Search Results (60)

This study presents a unified symbolic–numerical framework for the automatic generation and conversion of two-port network parameters, including Z, Y, H, F, T (A, B, C, and D), and S matrices. The method integrates Modified Nodal Analysis (MNA) with exact symbolic computation to derive transfer functions, poles, zeros, and parameter sensitivities directly from the circuit topology, eliminating the need for manual algebraic manipulation. Unlike conventional tools such as PSpice 9.1 or RF simulation software* which operate primarily on numerical models, the proposed approach provides closed-form expressions suitable for analytical design, optimization, and parameter-tolerance evaluation. The implemented software routines generate all parameter sets within a single workflow and enable bidirectional conversion between low-frequency formulations and high-frequency scattering representations. Numerical case studies on band-pass filters confirm the correctness of the generated expressions, with deviations below 1% relative to reference simulation results. Full article

The accelerating industrial demand for high-speed manipulation has necessitated the development of robotic architectures that effectively balance dynamic performance with workspace size. While serial SCARA robots offer large workspaces and parallel Delta robots provide high acceleration, existing architectures fail to combine these benefits effectively for specific four-degree-of-freedom (4-DoF) Schoenflies motion tasks. This study introduces and characterizes a novel 4-DoF parallel topology, having a symmetrical build-up, which is distinguished by its use of modular 2-DoF linear drive units. The research methodology entails the structural synthesis of the kinematic chain followed by kinematic analysis using vector algebra to derive closed-form inverse geometric models. Additionally, the Jacobian matrix is formulated to evaluate velocity transmission and systematically classify singular configurations, while the dexterity index is defined to assess the rotational capabilities of the mechanism. Numerical simulations of pick-and-place trajectory were also conducted, varying trajectory curvature to analyze kinematic behavior. The results demonstrate that the proposed modular architecture yields a highly symmetric and homogeneous workspace that can be scaled simply by adjusting the drive module lengths. Furthermore, the singularity and dexterity analyses reveal a substantial, singularity-free operational workspace, although tighter trajectory curvatures were found to impose higher velocity demands on the joints. In conclusion, the proposed mechanism successfully achieves the targeted Schoenflies motion, offering a solution for automated industrial tasks. Full article

In this paper we study the existence of Killing vector fields for right-invariant metrics on five-dimensional Lie groups. We begin by providing some explanation of the classification lists of the low-dimensional Lie algebras. Then we review some of the known results about Killing vector fields on Lie groups. We take as our invariant metric the sum of the squares of the right-invariant Maurer–Cartan one-forms, starting from a coordinate representation. A number of such metrics are uncovered that have one or more extra Killing vector fields, besides the left-invariant vector fields that are automatically Killing for a right-invariant metric. In each case the corresponding Lie algebra of Killing vector fields is found and identified to the extent possible on a standard list. The computations are facilitated by use of the symbolic manipulation package MAPLE. Full article

Solving algebraic word problems is an essential component of the school mathematics curriculum; nonetheless, many students still make mistakes in solving them. Several studies have largely focused on categorizing errors in solving algebraic word problems. However, relatively little attention has been given to the underlying learning obstacles that shape these errors. Addressing this gap, this study explores students’ learning obstacles in solving algebraic word problems through a hermeneutic phenomenological approach. Data were collected from 138 Indonesian students and two Indonesian mathematics teachers using written tests, document studies, and interviews. Data analysis was conducted alongside thematic analysis and the interpretative phenomenological analysis framework. The findings revealed five main errors: misunderstanding the problem’s meaning, incorrectly forming mathematical equations from the narrative, failing to solve the constructed mathematical model, providing incomplete or contextually inappropriate final answers, and failing to apply the trial-and-error method. These errors were traced to three categories of learning obstacles. Ontogenic obstacles included weaknesses in prerequisite skills such as reading comprehension, arithmetic, and algebraic manipulation, as well as a limited ability to transition from arithmetic to algebraic thinking. Epistemological obstacles arose when students’ understanding was tied to narrow contexts and could not be applied flexibly to new problem situations. Didactical obstacles reflected instructional gaps, particularly the emphasis on procedural routines over interpretation, reflection, and representational flexibility. This study extends the application of learning obstacle theory to the context of algebraic word problems and offers practical implications for teachers in designing adaptive instructional strategies to minimize students’ learning obstacles. Full article

This paper proposes a geometrically intuitive error modeling method for planar parallel mechanisms (PPMs) based on conformal geometric algebra (CGA). First, the end point of each limb is determined through rotational transformations in geometric algebra. Using this point as the center, the kinematic geometry body (KGB) of each limb is constructed. The end-effector position of the parallel mechanism is then obtained via intersection operations in CGA, while its orientation is derived by constructing the motion plane from the end points. Finally, the error model of the parallel mechanism is established through differential operations. To validate the proposed method, a kinematic calibration simulation was performed using a 3-RPR planar parallel mechanism as an example. The simulation results demonstrate a significant reduction in both position and orientation errors after calibration, indicating a substantial improvement in accuracy and verifying the correctness of the approach. Full article

Mathematical modeling competency is essential for engineering students, yet significant cognitive obstacles impede their ability to apply theoretical concepts like derivatives to real-world optimization problems. This study investigates the cognitive processes and obstacles encountered by Industrial Engineering and Management students when solving applied derivative problems, utilizing the Mathematical Modeling Cycle (MMC) and Duval’s theory of semiotic registers as analytical frameworks. A qualitative case study design was employed, analyzing students’ written exam responses to an applied optimization task involving tour organization with variable pricing structures. Three representative cases were examined in detail, revealing distinct patterns of cognitive engagement. Results identified specific cognitive obstacles including misunderstanding of variables and domains, weak connections between mathematical and economic contexts, difficulties in graphical representation of constraints, and deficits in validation and critical thinking. While students demonstrated procedural fluency in symbolic manipulation and mathematical work, they struggled to coordinate between different semiotic registers (verbal, algebraic, graphical, and contextual) and failed to complete the full modeling cycle, particularly in the crucial validation stages. These findings suggest that cognitive obstacles stem from representational gaps rather than general learning difficulties, indicating the need for targeted pedagogical interventions that explicitly address transitions between semiotic registers and emphasize the iterative nature of mathematical modeling in engineering contexts. Full article

This review is devoted to a comprehensive analysis of modern forms of information warfare in the context of digitalization and global interconnectedness. The work considers fundamental theoretical foundations—cognitive distortions, mass communication models, network theories and concepts of cultural code. The key tools of information influence are described in detail, including disinformation, the use of botnets, deepfakes, memetic strategies and manipulations in the media space. Particular attention is paid to methods of identifying and neutralizing information threats using artificial intelligence and digital signal processing, including partial digital convolutions, Fourier–Galois transforms, residue number systems and calculations in finite algebraic structures. The ethical and legal aspects of countering information attacks are analyzed, and geopolitical examples are given, demonstrating the peculiarities of applying various strategies. The review is based on a systematic analysis of 592 publications selected from the international databases Scopus, Web of Science and Google Scholar, covering research from fundamental works to modern publications of recent years (2015–2025). It is also based on regulatory legal acts, which ensures a high degree of relevance and representativeness. The results of the review can be used in the development of technologies for monitoring, detecting and filtering information attacks, as well as in the formation of national cybersecurity strategies. Full article

In recent years the use of delayed controllers has increased considerably, since they can attenuate noise, replace derivative actions, avoid the construction of observers, and reduce the use of extra sensors, while maintaining inherent insensitivity to high-frequency noise. Therefore, it is important to continue improving the tuning of these controllers, including properties such as performance, fragility and robustness that may be beneficial for this purpose. However, currently most studies prioritize tuning using only the performance property, some others only the fragility property, and some less only the robustness property. This work provides the first rigorous joint analysis of performance, fragility, and robustness for a class of systems whose characteristic equation is a quasi-polynomial of degree two, filling a gap in the current literature. Thus, necessary and sufficient conditions are proposed to improve the tuning of delayed-action controllers by ensuring a exponential decay rate on the convergence of the closed-loop system response (performance) and by ensuring stabilization and/or trajectory tracking in the face of changes in system parameters (robustness) and controllers gains (fragility). To illustrate and corroborate the effectiveness of the proposed theoretical results, a real-time implementation is presented on a mobile prototype consisting of an omnidirectional mobile robot, to streamline/guarantee trajectory tracking in response to variations in controller gains and robot parameters. This implementation and application of theoretical results are possible thanks to the proposal of a novel delayed nonlinear controller and some simple but strategic algebraic manipulations that reduce the original problem to the study of a quasi-polynomial of degree 9 with three commensurable delays. Finally, our results are compared with a classical proportional nonlinear controller showing that our proposal is relevant. Full article

This paper develops a theoretical framework for the computation of higher-order derivatives based on the algebra of hyper-dual numbers. Extending the classical dual number system, hyper-dual numbers provide a natural and rigorous mechanism for encoding and propagating derivative information through function composition and arithmetic operations. We formalize the underlying algebraic structure, define generalized hyper-dual extensions of scalar functions via multidimensional Taylor expansions, and establish consistency with standard differential calculus. The proposed approach enables exact computation of partial derivatives and mixed higher-order derivatives without resorting to symbolic manipulation or approximation schemes. We further investigate the algebraic properties and closure under differentiable operations, illustrating the method’s potential for unifying aspects of automatic differentiation with multivariable calculus. This study contributes to the theoretical foundation of algorithmic differentiation and highlights hyper-dual numbers as a precise and elegant tool in computational differential analysis. Full article

The double wishbone suspension (DWS) system is widely used in automotive engineering because of its favorable kinematic properties, which affect vehicle dynamics, handling, and ride comfort; hence, it is important to have an accurate 3D model, simulation, and analysis of the system in order to optimize its design. This requires efficient computational tools for parametric study. The development of effective computational tools that support parametric exploration stands as an essential requirement. Our research demonstrates a complete Wolfram Mathematica system that creates parametric 3D kinematic models and conducts simulations, performs analyses, and generates interactive visualizations of DWS systems. The system uses homogeneous transformation matrices to establish the spatial relationships between components relative to a global coordinate system. The symbolic geometric parameters allow designers to perform flexible design exploration and the kinematic constraints create an algebraic equation system. The numerical solution function NSolve computes linkage positions from input data, which enables fast evaluation of different design parameters. The integrated 3D visualization module based on Mathematica’s manipulate function enables users to see immediate results of geometric configurations and parameter effects while calculating exact 3D coordinates. The resulting robust, systematic, and flexible computational environment integrates parametric 3D design, kinematic simulation, analysis, and dynamic visualization for DWS, serving as a valuable and efficient tool for engineers during the design, development, assessment, and optimization phases of these complex automotive systems. Full article

This paper presents a spectral method to solve nonlinear distributed-order diffusion equations with both time-distributed-order and two-sided space-fractional terms. These are highly challenging to solve analytically due to the interplay between nonlinearity and the fractional distributed-order nature of the time and space derivatives. For this purpose, Hexic-kind Chebyshev polynomials (HCPs) are used as the backbone of the method to transform the primary problem into a set of nonlinear algebraic equations, which can be efficiently solved using numerical solvers, such as the Newton–Raphson method. The primary reason of choosing HCPs is due to their remarkable recurrence relations, facilitating their efficient computation and manipulation in mathematical analyses. A comprehensive convergence analysis was conducted to validate the robustness of the proposed method, with an error bound derived to provide theoretical guarantees for the solution’s accuracy. The method’s effectiveness is further demonstrated through two test examples, where the numerical results are compared with existing solutions, confirming the approach’s accuracy and reliability. Full article

This paper introduces Disturbance-Aware Redundant Control (DARC), a control framework addressing the challenge of human–robot co-transportation under disturbances. Our method integrates a disturbance-aware Model Predictive Control (MPC) framework with a proactive pose optimization mechanism. The robotic system, comprising a mobile base and a manipulator arm, compensates for uncertain human behaviors and internal actuation noise through a two-step iterative process. At each planning horizon, a candidate set of feasible joint configurations is generated using a Conditional Variational Autoencoder (CVAE). From this set, one configuration is selected by minimizing an estimated control cost computed via a disturbance-aware Discrete Algebraic Riccati Equation (DARE), which also provides the optimal control inputs for both the mobile base and the manipulator arm. We derive the disturbance-aware DARE and validate DARC with simulated experiments with a Fetch robot. Evaluations across various trajectories and disturbance levels demonstrate that our proposed DARC framework outperforms baseline algorithms that lack disturbance modeling, pose optimization, or both. Full article

White-box cryptography plays a vital role in untrusted environments where attackers can fully access the execution process and potentially expose cryptographic keys. It secures keys by embedding them within complex and obfuscated transformations, such as lookup tables and algebraic manipulations. However, existing white-box protection schemes for SM2 signatures face vulnerabilities, notably random number leakage, which compromises key security and diminishes overall effectiveness. This paper proposes an improved white-box implementation of the SM2 signature computation leveraging a Trusted Execution Environment (TEE) architecture. The scheme employs three substitution tables for SM2 key generation and signature processes, orchestrated by a random bit string k. The k value and lookup operations are securely isolated within the TEE, effectively mitigating the risk of k leakage and enhancing overall security. Experimental results show our scheme enhances security, reduces storage, and improves performance over standard SM2 signature processing, validating its efficacy with TEE and substitution tables in untrusted environments. Full article

To solve the nonlinear vibration problems of second- and third-order nonlinear oscillators, a modified harmonic balance method (HBM) is developed in this paper. In the linearized technique, we decompose the nonlinear terms of the governing equation on two sides via a constant weight factor; then, they are linearized with respect to a fundamental periodic function satisfying the specified initial conditions. The periodicity of nonlinear oscillation is reflected in the Mathieu-type ordinary differential equation (ODE) with periodic forcing terms appeared on the right-hand side. In each iteration of the linearized harmonic balance method (LHBM), we simply solve a small-size linear system to determine the Fourier coefficients and the vibration frequency. Because the algebraic manipulations required for the LHBM are quite saving, it converges fast with a few iterations. For the Duffing oscillator, a frequency–amplitude formula is derived in closed form, which improves the accuracy of frequency by about three orders compared to that obtained by the Hamiltonian-based frequency–amplitude formula. To reduce the computational cost of analytically solving the third-order nonlinear jerk equations, the LHBM invoking a linearization technique results in the Mathieu-type ODE again, of which the harmonic balance equations are easily deduced and solved. The LHBM can achieve quite accurate periodic solutions, whose accuracy is assessed by using the fourth-order Runge–Kutta numerical integration method. The optimal value of weight factor is chosen such that the absolute error of the periodic solution is minimized. Full article

This article presents a data-driven methodology for modeling DC–DC power electronic converters. Using the proposed methodology, the dynamics of a converter can be captured, thereby eliminating the need for explicit theoretical modeling methods. This approach only requires the acquisition of fundamental measurements: currents through inductors and voltages across capacitors. The acquired data are used to construct a linear difference system, which is algebraically manipulated to form a state–space representation of the converter under analysis. Three DC–DC converter topologies were analyzed, and their resulting models were tested and compared with simulation data, yielding an average error deviation of approximately $2\%$ for current signals and $4\%$ for voltage signals, demonstrating precise tracking of the actual dynamics. The proposed data-driven methodology could simplify the implementation of adaptive control strategies in larger-scale solutions or in the interconnection of multiple converters. Full article