Zentralblatt MATH (zbMATH)

The efficiency of robot control methods and the accuracy of their movements are often hindered by the complexity of defining motion paths. Commonly, these paths are represented by numerous linear segments, resulting in redundant motion commands, reduced smoothness, and velocity. To address these issues, this study investigates the application of mathematical algorithms, specifically the Ramer-Douglas-Peucker (RDP) method and higher-order polynomial interpolation, to optimize robot toolpaths. The RDP algorithm minimizes redundant points while retaining the trajectory’s overall shape, enhancing process speed and reducing energy costs. In addition, arc recognition is implemented to replace multiple linear operations with circular or arc-based motions, improving efficiency and reducing code complexity. The research employs RoboDK and Python API for offline programming, with experimental validation conducted on the Yaskawa Motoman HC10DTP robot. Results demonstrate that these methods can significantly reduce toolpath execution times – up to 3.7 times in certain cases – without significantly compromising trajectory accuracy. These approaches are applicable across various industries, including milling, painting, welding, and grinding, where smooth and precise motion is critical.

This paper presents and analyzes robust numerical algorithms for solving inverse problems for parabolic equations, specifically focusing on the determination of an unknown time-dependent source function from an integral flux condition. The study is motivated by mathematical models based on Navier-Stokes equations, particularly those exhibiting Poiseuille-type solutions. We employ a variational approach, formulating the inverse problem as the minimization of a Tikhonov regularization cost functional. Discrete approximation schemes are rigorously derived using finite volume methods in space and both backward Euler and Crank-Nicolson schemes in time. A key contribution of this work is the strict justification of the gradient formula for the cost functional by deriving the adjoint problem directly from the fully discrete scheme, rather than discretizing the continuous adjoint problem. This methodology is extended to problems involving fractional powers of elliptic operators and two-dimensional domains. Numerical experiments are conducted to compare the efficiency of Gradient Descent and Conjugate Gradient methods. The results demonstrate that the Conjugate Gradient method significantly outperforms standard gradient descent, maintaining high accuracy and convergence rates even with the inclusion of regularization terms and complex diffusion operators.

The Computer-Assisted Qualitative Data Analysis Software (CAQDAS) and mixed methods research integration propose a potential for advancing knowledge management and decision support processes. Therefore, this systematic literature review focuses on Web of Science (WoS) results related to the mixed methods and MAXQDA® software symbiosis. During the research period (at the end of 2024), 140 related articles were reduced to 16 most suitable based on the inclusion and exclusion criteria. However, the article faces some limitations, such as focusing solely on WoS data—articles in English, which could be solved in future studies. Based on the results, another potential research gap is evident, as few articles are related to the exploratory sequential mixed methods design and analysis of drawbacks using CAQDAS within mixed methods. Future studies could empirically analyze it.

Multi-criteria group decision-making has gained considerable attention due to its ability to aggregate diverse expert opinions and establish a preference order among alternatives. While probabilistic hesitant fuzzy (PHF) sets offer increased flexibility and generality for representing criteria values compared to traditional fuzzy and hesitant fuzzy set theories, existing aggregation techniques often fail to enhance consensus among biased expert judgments. Motivated by the need for more effective consensus-based decision-making, this paper proposes a new framework that integrates PHF set theory with Aczel-Alsina weighted averaging and geometric aggregation operators. These operators, known for their flexibility and the inclusion of an adjustable parameter, are particularly well-suited for addressing real-world decision-making challenges. The framework employs a cross-entropy based model to determine criteria weights and multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA) method to establish priority orders of alternatives. The proposed framework is demonstrated through a case study on manufacturing outsourcing vendor selection. The results show that Bertrandt is the most suitable vendor, with a score of 0.2390, and resources consumption is identified as the most critical criterion, with a weight of 0.20. To validate the robustness of the proposed framework, sensitivity and comparison analyses have also been conducted.

This research focuses on the modeling and lateral control of an autonomous vehicle, employing a novel robust fixed-time sliding mode control method. Prior to any further analysis, a detailed model of the lateral dynamics of an autonomous vehicle is developed in order to accurately represent its nonlinear behavior and dynamic characteristics. Furthermore, a novel fixed-time sliding mode controller is employed to control the vehicle’s movement, effectively addressing nonlinearities while reducing the impact of uncertainties and external disturbances. This approach is known for its ability to provide a specific time of convergence, which results in achieving high accuracy and fast response. Subsequently, the stability of the overall system must be maintained by applying Lyapunov functions. In order to validate the effectiveness of the proposed control method, it is tested through simulations and compared with classical fixed-time sliding mode control and fixed-time fast terminal sliding mode control techniques. The results confirm the superior robustness and performance of the proposed control method, thereby highlighting its potential for autonomous vehicle applications.

In this work, we investigate the stability conditions for four new high-order ADI type schemes proposed to solve 3D wave equations with a non-constant sound speed coefficient. This analysis is mainly based on the spectral method, therefore a basic benchmark problem is formulated with a constant sound speed coefficient. For a case of general non-constant coefficient the stability analysis is done by using the energy method. Our main conclusion states that the selected ADI type schemes use different factorization operators (mainly due to the need to approximate the artificial boundary conditions on the split time levels), but the general structure of the stability factors are similar for all schemes and thus the obtained CFL conditions are also very similar. The second goal is to compare the accuracy and efficiency of the selected ADI solvers. This analysis also includes parallel versions of these schemes. Two schemes are selected as the most effective and accurate.

The cultural economy sector's impact on the sustainable development of nations is widely recognized as a crucial aspect of national progress. This study explores the intricate relationship between the cultural economy and sustainability through a systematic literature review. Drawing from diverse scholarly sources, it delves into the economic, social, and ecological dimensions of sustainability within the cultural context. The analysis reveals that while there is a growing acknowledgement of culture's role in fostering sustainability, more comprehensive research must be done on the subject. Nonetheless, key indicators such as cultural workers, cultural tourism, products and services of the cultural and creative industries, and cultural heritage emerge as pivotal in assessing the sustainability of the cultural economy sector. By synthesizing findings from various publications, this study provides insights into the interplay between culture and sustainability, laying the groundwork for future research and policy formulation in this critical domain.

In the context of increasing environmental challenges and limitations of traditional energy resources, the development of energy innovations becomes a key factor in transitioning to a circular economy. This research is dedicated to examining the implementation of energy innovations by countries worldwide in the pursuit of Sustainable Development Goals. The transition to a circular economy requires a comprehensive understanding of the organizational and economic support for energy innovations, including ecological, technical, and socio-financial determinants of societal development. In this context, the advancement of energy innovations plays a crucial role in forming a sustainable economic system within its circulation. The research methodology includes bibliometric analysis to identify knowledge clusters regarding energy innovations. The economic indicators of energy innovations across different countries were analyzed. The impact of innovation and research and development (R&D) on the development of renewable energy was conducted. The insights were elaborated for the transition to a circular economy using a scenario-based approach. These insights outline the development trajectory of energy innovations in the context of a circular economy while considering ecological, technical, social, and economic challenges. Finally, the study provides a roadmap for implementing energy innovations in the context of economic decarbonization and the transition to a circular model while ensuring the achievement of the Sustainable Development Goals.

The characteristics of surface plasmon polaritons at the chiroplasmabased ellipsoidal nanowire metamaterial interface are examined in this study. Surface waves have been demonstrated to possess special characteristics, such as the dispersion maps’ dependency on chiroplasma parameters such as free carrier concentration. The influence of chiroplasma features on surface plasmon polaritons characteristics are studied. This suggests surface plasmon polaritons at chiroplasma-based ellipsoidal nanowire metamaterial interface may be exploited for Plasma-on-Chip for cancer treatment.

Studies on recycled materials emerged during recent years. This paper investigates the properties of sound absorption and transmission loss of the structures of the perforated plastic panel (PPP) backed with the rubber granule panel (RGP). Under production conditions, such a structure could be produced using only waste. The normal incidence sound absorption and transmission loss of the structure was measured using ISO 10534-2 and ASTM E2611-17 standard methods, respectively. In this study, the plastic panel perforation holes were tilted in steps of 15°–45° compared to the vertical axis of the sample. Different thickness rubber panels were used as backing (12 mm, 22 mm and 27 mm). The results showed that the sound absorption and transmission loss increased with the angle of the perforation pore. To compare the different structures, the multi-criteria analysis using the technique for order of preference by similarity to ideal solution (TOPSIS) approach was done. The RGP thickness, sound absorption coefficient (SAC) and sound transmission loss (STL) were weighted as a criterion. The results of the multi-criteria analysis showed that the optimal structure for a possible application is PPP45°+ RGP 22 mm, which was ranked highest of all alternatives. The first peak of SAC reached 0.97 at 1000 Hz. In the frequency range of 250–1000 Hz, STL values reached up to 10.4 dB and in the frequency range of 1–4 kHz – 20.1 dB. The results obtained using RGP and PPP show promising development potential for sound absorption and insulation applications.