Mathematics doi: 10.3390/math12203209

Authors: Juan José Font Sergio Macario Manuel Sanchis

This work aims to provide several versions of Dini&rsquo;s theorem for fuzzy number-valued continuous functions defined on a compact set K. In this context, there is a wide variety of possibilities since, unlike the real line, we can consider different topologies and orders on the set of fuzzy numbers. For example, we will show that the fuzzy Dini&rsquo;s theorem holds for the usual partial orders and the most commonly used topologies but does not hold for all orders in general.

]]>Mathematics doi: 10.3390/math12203208

Authors: Junhee Hong Youngjin Seol Seunghyun Lee Janghyeok Yoon Jiho Lee Ki-Su Park Ji-Wan Ha

Rapid elderly population growth has increased the number of patients with cognitive impairment (CI). Early detection and ongoing medical treatment can slow CI progression and significantly reduce the cost of managing patients. However, distinguishing CI from natural cognitive decline associated with aging is challenging. Previous studies conducted to identify patients with CI using lifelog data did not consider changes in lifelog data over time because each data point was learned individually. This study introduces a model that predicts patients with CI based on sleep lifelog data and analyzes significant sleep factors that influence cognitive decline. This study followed three steps: (1) collecting sleep lifelog data from elderly Korean people and reconstructing sleep lifelog data as time-series data; (2) building a model to classify CI using a time series of sleep lifelog data and a long short-term memory model; and (3) identifying sleep factors that influence the onset of CI using an explainable AI algorithm. The proposed CI classification model achieved a sensitivity of 0.89, a specificity of 0.80, and an area under the receiver operating characteristic curve of 0.92. This study will facilitate the noninvasive screening, diagnosis, and continuous monitoring of CI in the elderly.

]]>Mathematics doi: 10.3390/math12203207

Authors: Dumitru Vieru Constantin Fetecau Zulkhibri Ismail

Two classes of magnetohydrodynamic (MHD) motions of the incompressible Oldroyd-B fluids through an infinite cylinder are analytically investigated. General expressions are firstly established for shear stress and velocity fields corresponding to the motion induced by longitudinal shear stress on the boundary. For validation, the expression of the shear stress is determined by two different methods. Using an important remark regarding the governing equations for shear stress and fluid velocity corresponding to the two different motions, this expression is then used to provide the dimensionless velocity field of the MHD motion of the same fluids generated by a cylinder that rotates around its symmetry axis. Obtained results can generate exact solutions for any motion of this kind of Oldroyd-B fluids. Consequently, both types of motions are completely solved. For illustration, some case studies are considered, and adequate velocity fields are provided. The steady-state components of these velocities are presented in different forms whose equivalence is graphically proved. The influence of the magnetic field on the fluid behavior is graphically investigated. It was found that the fluid flows slower, and a steady state is earlier reached in the presence of a magnetic field. The fluid behavior when shear stress is given on the boundary is also investigated.

]]>Mathematics doi: 10.3390/math12203206

Authors: Edward Bormashenko

We applied the Ramsey analysis to the sets of points belonging to Riemannian manifolds. The points are connected with two kinds of lines: geodesic and non-geodesic. This interconnection between the points is mapped into the bi-colored, complete Ramsey graph. The selected points correspond to the vertices of the graph, which are connected with the bi-colored links. The complete bi-colored graph containing six vertices inevitably contains at least one mono-colored triangle; hence, a mono-colored triangle, built of the green or red links, i.e., non-geodesic or geodesic lines, consequently appears in the graph. We also considered the bi-colored, complete Ramsey graphs emerging from the intersection of two Riemannian manifolds. Two Riemannian manifolds, namely (M1,g1) and (M2,g2), represented by the Riemann surfaces which intersect along the curve (M1,g1)&cap;(M2,g2)=&#8466; were addressed. Curve &#8466; does not contain geodesic lines in either of the manifolds&nbsp;(M1,g1) and (M2,g2). Consider six points located on the &#8466;:&nbsp;{1,&hellip;6}&sub;&#8466;. The points {1,&hellip;6}&sub;&#8466; are connected with two distinguishable kinds of the geodesic lines, namely with the geodesic lines belonging to the Riemannian manifold (M1,g1)/red links, and, alternatively, with the geodesic lines belonging to the manifold (M2,g2)/green links. Points {1,&hellip;6}&sub;&#8466; form the vertices of the complete graph, connected with two kinds of links. The emerging graph contains at least one closed geodesic line. The extension of the theorem to the Riemann surfaces of various Euler characteristics is presented.

]]>Mathematics doi: 10.3390/math12203205

Authors: Mohammed N. Alshehri Saad Althobaiti Ali Althobaiti Rahmatullah Ibrahim Nuruddeen Halliru S. Sambo Abdulrahman F. Aljohani

The emergence of higher-dimensional evolution equations in dissimilar scientific arenas has been on the rise recently with a vast concentration in optical fiber communications, shallow water waves, plasma physics, and fluid dynamics. Therefore, the present study deploys certain improved analytical methods to perform a solitonic analysis of the newly introduced three-dimensional nonlinear dynamical equations (all within the current year, 2024), which comprise the new (3 + 1) Kairat-II nonlinear equation, the latest (3 + 1) Kairat-X nonlinear equation, the new (3 + 1) Boussinesq type nonlinear equation, and the new (3 + 1) generalized nonlinear Korteweg&ndash;de Vries equation. Certainly, a solitonic analysis, or rather, the admittance of diverse solitonic solutions by these new models of interest, will greatly augment the findings at hand, which mainly deliberate on the satisfaction of the Painleve integrability property and the existence of solitonic structures using the classical Hirota method. Lastly, this study is relevant to contemporary research in many nonlinear scientific fields, like hyper-elasticity, material science, optical fibers, optics, and propagation of waves in nonlinear media, thereby unearthing several concealed features.

]]>Mathematics doi: 10.3390/math12203204

Authors: Huanyin Su Shanglin Mo Huizi Dai Jincong Shen

Short-term origin&ndash;destination (OD) passenger flow forecasting is crucial for urban rail transit enterprises aiming to optimise transportation products and increase operating income. As there are large-scale OD pairs in an urban rail transit system, OD passenger flow cannot be obtained in real time (temporal hysteresis). Additionally, the distribution characteristics are also complex. Previous studies mainly focus on passenger flow prediction at metro stations, while few methods solve the OD passenger flow prediction problems of an urban rail transit system. In view of this, we propose a novel deep learning method fusing high-dimensional features (HDF-DL) with multi-source data. The HDF-DL method is combined with three modules. The temporal module incorporates the time-varying, trend, and cyclic characteristics of OD passenger flow, while the latest OD passenger flow time sequence (within 1 h) is excluded from the time-varying characteristics. In the spatial module, the K-means and K-shape algorithms are used to classify OD pairs from multiple perspectives and capture the spatial features, reducing the difficulty of OD passenger flow predictions with large-scale and complex characteristics. Weather factors are considered in the external feature module. The HDF-DL method is tested on a large-scale metro system in China, in which eight baseline models are designed. The results show that the HDF-DL method achieves high prediction accuracy across multiple time granularities, with a mean absolute percentage error of about 10%. OD passenger flow in every departure time interval can be predicted with high and stable accuracy, effectively capturing temporal characteristics. The modular design of HDF-DL, which fuses high-dimensional features and employs appropriate neural networks for different data types, significantly reduces prediction errors and outperforms baseline models.

]]>Mathematics doi: 10.3390/math12203203

Authors: Minghui Lv Xiaopeng Yan Ke Wang Xinhong Hao Jian Dai

Accurately estimating the modulation parameters of pseudorandom binary code&ndash;pulse amplitude modulation (PRBC&ndash;PAM) signals damaged by strong noise poses a significant challenge in emitter identification and countermeasure. Traditionally, weak signal detection methods based on chaos theory can handle situations with low signal-to-noise ratio, but most of them are developed for simple sin/cos waveform and cannot face PRBC&ndash;PAM signals commonly used in ultra-low altitude performance equipment. To address the issue, this article proposes a novel adaptive detection and estimation method utilizing the in-depth analysis of the Duffing oscillator&rsquo;s behaviour and output characteristics. Firstly, the short-time Fourier transform (STFT) is used for chaotic state identification and ternary processing. Then, two novel approaches are proposed, including the adjusting zero value (AZV) method and the chaotic state ratio (CSR) method. The proposed weak signal detection system exhibits unique capability to adaptively modify its internal periodic driving force frequency, thus altering the difference frequency to estimate the signal parameters effectively. Furthermore, the accuracy of the proposed method is substantiated in carrier frequency estimation under varying SNR conditions through extensive experiments, demonstrating that the method maintains high precision in carrier frequency estimation and a low bit error rate in both the pseudorandom sequence and carrier frequency, even at an SNR of &minus;30 dB.

]]>Mathematics doi: 10.3390/math12203196

Authors: Raydonal Ospina Patrícia L. Espinheira Leilo A. Arias Cleber M. Xavier Víctor Leiva Cecilia Castro

Residuals are essential in regression analysis for evaluating model adequacy, validating assumptions, and detecting outliers or influential data. While traditional residuals perform well in linear regression, they face limitations in exponential family models, such as those based on the binomial and Poisson distributions, due to heteroscedasticity and dependence among observations. This article introduces a novel standardized combined residual for linear and nonlinear regression models within the exponential family. By integrating information from both the mean and dispersion sub-models, the new residual provides a unified diagnostic tool that enhances computational efficiency and eliminates the need for projection matrices. Simulation studies and real-world applications demonstrate its advantages in efficiency and interpretability over traditional residuals.

]]>Mathematics doi: 10.3390/math12203200

Authors: Chao Cheng Weijun Wang He Di Xuedong Li Haotong Lv Zhiwei Wan

The improvement of information sciences promotes the utilization of data for process monitoring. As the core of modern automation, time-stamped signals are used to estimate the system state and construct the data-driven model. Many recent studies claimed that the effectiveness of data-driven methods relies greatly on data quality. Considering the complexity of the operating environment, process data will inevitably be affected. This poses big challenges to estimating faults from data and delivers feasible strategies for electrical systems of industry. This paper addresses the missing data problem commonly in traction systems by designing a martingale posterior-based data generation method for the state-space model. Then, a data-driven approach is proposed for fault detection and estimation via the subspace identification technique. It is a general scheme using the Bayesian framework, in which the Dirichlet process plays a crucial role. The data-driven method is applied to a pilot-scale traction motor platform. Experimental results show that the method has good estimation performance.

]]>Mathematics doi: 10.3390/math12203202

Authors: Balendu Bhooshan Upadhyay Shubham Kumar Singh Ioan Stancu-Minasian

In this article, we investigate a class of non-smooth semidefinite multiobjective programming problems with inequality and equality constraints (in short, NSMPP). We establish the convex separation theorem for the space of symmetric matrices. Employing the properties of the convexificators, we establish Fritz John (in short, FJ)-type necessary optimality conditions for NSMPP. Subsequently, we introduce a generalized version of Abadie constraint qualification (in short, NSMPP-ACQ) for the considered problem, NSMPP. Employing NSMPP-ACQ, we establish strong Karush-Kuhn-Tucker (in short, KKT)-type necessary optimality conditions for NSMPP. Moreover, we establish sufficient optimality conditions for NSMPP under generalized convexity assumptions. In addition to this, we introduce the generalized versions of various other constraint qualifications, namely Kuhn-Tucker constraint qualification (in short, NSMPP-KTCQ), Zangwill constraint qualification (in short, NSMPP-ZCQ), basic constraint qualification (in short, NSMPP-BCQ), and Mangasarian-Fromovitz constraint qualification (in short, NSMPP-MFCQ), for the considered problem NSMPP and derive the interrelationships among them. Several illustrative examples are furnished to demonstrate the significance of the established results.

]]>Mathematics doi: 10.3390/math12203201

Authors: Fabian Gnegel Stefan Schaudt Uwe Clausen Armin Fügenschuh

In recent years, parcel volumes have reached record highs, prompting the logistics industry to explore innovative solutions to meet growing demand. In densely populated areas, delivery robots offer a promising alternative to traditional truck-based delivery systems. These autonomous electric robots operate on sidewalks and deliver time-sensitive goods, such as express parcels, medicine and meals. However, their limited cargo capacity and battery life require a return to a depot after each delivery. This challenge can be modeled as an electric vehicle-routing problem with soft time windows and single-unit capacity constraints. The objective is to serve all customers while minimizing the quadratic sum of delivery delays and ensuring each vehicle operates within its battery limitations. To address this problem, we propose a mixed-integer quadratic programming model and introduce an enhanced formulation using a layered graph structure. For this layered graph, we present two solution approaches based on relaxations that reduce the number of nodes and arcs compared to the expanded formulation. The first approach, Iterative Refinement, solves the current relaxation to optimality and refines the graph when the solution is infeasible for the expanded formulation. This process continues until a proven optimal solution is obtained. The second approach, Branch and Refine, integrates graph refinement into a branch-and-bound framework, eliminating the need for restarts. Computational experiments on modified Solomon instances demonstrate the effectiveness of our solution approaches, with Branch and Refine consistently outperforming Iterative Refinement across all tested parameter configurations.

]]>Mathematics doi: 10.3390/math12203199

Authors: Yuan Bao Sibo Yang

In this work, we construct a theoretical framework to develop non C0 Morley type nonconforming high-convergence elements for biharmonic problems. For each element domain, P3 should be included in the space of shape functions. Besides the degrees of freedom of Morley elements, we add the integrals and first-order moments of the normal derivatives on edges. The choice of degrees of freedom and shape function space guarantees the possibility of improving the convergence order. As an application, we specifically construct a Morley type element on triangular meshes. Lastly, numerical experiments are carried out to verify the feasibility of the element.

]]>Mathematics doi: 10.3390/math12203197

Authors: Luciano Telesca Zbigniew Czechowski

In this study, we examined how the nonlinearity &alpha; of the Langevin equation influences the behavior of extremes in a generated time series. The extremes, defined according to run theory, result in two types of series, run lengths and surplus magnitudes, whose complex structure was investigated using the visibility graph (VG) method. For both types of series, the information measures of the Shannon entropy measure and Fisher Information Measure were utilized for illustrating the influence of the nonlinearity &alpha; on the distribution of the degree, which is the main topological parameter describing the graph constructed by the VG method. The main finding of our study was that the Shannon entropy of the degree of the run lengths and the surplus magnitudes of the extremes is mostly influenced by the nonlinearity, which decreases with with an increase in &alpha;. This result suggests that the run lengths and surplus magnitudes of extremes are characterized by a sort of order that increases with increases in nonlinearity.

]]>Mathematics doi: 10.3390/math12203198

Authors: Thierry E. Huillet

Life is on a razor&rsquo;s edge resulting from the random competitive forces of birth and death. We illustrate this aphorism in the context of three Markov chain population models where systematic random immigration events promoting growth are simultaneously balanced with random emigration ones provoking thinning. The origin of mass removals is either determined by external demands or by aging, leading to different conditions of stability.

]]>Mathematics doi: 10.3390/math12203195

Authors: Yihang Xu Junxi Wu Guoyan Zhao Meng Wang Xing Zhou

Rock mass discontinuities are an excellent information set for reflecting the geometric, spatial, and physical properties of the rock mass. Using clustering algorithms to analyze them is a significant way to select advantageous orientations of structural surfaces and provide a scientific theoretical basis for other rock mass engineering research. Traditional clustering algorithms often suffer from sensitivity to initialization and lack practical applicability, as discontinuity data are typically rough, low-precision, and unlabeled. Confronting these challenges, II-LA-KM, a learning-augmented clustering algorithm with improved initialization for rock discontinuity grouping, is proposed. Our method begins with heuristically selecting initial centers to ensure they are well-separated. Then, optimal transport is used to adjust these centers, minimizing the transport cost between them and other points. To enhance fault tolerance, a learning-augmented algorithm is integrated that iteratively reduces clustering costs, refining the initial results toward optimal clustering. Extensive experiments on a simulated artificial dataset and a real dataset from Woxi, Hunan, China, featuring both orientational and non-orientational attributes, demonstrate the effectiveness of II-LA-KM. The algorithm achieves a 97.5% accuracy on the artificial dataset and successfully differentiates between overlapping groups. Its performance is even more pronounced on the real dataset, underscoring its robustness for handling complex and noisy data. These strengths make our approach highly beneficial for practical rock discontinuity grouping applications.

]]>Mathematics doi: 10.3390/math12203194

Authors: Syeda Aunanya Mahmud Nazmul Islam Zahidul Islam Ziaur Rahman Sk. Tanzir Mehedi

The Internet of Things (IoT) has revolutionized various industries, but the increased dependence on all kinds of IoT devices and the sensitive nature of the data accumulated by them pose a formidable threat to privacy and security. While traditional IDSs have been effective in securing critical infrastructures, the centralized nature of these systems raises serious data privacy concerns as sensitive information is sent to a central server for analysis. This research paper introduces a Federated Learning (FL) approach designed for detecting intrusions in diverse IoT networks to address the issue of data privacy by ensuring that sensitive information is kept in the individual IoT devices during model training. Our framework utilizes the Federated Averaging (FedAvg) algorithm, which aggregates model weights from distributed devices to refine the global model iteratively. The proposed model manages to achieve above 90% accuracies across various metrics, including precision, recall, and F1 score, while maintaining low computational demands. The results show that the proposed system successfully identifies various types of cyberattacks, including Denial-of-Service (DoS), Distributed Denial-of-Service (DDoS), data injection, ransomware, and several others, showcasing its robustness. This research makes a great advancement to the IDSs by providing an efficient and reliable solution that is more scalable and privacy friendly than any of the existing models.

]]>Mathematics doi: 10.3390/math12203193

Authors: Askhat Diveev Elena Sofronova Nurbek Konyrbaev Oralbek Abdullayev

In this study, we consider the extended optimal control problem and search for a control function in the class of feasible functions for a real control object. Unlike the classical optimal control problem, the control function should depend on the state, not time. Therefore, the control synthesis problem for the initial-state domain should be solved, instead of the optimal control problem with one initial state. Alternatively, an optimal trajectory motion stabilisation system may be constructed. Both approaches&mdash;control and trajectory motion stabilisation system syntheses&mdash;cannot be applied to real-time control, as the task is too complex. The minimum threshold of quality criteria is searched for in the space of mathematical expression codes. Among other problems, the search space is difficult to define and the gradient is hard to determine. Therefore, the advanced control object model is used to obtain a feasible control function. The advanced model is firstly obtained before solving the optimal control problem and it already includes a trajectory motion stabilisation system; in particular, this stabilisation system is synthesised in advance at the control system design stage. When the optimal control problem appears, it is solved in real time in the classical statement, and a control function is searched for as a function of time. The advanced control object model also uses the reference model to generate the optimal trajectory. The search for the optimal control function is performed in real time and considers the synthesised stabilisation system of motion along a determined trajectory. Machine learning control via symbolic regression, namely, the network operator method, is used to directly solve the control synthesis problem. An example solution of the optimal control problem, with an advanced model moving in the environment with obstacles for a group of two mobile robots, is presented. The obtained solution is a control function for a reference model that generates a trajectory from a class of trajectories stabilised with the object&rsquo;s control system.

]]>Mathematics doi: 10.3390/math12203192

Authors: Zongwu Cai Pixiong Chen

In this paper, we propose utilizing machine learning methods to determine the expected aggregated stock market risk premium based on online investor sentiment and employing the multifold forward-validation method to select the relevant hyperparameters. Our empirical studies provide strong evidence that some machine learning methods, such as extreme gradient boosting or random forest, show significant predictive ability in terms of their out-of-sample performances with high-dimensional investor sentiment proxies. They also outperform the traditional linear models, which shows a possible unobserved nonlinear relationship between online investor sentiment and risk premium. Moreover, this predictability based on online investor sentiment has a better economic value, so it improves portfolio performance for investors who need to decide the optimal asset allocation in terms of the certainty equivalent return gain and the Sharpe ratio.

]]>Mathematics doi: 10.3390/math12203191

Authors: Zeqing Yang Kangni Xu Mingxuan Zhang Yingshu Chen Ning Hu Yi Zhang Yi Jin Yali Lv

(1) Background: Air rudders are used to control the flight attitude of aircraft, and their surface quality directly affects flight accuracy and safety. (2) Method: Traditional positioning methods can only obtain defect location information at the image level but cannot determine the defect&rsquo;s physical surface position on the air rudder, which lacks guidance for subsequent defect repair. We propose a defect physical surface positioning method based on a camera mapping model. (3) Results: Repeated positioning experiments were conducted on three typical surface defects of the air rudder, with a maximum absolute error of 0.53 mm and a maximum uncertainty of 0.26 mm. Through hardware systems and software development, the real-time positioning function for surface defects on the air rudder was realized, with the maximum axial positioning error for real-time defect positioning being 0.38 mm. (4) Conclusions: The proposed defect positioning method meets the required accuracy, providing a basis for surface defect repair in the air rudder manufacturing process. It also offers a new approach for surface defect positioning in similar products, with engineering application value.

]]>Mathematics doi: 10.3390/math12203190

Authors: Xiaogang Su George Ekow Quaye Yishu Wei Joseph Kang Lei Liu Qiong Yang Juanjuan Fan Richard A. Levine

Greedy search (GS) or exhaustive search plays a crucial role in decision trees and their various extensions. We introduce an alternative splitting method called smooth sigmoid surrogate (SSS) in which the indicator threshold function used in GS is approximated by a smooth sigmoid function. This approach allows for parametric smoothing or regularization of the erratic and discrete GS process, making it more effective in identifying the true cutoff point, particularly in the presence of weak signals, as well as less prone to the inherent end-cut preference problem. Additionally, SSS provides a convenient means of evaluating the best split by referencing a parametric nonlinear model. Moreover, in many variants of recursive partitioning, SSS can be reformulated as a one-dimensional smooth optimization problem, rendering it computationally more efficient than GS. Extensive simulation studies and real data examples are provided to evaluate and demonstrate its effectiveness.

]]>Mathematics doi: 10.3390/math12203189

Authors: Tariku Tesfaye Haile Fenglin Tian Ghada AlNemer Boping Tian

This paper studies the autoregressive integrated moving average (ARIMA) state space model combined with Kalman smoothing to impute missing values in a univariate time series before detecting change points. We estimate a scale-dependent time-average variance constant that depends on the length of the data section and is robust to mean shifts under serial dependence. The consistency of the proposed estimator is shown under the assumption allowing heavy tailedness. Integrating the proposed estimator with the moving sum and wild binary segmentation procedures to determine the number and locations of change points is discussed. Furthermore, the performance of the proposed methods is evaluated through extensive simulation studies and applied to the Beijing multi-site air quality dataset to impute missing values and detect mean changes in the data.

]]>Mathematics doi: 10.3390/math12203188

Authors: Ainur Ryskan Zafarjon Arzikulov Tuhtasin Ergashev Abdumauvlen Berdyshev

When studying the boundary value problems&rsquo; solvability for some partial differential equations encountered in applied mathematics, we frequently need to create systems of partial differential equations and explicitly construct linearly independent solutions explicitly for these systems. Hypergeometric functions frequently serve as solutions that satisfy these systems. In this study, we develop self-similar solutions for a third-order multidimensional degenerate partial differential equation. These solutions are represented using a generalized confluent Kamp&eacute; de F&eacute;riet hypergeometric function of the third order.

]]>Mathematics doi: 10.3390/math12203187

Authors: Vasile Berinde

This paper deals with the problem of finding a common solution for a fixed point problem for strictly pseudocontractive mappings and for a certain variational inequality problem. We propose a projection-type implicit averaged algorithm and establish the strong convergence of the sequences generated by this method to the common solution for the fixed point problem and the variational inequality problem. In order to illustrate the feasibility of the hypotheses and the superiority of our theoretical results over the existing literature, an example is also presented.

]]>Mathematics doi: 10.3390/math12203186

Authors: Jeongho Park Eunhee Kim

Angle estimation for low-altitude targets above the sea surface is a challenging problem due to multipath interference from surface reflection signals, and various approaches have been proposed. This paper proposes a matrix pencil method with multiple apertures. The matrix pencil method effectively responds to dynamic scenarios because it performs better when using a single snapshot than other methods. Also, employing multiple apertures is more economical than using one large aperture. Therefore, we propose a computationally efficient approach using this method and structures. The proposed two-stage MP method incrementally improves the resolution in two stages: in stage 1, we extract the denoised signals at each aperture level, and in stage 2, we further improve the resolution with those signals. In comparison with the angular resolution defined by the half-power beamwidth (HPBW) of a uniform linear array (ULA) antenna with an equivalent number of arrays, the proposed method demonstrated a superior resolution of less than 0.087 of the HPBW at a high signal-to-noise ratio (SNR) of 40 dB, and less than 0.31 of it even at a relatively low SNR of 15 dB, based on 90% of the resolving probability. For the multipath problem, the proposed scheme has the advantage of not requiring prior geometric information, and its performance is demonstrated through simulations to be better than the adaptive beamforming method and the composite monopulse method.

]]>Mathematics doi: 10.3390/math12203185

Authors: Van-Hien Nguyen Tri Cuong Do Kyoung-Kwan Ahn

In recent years, increasing attention has been given to reducing energy consumption in hydraulic excavators, resulting in extensive research in this field. One promising solution has been the integration of hydrostatic transmission (HST) and hydraulic pump/motor (HPM) configurations in parallel systems. However, these systems face challenges such as noise, throttling losses, and leakage, which can negatively impact both tracking accuracy and energy efficiency. To address these issues, this paper introduces an intelligent real-time prediction framework for system positioning, incorporating particle swarm optimization (PSO), long short-term memory (LSTM), a gated recurrent unit (GRU), and proportional&ndash;integral&ndash;derivative (PID) control. The process begins by analyzing real-time system data using Pearson correlation to identify hyperparameters with medium to strong correlations to the positioning parameters. These selected hyperparameters are then used as inputs for forecasting models. Independent LSTM and GRU models are subsequently developed to predict the system&rsquo;s position, with PSO optimizing four key hyperparameters of these models. In the final stage, the PSO-optimized LSTM-GRU models are employed to perform real-time intelligent predictions of motion trajectories within the system. Simulation and experimental results show that the model achieves a prediction deviation of less than 3 mm, ensuring precise real-time predictions and providing reliable data for system operators. Compared to traditional PID and LSTM-GRU-PID controllers, the proposed controller demonstrated superior tracking accuracy while also reducing energy consumption, achieving energy savings of up to 10.89% and 2.82% in experimental tests, respectively.

]]>Mathematics doi: 10.3390/math12203184

Authors: Lei He Qin Wang

This study presents an overlapping generation model to examine the impact of fertility incentive policies on economic growth in China, incorporating endogenous fertility, education, and technological advancement by integrating unified growth theory with an R&amp;D-based growth model. We analyze the impact of fertility incentive policies on economic growth by evaluating maternity insurance and public education. The results show that increasing the actual contribution rate of maternity insurance, maternity benefits, and public education expenditures can boost China&rsquo;s fertility rate; nevertheless, extending maternity leave would not incentivize an increase in the fertility rate. The impact of fertility incentives on economic growth is ambiguous, depending upon the extent to which increased fertility dilutes aggregate human capital via technical advancement. If the dilution effect is weak, the sign will turn positive, and vice versa. The simulation analysis of the benchmark model indicates that the fertility incentive policy, which encompasses increasing the actual contribution rate of maternity insurance, maternity benefits, and public education expenditure, can foster economic growth in China by enhancing the fertility rate in the long term.

]]>Mathematics doi: 10.3390/math12203182

Authors: Péter Korondi Nándor Fink Róbert Mikuska Péter Tamás Szemes Csaba Kézi Imre Kocsis

Modeling of various phenomena in engineering work is always a kind of simplification of real processes, aiming at a model where a certain level of mathematical theory and computational procedures is sufficient. If the complexity of the required theory corresponds to the general mathematical competence of engineers, then technical problems can be treated separately in engineering (or physical) models without regard to the mathematical background. However, in some advanced engineering fields, the harmonized development of engineering and mathematical models and toolboxes is necessary to find efficient solutions. For example, modeling variable structure systems in ideal sliding mode requires a mathematical toolbox that goes far beyond general engineering competence through the theory of discontinuous right-hand-side differential equations. Although sliding mode control is popular in practice and the concept of sliding mode allows a significant reduction of model complexity, its exact mathematical description is rarely encountered. The problem of friction compensation of a micro-telemanipulator using sliding mode control demonstrates a harmonized application of the mathematical and engineering approaches. Based on Filippov&rsquo;s theory, the ideal sliding mode can be discussed. Although an ideal system cannot be implemented in reality, the real systems can be kept close enough to it; therefore, the discussion of the solution of the ideal model is important for practical applications. Although several elements of the topic are available in the literature, in this paper a unique complex approach is given for users of sliding mode control with experimental considerations, different engineering models, and codes. The paper concludes that sliding mode control is a case where engineering and mathematical modeling are inseparable and requires the competence of both fields.

]]>Mathematics doi: 10.3390/math12203183

Authors: Yan-Kuen Wu Sy-Ming Guu Ya-Chan Chang

Min&ndash;max programming problems with addition&ndash;min constraints have been studied in the literature to model data transfer in BitTorrent-like peer-to-peer file-sharing systems. It is well known that the class of overlap functions contains various operators, including the &ldquo;min&rdquo; operator. The aim of this paper is to generalize the above min&ndash;max programming problem with addition&ndash;overlap function constraints. We demonstrate that this new optimization problem can be transformed into a simplified single-variable optimization problem, which makes it easier to find an optimal solution. The bisection method will be used to find this optimal solution. In addition, when the overlap function is explicitly specified, an iterative method is given to compute the optimal objective value with a polynomial time complexity. A numerical example is provided to illustrate the procedures.

]]>Mathematics doi: 10.3390/math12203181

Authors: Wenhao Liu Simiao Yuan Zhen Wang Xinyi Chang Limeng Gao Zhenrui Zhang

The image-recipe cross-modal retrieval task, which retrieves the relevant recipes according to food images and vice versa, is now attracting widespread attention. There are two main challenges for image-recipe cross-modal retrieval task. Firstly, a recipe&rsquo;s different components (words in a sentence, sentences in an entity, and entities in a recipe) have different weight values. If a recipe&rsquo;s different components own the same weight, the recipe embeddings cannot pay more attention to the important components. As a result, the important components make less contribution to the retrieval task. Secondly, the food images have obvious properties of locality and only the local food regions matter. There are still difficulties in enhancing the discriminative local region features in the food images. To address these two problems, we propose a novel framework named Dual Cross Attention Encoders for Cross-modal Food Retrieval (DCA-Food). The proposed framework consists of a hierarchical cross attention recipe encoder (HCARE) and a cross attention image encoder (CAIE). HCARE consists of three types of cross attention modules to capture the important words in a sentence, the important sentences in an entity and the important entities in a recipe, respectively. CAIE extracts global and local region features. Then, it calculates cross attention between them to enhance the discriminative local features in the food images. We conduct the ablation studies to validate our design choices. Our proposed approach outperforms the existing approaches by a large margin on the Recipe1M dataset. Specifically, we improve the R@1 performance by +2.7 and +1.9 on the 1k and 10k testing sets, respectively.

]]>Mathematics doi: 10.3390/math12203180

Authors: Qing Qin Lingxiao Li

This study evaluates the limitations of gravity models in constructing regional association networks, using China&rsquo;s interprovincial economic connections as a case study. Comparison between a gravity-model-based simulated network and an actual network reveals significant topological differences. The gravity model overestimates the influence of larger, inward-oriented provinces and fails to accurately represent external connections. Attempts to refine the model with additional variables proved ineffective. Further theoretical analysis attributes these deficiencies to measurement bias from the model&rsquo;s simplified binary perspective and information loss due to dimensional mismatch between pairwise predictions and complex network structures. These findings underscore the need for cautious application of gravity models and the development of more comprehensive analytical frameworks in regional network analysis.

]]>Mathematics doi: 10.3390/math12203179

Authors: Aris Magklaras Christos Gogos Panayiotis Alefragis Alexios Birbas

The extreme ultraviolet (EUV) photolithography process is a cornerstone of semiconductor manufacturing and operates under demanding precision standards realized via nanometer-level overlay (OVL) error modeling. This procedure allows the machine to anticipate and correct OVL errors before impacting the wafer, thereby facilitating near-optimal image exposure while simultaneously minimizing the overall OVL error. Such models are usually high dimensional and exhibit rigorous statistical phenomena such as collinearities that play a crucial role in the process of tuning their parameters. Ordinary least squares (OLS) is the most widely used method for parameters tuning of overlay models, but in most cases it fails to compensate for such phenomena. In this paper, we propose the usage of ridge regression, a widely known machine learning (ML) algorithm especially suitable for datasets that exhibit high multicollinearity. The proposed method was applied in perturbed data from a 300 mm wafer fab, and the results show reduced residuals when ridge regression is applied instead of OLS.

]]>Mathematics doi: 10.3390/math12203178

Authors: Hangyao Tu Zheng Wang Yanwei Zhao

Unpaired image translation with feature-level constraints presents significant challenges, including unstable network training and low diversity in generated tasks. This limitation is typically attributed to the following situations: 1. The generated images are overly simplistic, which fails to stimulate the network&rsquo;s capacity for generating diverse and imaginative outputs. 2. The images produced are distorted, a direct consequence of unstable training conditions. To address this limitation, the unpaired image-to-image translation with diffusion adversarial network (UNDAN) is proposed. Specifically, our model consists of two modules: (1) Feature fusion module: In this module, one-dimensional SVD features are transformed into two-dimensional SVD features using the convolutional two-dimensionalization method, enhancing the diversity of the images generated by the network. (2) Network convergence module: In this module, the generator transitions from the U-net model to a superior diffusion model. This shift leverages the stability of the diffusion model to mitigate the mode collapse issues commonly associated with adversarial network training. In summary, the CycleGAN framework is utilized to achieve unpaired image translation through the application of cycle-consistent loss. Finally, the proposed network was verified from both qualitative and quantitative aspects. The experiments show that the method proposed can generate more realistic converted images.

]]>Mathematics doi: 10.3390/math12203177

Authors: Jonatan Pena Ramirez Adrian Arellano-Delgado Rodrigo Méndez-Ramírez Hector Javier Estrada-Garcia

One of the earliest reports on synchronization of inert systems dates back to the time of the Dutch scientist Christiaan Huygens, who discovered that a pair of pendulum clocks coupled through a wooden bar oscillate in harmony. A remarkable feature in Huygens&rsquo; experiment is that different synchronous behaviors may be observed by just changing a parameter in the coupling. Motivated by this, in this paper, we propose a novel synchronization scheme for chaotic oscillators, in which the design of the coupling is inspired in Huygens&rsquo; experiment. It is demonstrated that the coupled oscillators may exhibit not only complete synchronization, but also mixed synchronization&mdash;some states synchronize in anti-phase whereas other states synchronize in-phase&mdash;depending on a single parameter of the coupling. Additionally, the stability of the synchronous solution is investigated by using the master stability function approach and the largest transverse Lyapunov exponent. The Lorenz system is considered as particular application example, and the performance of the proposed synchronization scheme is illustrated with computer simulations and validated by means of experiments using electronic circuits.

]]>Mathematics doi: 10.3390/math12203176

Authors: Sofia Holguin Jimenez Wajdi Trabelsi Christophe Sauvey

Production rescheduling involves re-optimizing production schedules in response to disruptions that render the initial schedule inefficient or unfeasible. This process requires simultaneous consideration of multiple objectives to develop new schedules that are both efficient and stable. However, existing review papers have paid limited attention to the multi-objective optimization techniques employed in this context. To address this gap, this paper presents a systematic literature review on multi-objective production rescheduling, examining diverse shop-floor environments. Adhering to the PRISMA guidelines, a total of 291 papers were identified. From this pool, studies meeting the inclusion criteria were selected and analyzed to provide a comprehensive overview of the problems tackled, dynamic events managed, objectives considered, and optimization approaches discussed in the literature. This review highlights the primary multi-objective optimization methods used in relation to rescheduling strategies and the dynamic disruptive events studied. Findings reveal a growing interest in this research area, with &ldquo;a priori&rdquo; and &ldquo;a posteriori&rdquo; optimization methods being the most commonly implemented and a notable rise in the use of the latter. Hybridized algorithms have shown superior performance compared to standalone algorithms by leveraging combined strengths and mitigating individual weaknesses. Additionally, &ldquo;interactive&rdquo; and &ldquo;Pareto pruning&rdquo; methods, as well as the consideration of human factors in flexible production systems, remain under-explored.

]]>Mathematics doi: 10.3390/math12203174

Authors: Ravil I. Mukhamediev

In September 2024, the Fashion-MNIST dataset will be 7 years old. Proposed as a replacement for the well-known MNIST dataset, it continues to be used to evaluate machine learning model architectures. This paper describes new results achieved with the Fashion-MNIST dataset using classical machine learning models and a relatively simple convolutional network. We present the state-of-the-art results obtained using the CNN-3-128 convolutional network and data augmentation. The developed CNN-3-128 model containing three convolutional layers achieved an accuracy of 99.65% in the Fashion-MNIST test image set. In addition, this paper presents the results of computational experiments demonstrating the dependence between the number of adjustable parameters of the convolutional network and the maximum acceptable classification quality, which allows us to optimise the computational cost of model training.

]]>Mathematics doi: 10.3390/math12203175

Authors: Junheng Fang Zhidong Xiao Xiaoqiang Zhu Lihua You Xiaokun Wang Jianjun Zhang

Dynamic simulation is widely applied in the real-time and realistic physical simulation field. How to achieve natural dynamic simulation results in real-time with small data sizes is an important and long-standing topic. In this paper, we propose a dynamic reconstruction and interpolation method grounded in physical principles for simulating dynamic deformations. This method replaces the deformation forces of the widely used eXtended Position-Based Dynamics (XPBD), which are traditionally derived from the gradient of the energy potential defined by the constraint function, with the elastic beam bending forces to more accurately represent the underlying deformation physics. By doing so, it establishes a mathematical model based on dynamic partial differential equations (PDE) for reconstruction, which are the differential equations involving both the parametric variable u and the time variable t. This model also considers the inertia forces caused by acceleration. The analytical solution to this model is then integrated with the XPBD framework, built upon Newton&rsquo;s equations of motion. This integration reduces the number of design variables and data sizes, enhances simulation efficiency, achieves good reconstruction accuracy, and makes deformation simulation more capable. The experiment carried out in this paper demonstrates that deformed shapes at about half of the keyframes simulated by XPBD can be reconstructed by the proposed PDE-based dynamic reconstruction algorithm quickly and accurately with a compact and analytical representation, which outperforms static B-spline-based representation and interpolation, greatly shortens the XPBD simulation time, and represents deformed shapes with much smaller data sizes while maintaining good accuracy. Furthermore, the proposed PDE-based dynamic reconstruction algorithm can generate continuous deformation shapes, which cannot be generated by XPBD, to raise the capacity of deformation simulation.

]]>Mathematics doi: 10.3390/math12203172

Authors: Haotian Wu Siya Chen Jun Fan Guang Jin

In the industrial sector, malfunctions of equipment that occur during the production and operation process typically necessitate human intervention to restore normal functionality. However, the question that follows is how to design and optimize the intervention measures based on the modeling of actual intervention scenarios, thereby effectively resolving the faults. In order to address the aforementioned issue, we propose an improved heuristic method based on a causal generative model for the design of optimal intervention, aiming to determine the best intervention measure by analyzing the causal effects among variables. We first construct a dual-layer mapping model grounded in the causal relationships among interrelated variables to generate counterfactual data and assess the effectiveness of intervention measures. Subsequently, given the developed fault intervention scenarios, an adaptive large neighborhood search (ALNS) algorithm employing the expected improvement strategy is utilized to optimize the interventions. This method provides guidance for decision-making during equipment operation and maintenance, and the effectiveness of the proposed model and search strategy have been validated through tests on the synthetic datasets and satellite attitude control system dataset.

]]>Mathematics doi: 10.3390/math12203173

Authors: Mohd Danish Siddiqi Fatemah Mofarreh

In this paper, we develop the concept of gradient r-Almost Newton-Ricci-Yamabe solitons (in brief, gradient r-ANRY solitons) immersed in a Riemannian manifold. We deduce the minimal and totally geodesic criteria for the hypersurface of a Riemannian manifold in terms of the gradient r-ANRY soliton. We also exhibit a Schur-type inequality and discuss the triviality of the gradient r-ANRY soliton in the case of a compact manifold. Finally, we demonstrate the completeness and noncompactness of the r-Newton-Ricci-Yamabe soliton on the hypersurface of the Riemannian manifold.

]]>Mathematics doi: 10.3390/math12203171

Authors: Fernando Lepe-Silva Broderick Crawford Felipe Cisternas-Caneo José Barrera-Garcia Ricardo Soto

This research presents a novel hybrid approach, which combines the White Shark Optimizer (WSO) metaheuristic algorithm with chaotic maps integrated into the binarization process. Inspired by the predatory behavior of white sharks, WSO has shown great potential to navigate complex search spaces for optimization tasks. On the other hand, chaotic maps are nonlinear dynamical systems that generate pseudo-random sequences, allowing for better solution diversification and avoiding local optima. By hybridizing WSO and chaotic maps through adaptive binarization rules, the complementary strengths of both approaches are leveraged to obtain high-quality solutions. We have solved the Set Covering Problem (SCP), a well-known NP-hard combinatorial optimization challenge with real-world applications in several domains, and experimental results indicate that LOG and TENT chaotic maps are better after statistical testing. This hybrid approach could have practical applications in telecommunication network optimization, transportation route planning, and resource-constrained allocation.

]]>Mathematics doi: 10.3390/math12203170

Authors: Ahmed Alhindi Meng-Sang Chew

The dimensional synthesis of compliant mechanisms (CMs) leverages the flexibility of their components to achieve precise motion and functionality. This study introduces a novel approach using the parametric fuzzy form of the Freudenstein equation with triangular fuzzy numbers (TFNs) to address the complexities and uncertainties inherent in CM design. By integrating fuzzy logic with advanced computational techniques such as Newton&rsquo;s method, the proposed methodology offers a robust framework for synthesizing CMs that can adapt to varying conditions. This approach enables the creation of flexible links modeled as fuzzy regions, allowing for optimized performance and reliability across a range of operational scenarios. Numerical examples illustrate the practical application and efficacy of the proposed methods, highlighting significant improvements in the design and synthesis of CMs. The integration of fuzzy logic in the synthesis process not only enhances the resilience of the mechanisms but also paves the way for future advancements in the field. This study demonstrates the potential of fuzzy logic principles in optimizing CM designs, ensuring they meet specific functional requirements with high precision.

]]>Mathematics doi: 10.3390/math12203169

Authors: Esteban Olivares Michel Curé Ignacio Araya Ernesto Fabregas Catalina Arcos Natalia Machuca Gonzalo Farias

This article presents a new algorithm that uses techniques from the field of artificial intelligence to automatically estimate the physical parameters of massive stars from a grid of stellar spectral models. This is the first grid to consider hydrodynamic solutions for stellar winds and radiative transport, containing more than 573 thousand synthetic spectra. The methodology involves grouping spectral models using deep learning and clustering techniques. The goal is to delineate the search regions and differentiate the &ldquo;species&rdquo; of spectra based on the shapes of the spectral line profiles. Synthetic spectra close to an observed stellar spectrum are selected using deep learning and unsupervised clustering algorithms. As a result, for each spectrum, we found the effective temperature, surface gravity, micro-turbulence velocity, and abundance of elements, such as helium and silicon. In addition, the values of the line force parameters were obtained. The developed algorithm was tested with 40 observed spectra, achieving 85% of the expected results according to the scientific literature. The execution time ranged from 6 to 13 min per spectrum, which represents less than 5% of the total time required for a one-to-one comparison search under the same conditions.

]]>Mathematics doi: 10.3390/math12203168

Authors: Yuhong Liu Liming Zheng Bohan Cai

Differential evolution is capable of searching for the optimum for different types of optimization problems with a few inputs, which has gained worldwide popularity. In this paper, we propose a parameters adaptation scheme based on the stagnation ratio (PASR), which regards the stagnation ratio (STR) as the indicator for adjusting the control parameters and greediness parameter. To be specific, when the STR is larger than the predefined threshold, exploration is advocated. In this circumstance, larger control parameters and a greediness parameter are adopted. However, when the STR is smaller than the predefined threshold, exploitation is preferred. In this case, smaller control parameters and a greediness parameter are utilized. Further, when the stagnation lasts for a long period, a generation-based selection (GBS) scheme is developed to help it escape from the local optimum and stagnation. Comparative experiments have been implemented on the CEC2017 to testify the effectiveness of adaptive differential evolution with the stagnation termination mechanism (STMDE) and its components. The competitiveness of the STMDE is also verified via comparing it to top-performing DE variants in the practical optimization problem selected from the CEC2011.

]]>Mathematics doi: 10.3390/math12203167

Authors: Shengnan He Xin Liu Zongbin Yin Xiaoli Sun

In this paper, we investigate the relationships among point transitivity, topological transitivity, Li&ndash;Yorke chaos, and the existence of irregular vectors for a linear semiflow {Tt}t&isin;&Delta; indexed with a complex sector. We reveal the equivalence between topological transitivity and point transitivity for a linear semiflow {Tt}t&isin;&Delta;, especially in case the range of some operator Tt,t&isin;&Delta; is not dense. We also prove that Li&ndash;Yorke chaos is equivalent to the existence of a semi-irregular vector and that point transitivity is stronger than the existence of an irregular vector for any linear semiflow Ttt&isin;&Delta;. At last, unlike the conclusion for traditional linear dynamical systems, we show that there exists a Li&ndash;Yorke chaotic C0-semigroup Ttt&isin;&Delta; without irregular vectors. The results and proof methods presented in this paper demonstrate the differences in the dynamical behavior between linear semiflows {Tt}t&isin;&Delta; and traditional linear systems with the acting semigroup S=Z+ and S=R+.

]]>Mathematics doi: 10.3390/math12203166

Authors: Xue Li Chao Ma

In this paper, we study the shrinking target problem regarding Q-Cantor series expansions of the formal Laurent series field. We provide the Hausdorff dimension of a very general shrinking target scheme generated by the nonautonomous dynamical system on the unit disk I.

]]>Mathematics doi: 10.3390/math12203165

Authors: Yubao Yuan Zhenghua Gao Lu He Zhen Lei

The vibration caused by blasting load may result in damage to high-rise buildings. In view of this consideration, an investigation of the vibration law was conducted in the context of an actual engineering project. The objective of this study was to analyze the peak particle velocity (PPV), vibration frequency, and peak particle stress (PPS) of the buildings within a range of 50 m to 250 m from the epicenter, under the condition of a single-shot charge of 30 kg. To achieve this, a combination of theoretical analysis, field tests, and numerical experiments was employed. Sadovsky&rsquo;s formula was used in combination with the least squares method to fit the propagation law of ground PPV. ANSYS 17.0/LS-DYNA and Origin 8.0 software were applied to study the amplification effect of building PPV and the relationship between PPV and PPS. Taking into account the difference between the height of the ground measuring point and the height of the explosive center, we investigated the PPV of high-rise buildings under three conditions of 36 m, 6 m, and &minus;24 m drop from the explosive center, to strengthen the in-depth understanding of resonance effect. The following conclusions were reached: the ground PPV decreases with increasing horizontal distance from the explosive center, with the radial PPV being the largest. The vertical PPV of buildings exhibits a height amplification effect, with a magnification factor of 2.66. The radial and tangential PPVs of buildings demonstrate that the middle layer exhibits a relatively modest speed, whereas the low and high layers demonstrate considerably higher speeds. The greater the vertical distance from the explosion center is, the greater is the PPV. The vibration frequency is irregular, with an average of 10 Hz. The PPV of buildings is not proportional to the PPS, which is the highest at the bottom. It is recommended that the PPS of buildings be included in the criteria for safety allowances in blasting vibration.

]]>Mathematics doi: 10.3390/math12203164

Authors: Ping-Hung Wu Thi Phuong Hoang Yen-Ting Chou Andres Philip Mayol Yu-Wei Lai Chih-Hsiang Kang Yu-Cheng Chan Siou-Zih Lin Ssu-Han Chen

Integrated circuits (ICs) are critical components in the semiconductor industry, and precise wafer defect inspection is essential for maintaining product quality and yield. This study addresses the challenge of insufficient sample patterns in wafer defect datasets by using the denoising diffusion probabilistic model (DDPM) to produce generated defects that elevate the performance of wafer defect inspection. The quality of the generated defects was evaluated using the Fr&eacute;chet Inception Distance (FID) score, which was then synthesized with real defect-free backgrounds to create an augmented defect dataset. Experimental results demonstrated that the augmented defect dataset significantly boosted performance, achieving 98.7% accuracy for YOLOv8-cls, 95.8% box mAP for YOLOv8-det, and 95.7% mask mAP for YOLOv8-seg. These results indicate that the generated defects produced by the DDPM can effectively enrich wafer defect datasets and enhance wafer defect inspection performance in real-world applications.

]]>Mathematics doi: 10.3390/math12203163

Authors: Sharief Deshmukh Nasser Bin Turki Ramesh Sharma

A nontrivial conformal vector field &omega; on an m-dimensional connected Riemannian manifold Mm,g has naturally associated with it the conformal potential &theta;, a smooth function on Mm, and a skew-symmetric tensor T of type (1,1) called the associated tensor. There is a third entity, namely the vector field T&omega;, called the orthogonal reflection field, and in this article, we study the impact of the condition that commutator &omega;,T&omega;=0; this condition that we refer to as the orthogonal reflection field is commutative. As a natural impact of this condition, we see the existence of a smooth function &rho; on Mm such that &nabla;&theta;=&rho;&omega;; this function &rho; is called the proportionality function. First, we show that an m-dimensional compact and connected Riemannian manifold Mm,g admits a nontrivial conformal vector field &omega; with a commuting orthogonal reflection T&omega; and constant proportionality function &rho; if and only if Mm,g is isometric to the sphere Sm(c) of constant curvature c. Secondly, we find three more characterizations of the sphere and two characterizations of a Euclidean space using these ideas. Finally, we provide a condition for a conformal vector field on a compact Riemannian manifold to be closed.

]]>Mathematics doi: 10.3390/math12203162

Authors: Li Shi Xiangjun Li Bingxue Jin Yingjie Li

Due to the security weaknesses of chaos-based pseudorandom number generators, in this paper, a new pseudorandom number generator (PRNG) based on mixing three-dimensional variables of a cat chaotic map is proposed. A uniformly distributed chaotic sequence by a logistic map is used in the mixing step. Both statistical tests and a security analysis indicate that our PRNG has good randomness and is more complex than any one-dimensional variable of a cat map. Furthermore, a new image encryption algorithm based on the chaotic PRNG is provided to protect the content of artwork images. The core of the algorithm is to use the sequence generated by the pseudorandom number generator to achieve the process of disruption and diffusion of the image pixels, so as to achieve the effect of obfuscation and encryption of the image content. Several security tests demonstrate that this image encryption algorithm has a high security level.

]]>Mathematics doi: 10.3390/math12203161

Authors: Siyu Liu Xiequan Fan Haijuan Hu Paul Doukhan

Let fn be the non-parametric kernel density estimator based on a kernel function K and a sequence of independent and identically distributed random vectors taking values in Rd. With some mild conditions, we establish sharp moderate deviations for the kernel density estimator. This means that we provide an equivalent for the tail probabilities of this estimator.

]]>Mathematics doi: 10.3390/math12193160

Authors: Hui-Ling Yang Chun-Tao Chang Yao-Ting Tseng

This study investigated non-instantaneous deteriorating items because not all products deteriorate immediately. In the high-tech product life cycle, the product demand increases linearly substantially in the growth stage and maintains a near-constant level in the maturity stage. This is a ramp-type demand rate. To satisfy the demand as shortages occur, partial backlogging is necessary. The advance-cash-credit payment scheme, comprising advance, cash, and credit payments, has gained popularity in business transactions to improve cash flow flexibility among supply chain participants. This study explored a partial backlogging inventory model with ramp-type demand for non-instantaneous deteriorating items under generalized payment. The proposed model also incorporated discounted cash flow analysis to account for the time value of the profit function. This study attempted to determine the optimal replenishment strategy to maximize the present value of the total profit. Finally, we conducted a sensitivity analysis to examine the efficacy of the proposed model and gain managerial insights. The optimal total profit rises with an increase in the permissible delay period and sale price but decreases with an increase in ordering and purchase costs. Then, the decision-maker can refer to the managerial insights to choose the appropriate parameter value for the operation.

]]>Mathematics doi: 10.3390/math12193159

Authors: Yajun Ge Jiannan Wang Bo Zhang Fan Peng Jing Ma Chenyu Yang Yue Zhao Ming Liu

Accurate traffic flow prediction in road networks is essential for intelligent transportation systems (ITS). Since traffic data are collected from the road network with spatial topological and time series sequences, the traffic flow prediction is regarded as a spatial&ndash;temporal prediction task. With the powerful ability to model the non-Euclidean data, the graph convolutional network (GCN)-based models have become the mainstream framework for traffic forecasting. However, existing GCN-based models either use the manually predefined graph structure to capture the spatial features, ignoring the heterogeneity of road networks, or simply perform 1-D convolution with fixed kernel to capture the temporal dependencies of traffic data, resulting in insufficient long-term temporal feature extraction. To solve those issues, a spatial&ndash;temporal correlation constrained dynamic graph convolutional network (STC-DGCN) is proposed for traffic flow forecasting. In STC-DGCN, a spatial&ndash;temporal embedding encoder module (STEM) is first constructed to encode the dynamic spatial relationships for road networks at different time steps. Then, a temporal feature encoder module with heterogeneous time series correlation modeling (TFE-HCM) and a spatial feature encoder module with dynamic multi-graph modeling (SFE-DCM) are designed to generate dynamic graph structures for effectively capturing the dynamic spatial and temporal correlations. Finally, a spatial&ndash;temporal feature fusion module based on a gating fusion mechanism (STM-GM) is proposed to effectively learn and leverage the inherent spatial&ndash;temporal relationships for traffic flow forecasting. Experimental results from three real-world traffic flow datasets demonstrate the superior performance of the proposed STC-DGCN compared with state-of-the-art traffic flow forecasting models.

]]>Mathematics doi: 10.3390/math12193158

Authors: Kuang-Hsun Shih Yi-Hsien Wang I-Chen Kao Fu-Ming Lai

The global financial landscape has witnessed a significant shift towards Exchange-Traded Funds (ETFs), with their market capitalization surpassing USD 10 trillion in 2023, due to advantages such as low management fees, high liquidity, and broad market exposure. As ETFs become increasingly central to investment strategies, accurately forecasting their performance has become crucial. This study addresses this need by comparing the efficacy of deep learning models against the traditional Fama-French three-factor model in predicting daily ETF returns. The methodology employs eight artificial neural network architectures, including ANN, LSTM, GRU, CNN, and their variants, implemented in Python and applied to data ranging from 2010 to 2020, while also exploring the impact of additional factors on forecast accuracy. Empirical results reveal that LSTM and the Fama-French three-factor model exhibit a superior performance in ETF return prediction. This study contributes to the literature on financial forecasting and offers practical insights into investment decision making. By leveraging advanced artificial intelligence techniques, this study aims to enhance the toolkit available for ETF performance analysis, potentially improving investment strategies in this dynamic market segment.

]]>Mathematics doi: 10.3390/math12193157

Authors: Xiao-Jun Yao Yu-Chun Lv Xiao-Mei Yang Feng-Yang Wang Yong-Xiang Zheng

Modal parameters are inherent characteristics of civil structures. Due to the effect of environmental factors and ambient loads, the physical and modal characteristics of a structure tend to change over time. Therefore, the effective identification of time-varying modal parameters has become an essential topic. In this study, an instantaneous modal identification method based on an adaptive chirp mode decomposition (ACMD) technique was proposed. The ACMD technique is highly adaptable and can accurately estimate the instantaneous frequencies of a structure. However, it is important to highlight that an initial frequency value must be selected beforehand in ACMD. If the initial frequency is set incorrectly, the resulting instantaneous frequencies may lack accuracy. To address the aforementioned problem, the Welch power spectrum was initially developed to extract a high-resolution time&ndash;frequency distribution from the measured signals. Subsequently, the time&ndash;frequency ridge was identified based on the maximum energy position in the time&ndash;frequency distribution plot, with the frequencies associated with the time&ndash;frequency ridge serving as the initial frequencies. Based on the initial frequencies, the measured signals with multiple degrees of freedom could be decomposed into individual time-varying components with a single degree of freedom. Following that, the instantaneous frequencies of each time-varying component could be calculated directly. Subsequently, a sliding window principal component analysis (PCA) method was introduced to derive instantaneous mode shapes. Finally, vibration data collected under various operational scenarios were used to validate the proposed method. The results demonstrated the effective identification of time-varying modal parameters in real-world civil structures, without missing modes.

]]>Mathematics doi: 10.3390/math12193156

Authors: Priyanka Majumder Valerio Antonio Pamplona Salomon

Multi-attribute decision-making (MADM) is a methodology for solving decision problems with a finite set of alternatives. The several methods of MADM require weights for the criteria and the alternatives to provide a solution. The Ordinal Priority Approach (OPA) is a recently proposed method for MADM that innovates; it does not require these inputs, just the rankings of criteria and alternatives. This article introduces a new hybrid method for MADM: the Intuitionistic Fuzzy Ordinal Priority Approach with Grey Relational Analysis (OPA-IF-GRA). OPA-IF-GRA combines GRA with OPA-IF, a newer extension of OPA that includes intuitionistic fuzzy sets to incorporate uncertainty into the decision-making process. The article presents an OPA-IF-GRA application for solving an electronics engineering problem, considering four criteria and six alternatives. The solution of OPA-IF-GRA is compared with the solutions obtained with three other MADM methods.

]]>Mathematics doi: 10.3390/math12193155

Authors: Alexander Zhdanok

We study Markov operators T, A, and T* of general Markov chains on an arbitrary measurable space. The operator, T, is defined on the Banach space of all bounded measurable functions. The operator A is defined on the Banach space of all bounded countably additive measures. We construct an operator T*, topologically conjugate to the operator T, acting in the space of all bounded finitely additive measures. We prove the main result of the paper that, in general, a Markov operator T* is quasi-compact if and only if T is quasi-compact. It is proved that the conjugate operator T* is quasi-compact if and only if the Doeblin condition (D) is satisfied. It is shown that the quasi-compactness conditions for all three Markov operators T, A, and T* are equivalent to each other. In addition, we obtain that, for an operator T* to be quasi-compact, it is necessary and sufficient that it does not have invariant purely finitely additive measures. A strong uniform reversible ergodic theorem is proved for the quasi-compact Markov operator T* in the space of finitely additive measures. We give all the proofs for the most general case. A detailed analysis of Lin&rsquo;s counterexample is provided.

]]>Mathematics doi: 10.3390/math12193154

Authors: Rui Li Weidong Huang

With the rapid growth of social media and live-streaming technology, live-stream selling has become integral to the digital economy. Using differential game theory, this paper examines how fairness concerns impact the profits of internet celebrities and brand manufacturers under the &ldquo;pure commission&rdquo; model. We analyzed no fairness concern, gap fairness concern, and self-due fairness concern models, to investigate the optimal decisions and corresponding profits for an internet celebrity and a brand manufacturer. The results show that the internet celebrity earned the highest profits with low commission rates under the self-due fairness concern model, whereas higher commission rates yielded higher profits for the internet celebrity under the gap fairness concern model. Simultaneously, fairness concerns significantly affected the cooperation stability and long-term benefits, motivating the internet celebrity to maintain efficient collaborations with the brand manufacturer. Furthermore, the self-due fairness concern model was more practical than the gap fairness concern model.

]]>Mathematics doi: 10.3390/math12193153

Authors: Faezeh Ataeiasad David Elizondo Saúl Calderón Ramírez Sarah Greenfield Lipika Deka

This paper proposes a novel method capable of both detecting OOD data and generating in-distribution data samples. To achieve this, a VAE model is adopted and augmented with a memory module, providing capacities for identifying OOD data and synthesising new in-distribution samples. The proposed VAE is trained on normal data and the memory stores prototypical patterns of the normal data distribution. At test time, the input is encoded by the VAE encoder; this encoding is used as a query to retrieve related memory items, which are then integrated with the input encoding and passed to the decoder for reconstruction. Normal samples reconstruct well and yield low reconstruction errors, while OOD inputs produce high reconstruction errors as their encodings get replaced by retrieved normal patterns. Prior works use memory modules for OOD detection with autoencoders, but this method leverages a VAE architecture to enable generation abilities. Experiments conducted with CIFAR-10 and MNIST datasets show that the memory-augmented VAE consistently outperforms the baseline, particularly where OOD data resembles normal patterns. This notable improvement is due to the enhanced latent space representation provided by the VAE. Overall, the memory-equipped VAE framework excels in identifying OOD and generating creative examples effectively.

]]>Mathematics doi: 10.3390/math12193151

Authors: Carlos Eduardo Loterio Matos Miguel Ângelo Lellis Moreira Maria Teresa Ribeiro Pereira Carlos Francisco Simões Gomes Marcos dos Santos Francisco J. G. Silva

Market competitiveness drives the electric motors industry, which in turn necessitates the selection of optimal production scenarios, particularly in the context of packaging. This is crucial for maintaining competitiveness and meeting the rigorous quality and logistical demands that are characteristic of this industry. This paper presents a systematic analysis of the packaging production chain for electric motors, employing the SAPEVO-M method as a decision aid tool. The study examines various strategic options, including outsourcing and internalizing processes, with a particular focus on their impacts on logistics, quality control, and overall supply-chain efficiency. The research conducts a comprehensive evaluation of these strategies to ascertain the most effective approach for managing the complexities of packaging production. The SAPEVO-M method facilitated a structured decision-making process, allowing for the aggregation and prioritization of diverse criteria such as cost, quality, flexibility, environmental impact, and supply risk. A sensitivity analysis was performed to validate the robustness of the decision-making outcomes under varying alternatives. The findings highlight the benefits of internalizing certain processes, particularly the assembly (with a score of 43.27%), to gain direct control over production variables, leading to enhanced operational efficiency and product competitiveness. This paper contributes to the literature by demonstrating the application of MCDA in enhancing strategic decisions within the electric motors industry, providing insights for analyzing other manufacturing factors in the improvement of supply-chain processes.

]]>Mathematics doi: 10.3390/math12193152

Authors: Abdalla Mansur Muhammad Shoaib Iharka Szücs-Csillik Daniel Offin Jack Brimberg Hedia Fgaier

This paper investigated the periodic and quasi-periodic orbits in the symmetric collinear four-body problem through a variational approach. We analyze the conditions under which homographic solutions minimize the action functional. We compute the minimal value of the action functional for these solutions and show that, for four equal masses organized in a linear configuration, these solutions are the minimizers of the action functional. Additionally, we employ numerical experiments using Poincar&eacute; sections to explore the existence and stability of periodic and quasi-periodic solutions within this dynamical system. Our results provide a deeper understanding of the variational principles in celestial mechanics and reveal complex dynamical behaviors, crucial for further studies in multi-body problems.

]]>Mathematics doi: 10.3390/math12193150

Authors: Shengkun Xie

This study examines how telematics variables such as annual percentage driven, total miles driven, and driving patterns influence the distributional behaviour of conventional rating factors when incorporated into predictive models for capturing auto insurance risk in rate regulation. To effectively manage the complexity inherent in telematics data, we advocate for the adoption of non-negative sparse principal component analysis (NSPCA) as a structured approach for data dimensionality reduction. By emphasizing sparsity and non-negativity constraints, NSPCA enhances the interpretability and predictive power of models concerning both loss severity and claim counts. This methodological innovation aims to advance statistical analyses within insurance pricing frameworks, ensuring the robustness of predictive models and providing insights crucial for rate regulation strategies specific to the auto insurance sector. Results show that, to enhance auto insurance risk pricing models, it is essential to address data dimension reduction challenges when integrating telematics data variables. Our findings underscore that integrating telematics variables into predictive models maintains the integrity of risk relativity estimates associated with traditional policy variables.

]]>Mathematics doi: 10.3390/math12193149

Authors: Ilhami Sel Davut Hanbay

This study focuses on the neural machine translation task for the TR-EN language pair, which is considered a low-resource language pair. We investigated fine-tuning strategies for pre-trained language models. Specifically, we explored the effectiveness of parameter-efficient adapter methods for fine-tuning multilingual pre-trained language models. Various combinations of LoRA and bottleneck adapters were experimented with. The combination of LoRA and bottleneck adapters demonstrated superior performance compared to other methods. This combination required only 5% of the pre-trained language model to be fine-tuned. The proposed method enhances parameter efficiency and reduces computational costs. Compared to the full fine-tuning of the multilingual pre-trained language model, it showed only a 3% difference in the BLEU score. Thus, nearly the same performance was achieved at a significantly lower cost. Additionally, models using only bottleneck adapters performed worse despite having a higher parameter count. Although adding LoRA to pre-trained language models alone did not yield sufficient performance, the proposed method improved machine translation. The results obtained are promising, particularly for low-resource language pairs. The proposed method requires less memory and computational load while maintaining translation quality.

]]>Mathematics doi: 10.3390/math12193148

Authors: Xianfeng Yu Yongming Li Shengling Geng

As an extension of quantitative temporal logic, uncertain temporal logic essentially describes the temporal behavior of uncertain and incomplete systems, thus better solving search and decision-making problems in such systems. Fuzzy linear temporal logic (FLTL) is a focal point in uncertain temporal logic research. However, there are evident shortcomings in the current research outcomes. First, in previous FLTL studies, the practice of obtaining path reachability and formula satisfaction values independently and subsequently selecting the smaller of the two as the satisfaction value metric led to information loss. Furthermore, this simplistic information fusion approach fails to reflect the varying importance of these two types of information to the requirements. Second, computing path reachability and temporal logic formula satisfaction values separately may result in a mismatch between the two pieces of information with respect to the same path segment. Thus, the primary challenge lies in accurately integrating the satisfaction values of temporal logic formulas with the path reachability of the segments that yields these satisfaction values, utilizing various reasonable information synthesis methods, to ensure synchronization between path reachability and formula satisfaction values without incurring information loss. Additionally, it is crucial to reflect the different preference requirements for these two types of information. Moreover, the temporal logic formula characterizes system properties, with its sub-formulas delineating distinct sub-properties. Consequently, considering the varying importance preferences of sub-formulas is also significant. To address these deficiencies, we introduced quality constraint operators into FLTL, resulting in quality-constrained fuzzy linear temporal logic (QFLTL). This incorporation enables the synchronization and comprehensive fusion of path-reachability information and formula satisfaction values within the final semantic metric, thereby resolving the issues related to information synchronization and loss. Furthermore, it can accommodate the differing preference requirements between the two types of information and sub-properties during the information synthesis process. We defined the syntax and semantics of QFLTL and examined its expressive power and properties. Notably, we investigated the decidability of logical decision problems in QFLTL, encompassing validity, satisfiability, and model-checking issues. We proposed corresponding solution algorithms and analyzed their complexities.

]]>Mathematics doi: 10.3390/math12193147

Authors: Yue Hu Shiyu Shen Hao Yang Weize Wang

The threat of quantum computing has spurred research into post-quantum cryptography. SQIsign, a candidate submitted to the standardization process of the National Institute of Standards and Technology, is emerging as a promising isogeny-based signature scheme. This work aimed to enhance SQIsign&rsquo;s practical deployment by optimizing its low-level arithmetic operations. Through hierarchical decomposition and performance profiling, we identified the ideal-to-isogeny translation, primarily involving elliptic curve operations, as the main bottleneck. We developed efficient 32-bit finite field arithmetic for elliptic curves, such as basic operations, like addition with carry, subtraction with borrow, and conditional move. We then implemented arithmetic operations in the Montgomery domain, and extended these to quadratic field extensions. Our implementation offers improved compatibility with 32-bit architectures and enables more fine-grained SIMD acceleration. Performance evaluations demonstrated the practicality in low-level operations. Our work has potential in easing the development of SQIsign in practice, making SQIsign more efficient and practical for real-world post-quantum cryptographic applications.

]]>Mathematics doi: 10.3390/math12193146

Authors: Wajdi Rajhi Ali B. M. Ali Dheyaa J. Jasim Omid Mehrabi Lotfi Ben Said Mahmoud Moradi

This work aims to analyze the effects of the main process parameters of fused filament fabrication (FFF) on the mechanical properties and part weight of 3D-printed thermoplastic polyurethane (TPU). Raster angle (RA), infill percentage (IP), and extruder temperature (FFF) in the ranges of 0&ndash;90&deg;, 15&ndash;55%, and 220&ndash;260 &deg;C, respectively, were considered as the FFF input parameters, and output variables part weight (PW), elongation at break (E), maximum failure load (MFL), ratio of the maximum failure load to part weight (Ratio), and build time (BT) were considered as responses. The Response Surface Methodology (RSM) and Design of Experiments (DOE) were applied in the analysis. Subsequently, the RSM approach was performed through multi-response optimizations with the help of Design-Expert software. The experimental results indicated a higher maximum failure load is achieved with an increased raster angle and decreased extruder temperature. ANOVA results show that ET has the most significant effect on elongation at break, with elongation at break decreasing as ET increases. The raster angle does not significantly affect the part weight of the TPU samples. The ratio of the maximum failure load to part weight of samples decreases with an increase in IP and ET. The results also indicated that the part weight and build time of FFF-printed TPU samples increase with an increase in IP. An ET of 220 &deg;C, RA of 0&deg;, and IP of 15% are the optimal combination of input variables for achieving the minimal part weight; minimal build time; and maximum elongation at break, maximum failure load, and ratio of the maximum failure load to part weight.

]]>Mathematics doi: 10.3390/math12193145

Authors: Yeudiel Lara Moreno Carlos Ignacio Hernández Castellanos

Traditional portfolio construction primarily revolves around a bi-objective approach, focusing on minimizing portfolio variance while maximizing expected returns. However, this approach leaves out other objectives that could interest decision makers. In this work, we incorporate an extra objective, namely the environmental, social, and governance index (ESG), as a secondary objective. This addition empowers investors to customize their portfolios by defining explicit trade-off thresholds between expected returns and risk, considering the ESG index. To achieve this goal, we make use of external archiving techniques and evolutionary algorithms. In particular, we first find approximate solutions to the bi-objective problem; then, we look for efficient solutions for ESG. We tested our approach with data on the Dow Jones, S&amp;P500, and Nasdaq100 from Yahoo Finance. The results show that the proposed methodology can identify portfolios with good returns and risks considering ESG.

]]>Mathematics doi: 10.3390/math12193144

Authors: Dingding Qi Yingjun Zhao Zhengjun Wang Wei Wang Li Pi Longyue Li

The logistics demands of industries represented by e-commerce have experienced explosive growth in recent years. Vehicle path-planning plays a crucial role in optimization systems for logistics and distribution. A path-planning scheme suitable for an actual scenario is the key to reducing costs and improving service efficiency in logistics industries. In complex application scenarios, however, it is difficult for conventional heuristic algorithms to ensure the quality of solutions for vehicle routing problems. This study proposes a joint approach based on the genetic algorithm and graph convolutional network for solving the capacitated vehicle routing problem with multiple distribution centers. First, we use the heuristic method to modularize the complex environment and encode each module based on the constraint conditions. Next, the graph convolutional network is adopted for feature embedding for the graph representation of the vehicle routing problem, and multiple decoders are used to increase the diversity of the solution space. Meanwhile, the REINFORCE algorithm with a baseline is employed to train the model, ensuring quick returns of high-quality solutions. Moreover, the fitness function is calculated based on the solution to each module, and the genetic algorithm is employed to seek the optimal solution on a global scale. Finally, the effectiveness of the proposed framework is validated through experiments at different scales and comparisons with other algorithms. The experimental results show that, compared to the single decoder GCN-based solving method, the method proposed in this paper improves the solving success rate to 100% across 15 generated instances. The average path length obtained is only 11% of the optimal solution produced by the GCN-based multi-decoder method.

]]>Mathematics doi: 10.3390/math12193143

Authors: Qiong Bao Minghao Gao Jianming Chen Xu Tan

The market share of electric vehicles (EVs) is growing rapidly. However, given the huge demand for parking and charging of electric vehicles, supporting facilities generally have problems such as insufficient quantity, low utilization efficiency, and mismatch between supply and demand. In this study, based on the actual EV operation data, we propose a driver travel-charging demand prediction method and a fuzzy bi-objective optimization method for location and size planning of charging parking lots (CPLs) based on existing parking facilities, aiming to reduce the charging waiting time of EV users while ensuring the maximal profit of CPL operators. First, the Monte Carlo method is used to construct a driver travel-charging behavior chain and a user spatiotemporal activity transfer model. Then, a user charging decision-making method based on fuzzy logic inference is proposed, which uses the fuzzy membership degree of influencing factors to calculate the charging probability of users at each road node. The travel and charging behavior of large-scale users are then simulated to predict the spatiotemporal distribution of charging demand. Finally, taking the predicted charging demand distribution as an input and the number of CPLs and charging parking spaces as constraints, a bi-objective optimization model for simultaneous location and size planning of CPLs is constructed, and solved using the fuzzy genetic algorithm. The results from a case study indicate that the planning scheme generated from the proposed methods not only reduces the travelling and waiting time of EV users for charging in most of the time, but also controls the upper limit of the number of charging piles to save construction costs and increase the total profit. The research results can provide theoretical support and decision-making reference for the planning of electric vehicle charging facilities and the intelligent management of charging parking lots.

]]>Mathematics doi: 10.3390/math12193142

Authors: Mojmir Uranjek Denis Imamović Iztok Peruš

This article aims to provide an accurate mathematical model with the minimum number of degrees of freedom for describing the floating sleeper phenomenon. This was accomplished using mathematical modeling supported by extensive field measurements of the railway track. Although the observed phenomenon is very complex, the simplified single degree of freedom (SDOF) mathematical model proved accurate enough for its characterization. The progression of the deterioration of the railway track was successfully correlated to changes in the maximal dynamic factor for different types of pulse loading. The results of the presented study might enable the enhanced construction and maintenance of railroads, particularly in karst areas.

]]>Mathematics doi: 10.3390/math12193141

Authors: Yang Zha Ying Li Xiao-Gang Lu

Large Language Models (LLMs) excel in fields such as natural language understanding, generation, complex reasoning, and biomedicine. With advancements in materials science, traditional manual annotation methods for phase diagrams have become inadequate due to their time-consuming nature and limitations in updating thermodynamic databases. To overcome these challenges, we propose a framework based on instruction tuning, utilizing LLMs for automated end-to-end annotation of phase diagrams. High-quality phase diagram images and expert descriptions are collected from handbooks and then preprocessed to correct errors, remove redundancies, and enhance information. These preprocessed data form a golden dataset, from which a subset are used to train LLMs through hierarchical sampling. The fine-tuned LLM is then tested for automated phase diagram annotation. Results show that the fine-tuned model achieves a cosine similarity of 0.8737, improving phase diagram comprehension accuracy by 7% compared to untuned LLMs. To the best of our knowledge, this is the first paper to propose using LLMs for the automated annotation of phase diagrams, replacing traditional manual annotation methods and significantly enhancing efficiency and accuracy.

]]>Mathematics doi: 10.3390/math12193140

Authors: Antoni Guerrero Angel A. Juan Alvaro Garcia-Sanchez Luis Pita-Romero

In urban logistics, effective maintenance is crucial for maintaining the reliability and efficiency of energy supply systems, impacting both asset performance and operational stability. This paper addresses the scheduling and routing plans for maintenance of power generation assets over a multi-period horizon. We model this problem as a multi-period team orienteering problem. To address this multi-period challenge, we propose a dual approach: a novel reinforcement learning (RL) framework and a biased-randomized heuristic algorithm. The RL-based method dynamically learns from real-time operational data and evolving asset conditions, adapting to changes in asset health and failure probabilities to optimize decision making. In addition, we develop and apply a biased-randomized heuristic algorithm designed to provide effective solutions within practical computational limits. Our approach is validated through a series of computational experiments comparing the RL model and the heuristic algorithm. The results demonstrate that, when properly trained, the RL-based model is able to offer equivalent or even superior performance compared to the heuristic algorithm.

]]>Mathematics doi: 10.3390/math12193139

Authors: Autcha Araveeporn

The multiple regression model statistical technique is employed to analyze the relationship between the dependent variable and several independent variables. The multicollinearity problem is one of the issues affecting the multiple regression model, occurring in regard to the relationship among independent variables. The ordinal least square is the standard method to evaluate parameters in the regression model, but the multicollinearity problem affects the unstable estimator. Liu regression is proposed to approximate the Liu estimators based on the Liu parameter, to overcome multicollinearity. In this paper, we propose a modified Liu parameter to estimate the biasing parameter in scaling options, comparing the ordinal least square estimator with two modified Liu parameters and six standard Liu parameters. The performance of the modified Liu parameter is considered, generating independent variables from the multivariate normal distribution in the Toeplitz correlation pattern as the multicollinearity data, where the dependent variable is obtained from the independent variable multiplied by a coefficient of regression and the error from the normal distribution. The mean absolute percentage error is computed as an evaluation criterion of the estimation. For application, a real Hepatitis C patients dataset was used, in order to investigate the benefit of the modified Liu parameter. Through simulation and real dataset analysis, the results indicate that the modified Liu parameter outperformed the other Liu parameters and the ordinal least square estimator. It can be recommended to the user for estimating parameters via the modified Liu parameter when the independent variable exhibits the multicollinearity problem.

]]>Mathematics doi: 10.3390/math12193137

Authors: Muvasharkhan Jenaliyev Akerke Serik Madi Yergaliyev

The work establishes the unique solvability of a boundary value problem for a 3D linearized system of Navier&ndash;Stokes equations in a degenerate domain represented by a cone. The domain degenerates at the vertex of the cone at the initial moment of time, and, as a consequence of this fact, there are no initial conditions in the problem under consideration. First, the unique solvability of the initial-boundary value problem for the 3D linearized Navier&ndash;Stokes equations system in a truncated cone is established. Then, the original problem for the cone is approximated by a countable family of initial-boundary value problems in domains represented by truncated cones, which are constructed in a specially chosen manner. In the limit, the truncated cones will tend toward the original cone. The Faedo&ndash;Galerkin method is used to prove the unique solvability of initial-boundary value problems in each of the truncated cones. By carrying out the passage to the limit, we obtain the main result regarding the solvability of the boundary value problem in a cone.

]]>Mathematics doi: 10.3390/math12193138

Authors: Purit Thammasiri Vasile Berinde Narin Petrot Kasamsuk Ungchittrakool

In this research paper, we present a novel theoretical technique, referred to as the double Tseng&rsquo;s algorithm with inertial terms, for finding a common solution to two monotone inclusion problems. Developing the double Tseng&rsquo;s algorithm in this manner not only comprehensively expands theoretical knowledge in this field but also provides advantages in terms of step-size parameters, which are beneficial for tuning applications and positively impact the numerical results. This new technique can be effectively applied to solve the problem of image deblurring and offers numerical advantages compared to some previously related results. By utilizing certain properties of a Lipschitz monotone operator and a maximally monotone operator, along with the identity associated with the convexity of the quadratic norm in the framework of Hilbert spaces, and by imposing some constraints on the scalar control conditions, we can achieve weak convergence to a common zero point of the sum of two monotone operators. To demonstrate the benefits and advantages of this newly proposed algorithm, we performed numerical experiments to measure the improvement in the signal&ndash;to&ndash;noise ratio (ISNR) and the structural similarity index measure (SSIM). The results of both numerical experiments (ISNR and SSIM) demonstrate that our new algorithm is more efficient and has a significant advantage over the relevant preceding algorithms.

]]>Mathematics doi: 10.3390/math12193136

Authors: Miroslav Ćirić Jelena Ignjatović Predrag S. Stanimirović

In the present paper, we introduce the concept of idempotent-aided factorization (I.-A. factorization) of a regular element of a semigroup, which can be understood as a semigroup-theoretical extension of full-rank factorization of matrices over a field. I.-A. factorization of a regular element d is defined by means of an idempotent e from its Green&rsquo;s D-class as decomposition into the product d=uv, so that the element u belongs to the Green&rsquo;s R-class of the element d and the Green&rsquo;s L-class of the idempotent e, while the element v belongs to the Green&rsquo;s L-class of the element d and the Green&rsquo;s R-class of the idempotent e. The main result of the paper is a theorem which states that each regular element of a semigroup possesses an I.-A. factorization with respect to each idempotent from its Green&rsquo;s D-class. In addition, we prove that when one of the factors is given, then the other factor is uniquely determined. I.-A. factorizations are then used to provide new existence conditions and characterizations of group inverses and (b,c)-inverses in a semigroup. In our further research, these factorizations will be applied to matrices with entries in a field, and efficient algorithms for realization of such factorizations will be provided.

]]>Mathematics doi: 10.3390/math12193135

Authors: Eberhard Mayerhofer

We establish lower norm bounds for multivariate functions within weighted Lebesgue spaces, characterised by a summation of functions whose components solve a system of nonlinear integral equations. This problem originates in portfolio selection theory, where these equations allow one to identify mean-variance optimal portfolios, composed of standard European options on several underlying assets. We elaborate on the Smirnov property&mdash;an integrability condition for the weights that guarantees the uniqueness of solutions to the system. Sufficient conditions on weights to satisfy this property are provided, and counterexamples are constructed, where either the Smirnov property does not hold or the uniqueness of solutions fails.

]]>Mathematics doi: 10.3390/math12193134

Authors: Zongbao Zou Lihao Chen Yuxin Liang

In the trade environment of a globalized economy, tariffs play a crucial role in transnational supply chains. At the same time, the power structure of the supply chain also plays an important role in the decision making and income distribution of a transnational supply chain. Therefore, we construct game-theoretic models to analyze the impacts of tariffs and power structures on the decision making and revenue distribution of transnational supply chains. First, we consider a bilateral monopoly model consisting of a Chinese manufacturer and a U.S. retailer and analyze the effects of tariffs and power structures on decision making and revenue distributions in this supply chain. Then, we extend the model to a duopoly competition model consisting of two Chinese manufacturers and one American retailer, further analyzing the roles of tariffs and power structures. The results indicate that in the bilateral monopoly model, the impact of tariffs on the manufacturer&rsquo;s profits is always greater than on the retailer&rsquo;s profits under a manufacturer-led circumstance. However, in a competitive model, when the market size is large, the impact of tariffs on the manufacturer&rsquo;s profits exceeds that of the retailer&rsquo;s profits; conversely, when the market size is smaller, the impact of tariffs on the retailer&rsquo;s profits is greater than on the manufacturer&rsquo;s profits. Furthermore, we find that in the duopoly competition model, under the manufacturer-led circumstance, both the manufacturer and the retailer earn the highest profits.

]]>Mathematics doi: 10.3390/math12193133

Authors: Nazeer Ansari Kholood Alnefaie Shakir Ali Adnan Abbasi Kh. Herachandra Singh

For a left module MR over a non-commutative ring R, the notion for the class of nilpotent elements (nilR(M)) was first introduced and studied by Sevviiri and Groenewald in 2014 (Commun. Algebra, 42, 571&ndash;577). Moreover, Armendariz and semicommutative modules are generalizations of reduced modules and nilR(M)=0 in the case of reduced modules. Thus, the nilpotent class plays a vital role in these modules. Motivated by this, we present the concept of nil-Armendariz modules as a generalization of reduced modules and a refinement of Armendariz modules, focusing on the class of nilpotent elements. Further, we demonstrate that the quotient module M/N is nil-Armendariz if and only if N is within the nilpotent class of MR. Additionally, we establish that the matrix module Mn(M) is nil-Armendariz over Mn(R) and explore conditions under which nilpotent classes form submodules. Finally, we prove that nil-Armendariz modules remain closed under localization.

]]>Mathematics doi: 10.3390/math12193132

Authors: Yushuang Fan Tao Zheng

We introduce the continuity equation of transverse K&auml;hler metrics on Sasakian manifolds and establish its interval of maximal existence. When the first basic Chern class is null (resp. negative), we prove that the solution of the (resp. normalized) continuity equation converges smoothly to the unique &eta;-Einstein metric in the basic Bott&ndash;Chern cohomological class of the initial transverse K&auml;hler metric (resp. first basic Chern class). These results are the transverse version of the continuity equation of the K&auml;hler metrics studied by La Nave and Tian, and also counterparts of the Sasaki&ndash;Ricci flow studied by Smoczyk, Wang, and Zhang.

]]>Mathematics doi: 10.3390/math12193131

Authors: Salman Saud Alsaeed Satyvir Singh

This paper investigates numerically the shock wave interaction with a V-shaped heavy/light interface. For numerical simulations, we choose six distinct vertex angles (&theta;=40&#8728;,60&#8728;,90&#8728;,120&#8728;,150&#8728;, and 170&#8728;), five distinct shock wave strengths (Ms=1.12,1.22,1.30,1.60, and 2.0), and three different Atwood numbers (At=&minus;0.32,&minus;0.77, and &minus;0.87). A two-dimensional space of compressible two-component Euler equations are solved using a third-order modal discontinuous Galerkin approach for the simulations. The present findings demonstrate that the vertex angle has a crucial influence on the shock wave interaction with the V-shaped heavy/light interface. The vertex angle significantly affects the flow field, interface deformation, wave patterns, spike generation, and vorticity production. As the vertex angle decreases, the vorticity production becomes more dominant. A thorough analysis of the vertex angle effect identifies the factors that propel the creation of vorticity during the interaction phase. Notably, smaller vertex angles lead to stronger vorticity generation due to a steeper density gradient, while larger angles result in weaker, more dispersed vorticity and a less complex interaction. Moreover, kinetic energy and enstrophy both dramatically rise with decreasing vortex angles. A detailed analysis is also carried out to analyze the vertex angle effects on the temporal variations of interface features. Finally, the impacts of different Mach and Atwood numbers on the V-shaped interface are briefly presented.

]]>Mathematics doi: 10.3390/math12193130

Authors: Yanlin Li M. S. Siddesha H. Aruna Kumara M. M. Praveena

In this work, we aim to investigate the characteristics of the Bach and Cotton tensors on Lorentzian manifolds, particularly those admitting a semi-symmetric metric &omega;-connection. First, we prove that a Lorentzian manifold admitting a semi-symmetric metric &omega;-connection with a parallel Cotton tensor is quasi-Einstein and Bach flat. Next, we show that any quasi-Einstein Lorentzian manifold admitting a semi-symmetric metric &omega;-connection is Bach flat.

]]>Mathematics doi: 10.3390/math12193129

Authors: Ladan Hatami-Moghaddam Mohammad Khalilzadeh Nasser Shahsavari-Pour Seyed Mojtaba Sajadi

Real-world projects encounter numerous issues, challenges, and assumptions that lead to changes in scheduling. This exposure has prompted researchers to develop new scheduling models, such as those addressing constrained resources, multi-skill resources, and activity pre-emption. Constrained resources arise from competition among projects for limited access to renewable resources. This research presents a scheduling model with constrained multi-skill and multi-mode resources, where activity durations vary under different scenarios and allow for partial pre-emption due to resource shortages. The main innovation is the pre-emption of activities when resources are unavailable, with defined minimum and maximum delivery time windows. For this purpose, a multi-objective mathematical programming model is developed that considers Bertsimas and Sim&rsquo;s robust model in uncertain conditions. The model aims to minimize resource consumption, idleness, and project duration. The proposed model was solved using a multi-objective genetic algorithm and finally, its validation was completed and confirmed. Analysis shows that limited renewable resources can lead to increased activity pre-emption and extended project timelines. Additionally, higher demand raises resource consumption, reducing availability and prolonging project duration. Increasing the upper time window extends project time while decreasing the lower bound pressures resources, leading to higher consumption and resource scarcity.

]]>Mathematics doi: 10.3390/math12193128

Authors: Tengfei Xiao

Complex physical processes, which could evolve in both spatial and temporal dimensions and be represented by partial difference equations, could also operate in a repetitive mode with iterative learning methods as suitable control laws. For these three-dimensional systems (of the spatial, temporal, and iterative dimensions), the stability in the iterative direction is critical for many applications, which can be analyzed and synthesized under the proposed concept of iterative dissipativity. The definition of iterative dissipativity, which is first introduced in this paper, encapsulates the dominant information in both the spatial and temporal dimensions, while also placing a particular emphasis on the iteration improvement. This property allows for the derivation of sufficient conditions for asymptotic stability in the iteration direction, which are represented by linear matrix inequality criteria that can be readily solved. Performance in both the spatial and temporal dimensions can also be satisfied under this iterative dissipativity concept, even in absence of real-time feedback. Moreover, the optimization solutions of the control parameters can be determined. Finally, a thermal process and a numeric example are presented to illustrate the effectiveness of the proposed iteratively dissipative learning control approach.

]]>Mathematics doi: 10.3390/math12193127

Authors: Sina Vafi

Parallel Concatenated Block (PCB) codes are conventionally represented as high-rate codes with low error correcting capability. To form a reliable and outstanding code, this paper presents a modification on the structure of PCB codes, which is accomplished by encoding some parity bits of one of their component codes. For the newly proposed code, named as the braided code, non-stuff bit-based convolutional interleavers are applied, aiming to minimize the design complexity while ensuring the proper permutations of the original message and selected parity bits. To precisely determine the error correcting capability, a tight bound for the minimum weight of braided code is presented. Additionally, further analyses are provided, which verify iterative decoding performance and the complexity of the constructed code. It is concluded that an outstanding braided code is formed by utilizing a reasonable number of iterations applied at its decoding processes, while maintaining its design complexity at a level similar to other well-known codes. The significant performance of short and long-length-based braided codes is evident in both waterfall and error floor regions.

]]>Mathematics doi: 10.3390/math12193126

Authors: Changyuan Luo Ling Sun

The specificity and complexity of space networks render the traditional key management mechanism no longer applicable. The certificate-less-based distributed spatial network key management scheme proposed in this paper combines the characteristics of space networks, solving the problems regarding the difficulty of implementing centralized key management in space networks and the excessive overhead required for maintaining public key certificates by constructing a distributed key generation center and establishing strategies such as private key updates, master key component updates, and session key negotiation. This method also avoids the key escrow problem inherent in existing identity-based key management schemes. This scheme provides the DPKG construction method for space networks; designs the update strategy for the DPKG node&rsquo;s master key sharing, providing a specific update algorithm; introduces the batch private key update mechanism; and uses the mapping function to evenly distribute the node&rsquo;s update requests throughout the update time period, avoiding the problem of overly concentrated update requests. After analysis and simulation verification, it was proven that the scheme can meet the necessary security requirements, offering good stability and scalability.

]]>Mathematics doi: 10.3390/math12193124

Authors: Roman Rodriguez-Aguilar Jose-Antonio Marmolejo-Saucedo Utku Köse

The first quarter of the 21st century has witnessed many technological innovations in various sectors. Likewise, the COVID-19 pandemic triggered the acceleration of digital transformation in organizations driven by artificial intelligence and communication technologies in Industry 4.0 and Industry 5.0. Aiming at the construction of digital twins, virtual representations of a physical system allow real-time bidirectional communication. This will allow the monitoring of operations, identification of possible failures, and decision making based on technical evidence. In this study, a fault diagnosis solution is proposed, based on the construction of a digital twin, for a cloud-based Industrial Internet of Things (IIoT) system contemplating the control of electro-hydrostatic actuators (EHAs). The system was supported by a deep learning model using Long Short-Term Memory (LSTM) networks for an effective diagnostic approach. The implemented study considers data preparation and integration and system development and application to evaluate the performance against the fault diagnosis problem. According to the results obtained, positive results are shown in the construction of the digital twin using a deep learning model for the fault diagnosis problem of an active EHA-IIoT configuration.

]]>Mathematics doi: 10.3390/math12193125

Authors: Tianqi Wang Hongquan Qu Chang’an Liu Tong Zheng Zhuoyang Lyu

With the continuous development of autonomous driving, traffic sign detection, as an essential subtask, has witnessed constant updates in corresponding technologies. Currently, traffic sign detection primarily confronts challenges such as the small size of detection targets and the complexity of detection scenarios. This paper focuses on detecting small traffic signs in low-light scenarios. To address these issues, this paper proposes a traffic sign detection method that integrates low-light image enhancement with small target detection, namely, LLE-STD. This method comprises two stages: low-light image enhancement and small target detection. Based on classic baseline models, we tailor the model structures by considering the requirements of lightweight traffic sign detection models and their adaptability to varying image qualities. The two stages are then coupled to form an end-to-end processing procedure. During experiments, we validate the performance of low-light image enhancement small target detection, and adaptability to images of different qualities using the public datasets GTSDB, TT-100K, and GLARE. Compared to classic models, LLE-STD demonstrates significant advantages. For example, the mAP results tested on the GLARE dataset show that LLE-STD outperforms RetinaNet by approximately 15%. This research can facilitate the practical application of deep learning-based intelligent methods in the field of autonomous driving.

]]>Mathematics doi: 10.3390/math12193123

Authors: Haseeb Wali Sohail Iqbal

In this paper, we construct two deformations of the Godeaux surface with &pi;1&cong;Z4, such that each central fibre contains a family of conics. We show that surfaces that are birational to these Godeaux surfaces exist in two connected components of the moduli space of the Campedelli surfaces with a fundamental group of order 8. The whole construction is simplified by the use of key varieties.

]]>Mathematics doi: 10.3390/math12193122

Authors: Jialiang Pan Chi-Jie Lu Wei-Jen Chen Kun-Shan Wu Chih-Te Yang

This study explores a supply chain product-inventory problem with advance sales under the omni-channel strategies (physical and online sales channels) based on the brand owner&rsquo;s business model and develops corresponding models that have not been proposed in previous studies. In addition, because the brand owner is a member of the supply chain, and has different handling methods for defective products or products returned by customers in various retail channels, defective products or returned products are included in the supply chain models to comply with actual operating conditions and fill the research gap in the handling of defective/returned products. Regarding the mathematical model&rsquo;s development, we first clarify the definition of model parameters and relevant data collection, and then establish the production-inventory models with omni-channel strategies and advance sales. The primary objective is to determine the optimal production, delivery, and replenishment decisions of the manufacturer, physical agent, and online e-commerce company in order to maximize the joint total profits of the entire supply chain system. Further, this study takes the supply chain system of mobile game steering wheel products as an example, uses data consistent with the actual situation to demonstrate the optimal solutions of the models, and conducts sensitivity analysis for the proposed model. The findings reveal that increased demand shortens the replenishment cycle and raises order quantity and shipment frequency in the physical channel, similar to the online channel during normal sales. However, during the online pre-order period, higher demand reduces order quantity and cycle length but still increases shipment frequency. Rising ordering or fixed shipping costs lead to higher order quantity and cycle length in both channels, but variable shipping costs in the online channel reduce them. Market price increases boost order quantity and frequency in the online channel, while customer return rates significantly impact inventory decisions.

]]>Mathematics doi: 10.3390/math12193121

Authors: Irena Hrastnik Ladinek

An L(d,1)-labeling of a graph G=(V,E) is a function f from the vertex set V(G) to the set of nonnegative integers such that the labels on adjacent vertices differ by at least d and the labels on vertices at distance two differ by at least one, where d&ge;1. The span of f is the difference between the largest and the smallest numbers in f(V). The &lambda;1d-number of G, denoted by &lambda;1d(G), is the minimum span over all L(d,1)-labelings of G. We prove that &lambda;1d(X)&le;2d+2, with equality if 1&le;d&le;4, for direct graph bundle X=Cm&times;&sigma;&#8467;Cn and Cartesian graph bundle X=Cm&#9633;&sigma;&#8467;Cn, if certain conditions are imposed on the lengths of the cycles and on the cyclic &#8467;-shift &sigma;&#8467;.

]]>Mathematics doi: 10.3390/math12193120

Authors: Nouf Al-Shenaifi Aqil M. Azmi Manar Hosny

This study harnesses the linguistic diversity of Arabic dialects to create two expansive corpora from X (formerly Twitter). The Gulf Arabic Corpus (GAC-6) includes around 1.7 million tweets from six Gulf countries&mdash;Saudi Arabia, UAE, Qatar, Oman, Kuwait, and Bahrain&mdash;capturing a wide range of linguistic variations. The Saudi Dialect Corpus (SDC-5) comprises 790,000 tweets, offering in-depth insights into five major regional dialects of Saudi Arabia: Hijazi, Najdi, Southern, Northern, and Eastern, reflecting the complex linguistic landscape of the region. Both corpora are thoroughly annotated with dialect-specific seed words and geolocation data, achieving high levels of accuracy, as indicated by Cohen&rsquo;s Kappa scores of 0.78 for GAC-6 and 0.90 for SDC-5. The annotation process leverages AI-driven techniques, including machine learning algorithms for automated dialect recognition and feature extraction, to enhance the granularity and precision of the data. These resources significantly contribute to the field of Arabic dialectology and facilitate the development of AI algorithms for linguistic data analysis, enhancing AI system design and efficiency. The data provided by this research are crucial for advancing AI methodologies, supporting diverse applications in the realm of next-generation AI technologies.

]]>Mathematics doi: 10.3390/math12193119

Authors: Wihan van der Heever Ranjan Satapathy Ji Min Park Erik Cambria

This study leverages explainable artificial intelligence (XAI) techniques to analyze public sentiment towards Environmental, Social, and Governance (ESG) factors, climate change, and green finance. It does so by developing a novel multi-task learning framework combining aspect-based sentiment analysis, co-reference resolution, and contrastive learning to extract nuanced insights from a large corpus of social media data. Our approach integrates state-of-the-art models, including the SenticNet API, for sentiment analysis and implements multiple XAI methods such as LIME, SHAP, and Permutation Importance to enhance interpretability. Results reveal predominantly positive sentiment towards environmental topics, with notable variations across ESG categories. The contrastive learning visualization demonstrates clear sentiment clustering while highlighting areas of uncertainty. This research contributes to the field by providing an interpretable, trustworthy AI system for ESG sentiment analysis, offering valuable insights for policymakers and business stakeholders navigating the complex landscape of sustainable finance and climate action. The methodology proposed in this paper advances the current state of AI in ESG and green finance in several ways. By combining aspect-based sentiment analysis, co-reference resolution, and contrastive learning, our approach provides a more comprehensive understanding of public sentiment towards ESG factors than traditional methods. The integration of multiple XAI techniques (LIME, SHAP, and Permutation Importance) offers a transparent view of the subtlety of the model&rsquo;s decision-making process, which is crucial for building trust in AI-driven ESG assessments. Our approach enables a more accurate representation of public opinion, essential for informed decision-making in sustainable finance. This paper paves the way for more transparent and explainable AI applications in critical domains like ESG.

]]>Mathematics doi: 10.3390/math12193118

Authors: Fu Cheng Chenyao Huang Shanshan Ji

The determination of the capital structure is a critical component of a company&rsquo;s financial decision-making process. The question of how to optimize a firm&rsquo;s capital structure to increase its value has been a significant topic of interest within the financial community. The employee stock ownership plan (ESOP) has developed rapidly in China&rsquo;s capital market over the past decade, providing a suitable context for studying the impact of employee equity incentives on capital structure decisions. This paper employs cross-sectional ordinary least squares regression models and unbalanced panel fixed effect models to investigate the impact of employee stock ownership plans (ESOPs) on firms&rsquo; capital structure decisions. The analysis is conducted on a sample of Chinese A-share listed companies on the Shanghai and Shenzhen Stock Exchanges. The research considers both static capital structure choice and dynamic capital structure adjustment. We find that the implementation of an ESOP reduces the level of corporate debt and accelerates the dynamic adjustment of capital structure, suggesting that employee equity incentives play a role in optimizing firms&rsquo; capital structure decisions. We also find that the impact of ESOPs on the dynamic adjustment of capital structure is asymmetric. Specifically, the implementation of ESOPs markedly accelerates the downward adjustment of capital structure, yet has no impact on the upward adjustment of capital structure. Further analysis demonstrates that the impact of ESOPs on capital structure decisions is contingent upon the macroeconomic environment, industry characteristics, corporate governance, and ESOP contract designs. First, the optimization of ESOPs on capital structure decisions is more pronounced in an economic boom environment, in a poor market climate, or in competitive industries. Second, the reduction effect of ESOPs on corporate debt is more pronounced in non-state-owned companies, high-tech companies and those with lower ownership concentration. In contrast, the acceleration effect of ESOPs on capital structure adjustment is more pronounced in state-owned companies, non-high-tech companies and those with higher ownership concentration. Ultimately, ESOPs financed by loans from a firm&rsquo;s major shareholders&mdash;or with a longer lock-up period, smaller shareholding size or executive subscription ratio&mdash;demonstrate a more pronounced optimization effect on capital structure decisions. This paper not only contributes to the existing literature on the relationship between equity incentives and capital structure decisions, but also provides guidance for listed companies on the reasonable design of their ESOPs and the optimization of their capital structure decisions.

]]>Mathematics doi: 10.3390/math12193117

Authors: Lin Hu Long Jian

This article investigates a class of multi-agent systems (MASs) with known dynamics external disturbances, where the communication graph is directed, and the followers have undirected connections. To eliminate the impacts of external disturbance, the technologies of disturbance observer-based control are introduced into the containment control problems. Additionally, to save communication costs and energy consumption, a distributed disturbance observer-based event-triggered controller is employed to achieve containment control and reject disturbance. Furthermore, designing the event-triggered function using an exponential function is beneficial for a time-dependent term while ensuring the exclusion of Zeno behavior. Finally, a numerical simulation is provided to validate the effectiveness of the theoretical analysis.

]]>Mathematics doi: 10.3390/math12193116

Authors: Shenzi Yang Guoqing Zhao Fan Li

The data envelopment analysis (DEA) models have been widely recognized and applied in various fields. However, these models have limitations, such as their inability to globally rank DMUs, the efficiency values are definite numerical values, they are unable to reflect potential efficiency changes, and they fail to adequately reflect the degree of the decision maker&rsquo;s preference. In order to address these shortcomings, this paper combines possibility theory with self-interest and non-self-interest principles to improve the DEA model to provide a more detailed reflection of the differences between DMUs. First, the self-interest and non-self-interest principles are employed to establish the DEA evaluation model, and the determined numerical efficiency is transformed into efficiency intervals. Second, an attitude function is added to the common possible-degree formula to reflect the decision maker&rsquo;s preference, and a more reasonable method for solving the attitude function is presented. Finally, the improved possible-degree formula proposed in this paper is used to rank and compare the interval efficiencies. This improved method not only provides more comprehensive ranking information but also better captures the decision maker&rsquo;s preferences. This model takes preference issues into account and has improved stability and accuracy compared with existing models. The application of the improved model in airlines shows that the model proposed in this paper effectively achieved a full ranking. From a developmental perspective, the efficiency levels of Chinese airlines were generally comparable. Joyair and One Two Three performed poorly, exhibiting significant gaps compared with other airlines.

]]>Mathematics doi: 10.3390/math12193115

Authors: Ibrahim A. Nafisah Irsa Sajjad Mohammed A. Alshahrani Osama Abdulaziz Alamri Mohammed M. A. Almazah Javid Gani Dar

This study introduces an enhanced version of the discrete choice model combining embedded neural architecture to enhance predictive accuracy while preserving interpretability in choice modeling across temporal dimensions. Unlike the traditional architectures, which directly utilize raw data without intermediary transformations, this study introduces a modified approach incorporating temporal embeddings for improved predictive performance. Leveraging the Phones Accelerometer dataset, the model excels in predictive accuracy, discrimination capability and robustness, outperforming traditional benchmarks. With intricate parameter estimates capturing spatial orientations and user-specific patterns, the model offers enhanced interpretability. Additionally, the model exhibits remarkable computational efficiency, minimizing training time and memory usage while ensuring competitive inference speed. Domain-specific considerations affirm its predictive accuracy across different datasets. Overall, the subject model emerges as a transparent, comprehensible, and powerful tool for deciphering accelerometer data and predicting user activities in real-world applications.

]]>Mathematics doi: 10.3390/math12193114

Authors: Jinyu Zhu Yu Zhang Yunan Wang Hongli Zhang Binxing Fang

To facilitate a direct comparison of the differences in network resources among countries worldwide, this paper proposes a method for quantifying the relationship between autonomous systems and territorial networks from the perspective of network topology. Using global router-level network topology data as the foundational data for the network resources of various countries, we abstract the dual mapping information of router geographic distribution and operational ownership into a matrix-form mathematical model. By employing relevant indicators from both network scale and border connectivity, we compare matrix model data from different periods to quantitatively assess changes in the network structures of countries globally. The study results show that internet resources are concentrated in the United States, which owns 38.04% of the global routers, distributed across 87.88% of the countries, significantly impacting the global network. Compared to the average quantitative indicators of each country, 67.00% of the countries exhibit higher deployment consistency, 37.30% show higher border connection consistency, 23.81% perform prominently in terms of impact, and 46.20% have outstanding border node degrees. From a continental perspective, the analysis indicates that Asian and African countries have a closer relationship between AS and territorial networks, while Europe&rsquo;s connections are relatively sparse. Over time, we observe a slight decline in deployment consistency in Asia, Africa, and Europe, a slight increase in border connection consistency in Asia, Africa, and North America, and enhanced impact in Asia, Africa, Europe, and South America. These trends suggest that the integration between AS and territorial networks is intensifying in most countries.

]]>Mathematics doi: 10.3390/math12193113

Authors: Ekambaram Chandrasekaran George E. Chatzarakis Radhakrishnan Sakthivel Ethiraju Thandapani

This paper focuses on the oscillatory properties of the third-order semi-canonical nonlinear delay differential equation. By using the new canonical transform method, we transformed the studied equation into a canonical-type equation, which simplified the examination of the studied equation. The obtained oscillation results are new and complement the existing results mentioned in the literature. Examples are provided to illustrate the importance and novelty of the main results.

]]>Mathematics doi: 10.3390/math12193112

Authors: Muhammad Amer Latif

In this study, trapezoidal-type inequalities in fuzzy settings have been investigated. The theory of fuzzy analysis has been discussed in detail. The integration by parts formula of analysis of fuzzy mathematics has been employed to establish an equality. Trapezoidal-type inequality for functions with values in the fuzzy number-valued space is proven by applying the proven equality together with the properties of a metric defined on the set of fuzzy number-valued space and H&ouml;ler&rsquo;s inequality. The results proved in this research provide generalizations of the results from earlier existing results in the field of mathematical inequalities. An example is designed by defining a function that has values in fuzzy number-valued space and validated the results numerically using the software Mathematica (latest v. 14.1). The p-levels of the defined fuzzy number-valued mapping have been shown graphically for different values of p&isin;0,1.

]]>Mathematics doi: 10.3390/math12193111

Authors: Dimitrios Nikolopoulos Ermioni Petraki

This paper reports fractal patterns identified in the complex musical composition DIAPHONIES by Michael Paouris via power-law fractal analysis with sliding-windows of size 1024. From 7,647,232 analysed musical segments of DIAPHONIES, 3,222,832 (42.4%) are fractional Brownian motion (fBm) fractal segments and 4,424,400 (57.6%) are fractional Gaussian noise (fGn) stochastic ones. From the fBm fractal segments 295,294 (9.1%) exhibit strong persistency-P with power-law segments in the range of 2.3&le;b&le;3. These are the very strong fractal areas in DIAPHONIES. Numerous segments with strong antipersistency 1.7&le;b&lt;2 are reported together with segments with AP changes (1.7&le;b&lt;2.3). In DIAPHONIES continuous fractal fBm areas are dipped in non-fractal fGn areas of deterministic music. The results are within the fBm fractal areas reported in existing papers. Very importantly, the simple composition called Nocturnal-Angel by Michael Paouris, exhibited limited fBm areas of average b&macr;=1.98 (&sigma;=0.3), namely of pure statistical, deterministic music, while simultaneously, the fractal analysis profile was completely different from the profiles of DIAPHONIES, hence reinforcing, the fractal findings of DIAPHONIES in relation to trivial music harmony.

]]>Mathematics doi: 10.3390/math12193109

Authors: Zhanggen Zhu Lefeng Cheng Teng Shen

In the context of increasing global efforts to mitigate climate change, effective carbon emission reduction is a pressing issue. Governments and power companies are key stakeholders in implementing low-carbon strategies, but their interactions require careful management to ensure optimal outcomes for both economic development and environmental protection. This paper addresses this real-world challenge by utilizing evolutionary game theory (EGT) to model the strategic interactions between these stakeholders under a low-carbon trading mechanism. Unlike classical game theory, which assumes complete rationality and perfect information, EGT allows for bounded rationality and learning over time, making it particularly suitable for modeling long-term interactions in complex systems like carbon markets. This study builds an evolutionary game model between the government and power companies to explore how different strategies in carbon emission reduction evolve over time. Using payoff matrices and replicator dynamics equations, we determine the evolutionarily stable equilibrium (ESE) points and analyze their stability through dynamic simulations. The findings show that in the absence of a third-party regulator, neither party achieves an ideal ESE. To address this, a third-party regulatory body is introduced into the model, leading to the formulation of a tripartite evolutionary game. The results highlight the importance of regulatory oversight in achieving stable and optimal low-carbon strategies. This paper offers practical policy recommendations based on the simulation outcomes, providing a robust theoretical framework for government intervention in carbon markets and guiding enterprises towards sustainable practices.

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