Search Results (127)

Fiber Bragg grating (FBG) exhibits strong resistance to electromagnetic interference and excellent linear strain response, making it highly promising for structural health monitoring (SHM) in pavement. This research investigates the strain transfer characteristics of embedded FBG in pavement structure and materials by using the relevant theoretical models. Results indicate adhesive layer thickness and sheath modulus are the primary factors influencing the strain transfer coefficient. A thinner adhesive layer and high modulus of sheath enhance the coefficient. Additionally, the strain distribution of sheath significantly affects the transfer efficiency. When the stress level near the grating region is lower than the both ends, the coefficient increases and even exceeds 1, which typically occurs under multi-axle conditions. As for asphalt mixture, high temperature leads to lower efficiency, while accumulated plastic strain improves it. Although the increased load frequency results a higher strain transfer coefficient, the magnitude of this change is negligible. By employing polynomial fitting to the sheath strain distribution, the boundary condition of theoretical equation could be removed. The theoretical and numerical results of strain transfer coefficient for pavement embedded FBG demonstrate good consistency, indicating the polynomial fitting is adoptable for the theoretical calculation with non-uniform strain distribution. This study utilizes the FEM to clarify the evolution of FBG strain transfer in pavement structures and materials, providing a theoretical basis for the design and implementation of embedded FBG in pavement. Full article

The study of neuronal electrical activity and spatial organization is essential for uncovering the mechanisms that regulate neuronal electrophysiology and function. Mathematical models have been utilized to analyze the structural properties of neuronal networks, predict connectivity patterns, and examine how morphological changes impact neural network function. In this study, we aimed to explore the role of the actin cytoskeleton in neuronal signaling via primary cilia and to elucidate the role of the actin network in conjunction with neuronal electrical activity in shaping spatial neuronal formation and organization, as demonstrated by relevant mathematical models. Our proposed model is based on the polygamma function, a mathematical application of ramification, and a geometrical definition of the actin cytoskeleton via complex numbers, ring polynomials, homogeneous polynomials, characteristic polynomials, gradients, the Dirac delta function, the vector Laplacian, the Goldman equation, and the Lie bracket of vector fields. We were able to reflect the effects of neuronal electrical activity, as modeled by the Van der Pol equation in combination with the actin cytoskeleton, on neuronal morphology in a 2D model. In the next step, we converted the 2D model into a 3D model of neuronal electrical activity, known as a core-shell model, in which our generated membrane potential is compatible with the neuronal membrane potential (in millivolts, mV). The generated neurons can grow and develop like an organoid brain based on the developed mathematical equations. Furthermore, we mathematically introduced the signal transduction of primary cilia in neurons. Additionally, we proposed a geometrical model of the neuronal branching pattern, which we described as ramification, that could serve as an alternative mathematical explanation for the branching pattern emanating from the neuronal soma. In conclusion, we highlighted the relationship between the actin cytoskeleton and the signaling processes of primary cilia. We also developed a 3D model that integrates the geometric organization unique to neurons, which contains soma and branches, such that the mathematical model represents the interaction between the actin cytoskeleton and neuronal electrical activity in generating action potentials. Next, we could generalize the model into a cluster of neurons, similar to an organoid brain model. This mathematical framework offers promising applications in artificial intelligence and advancements in neural networks. Full article

Blasting-induced seismic waves are typically nonlinear and non-stationary signals. The EMD-Hilbert transform is commonly used for time–frequency analysis of such signals. However, during the empirical mode decomposition (EMD) processing of blasting-induced seismic waves, endpoint effects occur, resulting in varying degrees of divergence in the obtained intrinsic mode function (IMF) components at both ends. The further application of the Hilbert transform to these endpoint-divergent IMFs yield artificial time–frequency analysis results, adversely impacting the assessment of blasting-induced seismic wave hazards. This paper proposes an improved EMD endpoint effect suppression algorithm that considers local endpoint development trends, global time distribution, energy matching, and waveform matching. The method first analyzes global temporal characteristics and endpoint amplitude variations to obtain left and right endpoint extension signal fragment S(t)_L and S(t)_R. Using these as references, the original signal is divided into “b” equal segments S(t)₁, S(t)₂ … S(t)_b. Energy matching and waveform matching functions are then established to identify signal fragments S(t)_i and S(t)_j that match both the energy and waveform characteristics of S(t)_L and S(t)_R. Replacing S(t)_L and S(t)_R with S(t)_i and S(t)_j effectively suppresses the EMD endpoint effects. To verify the algorithm’s effectiveness in suppressing EMD endpoint effects, comparative studies were conducted using simulated signals to compare the proposed method with mirror extension, polynomial fitting, and extreme value extension methods. Three evaluation metrics were utilized: error standard deviation, correlation coefficient, and computation time. The results demonstrate that the proposed algorithm effectively reduces the divergence at the endpoints of the IMFs and yields physically meaningful IMF components. Finally, the method was applied to the analysis of actual blasting seismic signals. It successfully suppressed the endpoint effects of EMD and improved the extraction of time–frequency characteristics from blasting-induced seismic waves. This has significant practical implications for safety assessments of existing structures in areas affected by blasting. Full article

This paper presents a novel generalization of the mth-order Laguerre and Laguerre-based Appell polynomials and examines their fundamental properties. By establishing quasi-monomiality, we derive key results, including recurrence relations, multiplicative and derivative operators, and the associated differential equation. Additionally, both series and determinant representations are provided for this new class of polynomials. Within this framework, several subpolynomial families are introduced and analyzed including the generalized mth-order Laguerre–Hermite Appell polynomials. Furthermore, the generalized mth-order Laguerre–Gould–Hopper-based Appell polynomials are defined using fractional operators and we investigate their structural characteristics. New families are also constructed, such as the mth-order Laguerre–Gould–Hopper–based Bernoulli, Laguerre–Gould–Hopper–based Euler, and Laguerre–Gould–Hopper–based Genocchi polynomials, exploring their operational and algebraic properties. The results contribute to the broader theory of special functions and have potential applications in mathematical physics and the theory of differential equations. Full article

This paper introduces a novel recursive algorithm for inverting matrix polynomials, developed as a generalized extension of the classical Leverrier–Faddeev scheme. The approach is motivated by the need for scalable and efficient inversion techniques in applications such as system analysis, control, and FEM-based structural modeling, where matrix polynomials naturally arise. The proposed algorithm is fully numerical, recursive, and division free, making it suitable for large-scale computation. Validation is performed through a finite element simulation of the transverse vibration of a fighter aircraft wing. Results confirm the method’s accuracy, robustness, and computational efficiency in computing characteristic polynomials and adjugate-related forms, supporting its potential for broader application in control, structural analysis, and future extensions to structured or nonlinear matrix systems. Full article

To address the resource utilization challenges of residual plastic film in Xinjiang and the issues of low reliability, poor cutting length qualification rates, and high energy consumption in existing film-mixed residue choppers, a rotary knife-type mixed film residue chopper was designed based on the “single support cutting + sliding cutting” principle. The device primarily consists of an adaptive feeding mechanism, a chopping mechanism, and a transmission system. The main structural and motion parameters of the mechanisms were determined through the analysis of feeding and chopping conditions. The primary factors affecting the cotton stalk chopping length qualification rate (CLCR-CS), residual film chopping length qualification rate (CFCR-RF), and specific energy consumption (SEC) were identified as the feeding roller speed, chopper speed, and the gap between the moving and fixed blades. Vibration characteristic analysis of the chopper was conducted using ANSYS software. The first six natural frequencies of the chopper were found to range from 112.54 to 186.65 Hz, with maximum deformation ranging from 0.885 to 1.237 mm. The excitation frequency was significantly lower than the first natural frequency, ensuring that the chopper met reliability and operational performance standards. A prototype was fabricated, and a second-order rotational orthogonal experiment was performed with CLCR-CS, CFCR-RF, and SEC as the test indicators and feeding roller speed, chopper speed, and the gap between the moving and fixed blades as the experimental factors. Variance and response surface analyses were conducted using Design-Expert software to clarify the effects and interactions of experimental factors on the test indicators. The second-order polynomial response surface model was optimized, and the optimal factor values were derived based on practical operational conditions. Verification experiments confirmed that the optimal operating parameters were a feeding roller speed of 32.40 r/min, a chopper speed of 222.0 r/min, and a blade gap of 1.0 mm. Under these conditions, CLCR-CS was 89.96%, CFCR-RF was 91.62%, and SEC was 5.36 kJ/kg, meeting the design specifications of the mixed film residue chopper. Full article

This paper explores the common neighborhood energy ($E_{CN}\left(\mathsf{\Gamma }\right)$) of graphs derived from the dihedral group $D_{2n}$ and generalized quaternion group $Q_{4n}$, specifically the non-commuting graph (NCM-graph) and the commuting graph (CM-graph). Studying graphs associated with groups offers a powerful approach to translating algebraic properties into combinatorial structures, enabling the application of graph-theoretic tools to understand group behavior. The common neighborhood energy, defined as the sum of the absolute values of the eigenvalues of the common neighborhood (CN) matrix, i.e., ${\sum }_{i=1}^p\left|{\zeta }_i\right|$, where ${\left\{{\zeta }_i\right\}}_{i=1}^p$ are the CN eigenvalues, provides insights into the structural properties of these graphs. We derive explicit formulas for the CN characteristic polynomials and corresponding CN eigenvalues for both the NCM-graph and CM-graph as functions of n. Consequently, we establish closed-form expressions for the $E_{CN}$ of these graphs, which are parameterized by n. The validity of our theoretical results is confirmed through computational examples. This study contributes to the spectral analysis of algebraic graphs, demonstrating a direct connection between the group-theoretic structure of $D_{2n}$ and $Q_{4n}$, as well as the combinatorial energy of their associated graphs, thus furthering the understanding of group properties through spectral graph theory. Full article

Motors, as the core carriers of pollution-free power, realize efficient electric energy conversion in clean energy systems such as electric vehicles and wind power generation, and are widely used in industrial automation, smart home appliances, and rail transit fields with their low-noise and zero-emission operating characteristics, significantly reducing the dependence on fossil energy. As the requirements of various application scenarios become increasingly complex, it becomes particularly important to accurately and quickly design the sealing structure of motors. However, traditional design methods show many limitations when facing such challenges. To solve this problem, this paper proposes hybrid models of machine learning that contain polynomial regression and optimization XGBOOST models to rapidly and accurately predict the sealing performance of motors. Then, the hybrid model is combined with the simulated annealing algorithm and multi-objective particle swarm optimization algorithm for optimization. The reliability of the results is verified by the mutual verification of the results of the simulated annealing algorithm and the particle swarm optimization algorithm. The prediction accuracy of the hybrid model for data outside the training set is within 2.881%. Regarding the prediction speed of this model, the computing time of ML is less than 1 s, while the computing time of FEA is approximately 9 h, with an efficiency improvement of 32,400 times. Through the cross-validation of single-objective optimization and multi-objective optimization algorithms, the optimal design scheme is a groove depth of 0.8–0.85 mm and a pre-tightening force of 80 N. The new method proposed in this paper solves the limitations in the design of motor sealing structures, and this method can be extended to other fields for application. Full article

Particulate matter affects both the light environment and air quality in greenhouses, obstructing normal gas exchange and hindering efficient physiological activities such as photosynthesis. This study focused on young Chinese cabbage (Brassica rapa L. Chinensis Group) in a greenhouse at harvest time, monitoring and comparing hyperspectral information, net photosynthetic rate, and microscopic leaf structure under two conditions: a quantitative artificial particulate matter environment and a healthy environment. Based on microscopic results combined with spectral responses and changes in photosynthetic physiological information, it is believed that particulate matter enters plant cells through stomata. Through retention and transport pathways, it disrupts the membrane structure, organelles, and other components of plant cells, resulting in adverse effects on the plant’s physiological functions. The study analyzed the mechanisms by which particulate matter influences the photosynthesis, spectral characteristics, and physiological responses of young Chinese cabbage. Physiological Reflectance Index (PRI), Modified Chlorophyll Absorption Ratio Index (MCARI), spectral red-edge position (λr), and spectral sensitive bands were used as spectral feature variables. Through cubic polynomial and 24 combinations of spectral preprocessing and modeling methods, an inversion model of spectral features and net photosynthetic rate was established. The optimal combination of spectral preprocessing and modeling methods was finally selected as SG + SD + PLS + MSC, which consists of Savitzky-Golay smooth (SG), second derivative (SD), partial least squares (PLS), and multiplicative scatter correction (MSC). The coefficient of determination (R²) of the model is 0.9513. The results indicate that particulate matter affects plant photosynthesis. The SG + SD + PLS + MSC combination method is relatively advantageous for processing the photosynthetic spectral physiological information of plants under the influence of particulate matter. The results of this study will deepen the understanding of the mechanisms by which particulate matter affects plants and provide a reference for the physiological information inversion of greenhouse vegetables under particulate matter pollution. Full article

The degree of tree curvature exerts a significant influence on the utilization of forestry resources. This study proposes an enhanced quantitative structural modeling (QSM) method, founded upon terrestrial laser scanning (TLS) point cloud data, for the precise extraction of 3D curvature characteristics of tree trunks. The conventional approach operates under the assumption that the tree trunk constitutes an upright rotating body, thereby disregarding the tree trunk’s true curvature morphology. The proposed method is founded on the classical QSM algorithm and introduces two zoom factors that can dynamically adjust the fitting parameters. This improvement leads to enhanced accuracy in the representation of tree trunk curvature and reduced computational complexity. The study utilized 146 sample trees from 13 plots in Jixi, Anhui Province, which were collected and pre-processed by TLS. The study combines point cloud segmentation, manual labeling of actual curvature and dual-factor experiments, and uses quadratic polynomials and simulated annealing algorithms to determine the optimal model factors. The validation results demonstrate that the enhanced method exhibits a greater degree of concordance between the predicted and actual curvature values within the validation set. In the regression equation, the coefficient of the two-factor method for fitting a straight line is 0.95, which is substantially higher than the 0.75 of the one-factor method. Furthermore, the two-factor model has an R² of 0.21, indicating that the two-factor optimization method generates a significantly smaller error compared to the one-factor model (with an R² of 0.12). In addition, this study discusses the possible reasons for the error in the results, as well as the shortcomings and outlook. The experimental results demonstrate the augmented method’s capacity to accurately reconstruct the 3D curvature of tree trunks in most cases. This study provides an efficient and accurate method for conducting fine-grained forest resource measurements and tree bending studies. Full article

In this study, firstly the definitions and basic algebraic properties of k-Oresme and k-Oresme–Lucas sequences are given. Then, various summation formulae are derived with the help of the first and second derivatives of two polynomials with k-Oresme and k-Oresme–Lucas number coefficients. The main aim of this study is to establish the relations between the generalized Fibonacci and generalized Lucas sequences and the k-Oresme and k-Oresme–Lucas sequences, respectively. These connections allow us to obtain different combinatorial identities of these sequences using the characteristic equation of the k-Oresme and k-Oresme–Lucas sequences. In this way, the discovered combinatorial identities reveal the arithmetic and structural symmetries in the sequences, through the regularities and recurring patterns observed in the algebraic structures of the considered number sequences. The results obtained in this study enable the development of new symmetric approaches in areas such as numerical analysis, cryptography and optimization algorithms, and the algebraic relations derived in this study can contribute to the solution of different problems in disciplines such as mathematical modelling and theoretical physics. Full article

The homogeneous polynomial defined by a tensor, $\mathcal{A}{\mathbf{x}}^{m-1}$ for $\mathbf{x}\in {\mathbb{R}}^n$, has been used in many recent problems in the context of tensor analysis and optimization, including the tensor eigenvalue problem, tensor equation, tensor complementary problem, tensor eigenvalue complementary problem, tensor variational inequality problem, and least element problem of polynomial inequalities defined by a tensor, among others. However, conventional computation methods use the definition directly and neglect the structural characteristics of homogeneous polynomials involving tensors, leading to a high computational burden (especially when considering iterative algorithms or large-scale problems). This motivates the need for efficient methods to reduce the complexity of relevant algorithms. First, considering the symmetry of each monomial in the canonical basis of homogeneous polynomials, we propose a calculation method using the merge tensor of the involved tensor to replace the original tensor, thus reducing the computational cost. Second, we propose a calculation method that combines sparsity to further reduce the computational cost. Finally, a simplified algorithm that avoids duplicate calculations is proposed. Extensive numerical experiments demonstrate the effectiveness of the proposed methods, which can be embedded into algorithms for use by the tensor optimization community, improving computational efficiency in magnetic resonance imaging, n-person non-cooperative games, the calculation of molecular orbitals, and so on. Full article

This paper extends the research on cascaded-resonator (CR)-based filter banks introduced in previous studies. These IIR filter banks are online adaptive, making them highly suitable for spectral decomposition and signal analysis. The multiple-resonator-based structure offers an efficient design with low side lobes and high stopband attenuation. While earlier works focused on the fundamental structure and principles of these filter banks, the efficiency of their design was not thoroughly explored. In this study, thanks to the full periodicity of the frequency response, significant improvements in the modeling of the characteristic polynomial (the denominator of the transfer function) and preprocessing filters are introduced, resulting in an enhanced sparsity and a computational efficiency. Additionally, the previously employed linear programming algorithm for solving semi-infinite problems including a large number of linear constraints is replaced by more advanced quadratic programming (QP) or linear least-squares (LLS) optimization methods. These changes lead to a much faster and more powerful design process, even for filter banks with a larger number of resonator cascades and/or resonators per cascade. Furthermore, additional enhancements to the design methodology are proposed, further improving the robustness and applicability of the filters. These advancements enable the creation of highly efficient filter banks capable of handling complex and dynamic spectral analysis tasks in real time. Full article

This study explores the degree energy of fuzzy graphs to establish fundamental spectral bounds and characterize adjacency structures. We derive upper bounds on the sum of squared degree eigenvalues based on vertex degree distributions and formulate constraints using the characteristic polynomial of the maximum degree matrix. Furthermore, we demonstrate that the average degree energy of a connected fuzzy graph remains strictly positive. The proposed framework is applied to protein–protein interaction networks, identifying critical proteins and enhancing network resilience analysis. Full article

This study investigates the relationship between surface properties and microstructural characteristics of photocatalytic composites and their impact on air purification efficiency. High-resolution energy-dispersive X-ray spectroscopy (EDS) mapping and mercury intrusion porosimetry (MIP) were employed to analyze photocatalyst distribution and pore structure quantitatively. The findings demonstrated a strong correlation between TiO₂ coverage on the photoactive surface and NO removal rates and between pore structure characteristics and NO₂ generation rates. Two predictive models were developed to link NOx removal rates with photocatalytic cementitious mortars’ surface and structural properties. A stepwise regression approach produced a second-degree polynomial model with an adjusted R² of 0.98 and a Mean Absolute Percentage Error (MAPE) of 8.34%, indicating high predictive accuracy. The results underscore the critical role of uniform photocatalyst distribution and optimized pore structure in enhancing NOx removal efficiency while promoting the generation of desirable products (NO₃⁻) and minimizing the formation of undesirable byproducts (NO₂). Full article