must verify and approve all AI-generated NDT documentation to ensure industrial safety and regulatory compliance…

Trace theory is a fundamental tool in linear algebra, spectral theory, homological algebra, and related areas of modern mathematics. While the additivity of trace is classical in finite-dimensional settings, a unified structural principle for its behavior under measurable decomposition is less explicitly formulated across categorical and analytic frameworks. [8,9].
The paper introduces a compact trace reciprocity framework for trace-class exact endofunctors admitting measurable decomposition over a σ-finite measure space. Under suitable measurability, integrability, and boundedness assumptions, the global trace can be recovered from the local traces of the measurable components. The report summarizes the formal setting, states the main theorem, and outlines the proof strategy based on approximation by simple families, trace additivity, and convergence arguments. [6,4]
Representative examples are included to show how the framework recovers familiar identities in finite-dimensional and operator-theoretic settings. The goal is to provide a concise conference-style presentation of the main reciprocity principle, its mathematical scope, and its structural significance. [7,3]
Keywords – Trace theory; trace reciprocity; measurable decomposition; trace-class endofunctors; stable categories; exact endofunctors; categorical invariants; operator theory.

This paper proposes a hybrid artificial intelligence architecture for autonomous structural inspection using unmanned aerial vehicles, multimodal large language models and image embeddings. A UAV is an unmanned aerial vehicle; in this paper it denotes a drone carrying imaging sensors for close visual inspection of infrastructure assets. Images are uploaded to Azure cloud storage, transformed into multimodal evidence and evaluated by a Microsoft Foundry agent under deterministic risk rules. A preliminary simulated benchmark shows improved recall, fewer false alerts and shorter engineer review time while preserving auditable human-supervised decisions.

Digital twin technology has rapidly evolved into a foundational pillar of modern engineering practice. By creating high-fidelity, data-driven virtual replicas of physical systems, digital twins enable continuous monitoring, predictive analytics, and advanced optimization throughout the lifecycle of assets. This extended article expands on the conceptual, technical, and practical dimensions of digital twins, providing deeper insights into architectures, data frameworks, integration strategies, real-world case studies, economic implications, and emerging research directions.

Pre-university education in general is facing various challenges, but in the schools of the Municipality of Kamenica the challenges are even greater in improving learning outcomes in teaching and learning, these challenges range from identifying individual student needs and optimizing learning resources.
This paper examines the role and impact of artificial intelligence (AI) in improving and facilitating learning circumstances in schools in the Municipality of Kamenica in Kosovo. The main goal is to analyze how AI solutions can improve the level of learning, support effective teaching and help in assessing and attracting students by increasing their level of concentration.
In this paper, we have taken an empirical approach using real data from several pre-university education schools in Kamenica, which include test scores, attendance statistics, and information on learning activities. With the help of machine learning techniques, models have been built that identify student profiles with different performance and recommend personalized learning strategies for each profile. An AIbased recommender system has also been developed that suggests teaching materials and relevant exercises using virtual laboratories according to the needs and individual progress of students.
The results show that the use of AI tools helps in identifying student weaknesses more quickly, in creating personalized lesson plans and in facilitating the work of teachers for continuous monitoring and evaluation. The analysis also shows the perception of teachers and parents across the Municipality of Kamenica towards the integration of AI in teaching practice, highlighting the challenges and opportunities for wider implementation in pre-university education in Kosovo.
This case study that we have conducted in the Municipality of Kamenica offers a practical and strategic contribution to municipal education policies towards the effective use of advanced technologies in the teaching process not only in the Municipality of Kamenica but also beyond.

World-model reinforcement learning agents plan by imagining future trajectories through a learned latent dynamics model. In safety-critical driving tasks, the quality of these imagined rollouts — particularly their representation of vulnerable road users — directly determines whether the agent can anticipate and avoid dangerous situations. We analyze the imagined rollouts of a DreamerV3 agent trained to navigate urban environments in CARLA using semantic segmentation and depth observations. By decoding the agent’s latent imagination into observation space, we qualitatively and quantitatively examine how pedestrians are represented in imagined futures, comparing episodes that result in collision against those where the agent successfully avoids. We investigate whether the world model accurately predicts pedestrian presence and motion in its imagined horizon, and whether reconstruction fidelity of pedestrian regions correlates with avoidance outcomes. Our analysis provides insight into the internal representations that underlie emergent safety behaviors in model-based driving agents and highlights limitations of finite imagination horizons for pedestrian safety.

Nonlinear dynamical systems arise in numerous scientific and engineering domains, including physics, economics, biology, and control theory. Their complex behavior, sensitivity to initial conditions, and possible chaotic dynamics make accurate modeling and prediction challenging using traditional analytical approaches alone. In recent years, artificial intelligence (AI) techniques have demonstrated strong potential for modeling nonlinear and complex systems through data-driven methods. This paper explores artificial intelligence approaches for modeling nonlinear dynamical systems, focusing on the integration of machine learning techniques with classical mathematical modeling. We consider representative nonlinear systems and analyze how neural networks, regression models, and hybrid AI–mathematical frameworks can be used to approximate system behavior, predict future states, and capture hidden structures in time-series data. Special attention is given to systems exhibiting chaotic behavior, where small perturbations in initial conditions can lead to significant divergence in trajectories. The study presents numerical simulations and comparative analyses between traditional mathematical models and AI-based approaches. The results highlight the advantages of machine learning methods in capturing nonlinear patterns and improving predictive accuracy, especially when analytical solutions are difficult or unavailable. Additionally, we discuss the interpretability of AI models in the context of dynamical systems and outline potential applications in engineering, intelligent control, and data-driven system identification. The proposed framework contributes to the growing intersection between dynamical systems theory and artificial intelligence by demonstrating how AI tools can support the analysis and modeling of complex nonlinear phenomena. This work aims to provide a foundation for future research on hybrid mathematical–AI methods for understanding and predicting complex systems.

Data fusion is the process of integrating multiple heterogeneous data sources to produce more accurate, comprehensive, and useful information than any single source alone. For the medical data fusion, this information may come from imaging, genomic data, clinical records, and physiological signals. It has emerged as a cornerstone of modern precision medicine. Information theory provides a rigorous mathematical framework for quantifying uncertainty, measuring information gain, and can thus be used to optimize fusion strategies across diverse clinical contexts. This paper presents a review of information-theoretic approaches suitable for medical data fusion, covering: fundamental concepts (entropy, mutual information, Kullback-Leibler divergence, rate-distortion), theoretical frameworks (information bottleneck, transfer entropy, partial information decomposition), and their application across major clinical domains. We synthesize recent advances in fusion-based architectures, discuss the critical challenges of uncertainty quantification, and provide practical guidelines for implementing information-theoretic fusion in clinical settings. Through a systematic analysis, we identify key challenges, including parameter sensitivity, missing modalities, and clinical interpretability, to outline promising directions for future research. This review aims to provide clinicians, researchers, and developers with a comprehensive understanding of how information theory can transform medical data for improved diagnostic accuracy, prognostic precision, and personalized patient care.