Mathematics

This paper proposes a modification of a Sliding Mode Classical Observer (SMCO) to adapt it to the fractional approach. This adaptation involves using a set of definitions based on fractional calculus theory, particularly the approach developed by Riemann–Liouville, resulting in a Sliding Mode Fractional Observer (SMFO). Both observers are used to perform disturbance reconstruction considered additive in a Quadrotor Unmanned Aerial Vehicle (UAV) model. Then, this work presents the fractional-order sliding mode observer’s mathematical formulation and integration into the Quadrotor UAV model. To validate the quality of the disturbance reconstruction process of the proposed SMFO observer scheme, numerical simulations are carried out, where a reconstruction quality indicator (BQR) is proposed based on the analysis of performance indices such as the Mean Square Error (MSE), the First Probability Moment (FPM), and Second Probability Moment (SPM), which were obtained for both the SMCO and the SMFO. The simulation results demonstrate the efficacy of the proposed observer in accurately reconstructing disturbances under various environmental conditions. Comparative analyses with SMCO highlight the advantages of the fractional-order approach in terms of reconstruction accuracy and improvement of its transitory performance. Finally, the presented SMFO offers a promising avenue for enhancing the reliability and precision of disturbance estimation, ultimately contributing to the advancement of robust control strategies for Quadrotor UAV systems. Full article

The aim of the present research work is to investigate the solution of Urysohn integral equation by common fixed point result in the setting of complex valued b-metric space. To obtain the objective, we used a generalized rational contraction involving control functions and a pair of self-mappings. In this way, we generalize some well-known results of literature. Some non-trivial examples are also flourished to demonstrate the innovation of our principal result. Full article

Emissions of maritime transport have been a critical research topic with the substantial growth in the global shipping industry, encompassing both the expansion of the world fleet and the increased distances it has been covering recently. The International Maritime Organization (IMO) has enforced some regulations to mitigate ship Greenhouse Gas (GHG) emissions, which affect vessels’ operational practice, and further affect service reliability. In this paper, some compliance methods (two-speed strategy, fuel switching, and LNG) against Emission Control Areas (ECAs) at the operational level are examined regarding if and how they impact the liner shipping schedule and service reliability; meanwhile, uncertain weather conditions and port times, as the main uncertain factors, are also involved. Then, a bi-objective fuzzy programming model is formulated and solved by the augmented $\epsilon$-constraint approach, which generates a set of Pareto solutions by balancing the economic and environmental sustainability. Some findings can be concluded through the experimental results, including that, firstly, to meet uncertain weather conditions at sea requires strong robustness; secondly, ECA regulations can negatively affect the liner shipping service level; moreover, slow steaming is an immediate and effective measure to reduce GHG emissions; and, furthermore, ship routing choice could have a significant influence on ship emissions and service reliability. Full article

The main purpose of this study is to provide a comparative analysis of several possible approaches to applying data envelopment analysis (DEA) in the case where some decision making units (DMUs) in the original sample have negative system outputs. In comparison to the traditional model of Charnes, Cooper, and Rhodes (CCR) and the CCR model with a scale shift to measure second-stage outputs, the range directional measure (RDM) model produces the most appropriate results. In this paper, an approach is proposed for estimating returns to scale. The study applies a two-stage DEA model with negative second-stage outputs to assess the public support for research, development, and demonstration projects in the energy sector in 23 countries over the period from 2010 to 2018. The assessment of government performance depends on its contribution to the growth of energy efficiency in the national economy and the reduction of its carbon intensity. Intermediate outputs (patents in the energy sector) are included in the analysis as both outputs of the first stage and inputs of the second stage. Taking the similarity between the calculations obtained without stage separation and the system efficiency calculations from the two-stage model as a measure of model adequacy, the RDM model shows the highest similarity scores. Full article

In the pursuit of energy efficiency and reduced environmental impact, adequate ventilation in enclosed spaces is essential. This study presents a hybrid neural network model designed for monitoring and prediction of environmental variables. The system comprises two phases: An IoT hardware–software platform for data acquisition and decision-making and a hybrid model combining short-term memory and convolutional recurrent structures. The results are promising and hold potential for integration into parallel processing AI architectures. Full article

The fusion of evolutionary algorithms and the solution concepts of cooperative game theory is proposed in this paper to solve the fuzzy optimization problems. The original fuzzy optimization problem is transformed into a scalar optimization problem by assigning some suitable coefficients. The assignment of those coefficients is frequently determined by the decision-makers via their subjectivity, which may cause some biases. In order to avoid these subjective biases, a cooperative game is formulated by considering the $\alpha$-level functions of the fuzzy objective function. Using the Shapley values of this formulated cooperative game, the suitable coefficients can be reasonably set up. Under these settings, the transformed scalar optimization problem is solved to obtain the nondominated solution, which will depend on the coefficients. In other words, we shall obtain a bunch of nondominated solutions depending on the coefficients. Finally, the evolutionary algorithms are invoked to find the best nondominated solution by evolving the coefficients. Full article

In this study, considering the delays for a susceptible individual becoming an alcoholic and the relapse of a recovered individual back into being an alcoholic, we formulate an epidemic model for alcoholism with distributed delays and relapse. The basic reproduction number $R_0$ is calculated, and the threshold property of $R_0$ is established. By analyzing the characteristic equation, we demonstrate the local asymptotic stability of the different equilibria under various conditions: when $R_0<1$, the alcoholism-free equilibrium is locally asymptotically stable; when $R_0>1$, the alcoholism equilibrium exists and is locally asymptotically stable. Furthermore, we demonstrate the global asymptotic stability at each equilibrium using a suitable Lyapunov function. Specifically, when $R_0<1$, the alcoholism-free equilibrium is globally asymptotically stable; when $R_0>1$, the alcoholism equilibrium is globally asymptotically stable. The sensitivity analysis of $R_0$ shows that reducing exposure is more effective than treatment in controlling alcoholism. Interestingly, we found that extending the latency delay $h_1$ and relapse delay $h_2$ also effectively contribute to the control of the spread of alcoholism. Numerical simulations are also provided to support our theoretical results. Full article

An important action-planning problem is considered for participants of the pursuit–evasion game with multiple pursuers and a high-speed evader. The objects of study are mobile robotic systems and specifically small unmanned aerial vehicles (UAVs). The problem is complicated by the presence of significant wind loads that affect the trajectory and motion strategies of the players. It is assumed that UAVs have limited computing resources, which involves the use of computationally fast and real-time heuristic approaches. A novel and rapidly developing intelligent–geometric theory is applied to address the discussed problem. To accurately calculate the points of the participant’s rapprochement, we use a geometric approach based on the construction of circles or spheres of Apollonius. Intelligent control methods are applied to synthesize complex motion strategies of participants. A method for quickly predicting the evader’s trajectory is proposed based on a two-layer neural network containing a new activation function of the “s-parabola” type. We consider a special backpropagation training scheme for the model under study. A simulation scheme has been developed and tested, which includes mathematical models of dynamic objects and wind loads. The conducted simulations on pursuit–evasion games in close to real conditions showed the prospects and expediency of the presented approach. Full article

Automated segmentation of abdominal organs and tumors in medical images is a challenging yet essential task in medical image analysis. Deep learning has shown excellent performance in many medical image segmentation tasks, but most prior efforts were fragmented, addressing individual organ and tumor segmentation tasks with specialized networks. To tackle the challenges of abdominal organ and tumor segmentation using partially labeled datasets, we introduce Re-parameterizing Mixture-of-Diverse-Experts (RepMode) to abdominal organ and tumor segmentation. Within the RepMode framework, the Mixture-of-Diverse-Experts (MoDE) block forms the foundation, learning generalized parameters applicable across all tasks. We seamlessly integrate the MoDE block into a U-shaped network with dynamic heads, addressing multi-scale challenges by dynamically combining experts with varying receptive fields for each organ and tumor. Our framework incorporates task encoding in both the encoder–decoder section and the segmentation head, enabling the network to adapt throughout the entire system based on task-related information. We evaluate our approach on the multi-organ and tumor segmentation (MOTS) dataset. Experiments show that DoDRepNet outperforms previous methods, including multi-head networks and single-network approaches, giving a highly competitive performance compared with the original single network with dynamic heads. DoDRepNet offers a promising approach to address the complexities of abdominal organ and tumor segmentation using partially labeled datasets, enhancing segmentation accuracy and robustness. Full article

This study proposes an interface localizing scheme to enhance the performance of the previous hybrid-level interface-reduction method. The conventional component mode synthesis (CMS) only focuses on interior reduction, while the interface is fully retained for convenient synthesis. Thus, various interface-reduction methods have been suggested to obtain a satisfactory size for the reduced systems. Although previous hybrid-level interface-reduction approaches have addressed major issues associated with conventional interface-reduction methods—in terms of accuracy and efficiency through considering partial substructure synthesis—this method can be applied to limited modeling conditions where interfaces and substructures are independently defined. To overcome this limitation, an interface localizing algorithm is developed to ensure an enhanced performance in the conventional hybrid-level interface-reduction method. The interfaces are discriminated through considering the Boolean operation of substructures, and the interface reduction basis is computed at the localized interface level, which is constructed by a partially coupled system. As a result, a large amount of computational resources are saved, achieving the possibility of efficient design modifications at the semi-substructural level. Full article

The Cholesky factorization of the moment matrix is considered for the Gauss hypergeometric discrete orthogonal polynomials. This family of discrete orthogonal polynomials has a weight with first moment given by ${\rho }_0={}_2{F}_1\left[\begin{array}{c}a,b\\ c+1\end{array};\eta \right]$. For the Gauss hypergeometric discrete orthogonal polynomials, also known as generalized Hahn of type I, Laguerre–Freud equations are found, and the differences with the equations found by Dominici and by Filipuk and Van Assche are provided. Full article

This paper presents a transformative methodology that harnesses the power of digital twin (DT) technology for the advanced condition monitoring of lithium-ion batteries (LIBs) in electric vehicles (EVs). In contrast to conventional solutions, our approach eliminates the need to calibrate sensors or add additional hardware circuits. The digital replica works seamlessly alongside the embedded battery management system (BMS) in an EV, delivering real-time signals for monitoring. Our system is a significant step forward in ensuring the efficiency and sustainability of EVs, which play an essential role in reducing carbon emissions. A core innovation lies in the integration of the digital twin into the battery monitoring process, reshaping the landscape of energy storage and alternative power sources such as lithium-ion batteries. Our comprehensive system leverages a cloud-based IoT network and combines both physical and digital components to provide a holistic solution. The physical side encompasses offline modeling, where a long short-term memory (LSTM) algorithm trained with various learning rates (LRs) and optimized by three types of optimizers ensures precise state-of-charge (SOC) predictions. On the digital side, the digital twin takes center stage, enabling the real-time monitoring and prediction of battery activity. A particularly innovative aspect of our approach is the utilization of a time-series generative adversarial network (TS-GAN) to generate synthetic data that seamlessly complement the monitoring process. This pioneering use of a TS-GAN offers an effective solution to the challenge of limited real-time data availability, thus enhancing the system’s predictive capabilities. By seamlessly integrating these physical and digital elements, our system enables the precise analysis and prediction of battery behavior. This innovation—particularly the application of a TS-GAN for data generation—significantly contributes to optimizing battery performance, enhancing safety, and extending the longevity of lithium-ion batteries in EVs. Furthermore, the model developed in this research serves as a benchmark for future digital energy storage in lithium-ion batteries and comprehensive energy utilization. According to statistical tests, the model has a high level of precision. Its exceptional safety performance and reduced energy consumption offer promising prospects for sustainable and efficient energy solutions. This paper signifies a pivotal step towards realizing a cleaner and more sustainable future through advanced EV battery management. Full article

Solving optimization problems in a fuzzy environment is an area widely addressed in the recent literature. De-fuzzification of data, construction of crisp more or less equivalent problems, unification of multiple objectives, and solving a single crisp optimization problem are the general descriptions of many procedures that approach fuzzy optimization problems. Such procedures are misleading (since relevant information is lost through de-fuzzyfication and aggregation of more objectives into a single one), but they are still dominant in the literature due to their simplicity. In this paper, we address the full fuzzy linear programming problem, and provide solutions in full accordance with the extension principle. The main contribution of this paper is in modeling the conjunction of the fuzzy sets using the “product” operator instead of “min” within the definition of the solution concept. Our theoretical findings show that using a generalized “min” operator within the extension principle assures thinner shapes to the derived fuzzy solutions compared to those available in the literature. Thinner shapes are always desirable, since such solutions provide the decision maker with more significant information. Full article

Predator–prey interactions do not solely depend on biotic factors: rather, they depend on many other abiotic factors also. One such abiotic factor is wind speed, which can crucially change the predation efficiency of the predator population. In this article, the impact of wind speed along with seasonality on various parameters has been investigated. Here, we present two continuous-time models with specialist and generalist type predators incorporating the effect of wind and the seasonality on the model parameters. It has been observed that wind speed plays a significant role in controlling the system dynamics for both systems. It makes the systems stable for both of the seasonally unperturbed systems. However, it controls the chaotic dynamics that occur in case of no wind for the seasonally perturbed system with the predator as a specialist. On the other hand, for the seasonally perturbed system with a generalist predator, it controls period-four oscillations (which occur considering no wind speed) to simple limit-cycle oscillations. Furthermore, the wind parameter has a huge impact on the survival of predator species. The survival of predator species may be achieved by ensuring a suitable range of wind speeds in the ecosystem. Therefore, we observe that seasonality introduces chaos, but wind reduces it. These results may be very useful for adopting necessary management for the conservation of endangered species that are massively affected by wind speed in an ecosystem. Full article

Distracted behavior detection is an important task in computer-assisted driving. Although deep learning has made significant progress in this area, it is still difficult to meet the requirements of the real-time analysis and processing of massive data by relying solely on local computing power. To overcome these problems, this paper proposes a driving distraction detection method based on cloud–fog computing architecture, which introduces scalable modules and a model-driven optimization based on greedy pruning. Specifically, the proposed method makes full use of cloud–fog computing to process complex driving scene data, solves the problem of local computing resource limitations, and achieves the goal of detecting distracted driving behavior in real time. In terms of feature extraction, scalable modules are used to adapt to different levels of feature extraction to effectively capture the diversity of driving behaviors. Additionally, in order to improve the performance of the model, a model-driven optimization method based on greedy pruning is introduced to optimize the model structure to obtain a lighter and more efficient model. Through verification experiments on multiple driving scene datasets such as LDDB and Statefarm, the effectiveness of the proposed driving distraction detection method is proved. Full article

Economic growth is essential for nations endowed with natural resources as it reflects how well those resources are utilized in an efficient and sustainable way. For instance, OPEC member nations, which hold a large proportion of the world’s oil and gas reserves, may require a frequent evaluation of economic growth patterns to ensure that the natural resources are best used. For this purpose, this study proposes an inverse data envelopment analysis model for assessing the optimal increase in input resources required for economic growth among OPEC member nations. In this context, economic growth is reflected in the GDP per capita, taking into account possible environmental degradation. Such a model is applied to the selected OPEC member nations, which suggests that in terms of increasing the GDP per capita, only one member was able to achieve the best efficiency (i.e., reaching the efficiency frontier), resulting in a hierarchy or dominance within the sample countries. The analysis results further identify the economic growth potential for each member country. For the case of Indonesia, the analysis suggests that further economic growth may be achieved for Indonesia without additional input resources. This calls for diversification of the nation’s economy or investment in other input resources. In addition, the overall results indicated that each member nation could increase its GDP per capita while experiencing minimal environmental degradation. Our analysis not only benchmarks the growth efficiency of countries, but also identifies opportunities for more efficient and sustainable growth. Full article

A multivariate folded normal distribution is a distribution of the absolute value of a Gaussian random vector. In this paper, we provide the marginal and conditional distributions of the multivariate folded normal distribution, and also prove that independence and non-correlation are equivalent for it. In addition, we provide a numerical approach using the R language to fit a multivariate folded normal distribution. The accuracy of the estimated mean and variance parameters is then examined. Finally, a real data application to body mass index data are presented. Full article

This paper is devoted to the numerical treatment of two-dimensional Fredholm integral equations, defined on general curvilinear domains of the plane. A Nyström method, based on a suitable Gauss-like cubature formula, recently proposed in the literature is proposed. The convergence, stability and good conditioning of the method are proved in suitable subspaces of continuous functions of Sobolev type. The cubature formula, on which the Nyström method is constructed, has an error that behaves like the best polynomial approximation of the integrand function. Consequently, it is also shown how the Nyström method inherits this property and, hence, the proposed numerical strategy is fast when the involved known functions are smooth. Some numerical examples illustrate the efficiency of the method, also in comparison with other methods known in the literature. Full article

Computing an element of the Clarke subdifferential of a function represented by a program is an important problem in modern non-smooth optimization. Existing algorithms either are computationally inefficient in the sense that the computational cost depends on the input dimension or can only cover simple programs such as polynomial functions with branches. In this work, we show that a generalization of the latter algorithm can efficiently compute an element of the Clarke subdifferential for programs consisting of analytic functions and linear branches, which can represent various non-smooth functions such as max, absolute values, and piecewise analytic functions with linear boundaries, as well as any program consisting of these functions such as neural networks with non-smooth activation functions. Our algorithm first finds a sequence of branches used for computing the function value at a random perturbation of the input; then, it returns an element of the Clarke subdifferential by running the backward pass of the reverse-mode automatic differentiation following those branches. The computational cost of our algorithm is at most that of the function evaluation multiplied by some constant independent of the input dimension n, if a program consists of piecewise analytic functions defined by linear branches, whose arities and maximum depths of branches are independent of n. Full article