In this editorial, we introduce “Mathematical Methods in Applied Sciences”, a Special Issue of Axioms comprising 17 articles [...]

Mathematical Methods in Applied Sciences

Inter-robot management via neighboring robot sensing and measurement using a zeroing neural dynamics approach

The energy industry worldwide is today confronted with several challenges, including heightened levels of consumption and inefficiency, volatile patterns in demand and supply, and a dearth of crucial data necessary for effective management. Developing countries face significant challenges due to the widespread occurrence of unauthorized connections to the electricity grid, resulting in substantial amounts of unmeasured and unpaid energy consumption. Nevertheless, the implementation of artificial intelligence (AI) and machine learning (ML) technologies has the potential to improve energy management, efficiency, and sustainability. Therefore, this study aims to evaluate the potential influence of AI and ML technologies on the progress of the energy industry. The present study employed the systematic literature review methodology to examine the challenges arising from frequent power outages and limited energy accessibility in various developing nations. The results of this study indicate that AI and ML possess significant potential in various domains, including predictive maintenance of turbines, optimization of energy consumption, management of power grids, prediction of energy prices, and assessment of energy demand and efficiency in residential buildings. This study concluded with a discussion of the necessary measures to enable developing nations to harness the advantages of AI and ML in the energy sector.

A comprehensive review of artificial intelligence and machine learning applications in energy consumption and production

The field of computer science has undergone rapid expansion due to the increasing interest in improving system performance. This has resulted in the emergence of advanced techniques, such as neural networks, intelligent systems, optimization algorithms, and optimization strategies. These innovations have created novel opportunities and challenges in various domains. This paper presents a thorough examination of three intelligent methods: neural networks, intelligent systems, and optimization algorithms and strategies. It discusses the fundamental principles and techniques employed in these fields, as well as the recent advancements and future prospects. Additionally, this paper analyzes the advantages and limitations of these intelligent approaches. Ultimately, it serves as a comprehensive summary and overview of these critical and rapidly evolving fields, offering an informative guide for novices and researchers interested in these areas.

/pdf/advances-on-intelligent-algorithms-for-scientific-computing-1e8luwnm.pdf

Advances on intelligent algorithms for scientific computing: an overview

Heavy metals (HMs) enter waterbodies through various means, which, when exceeding a threshold limit, cause toxic effects both on the environment and in humans upon entering their systems. Recent times have seen an increase in such HM influx incident rates. This requires an instant response in this regard to review the challenges in the available classical methods for HM detection and removal. As well as provide an opportunity to explore the applications of artificial intelligence (AI) and machine learning (ML) for the identification and further redemption of water and wastewater from the HMs. This review of research focuses on such applications in conjunction with the available in-silico models producing worldwide data for HM levels. Furthermore, the effect of HMs on various disease progressions has been provided, along with a brief account of prediction models analysing the health impact of HM intoxication. Also discussing the ethical and other challenges associated with the use of AI and ML in this field is the futuristic approach intended to follow, opening a wide scope of possibilities for improvement in wastewater treatment methodologies. 

Artificial intelligence and machine learning algorithms in the detection of heavy metals in water and wastewater: Methodological and ethical challenges

Complex time-dependent Lyapunov equation (CTDLE), as an important means of stability analysis of control systems, has been extensively employed in mathematics and engineering application fields. Recursive neural networks (RNNs) have been reported as an effective method for solving CTDLE. In the previous work, zeroing neural networks (ZNNs) have been established to find the accurate solution of time-dependent Lyapunov equation (TDLE) in the noise-free conditions. However, noises are inevitable in the actual implementation process. In order to suppress the interference of various noises in practical applications, in this paper, a complex noise-resistant ZNN (CNRZNN) model is proposed and employed for the CTDLE solution. Additionally, the convergence and robustness of the CNRZNN model are analyzed and proved theoretically. For verification and comparison, three experiments and the existing noise-tolerant ZNN (NTZNN) model are introduced to investigate the effectiveness, convergence and robustness of the CNRZNN model. Compared with the NTZNN model, the CNRZNN model has more generality and stronger robustness. Specifically, the NTZNN model is a special form of the CNRZNN model, and the residual error of CNRZNN can converge rapidly and stably to order 10−5 when solving CTDLE under complex linear noises, which is much lower than order 10−1 of the NTZNN model. Analogously, under complex quadratic noises, the residual error of the CNRZNN model can converge to 2∥A∥F/ζ3 quickly and stably, while the residual error of the NTZNN model is divergent.

/pdf/complex-noise-resistant-zeroing-neural-network-for-computing-151sub91.pdf

Complex Noise-Resistant Zeroing Neural Network for Computing Complex Time-Dependent Lyapunov Equation

Real‐Time Solutions for Dynamic Complex Matrix Inversion and Chaotic Control Using ODE‐Based Neural Computing Methods

In recent years, neural networks have become a common practice in academia for handling complex problems. Numerous studies have indicated that complex problems can generally be formulated as a single or a set of time-varying equations. Dynamic neural networks, as powerful tools for processing time-varying problems, play an essential role in their online solution. This paper reviews recent advances in real-valued, complex-valued, and noise-tolerant dynamic neural networks for solving various time-varying problems, discusses the finite-time convergence, fixed/varying parameters, and noise tolerance properties of dynamic neural network models. This review is highly relevant for researchers and novices interested in using dynamic neural networks to solve time-varying problems.

Dynamic Neural Network Models for Time-Varying Problem Solving: A Survey on Model Structures

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