Mathematics doi: 10.3390/math12071023
Authors: Markus Neumayer Thomas Suppan Thomas Bretterklieber Hannes Wegleiter Colin Fox
The reconstruction of the spatial complex conductivity σ+jωε0εr from complex valued impedance measurements forms the inverse problem of complex electrical impedance tomography or complex electrical capacitance tomography. Regularized Gauß-Newton schemes have been proposed for their solution. However, the necessary computation of the Jacobian is known to be computationally expensive, as standard techniques such as adjoint field methods require additional simulations. In this work, we show a more efficient way to computationally access the Jacobian matrix. In particular, the presented techniques do not require additional simulations, making the use of the Jacobian, free of additional computational costs.
]]>Mathematics doi: 10.3390/math12071022
Authors: Jie Liu Jian-Ping Sun
In this paper, the problem of clustering component synchronization of nonlinearly coupled complex networks with nonidentical nodes and asymmetric couplings is investigated. A pinning control strategy is designed to achieve the clustering component synchronization with respect to the specified components. Based on matrix analysis and stability theory, clustering component synchronization criteria are established. Two numerical simulations are also provided to show the effectiveness of the theoretical results.
]]>Mathematics doi: 10.3390/math12071021
Authors: Mao Luo Huigang Qin Xinyun Wu Caiquan Xiong Dahai Xia Yuanzhi Ke
This paper presents an algorithm for effectively maintaining the minimum spanning tree in dynamic weighted undirected graphs. The algorithm efficiently updates the minimum spanning tree when the underlying graph structure changes. By identifying the portion of the original tree that can be preserved in the updated tree, our algorithm avoids recalculating the minimum spanning tree from scratch. We provide proof of correctness for the proposed algorithm and analyze its time complexity. In general scenarios, the time complexity of our algorithm is comparable to that of Kruskal’s algorithm. However, the experimental results demonstrate that our algorithm outperforms the approach of recomputing the minimum spanning tree by using Kruskal’s algorithm, especially in medium- and large-scale dynamic graphs where the graph undergoes iterative changes.
]]>Mathematics doi: 10.3390/math12071020
Authors: Aleksandar Kemiveš Lidija Barjaktarović Milan Ranđelović Milan Čabarkapa Dragan Ranđelović
Many methods exist for solving the problem of evaluating efficiency in different processes. They are divided into two basic groups, parametric and non-parametric methods, which can have significant differences in the results. In this study, the authors consider the process of assessing the business climate depending on realized foreign investments. Due to the expected difference in efficiency assessment using different approaches, the goal of this paper is to create an optimization model of an ensemble for efficiency assessment that uses both types of methods with the aim of creating a symmetrical approach that achieves better results than each type of method individually. The proposed solution simultaneously analyzes the impact of different factors on foreign investments in order to determine the most important factors and thus enable each local government to ensure the best possible efficiency in this process. The innovative idea of this study is in the inclusion of classification and feature selection methods of machine learning to fulfill the set goal. Our research, focused on a specific case study in various cities across the Republic of Serbia, evaluated the effectiveness of that process. This study extends previous research and confirms the published results, highlighting the advantages of the newly proposed model.
]]>Mathematics doi: 10.3390/math12071019
Authors: Yunlong Qiu Haiyang Wu Yuntong Dai Kai Li
Self-oscillatory systems have great utility in energy harvesting, engines, and actuators due to their ability to convert ambient energy directly into mechanical work. This characteristic makes their design and implementation highly valuable. Due to the complexity of the motion process and the simultaneous influence of multiple parameters, computing self-oscillatory systems proves to be challenging, especially when conducting inverse parameter design. To simplify the computational process, a combined approach o0f Random Forest (RF) and Backpropagation Neural Network (BPNN) algorithms is employed. The example used is a self-rotating skipping rope made of liquid crystal elastomer (LCE) fiber and a mass block under illumination. Numerically solving the governing equations yields precise solutions for the rotation frequency of the LCE skipping rope under various system parameters. A database containing 138,240 sets of parameter conditions and their corresponding rotation frequencies is constructed to train the RF and BPNN models. The training outcomes indicate that RF and BPNN can accurately predict the self-rotating skipping rope frequency under various parameters, demonstrating high stability and computational efficiency. This approach allows us to discover the influences of distinct parameters on the rotation frequency as well. Moreover, it is capable of inverse design, meaning it can derive the corresponding desired parameter combination from a given rotation frequency. Through this study, a deeper understanding of the dynamic behavior of self-oscillatory systems is achieved, offering a new approach and theoretical foundation for their implementation and construction.
]]>Mathematics doi: 10.3390/math12071018
Authors: Bernardo G. Rodrigues Francesco G. Russo
We describe the nonabelian exterior square G∧^G of a pro-p-group G (with p arbitrary prime) in terms of quotients of free pro-p-groups, providing a new method of construction of G∧^G and new structural results for G∧^G. Then, we investigate a generalization of the probability that two randomly chosen elements of G commute: this notion is known as the “ complete exterior degree” of a pro-p-group and we will use it to characterize procyclic groups. Among other things, we present a new formula, which simplifies the numerical aspects which are connected with the evaluation of the complete exterior degree.
]]>Mathematics doi: 10.3390/math12071017
Authors: Liang Li Yiqiu Mao
The current article focuses on the examination of nonlinear instability and dynamic transitions in a double-diffusive rotating couple-stress fluid layer. The analysis was based on the newly developed dynamic transition theory by T. Ma and S. Wang. Through a comprehensive linear spectrum analysis and investigation of the principle of exchange of stability (PES) as the thermal Rayleigh number crosses a threshold, the nonlinear orbital changes during the transition were rigorously elucidated utilizing reduction methods. For both single real and complex eigenvalue crossings, local pitch-fork and Hopf bifurcations were discovered, and directions of these bifurcations were identified along with transition types. Furthermore, nondimensional transition numbers that signify crucial factors during the transition were calculated and the orbital structures were illustrated. Numerical studies were performed to validate the theoretical results, revealing the relations between key parameters in the system and the types of transition. The findings indicated that the presence of couple stress and a slow diffusion rate of solvent and temperature led to smoother nonlinear transitions during convection.
]]>Mathematics doi: 10.3390/math12071016
Authors: Omar Mutab Alsalami Efat Yousefpoor Mehdi Hosseinzadeh Jan Lansky
A flying ad hoc network (FANET) is formed from a swarm of drones also known as unmanned aerial vehicles (UAVs) and is currently a popular research subject because of its ability to carry out complicated missions. However, the specific features of UAVs such as mobility, restricted energy, and dynamic topology have led to vital challenges for making reliable communications between drones, especially when designing routing methods. In this paper, a novel optimized link-state routing scheme with a greedy and perimeter forwarding capability called OLSR+GPSR is proposed in flying ad hoc networks. In OLSR+GPSR, optimized link-state routing (OLSR) and greedy perimeter stateless routing (GPSR) are merged together. The proposed method employs a fuzzy system to regulate the broadcast period of hello messages based on two inputs, namely the velocity of UAVs and position prediction error so that high-speed UAVs have a shorter hello broadcast period than low-speed UAVs. In OLSR+GPSR, unlike OLSR, MPR nodes are determined based on several metrics, especially neighbor degree, node stability (based on velocity, direction, and distance), the occupied buffer capacity, and residual energy. In the last step, the proposed method deletes two phases in OLSR, i.e., the TC message dissemination and the calculation of all routing paths to reduce routing overhead. Finally, OLSR+GPSR is run on an NS3 simulator, and its performance is evaluated in terms of delay, packet delivery ratio, throughput, and overhead in comparison with Gangopadhyay et al., P-OLSR, and OLSR-ETX. This evaluation shows the superiority of OLSR+GPSR.
]]>Mathematics doi: 10.3390/math12071015
Authors: Cecilia Leal-Ramírez Héctor Alonso Echavarría-Heras
Background: The evaluation of the development of a student’s abilities and skills through a learning activity is a topic strongly questioned by the education system in Mexico. Several instruments have been developed to achieve said evaluation. However, these involve both qualitative and subjective assessment, thereby avoiding the possibility of unambiguously verifying the development of a student’s aptitudes. Methods: We developed a new instrument composed of an integrated instruction and a dynamic fuzzy inference system. Integrated instruction is a table that contains a set of instructions and a set of indicators that make it possible to evaluate knowledge, procedure, and attitude without establishing qualitative or subjective criteria to rank them. The dynamic fuzzy inference system assesses indicators under a criterion to demonstrate the development of a student’s abilities and skills. Results: The method was applied to three different learning activities, where the assessment was precise and transparent for the student, contributing to an extraordinary identification of the acquainted knowledge, procedure, and attitude that the student displayed to develop the activity. Conclusions: Our instrument evaluates the development of abilities and skills without ambiguity or subjectivity, making efficient feedback possible and allowing it to be perfected without difficulties for future adaptations.
]]>Mathematics doi: 10.3390/math12071014
Authors: Kazeem Babatunde Akande Samuel Tosin Akinyemi Nneka O. Iheonu Alogla Monday Audu Folashade Mistura Jimoh Atede Anne Ojoma Victoria Iyabode Okeowo Abdulrahaman Lawal Suleiman Kayode Oshinubi
Anthrax, a zoonotic disease with serious public health consequences, has been the subject of rigorous mathematical and statistical modeling to better understand its dynamics and to devise effective control techniques. In this study, we propose a novel mathematical risk-structured model for anthrax disease spread that includes both qualitative and quantitative evaluations. Our research focuses on the complex interplay between host–anthrax interactions and zoonotic transmission. Our mathematical approach incorporates bifurcation analysis and stability considerations. We investigate the dynamic behavior of the proposed model under various settings, shedding light on the important parameters that determine anthrax transmission and persistence. The normalized forward sensitivity analysis method is used to determine the parameters that are relevant to reducing Rc and, by extension, disease spread. Through scenario simulation of our model, we identify intervention techniques, such as enlightenment of the populace, that will effectively minimize disease transmission. Our findings provide insights into anthrax epidemiology and emphasize the importance of effective disease management. Bifurcation investigations reveal the existence and stability of numerous equilibria, allowing for a better understanding of the behavior of the system under various scenarios. This study adds to the field of anthrax modeling by providing a foundation for informed decision-making regarding public health measures. The use of a mathematical modeling approach improves our ability to anticipate and control anthrax epidemics, ultimately helping to protect both human and animal populations.
]]>Mathematics doi: 10.3390/math12071013
Authors: Jie Yang Byung Gook Lee
The distributed leader-follower control of multi-agent systems is discussed. Each agent is expressed in a discrete-time and non-linear dynamic model with an unknown parameter and can be affected by its neighbors’ history information. For each agent, to identify the parameter, one switching set of the parameter estimates is constructed and the optimal parameter estimate is chosen based on the index switching function. Using the given desired reference signal, the leader agent’s control law is designed, and relying on the neighbors’ history information, each follower agent’s local control law is designed. With the designed distributed tracking adaptive control laws, the whole system tracks the given desired reference signal, and in the face of strong couplings the closed-loop system ultimately reaches an agreement. Finally, by comparing simulations of the control strategy with a normal projection algorithm, the results indicate that the adaptive control method with a switching set of the parameter estimates is effective in improving the control performance.
]]>Mathematics doi: 10.3390/math12071012
Authors: Tjaša Heričko Boštjan Šumak Sašo Karakatič
Software evolution is driven by changes made during software development and maintenance. While source control systems effectively manage these changes at the commit level, the intent behind them are often inadequately documented, making understanding their rationale challenging. Existing commit intent classification approaches, largely reliant on commit messages, only partially capture the underlying intent, predominantly due to the messages’ inadequate content and neglect of the semantic nuances in code changes. This paper presents a novel method for extracting semantic features from commits based on modifications in the source code, where each commit is represented by one or more fine-grained conjoint code changes, e.g., file-level or hunk-level changes. To address the unstructured nature of code, the method leverages a pre-trained transformer-based code model, further trained through task-adaptive pre-training and fine-tuning on the downstream task of intent classification. This fine-tuned task-adapted pre-trained code model is then utilized to embed fine-grained conjoint changes in a commit, which are aggregated into a unified commit-level vector representation. The proposed method was evaluated using two BERT-based code models, i.e., CodeBERT and GraphCodeBERT, and various aggregation techniques on data from open-source Java software projects. The results show that the proposed method can be used to effectively extract commit embeddings as features for commit intent classification and outperform current state-of-the-art methods of code commit representation for intent categorization in terms of software maintenance activities undertaken by commits.
]]>Mathematics doi: 10.3390/math12071010
Authors: Baoli Xie Jianxiang Dong Caochuan Ma
We characterize the boundedness and compactness of dual Toeplitz operators on the orthogonal complement of the generalized Fock space. We study the problem when the finite sum of the dual Toeplitz products is compact. Additionally, we also consider when the sum of the dual Toeplitz operators is equal to another dual Toeplitz operator.
]]>Mathematics doi: 10.3390/math12071011
Authors: Ping Zhang
COPA, introduced by Andreeva et al., is the first online authenticated encryption (AE) mode with nonce-misuse resistance, and it is covered in COLM, which is one of the final CAESAR portfolios. However, COPA has been proven to be insecure in the releasing unverified plaintext (RUP) setting. This paper mainly focuses on the integrity under RUP (INT-RUP) defect of COPA. Firstly, this paper revisits the INT-RUP security model for adaptive adversaries, investigates the possible factors of INT-RUP insecurity for “Encryption-Mix-Encryption”-type checksum-based AE schemes, and finds that these AE schemes with INT-RUP security vulnerabilities utilize a common poor checksum technique. Then, this paper introduces an improved checksum technique named polynomial intermediate checksum (PIC) for INT-RUP security and emphasizes that PIC is a sufficient condition for guaranteeing INT-RUP security for “Encryption-Mix-Encryption”-type checksum-based AE schemes. PIC is generated by a polynomial sum with full terms of intermediate internal states, which guarantees no information leakage. Moreover, PIC ensures the same level between the plaintext and the ciphertext, which guarantees that the adversary cannot obtain any useful information from the unverified decryption queries. Again, based on PIC, this paper proposes a modified scheme COPA-PIC to fix the INT-RUP defect of COPA. COPA-PIC is proven to be INT-RUP up to the birthday-bound security if the underlying primitive is secure. Finally, this paper discusses the properties of COPA-PIC and makes a comparison for AE modes with distinct checksum techniques. The proposed work is of good practical significance. In an interactive system where two parties communicate, the receiver can effectively determine whether the information received from the sender is valid or not, and thus perform the subsequent operation more effectively.
]]>Mathematics doi: 10.3390/math12071009
Authors: Ndivhuwo Ndou Phumlani Dlamini Byron Alexander Jacobs
In this paper, the enhanced higher-order unconditionally positive finite difference method is developed to solve the linear, non-linear and system advection diffusion reaction equations. Investigation into the effectiveness and efficiency of the proposed method is carried out by calculating the convergence rate, error and computational time. A comparison of the solutions obtained by the enhanced higher-order unconditionally positive finite difference and exact solution is conducted for validation purposes. The numerical results show that the developed method reduced the time taken to solve the linear and non-linear advection diffusion reaction equations as compared to the results obtained by the higher-order unconditionally positive finite difference method.
]]>Mathematics doi: 10.3390/math12071008
Authors: Bhuwan Chandra Joshi Murari Kumar Roy Abdelouahed Hamdi
In this paper, we examine a semi-infinite interval-valued optimization problem with vanishing constraints (SIVOPVC) that lacks differentiability and involves constraints that tend to vanish. We give definitions of generalized convex functions along with supportive examples. We investigate duality theorems for the SIVOPVC problem. We establish these theorems by creating duality models, which establish a relationship between SIVOPVC and its corresponding dual models, assuming generalized convexity conditions. Some examples are also given to illustrate the results.
]]>Mathematics doi: 10.3390/math12071007
Authors: Shiying Liu Fang Yang Tailin Liu Mengli Li
This study designs a two-stage algorithm to address the bid generation problem of carriers when adding new vehicle routes in the presence of the existing vehicle routes to provide transportation service. To obtain the best auction combination and bid price of the carrier, a hybrid integer nonlinear programming model is introduced. According to the characteristics of the problem, a set of two-stage hybrid algorithms is proposed, innovatively integrating block coding within a genetic algorithm framework with a depth-first search approach. This integration effectively manages routing constraints, enhancing the algorithm’s efficiency. The block coding and each route serve as decision variables in the set partition formula, enabling a comprehensive exploration of potential solutions. After a simulation-based analysis, the algorithm has been comprehensively validated analytically and empirically. The improvement of this research lies in the effectiveness of the proposed algorithm, i.e., the ability to handle a broader range of problem scales with less time in addressing complex operator bid generation in combinatorial auctions.
]]>Mathematics doi: 10.3390/math12071006
Authors: Andrey Tsyganov Yulia Tsyganova
This paper addresses the problem of parameter identification for discrete-time stochastic systems with unknown exogenous inputs. These systems form an important class of dynamic stochastic system models used to describe objects and processes under a high level of a priori uncertainty, when it is not possible to make any assumptions about the evolution of the unknown input signal or its statistical properties. The main purpose of this paper is to construct a new SVD-based modification of the existing Gillijns and De Moor filtering algorithm for linear discrete-time stochastic systems with unknown exogenous inputs. Using the theoretical results obtained, we demonstrate how this modified algorithm can be applied to solve the problem of parameter identification. The results of our numerical experiments conducted in MATLAB confirm the effectiveness of the SVD-based parameter identification method that was developed, under conditions of unknown exogenous inputs, compared to maximum likelihood parameter identification when exogenous inputs are known.
]]>Mathematics doi: 10.3390/math12071005
Authors: Zhoubao Sun Kai Zhang Yan Zhu Yanzhe Ji Pingping Wu
The interest of advertising designers and operators in crafting appealing images is steadily increasing. With a primary focus on image attractiveness, this study endeavors to uncover the correlation between image features and attractiveness. The ultimate objective is to enhance the accuracy of predicting image attractiveness to achieve visually captivating effects. The experimental subjects encompass images sourced from the Shutterstock website, and the correlation between image features and attractiveness is analyzed through image attractiveness scores. In our experiments, we extracted traditional features such as color, shape, and texture from the images. Through a detailed analysis and comparison of the accuracy in predicting image attractiveness before and after feature selection using Lasso and LassoNet,, we confirmed that feature selection is an effective method for improving prediction accuracy. Subsequently, the Lasso and LassoNet feature selection methods were applied to a dataset containing image content features. The results verified an enhancement in the model’s accuracy for predicting image attractiveness with the inclusion of image content features. Finally, through an analysis of the four-dimensional features of color, texture, shape, and content, we identified specific features influencing image attractiveness, providing a robust reference for image design.
]]>Mathematics doi: 10.3390/math12071004
Authors: Susana Aberturas Juan Diego Aguilera José Luis Olazagoitia Miguel Ángel García Antonio Hernando
This study explores the advanced mathematical modeling of electromagnetic energy harvesting in vehicle suspension systems, addressing the pressing need for sustainable transportation and improved energy efficiency. We focus on the complex challenge posed by the non-linear behavior of magnetic flux in relation to displacement, a critical aspect often overlooked in conventional approaches. Utilizing Taylor expansion and Fourier analysis, we dissect the intricate relationship between oscillation and electromagnetic damping, crucial for optimizing energy recovery. Our rigorous mathematical methodology enables the precise calculation of the average power per cycle and unit mass, providing a robust metric for evaluating the effectiveness of energy harvesting. Further, the study extends to the practical application in a combined system of passive and electromagnetic suspension, demonstrating the real-world viability of our theoretical findings. This research not only offers a comprehensive solution for enhancing vehicle efficiency through advanced suspension systems but also sets a precedent for the integration of complex mathematical techniques in solving real-world engineering challenges, contributing significantly to the future of energy-efficient automotive technologies. The cases reviewed in this article and listed as references are those commonly found in the literature.
]]>Mathematics doi: 10.3390/math12071003
Authors: Petar Popivanov Angela Slavova
In this paper, exact solutions of semilinear equations having exponential growth in the space variable x are found. Semilinear Schrödinger equation with logarithmic nonlinearity and third-order evolution equations arising in optics with logarithmic and power-logarithmic nonlinearities are investigated. In the parabolic case, the solution u is written as u=be−ax2, a<0, a,b being real-valued functions. We are looking for the solutions u of Schrödinger-type equation of the form u=be−ax22, respectively, for the third-order PDE, u=AeiΦ, where the amplitude b and the phase function a are complex-valued functions, A>0, and Φ is real-valued. In our proofs, the method of the first integral is used, not Hirota’s approach or the method of simplest equation.
]]>Mathematics doi: 10.3390/math12071002
Authors: Xiao Pan Dongna Lu Ning Li
China’s policies about reducing carbon emissions mainly focus on saving energy and reducing pollutant emissions. However, the carbon emissions of the logistics industry remain high. Thus, logistics companies should not only reduce distribution costs, but also consider the impact of carbon emissions when planning distribution routes. This paper studies the supermarket delivery distribution route planning problem considering carbon emissions. Aiming at the lowest economic operating cost composed of fixed cost, driving cost, and carbon emission cost, we propose a grey wolf optimized genetic algorithm to generate delivery route plans, where the social rank and hunting behavior of the grey wolf optimization algorithm are integrated into the selection operation of the genetic algorithm. Finally, a real case of a large third-party logistics enterprise in Beijing is studied. The case study results verify the effectiveness and applicability of the model and algorithm.
]]>Mathematics doi: 10.3390/math12071001
Authors: Xuebin Xie Yingling Huang
Landslide displacement prediction is of great significance for the prevention and early warning of slope hazards. In order to enhance the extraction of landslide historical monitoring signals, a landslide displacement prediction method is proposed based on the decomposition of monitoring data before prediction. Firstly, based on the idea of temporal addition, the sparrow search algorithm (SSA) coupled with the variational modal decomposition (VMD) algorithm is used to decompose the total landslide displacement into trend item, periodic item and random item; then, the displacement values of the subitems are fitted by using the long and short-term memory (LSTM) neural network, and the predicted cumulative landslide displacement is obtained by adding up the predicted values of the three subsequences. Finally, the historical measured data of the Shuping landslide is taken as an example. Considering the effects of seasonal rainfall and reservoir water level rise and fall, the displacement of this landslide is predicted, and the prediction results of other traditional models are compared. The results show that the landslide displacement prediction model of SSA-VMD coupled with LSTM can predict landslide displacement more accurately and capture the characteristics of historical signals, which can be used as a reference for landslide displacement prediction.
]]>Mathematics doi: 10.3390/math12071000
Authors: Paul W. Eloe Yulong Li Jeffrey T. Neugebauer
Sufficient conditions are obtained for a signed maximum principle for boundary value problems for Riemann–Liouville fractional differential equations with analogues of Neumann or periodic boundary conditions in neighborhoods of simple eigenvalues. The primary objective is to exhibit four specific boundary value problems for which the sufficient conditions can be verified. To show an application of the signed maximum principle, a method of upper and lower solutions coupled with monotone methods is developed to obtain sufficient conditions for the existence of a maximal solution and a minimal solution of a nonlinear boundary value problem. A specific example is provided to show that sufficient conditions for the nonlinear problem can be realized.
]]>Mathematics doi: 10.3390/math12070999
Authors: Piotr Krylov Askar Tuganbaev
We study the derivations of the incidence algebra I(X,R), where X is a preordered set and R is an algebra over some commutative ring T. A satisfactory description of the T-module of derivations and the T-module of outer derivations of this algebra is given.
]]>Mathematics doi: 10.3390/math12070998
Authors: Benet Eiximeno Arnau Miró Ivette Rodríguez Oriol Lehmkuhl
This study introduces a deep learning surrogate model designed to predict the evolution of the mean pressure coefficient on the back face of a Windsor body across a range of yaw angles from 2.5∘ to 10∘. Utilizing a variational autoencoder (VAE), the model effectively compresses snapshots of back pressure taken at yaw angles of 2.5∘, 5∘, and 10∘ into two latent vectors. These snapshots are derived from wall-modeled large eddy simulations (WMLESs) conducted at a Reynolds number of ReL=2.9×106. The frequencies that dominate the latent vectors correspond closely with those observed in both the drag’s temporal evolution and the dynamic mode decomposition. The projection of the mean pressure coefficient to the latent space yields an increasing linear evolution of the two latent variables with the yaw angle. The mean pressure coefficient distribution at a yaw angle of 7.5∘ is predicted with a mean error of e¯=3.13% when compared to the WMLESs results after obtaining the values of the latent space with linear interpolation.
]]>Mathematics doi: 10.3390/math12070997
Authors: Sio-Kei Im Ka-Hou Chan
The attention mechanism performs well for the Neural Machine Translation (NMT) task, but heavily depends on the context vectors generated by the attention network to predict target words. This reliance raises the issue of long-term dependencies. Indeed, it is very common to combine predicates with postpositions in sentences, and the same predicate may have different meanings when combined with different postpositions. This usually poses an additional challenge to the NMT study. In this work, we observe that the embedding vectors of different target tokens can be classified by part-of-speech, thus we analyze the Natural Language Processing (NLP) related Content-Adaptive Recurrent Unit (CARU) unit and apply it to our attention model (CAAtt) and embedding layer (CAEmbed). By encoding the source sentence with the current decoded feature through the CARU, CAAtt is capable of achieving translation content-adaptive representations, which attention weights are contributed and enhanced by our proposed L1expNx normalization. Furthermore, CAEmbed aims to alleviate long-term dependencies in the target language through partial recurrent design, performing the feature extraction in a local perspective. Experiments on the WMT14, WMT17, and Multi30k translation tasks show that the proposed model achieves improvements in BLEU scores and enhancement of convergence over the attention-based plain NMT model. We also investigate the attention weights generated by the proposed approaches, which indicate that refinement over the different combinations of adposition can lead to different interpretations. Specifically, this work provides local attention to some specific phrases translated in our experiment. The results demonstrate that our approach is effective in improving performance and achieving a more reasonable attention distribution compared to the state-of-the-art models.
]]>Mathematics doi: 10.3390/math12070996
Authors: Nelson Martins-Ferreira Rui A. P. Perdigão
A generalized construction procedure for algebraic number systems is hereby presented. This procedure offers an efficient representation and computation method for complex numbers, quaternions, and other algebraic structures. The construction method is then illustrated across a range of examples. In particular, the novel developments reported herein provide a generalized form of the Cayley–Dickson construction through involutive dimagmas, thereby allowing for the treatment of more general spaces other than vector spaces, which underlie the associated algebra structure.
]]>Mathematics doi: 10.3390/math12070995
Authors: Yao Zhai Wei Liu Yunzhi Jin Yanqing Zhang
The Hidden Markov Model (HMM) is a crucial probabilistic modeling technique for sequence data processing and statistical learning that has been extensively utilized in various engineering applications. Traditionally, the EM algorithm is employed to fit HMMs, but currently, academics and professionals exhibit augmenting enthusiasm in Bayesian inference. In the Bayesian context, Markov Chain Monte Carlo (MCMC) methods are commonly used for inferring HMMs, but they can be computationally demanding for high-dimensional covariate data. As a rapid substitute, variational approximation has become a noteworthy and effective approximate inference approach, particularly in recent years, for representation learning in deep generative models. However, there has been limited exploration of variational inference for HMMs with high-dimensional covariates. In this article, we develop a mean-field Variational Bayesian method with the double-exponential shrinkage prior to fit high-dimensional HMMs whose hidden states are of discrete types. The proposed method offers the advantage of fitting the model and investigating specific factors that impact the response variable changes simultaneously. In addition, since the proposed method is based on the Variational Bayesian framework, the proposed method can avoid huge memory and intensive computational cost typical of traditional Bayesian methods. In the simulation studies, we demonstrate that the proposed method can quickly and accurately estimate the posterior distributions of the parameters with good performance. We analyzed the Beijing Multi-Site Air-Quality data and predicted the PM2.5 values via the fitted HMMs.
]]>Mathematics doi: 10.3390/math12070994
Authors: Ivan Babkin Vyacheslav Rybin Valery Andreev Timur Karimov Denis Butusov
Computer simulation of continuous chaotic systems is usually performed using numerical methods. The discretization may introduce new properties into finite-difference models compared to their continuous prototypes and can therefore lead to new types of dynamical behavior exhibited by discrete chaotic systems. It is known that one can control the dynamics of a discrete system using a special class of integration methods. One of the applications of such a phenomenon is chaos-based communication systems, which have recently attracted attention due to their high covertness and broadband transmission capability. Proper modulation of chaotic carrier signals is one of the key problems in chaos-based communication system design. It is challenging to modulate and demodulate a chaotic signal in the same way as a conventional signal due to its noise-like shape and broadband characteristics. Therefore, the development of new modulation–demodulation techniques is of great interest in the field. One possible approach here is to use adaptive numerical integration, which allows control of the properties of the finite-difference chaotic model. In this study, we describe a novel modulation technique for chaos-based communication systems based on generalized explicit second-order Runge–Kutta methods. We use a specially designed test bench to evaluate the efficiency of the proposed modulation method and compare it with state-of-the-art solutions. Experimental results show that the proposed modulation technique outperforms the conventional parametric modulation method in both coverage and noise immunity. The obtained results can be efficiently applied to the design of advanced chaos-based communication systems as well as being used to improve existing architectures.
]]>Mathematics doi: 10.3390/math12070992
Authors: Adham Salih Joseph Gabbay Amiram Moshaiov
This study is motivated by the need to develop generic neuro-fuzzy motion controllers for autonomous vehicles that may traverse rugged terrains. Three types of target problems are investigated. These problems differ in terms of the expected motion behavior, including cautious, intermediate, and courageous behaviors. The target problems are defined as evolutionary multi-objective problems aiming to evolve near optimal neuro-fuzzy controllers that can operate in a variety of scenarios. To enhance the evolution, sequential transfer optimization is considered, where each of the source problems is defined and solved as a bi-objective problem. The performed experimental study demonstrates the ability of the proposed search approach to find neuro-fuzzy controllers that produce the required motion behaviors when operating in various environments with different motion difficulties. Moreover, the results of this study substantiate the hypothesis that solutions with performances near the edges of the obtained approximated bi-objective Pareto fronts of the source problems provide better transferability as compared with those that are associated with performances near the center of the obtained fronts.
]]>Mathematics doi: 10.3390/math12070993
Authors: Shuangmin Chen Nailei Hei Shun Hu Zijia Yue Ying He
Querying the geodesic distance field on a given smooth surface is a fundamental research pursuit in computer graphics. Both accuracy and smoothness serve as common indicators for evaluating geodesic algorithms. In this study, we argue that ensuring that the norm of the triangle-wise estimated gradients is not larger than 1 is preferable compared to the widely used eikonal condition. Inspired by this, we formulate the geodesic distance field problem as a Quadratically Constrained Linear Programming (QCLP) problem. This formulation can be further adapted into a Quadratically Constrained Quadratic Programming (QCQP) problem by incorporating considerations for smoothness requirements. Specifically, when enforcing a Hessian-energy-based smoothing term, our formulation, named QCQP-Hessian, effectively mitigates the cusps in the geodesic isolines within the near-ridge area while maintaining accuracy in the off-ridge area. We conducted extensive experiments to demonstrate the accuracy and smoothness advantages of QCQP-Hessian.
]]>Mathematics doi: 10.3390/math12070991
Authors: Federico Alonso-Pecina Irma Yazmín Hérnandez-Báez Roberto Enrique López-Díaz Martin H. Cruz-Rosales
We address an inventory-routing problem that arises in a liquid oxygen-producing company. Decisions must be made for the efficient transport of the product from sources to destinations by means of a heterogeneous fleet of trucks. This combinatorial problem has been stated as a constrained minimization one, whose objective function is the quotient of the operating cost divided by the total amount of delivered product. The operating cost comes from the distances traveled, the drivers’ salary, and the drivers’ overnight accommodation. The constraints include time windows for drivers and destinations, inventory safety levels, lower bounds for the quantity of product delivered to destinations, and maximum driving times. To approximate the optimal solution of this challenging problem, we developed a heuristic algorithm that first finds a feasible solution, and then iteratively improves it by combining the Metropolis criterion with local search. Our results are competitive with the best proposals in the literature.
]]>Mathematics doi: 10.3390/math12070990
Authors: Artem E. Konkov Pavel S. Korenev Valerii I. Kruzhkov Evgeniia A. Pavlova
On 22 January 2024, at the age of 78, Yuri Vladimirovich Mitrishkin (Figure 1), an outstanding scientist and remarkable educator with half a century of experience, passed away unexpectedly [...]
]]>Mathematics doi: 10.3390/math12070989
Authors: Miao He Changtian Wu Jinsong Leng
When studying signal reconstruction, the frames are often selected in advance as encoding tools. However, in practical applications, this encoding frame may be subject to attacks by intermediaries and generate errors. To solve this problem, in this paper, the erasure recovery matrices for data erasures and rearrangements are analyzed. Unlike the previous research, first of all, we introduce a kind of frame and its erasure recovery matrix M so that MI,Λ=Im×m, where Im×m is a unit matrix. In this case, we do not need to invert the matrix of the frame operator and the erasure recovery matrix, and this greatly simplifies reconstruction problems and calculations. Then three different construction algorithms of the above erasure recovery matrix M and the frame are proposed, and each of them has advantages. Furthermore, some restrictions on M so that the constructed frame and erasure recovery matrix M can recover coefficients from rearrangements are imposed. We prove that in some cases, the above M and frame can recover coefficients stably from m rearrangements.
]]>Mathematics doi: 10.3390/math12070988
Authors: Alexander V. Aksenov Anatoly A. Kozyrev
Unsteady equations of flat and axisymmetric boundary layers are considered. For the unsteady axisymmetric boundary layer equation, the problem of group classification is solved. It is shown that the kernel of symmetry operators can be extended by no more than four-dimensional Lie algebra. The kernel of symmetry operators of the unsteady flat boundary layer equation is found and it is shown that it can be extended by no more than a five-dimensional Lie algebra. The non-existence of the unsteady analogue of the Stepanov–Mangler transformation is proved.
]]>Mathematics doi: 10.3390/math12070987
Authors: Maciej Leszczynski Przemyslaw Perlikowski Piotr Brzeski
This paper explores two sample-based methods for analysing multistable systems: basin stability and basin entropy. Both methods rely on many numerical integration trials conducted with diverse initial conditions. The collected data is categorised and used to compute metrics that characterise solution stability, phase space structure, and system dynamics predictability. Basin stability assesses the overall likelihood of reaching specific solutions, while the basin entropy measure aims to capture the structure of attraction basins and the complexity of their boundaries. Although these two metrics complement each other effectively, their original procedures for computation differ significantly. This paper introduces a universal approach and algorithm for calculating basin stability and entropy measures. The suitability of these procedures is demonstrated through the analysis of two non-linear systems.
]]>Mathematics doi: 10.3390/math12070986
Authors: Jun Long Shangpeng Wang Yakun Huo Limin Liu Huilong Fan
The purpose of constructing onboard observation mission queues is to improve the execution efficiency of onboard tasks and reduce energy consumption, representing a significant challenge in achieving efficient global military reconnaissance and target tracking. Existing research often focuses on the aspect of task scheduling, aiming at optimizing the efficiency of single-task execution, while neglecting the complex dependencies that might exist between multiple tasks and payloads. Moreover, traditional task scheduling schemes are no longer suitable for large-scale tasks. To effectively reduce the number of tasks within the network, we introduce a network aggregation graph model based on multiple satellites and tasks, and propose a task aggregation priority dynamic calculation algorithm based on graph computations. Subsequently, we present a dynamic merging-based method for multi-satellite, multi-task aggregation, a novel approach for constructing onboard mission queues that can dynamically optimize the task queue according to real-time task demands and resource status. Simulation experiments demonstrate that, compared to baseline algorithms, our proposed task aggregation method significantly reduces the task size by approximately 25% and effectively increases the utilization rate of onboard resources.
]]>Mathematics doi: 10.3390/math12070985
Authors: Silvério Rosa Faïçal Ndaïrou
A recently proposed fractional-order mathematical model with Caputo derivatives was developed for Ebola disease. Here, we extend and generalize this model, beginning with its correction. A fractional optimal control (FOC) problem is then formulated and numerically solved with the rate of vaccination as the control measure. The research presented in this work addresses the problem of fitting real data from Guinea, Liberia, and Sierra Leone, available at the World Health Organization (WHO). A cost-effectiveness analysis is performed to assess the cost and effectiveness of the control measure during the intervention. We come to the conclusion that the fractional control is more efficient than the classical one only for a part of the time interval. Hence, we suggest a system where the derivative order changes over time, becoming fractional or classical when it makes more sense. This type of variable-order fractional model, known as piecewise derivative with fractional Caputo derivatives, is the most successful in managing the illness.
]]>Mathematics doi: 10.3390/math12070984
Authors: Naiara P. V. Sebbe Francisco J. G. Silva Alcinda M. S. Barreiras Isabel M. Pinto Rita C. M. Sales-Contini Luis P. Ferreira Ana B. M. Machado
Logistics and the supply chain are areas of great importance within organizations. Due to planning gaps, an increase in extra and unnecessary transport costs is usually observed in several companies due to their commercial commitments and need to comply with the delivery time and the batch quantity of products, leading to a negative economic impact. Thus, the objective of this work was to adjust an optimization model to maximize the shipments usually carried out by the companies. To validate the model, an automotive components manufacturer was selected, allowing us to apply the model to a real case study and evaluate the advantages and drawbacks of this tool. It was found that the company to validate the model exports most of its products, and most pallets sent are not fully optimized, generating excessive expense for the company in terms of urgent transport. To solve this problem, two mathematical optimization models were used for the company’s current reality, optimizing the placement of boxes per pallet and customer. With the use of the new tool, it was possible to determine that five pallets should be sent to the customer weekly, which correspond to their needs, and that have the appropriate configurations so that the pallet is sent completely.
]]>Mathematics doi: 10.3390/math12070983
Authors: Minghui Sheng Hui Wang Maode Ma Yiying Sun Run Zhou
The rapid growth of edge devices and mobile applications has driven the adoption of edge computing to handle computing tasks closer to end-users. However, the heterogeneity of edge devices and their limited computing resources raise challenges in the efficient allocation of computing resources to complete services with different characteristics and preferences. In this paper, we delve into an edge scenario comprising multiple Edge Computing Servers (ECSs), multiple Device-to-Device (D2D) Edge Nodes (ENs), and multiple edge devices. In order to address the resource allocation challenge among ECSs, ENs, and edge devices in high-workload environments, as well as the pricing of edge resources within the resource market framework, we propose a Risk Assessment Contract Algorithm (RACA) based on risk assessment theory. The RACA enables ECSs to assess risks associated with local users by estimating their future revenue potential and updating the contract autonomously at present and in the future. ENs acquire additional resources from ECSs to efficiently complete local users’ tasks. Simultaneously, ENs can also negotiate reasonable resource requests and pricing with ECSs by a Stackelberg game algorithm. Furthermore, we prove the unique existence of Nash equilibrium in the established game, implying that equilibrium solutions can stably converge through computational methods in heterogeneous environments. Finally, through simulation experiments on the dataset, we demonstrate that risk assessment can better enhance the overall profit capability of the system. Moreover, through multiple experiments, we showcase the stability of the contract’s autonomous update capability. The RACA exhibits better utility in terms of system profit capabilities, stability in high-workload environments, and energy consumption. This work provides a more dynamic and effective solution to the resource allocation problem in edge systems under high-workload environments.
]]>Mathematics doi: 10.3390/math12070982
Authors: Chong-Quan Zhang Qing-Wen Wang Xiang-Xiang Wang Zhuo-Heng He
We investigate and discuss in detail the structure of the restricted singular value decomposition for a tensor triplet under t-product (T-RSVD). The algorithm is provided with a numerical example illustrating the main result. For applications, we consider color image watermarking processing with T-RSVD.
]]>Mathematics doi: 10.3390/math12070981
Authors: Yu-Jing Chiu Ling-Shiuan Hong So-Ra Song Yu-Chao Cheng
In recent years, influencer marketing has taken over traditional brand advertisements on social media platforms, combining word-of-mouth marketing with celebrity endorsements. However, there has been limited academic research on the key success factors in influencer marketing. This paper used a hybrid MCDM model that integrates the Delphi method and the decision-making trial and evaluation laboratory (DEMATEL) approach. Through a two-stage empirical study, the research aims to explore the crucial success factors in influencer marketing. This study focuses on the Taiwanese market. The target respondents for the survey are consumers in Taiwan who have purchased products or services based on recommendations from key opinion leaders (KOLs) or internet celebrities. This systematic research framework not only pinpoints key factors that capture consumer attention towards influencers, but it also illustrates the inter-relationship of structure and improvement directions among these factors. According to results, the key factors include influencer reputation, credibility, degree of key opinion influence, attractiveness, popularity, consistency between influencers and brands, fan engagement level, and informativeness. Finally, businesses can consider five aspects to be the purpose of collaboration, product type, target audience for the product, characteristics of the influencer’s creative content, and media attributes. By comprehensively considering these aspects, businesses can determine the appropriate format for collaborative content. This decision can then guide how influencers communicate with consumers, effectively conveying brand information to the relevant target audience. The research findings provide fresh and significant insights in the field of influencer marketing studies.
]]>Mathematics doi: 10.3390/math12070979
Authors: Miroslav Stoenchev Venelin Todorov Slavi Georgiev
This paper examines the relationship between the overconvergence of Fourier series and the existence of Hadamard–Ostrowski gaps. Ostrowski’s result on the overconvergence of power series serves as a motivating factor for obtaining a natural generalization: the overconvergence of Fourier series. The connection between Hadamard–Ostrowski gaps and the overconvergence of Fourier series is clarified by applying the Hadamard three-circle theorem and the theory of orthogonal polynomials. Our main result is obtained by applying the Hadamard three-circle theorem.
]]>Mathematics doi: 10.3390/math12070980
Authors: Zhi-Jie Jiang
One of the aims of this paper is to characterize 3-complex symmetric weighted composition operators induced by three types of symbols on the weighted Bergman space of the right half-plane with the conjugation Jf(z)=f(z¯)¯. It is well known that the complex symmetry is equivalent to 2-complex symmetry for the weighted composition operators studied in the paper. However, the interesting fact that 3-complex symmetry is not equivalent to 2-complex symmetry for such operators is found in the paper. Finally, the complex normal of such operators on the weighted Bergman space of the right half-plane with the conjugation J is characterized.
]]>Mathematics doi: 10.3390/math12070978
Authors: Yufeng Shi Jinghan Wang
In this paper, we consider the general mean-field backward doubly stochastic differential equations (mean-field BDSDEs) whose generator f can be discontinuous in y. We prove the existence theorem of solutions under stochastic linear growth conditions and also obtain the related comparison theorem. Naturally, we present those results under the linear growth condition, which is a special case of the stochastic condition. Finally, a financial claim sale problem is discussed, which demonstrates the application of the general mean-field BDSDEs in finance.
]]>Mathematics doi: 10.3390/math12070976
Authors: Dejan Andjelković Gordan Stojić Nikola Nikolić Dillip Kumar Das Marko Subotić Željko Stević
The capacity of transport infrastructure is one of the very important tasks in transport engineering, which depends mostly on the geometric characteristics of road and headway analysis. In this paper, we have considered 14 road sections and determined their efficiency based on headway analysis. We have developed a novel interval fuzzy-rough-number decision-making model consisting of DEA (data envelopment analysis), IFRN SWARA (interval-valued fuzzy-rough-number stepwise weight-assessment-ratio analysis), and IFRN WASPAS (interval-valued fuzzy-rough-number weighted-aggregate sum–product assessment) methods. The main contribution of this study is a new extension of WASPAS method with interval fuzzy rough numbers. Firstly, the DEA model was applied to determine the efficiency of 14 road sections according to seven input–output parameters. Seven out of the fourteen alternatives showed full efficiency and were implemented further in the model. After that, the IFRN SWARA method was used for the calculation of the final weights, while IFRN WASPAS was applied for ranking seven of the road sections. The results show that two sections are very similar and have almost equal efficiency, while the other results are very stable. According to the results obtained, the best-ranked is a measuring segment of the Ivanjska–Šargovac section, with a road gradient = −5.5%, which has low deviating values of headways according to the measurement classes from PC-PC to AT-PC, which shows balanced and continuous traffic flow. Finally, verification tests such as changing the criteria weights, comparative analysis, changing the λ parameter, and reverse rank analysis have been performed.
]]>Mathematics doi: 10.3390/math12070977
Authors: Xiaolong Wang Zhijian He Xiaojiang Peng
Diffusion models have swiftly taken the lead in generative modeling, establishing unprecedented standards for producing high-quality, varied outputs. Unlike Generative Adversarial Networks (GANs)—once considered the gold standard in this realm—diffusion models bring several unique benefits to the table. They are renowned for generating outputs that more accurately reflect the complexity of real-world data, showcase a wider array of diversity, and are based on a training approach that is comparatively more straightforward and stable. This survey aims to offer an exhaustive overview of both the theoretical underpinnings and practical achievements of diffusion models. We explore and outline three core approaches to diffusion modeling: denoising diffusion probabilistic models, score-based generative models, and stochastic differential equations. Subsequently, we delineate the algorithmic enhancements of diffusion models across several pivotal areas. A notable aspect of this review is an in-depth analysis of leading generative models, examining how diffusion models relate to and evolve from previous generative methodologies, offering critical insights into their synergy. A comparative analysis of the merits and limitations of different generative models is a vital component of our discussion. Moreover, we highlight the applications of diffusion models across computer vision, multi-modal generation, and beyond, culminating in significant conclusions and suggesting promising avenues for future investigation.
]]>Mathematics doi: 10.3390/math12070974
Authors: Yuya Note Masahito Watanabe Hiroaki Yoshimura Takaharu Yaguchi Toshiaki Omori
Estimating governing equations from observed time-series data is crucial for understanding dynamical systems. From the perspective of system comprehension, the demand for accurate estimation and interpretable results has been particularly emphasized. Herein, we propose a novel data-driven method for estimating the governing equations of dynamical systems based on machine learning with high accuracy and interpretability. The proposed method enhances the estimation accuracy for dynamical systems using sparse modeling by incorporating physical constraints derived from Hamiltonian mechanics. Unlike conventional approaches used for estimating governing equations for dynamical systems, we employ a sparse representation of Hamiltonian, allowing for the estimation. Using noisy observational data, the proposed method demonstrates a capability to achieve accurate parameter estimation and extraction of essential nonlinear terms. In addition, it is shown that estimations based on energy conservation principles exhibit superior accuracy in long-term predictions. These results collectively indicate that the proposed method accurately estimates dynamical systems while maintaining interpretability.
]]>Mathematics doi: 10.3390/math12070975
Authors: Weiwei Mao Kaijie Xu
As an information granulation technology, clustering plays a pivotal role in unsupervised learning, serving as a fundamental cornerstone for various data mining techniques. The effective and accurate classification of data is a central focus for numerous researchers. For a dataset, we assert that the classification performance of a clustering method is significantly influenced by uncertain data, particularly those situated at the cluster boundaries. It is evident that uncertain data encapsulate richer information compared with others. Generally, the greater the uncertainty, the more information the data holds. Therefore, conducting a comprehensive analysis of this particular subset of data carries substantial significance. This study presents an approach to characterize data distribution properties using fuzzy clustering and defines the boundary and non-boundary characteristics (certainty and uncertainty) of the data. To improve the classification performance, the strategy focuses on reducing the uncertainty associated with boundary data. The proposed scheme involves inserting data points with the cloud computing technology based on the distribution characteristics of the membership functions to diminish the uncertainty of uncertain data. Building upon this, the contribution of boundary data is reassigned to the prototype in order to diminish the proportion of uncertain data. Subsequently, the classifier is optimized through data label (classification error) supervision. Ultimately, the objective is to leverage clustering algorithms for classification, thereby enhancing overall classification accuracy. Experimental results substantiate the effectiveness of the proposed scheme.
]]>Mathematics doi: 10.3390/math12070973
Authors: Ruixue Zhang Yongtao Hao
Time series data are prevalent in the real world, particularly playing a crucial role in key domains such as meteorology, electricity, and finance. Comprising observations at historical time points, these data, when subjected to in-depth analysis and modeling, enable researchers to predict future trends and patterns, providing support for decision making. In current research, especially in the analysis of long time series, effectively extracting and integrating long-term dependencies with short-term features remains a significant challenge. Long-term dependencies refer to the correlation between data points spaced far apart in a time series, while short-term features focus on more recent changes. Understanding and combining these two features correctly are crucial for constructing accurate and reliable predictive models. To efficiently extract and integrate long-term dependencies and short-term features in long time series, this paper proposes a pyramid attention structure model based on multi-scale feature extraction, referred to as the MSFformer model. Initially, a coarser-scale construction module is designed to obtain coarse-grained information. A pyramid data structure is constructed through feature convolution, with the bottom layer representing the original data and each subsequent layer containing feature information extracted across different time step lengths. As a result, nodes higher up in the pyramid integrate information from more time points, such as every Monday or the beginning of each month, while nodes lower down retain their individual information. Additionally, a Skip-PAM is introduced, where a node only calculates attention with its neighboring nodes, parent node, and child nodes, effectively reducing the model’s time complexity to some extent. Notably, the child nodes refer to nodes selected from the next layer by skipping specific time steps. In this study, we not only propose an innovative time series prediction model but also validate the effectiveness of these methods through a series of comprehensive experiments. To comprehensively evaluate the performance of the designed model, we conducted comparative experiments with baseline models, ablation experiments, and hyperparameter studies. The experimental results demonstrate that the MSFformer model improves by 35.87% and 42.6% on the MAE and MSE indicators, respectively, compared to traditional Transformer models. These results highlight the outstanding performance of our proposed deep learning model in handling complex time series data, particularly in capturing long-term dependencies and integrating short-term features.
]]>Mathematics doi: 10.3390/math12070972
Authors: Vasily E. Tarasov
In this paper, a short review of the calculus of exact finite-differences of integer order is proposed. The finite-difference operators are called the exact finite-differences of integer orders, if these operators satisfy the same characteristic algebraic relations as standard differential operators of the same order on some function space. In this paper, we prove theorem that this property of the exact finite-differences is satisfies for the space of simple entire functions on the real axis (i.e., functions that can be expanded into power series on the real axis). In addition, new results that describe the exact finite-differences beyond the set of entire functions are proposed. A generalized expression of exact finite-differences for non-entire functions is suggested. As an example, the exact finite-differences of the square root function is considered. The use of exact finite-differences for numerical and computer simulations is not discussed in this paper. Exact finite-differences are considered as an algebraic analog of standard derivatives of integer order.
]]>Mathematics doi: 10.3390/math12070971
Authors: Xinmin Zhou Wenhao Rao Yaqiong Liu Shudong Sun
The optimization of job shop scheduling is pivotal for improving overall production efficiency within a workshop. In demand-driven personalized production modes, achieving a balance between workshop resources and the diverse demands of customers presents a challenge in scheduling. Additionally, considering the self-interested behaviors of agents, this study focuses on tackling the problem of multi-agent job shop scheduling with private information. Multiple consumer agents and one job shop agent are considered, all of which are self-interested and have private information. To address this problem, a two-stage decentralized algorithm rooted in the genetic algorithm is developed to achieve a consensus schedule. The algorithm allows agents to evolve independently and concurrently, aiming to satisfy individual requirements. To prevent becoming trapped in a local optimum, the search space is broadened through crossover between agents and agent-based block insertion. Non-dominated sorting and grey relational analysis are applied to generate the final solution with high social welfare. The proposed algorithm is compared using a centralized approach and two state-of-the-art decentralized approaches in computational experiments involving 734 problem instances. The results validate that the proposed algorithm generates non-dominated solutions with strong convergence and uniformity. Moreover, the final solution produced by the developed algorithm outperforms those of the decentralized approaches. These advantages are more pronounced in larger-scale problem instances with more agents.
]]>Mathematics doi: 10.3390/math12070970
Authors: Ayman M. Alneamy Hassen M. Ouakad
The present investigation focuses on the design and mathematical modeling of a microelectromechanical (MEMS) mode-localized based sensor/actuator system. This device incorporates a sensitive clamped–clamped shallow arch microbeam with an initial curvature shaped to resemble one of the first two symmetric and asymmetric modes of free oscillations of a clamped–clamped beam. The analysis reveals that with a suitable arrangement of the initial shape of the device flexible electrode and a proper tuning of the maximum initial rise and the actuating dc load enables the transition to display certain bistable behavior. This could be a better choice to build a device with a large stroke. Furthermore, the generated data showed the occurrence of mode-veering, indicating a coupling between the concerned symmetric and asymmetric modes of vibrations, and offering the possibility for such a device to be used as a mode-localized MEMS-based sensor utilizing veering and crossing phenomena. Indeed, where a certain energy is exchanged between symmetric and asymmetric modes of a microbeam, it can be utilized to serve as a foundation for the development of a new class of highly precise resonant sensors that can capture, with a certain level of precision, any of the sensed signal amplitudes.
]]>Mathematics doi: 10.3390/math12070969
Authors: Rui Wang Yang Gao Yilin Jia Hai He Junjie Wu Weisheng Wang
Although the stability regions of wind turbines in the islanding mode have been widely researched, small-signal modeling of grid-forming wind turbines (GFWTs) in the islanding mode has yet to be explored. In addition, the state-space matrix of the wind turbine system has yet to be fully represented. Therefore, this paper proposes a small-signal modeling of GFWT and a method for identifying the stabilization region of a system with variable parameters. First, small-signal modeling of a GFWT based on virtual synchronous generator control is developed. Second, the bialternate sum matrix approach is used to determine the system stabilization region. The system matrix with multiple variable parameters is first decomposed into the sum of several matrices in this paper. Furthermore, the rotor-side generator control is simplified. It can reduce the dimensionality of the system matrix model. Finally, the simulation shows that the proposed method for determining the stabilization region of the variable system is accurate.
]]>Mathematics doi: 10.3390/math12070968
Authors: Yuan Hong Shaojian Qu
Operational risk assessment has received considerable attention in bank risk management. However, current assessment methods are primarily designed to assess the risk profile of individual banks. To enable cross-bank operational risk assessment, we propose an integrated AHP-DEA (analytic hierarchy process–data envelopment analysis) method. This method determines the importance of assessment criteria by calculating the weighted sum of rank votes after obtaining the importance values for specific rankings with DEA. This procedure replaces the pairwise comparisons in AHP and addresses the challenge of traditional AHPs in determining appropriate importance values when dealing with a large number of indicators. We applied this method to assess the operational risks of three Chinese commercial banks, and the empirical results indicate that this integrated AHP-DEA method is simple and user-friendly, making it suitable for cross-bank operational risk assessment.
]]>Mathematics doi: 10.3390/math12070967
Authors: Huimin Wang Yanhong Liu Xiuling Li Hengjia Chen
The generalized Zakharov equation is a widely used and crucial model in plasma physics, which helps to understand wave particle interactions and nonlinear wave propagation in plasma. The solitary wave solution of this equation provides insights into phenomena such as electron and ion acoustic waves, as well as magnetic field disturbances in plasma. The numerical simulation of solitary wave solutions to the generalized Zakharov equation is an interesting problem worth studying. This is crucial for plasma-based technology, as well as for understanding nonlinear wave propagation in plasma physics and other fields. In this study, a numerical investigation of the generalized Zakharov equation using the lattice Boltzmann method has been conducted. The lattice Boltzmann method is a new modeling and simulating method at the mesoscale. A lattice Boltzmann model was constructed by performing Taylor expansion, Chapman–Enskog expansion, and time multiscale expansion on the lattice Boltzmann equation. By defining the moments of the equilibrium distribution function appropriately, the macroscopic equation can be restored. Furthermore, the numerical experiments for the equation are carried out with the parameter lattice size m=100, time step Δt=0.001, and space step size Δx=0.4. The solitary wave solution of the equation is numerically simulated. Numerical results under different parameter values are compared, and the convergence and effectiveness of the model are numerically verified. It is obtained that the model is convergent in time and space, and the convergence orders are all 2.24881. The effectiveness of our model was also verified by comparing the numerical results of different numerical methods. The lattice Boltzmann method demonstrates advantages in both accuracy and CPU time. The results indicate that the lattice Boltzmann method is a good tool for computing the generalized Zakharov equation.
]]>Mathematics doi: 10.3390/math12070966
Authors: Glykeria Stamatopoulou Eva Tsouparopoulou Maria Symeonaki
This paper investigates the transmission of educational attainment from parents to offspring as a mediator of intergenerational class mobility in Europe. The study covers the last two decades with data drawn from a cross-national large-scale sample survey, namely the European Social Survey (ESS), for the years 2002–2018. Interest has focused on the question of the persistence of inequality of educational opportunities by examining the attainment of nominal levels of education and the association between the educational attainment of the parent with the highest level of education and their descendants. The study also covers new trends in social mobility that consider education as a “positional good”, and a novel method of incorporating educational expansion into the transition probabilities is proposed, providing answers to whether the rising accessibility of educational qualifications attenuates the association between social origin and educational attainment. Therefore, the concept of positionality is taken into account in the estimation of intergenerational transition probabilities, and to complement the analysis, mobility measures are provided for both methods, nominal and positional. The proposed positional method is validated through a correlation analysis between the upward mobility scores (nominal and positional) with the Education Expansion Index (EEI) for the respective years. The upward mobility scores estimated via the positional method are more highly correlated with the EEI for all years, indicating a better alignment with the broader trends in educational participation and achievement.
]]>Mathematics doi: 10.3390/math12070965
Authors: Huimin Wang Yuelin Gao Yahua He
Particle Swarm Optimization (PSO) is facing more challenges in solving high-dimensional global optimization problems. In order to overcome this difficulty, this paper proposes a novel PSO variant of the hybrid Sine Cosine Algorithm (SCA) strategy, named Velocity Four Sine Cosine Particle Swarm Optimization (VFSCPSO). The introduction of the SCA strategy in the velocity formulation ensures that the global optimal solution is found accurately. It increases the flexibility of PSO. A series of experiments are conducted on the CEC2005 test suite with compositional algorithms, algorithmic variants, and good intelligent algorithms. The experimental results show that the algorithm effectively improves the overall performance of compositional algorithms; the Friedman test proves that the algorithm has good competitiveness. The algorithm also performs better in PID parameter tuning. Therefore, the VFSCPSO is able to solve the high-dimensional global optimization problems in a better way.
]]>Mathematics doi: 10.3390/math12070964
Authors: Guillaume Leduc
Oscillations in option price convergence have long been a problematic aspect of tree methods, inhibiting the use of repeated Richardson extrapolation that could otherwise greatly accelerate convergence, a feature integral to some of the most efficient modern methods. These oscillations are typically caused by the fluctuating positions of nodes around the discontinuities in the payoff function or its derivatives. Our paper addresses this crucial gap that typically prohibits the use of lattice methods when high efficiency is needed. Focusing on double barrier options, we develop a trinomial tree in which the positions of the nodes are precisely adjusted to align with these discontinuities throughout the option’s lifespan and across various time steps. This alignment enables the use of repeated extrapolation to achieve high order convergence, including near barriers, a well-known challenge in many tree methods. Maintaining the inherent simplicity and adaptability of tree methods, our approach is easily applicable to other models and option types.
]]>Mathematics doi: 10.3390/math12070963
Authors: Yunki Gwak Sy-Ngoc Nguyen Jun-Sik Kim Hyungbum Park Jaehun Lee Jang-Woo Han
This paper proposes a simple yet accurate finite element (FE) formulation for the thermomechanical analysis of laminated composites and sandwich plates. To this end, an enhanced first-order shear deformation theory including the transverse normal effect based on the mixed variational theorem (EFSDTM_TN) was employed in the FE implementation. The primary objective of the FE formulation was to systematically interconnect the displacement and transverse stress fields using the mixed variational theorem (MVT). In the MVT, the transverse stress field is derived from the efficient higher-order plate theory including the transverse normal effect (EHOPT_TN), to enhance the solution accuracy, whereas the displacement field is defined by the first-order shear deformation theory including the transverse normal effect (FSDT_TN), to amplify the numerical efficiency. Furthermore, the transverse displacement field is modified by incorporating the components of the external temperature loading, enabling the consideration of the transverse normal strain effect without introducing additional unknown variables. Based on the predefined relationships, the proposed FE formulation can extract the C0-based computational benefits of FSDT_TN, while improving the solution accuracy for thermomechanical analysis. The numerical performance of the proposed FE formulation was demonstrated by comparing the obtained solutions with those available in the literature, including 3-D exact solutions.
]]>Mathematics doi: 10.3390/math12070962
Authors: Fengjie Xie Zhiting Chen Zhuan Zhang
For the dynamic takeout delivery vehicle routing problem, which faces fluctuating order demand and time-varying speeds, this study presents a novel approach. We analyze the time distribution of takeout orders and apply a Receding Horizon Control (RHC) strategy to convert the dynamic challenge into a static one. The driving speed of delivery vehicles on different roads at different times is determined based on the subdivision criteria of the urban road network and a traffic congestion measurement method. We propose a dynamic takeout delivery vehicle routing optimization model and a time-varying subdivision road network is established to minimize the total delivery cost. We validated the model through simulation examples. The optimization results show that the total distribution cost is reduced after considering the time-varying subdivision road network, with the penalty cost decreasing by 39%. It is evident that considering the subdivision of the road network can enhance order delivery efficiency and optimize the overall dining experience. The sensitivity analysis of various parameters reveals that the delivery platform must appropriately determine the time domain and allocate the number of delivery personnel based on order scale to avoid escalating delivery costs. These findings provide theoretical guidance for vehicle routing planning in the context of delivery platforms.
]]>Mathematics doi: 10.3390/math12070961
Authors: Ghiocel Groza Marilena Jianu Ion Mierluş-Mazilu
The α-fractional power moduli series are introduced as a generalization of α-fractional power series and the structural properties of these series are investigated. Using the fractional Taylor’s formula, sufficient conditions for a function to be represented as an α-fractional power moduli series are established. Beyond theoretical formulations, a practical method to represent solutions to boundary value problems for fractional differential equations as α-fractional power series is discussed. Finally, α-analytic functions on an open interval I are defined, and it is shown that a non-constant function is α-analytic on I if and only if 1/α is a positive integer and the function is real analytic on I.
]]>Mathematics doi: 10.3390/math12070960
Authors: Manuel De la Sen
This research relies on several kinds of Volterra-type integral differential systems and their associated stability concerns under the impulsive effects of the Volterra integral terms at certain time instants. The dynamics are defined as delay-free dynamics contriobution together with the contributions of a finite set of constant point delay dynamics, plus a Volterra integral term of either a finite length or an infinite one with intrinsic memory. The global asymptotic stability is characterized via Krasovskii–Lyapuvov functionals by incorporating the impulsive effects of the Volterra-type terms together with the effects of the point delay dynamics.
]]>Mathematics doi: 10.3390/math12070959
Authors: Jamshaid Ul Rahman Sana Danish Dianchen Lu
The motivation behind this study is to overcome the complex mathematical formulation and time-consuming nature of traditional numerical methods used in solving differential equations. It seeks an alternative approach for more efficient and simplified solutions. A Deep Neural Network (DNN) is utilized to understand the intricate correlations between the oscillator’s variables and to precisely capture their dynamics by being trained on a dataset of known oscillator behaviors. In this work, we discuss the main challenge of predicting the behavior of oscillators without depending on complex strategies or time-consuming simulations. The present work proposes a favorable modified form of neural structure to improve the strategy for simulating linear and nonlinear harmonic oscillators from mechanical systems by formulating an ANN as a DNN via an appropriate oscillating activation function. The proposed methodology provides the solutions of linear and nonlinear differential equations (DEs) in differentiable form and is a more accurate approximation as compared to the traditional numerical method. The Van der Pol equation with parametric damping and the Mathieu equation are adopted as illustrations. Experimental analysis shows that our proposed scheme outperforms other numerical methods in terms of accuracy and computational cost. We provide a comparative analysis of the outcomes obtained through our proposed approach and those derived from the LSODA algorithm, utilizing numerical techniques, Adams–Bashforth, and the Backward Differentiation Formula (BDF). The results of this research provide insightful information for engineering applications, facilitating improvements in energy efficiency, and scientific innovation.
]]>Mathematics doi: 10.3390/math12070958
Authors: Zhuoran Duan Chao Xu Zhengping Li Bo Feng Chao Nie
Cervical cancer, as the fourth most common cancer in women, poses a significant threat to women’s health. Vaginal colposcopy examination, as the most cost-effective step in cervical cancer screening, can effectively detect precancerous lesions and prevent their progression into cancer. The size of the lesion areas in the colposcopic images varies, and the characteristics of the lesions are complex and difficult to discern, thus heavily relying on the expertise of the medical professionals. To address these issues, this paper constructs a vaginal colposcopy image dataset, ACIN-3, and proposes a Fusion Multi-scale Attention Network for the detection of cervical precancerous lesions. First, we propose a heterogeneous receptive field convolution module to construct the backbone network, which utilizes combinations of convolutions with different structures to extract multi-scale features from multiple receptive fields and capture features from different-sized regions of the cervix at different levels. Second, we propose an attention fusion module to construct a branch network, which integrates multi-scale features and establishes connections in both the spatial and channel dimensions. Finally, we design a dual-threshold loss function and introduce positive and negative thresholds to improve sample weights and address the issue of data imbalance in the dataset. Multiple experiments are conducted on the ACIN-3 dataset to demonstrate the superior performance of our approach compared to some classical and recent advanced methods. Our method achieves an accuracy of 92.2% in grading and 94.7% in detection, with average AUCs of 0.9862 and 0.9878. Our heatmap illustrates the accuracy of our approach in focusing on the locations of lesions.
]]>Mathematics doi: 10.3390/math12070957
Authors: Bo Yu Qi Li Wenhua Jiao Shiyang Zhang Yongjun Zhu
Surface defects on the permanent magnetic ferrite magnet rotor are the primary cause for the decline in performance and safety hazards in permanent magnet motors. Machine-vision methods offer the possibility to identify defects automatically. In response to the challenges in the permanent magnetic ferrite magnet rotor, this study proposes an improved You Only Look Once (YOLO) algorithm named SAB-YOLOv5. Utilizing a line-scan camera, images capturing the complete surface of a general object are obtained, and a dataset containing surface defects is constructed. Simultaneously, an improved YOLOv5-based surface defect algorithm is introduced. Firstly, the algorithm enhances the capability to extract features at different scales by incorporating the Atrous Spatial Pyramid Pooling (ASPP) structure. Then, the fusion of features is improved by combining the tensor concatenation operation of the feature-melting network with the Bidirectional Feature Pyramid Network (BiFPN) structure. Finally, the introduction of the spatial pyramid dilated (SPD) convolutional structure into the backbone network and output end enhances the detection performance for minute defects on the target surface. In the study, the SAB-YOlOv5 algorithm shows an obvious increase from 84.2% to 98.3% in the mean average precision (mAP) compared to that of the original YOLOv5 algorithm. The results demonstrate that the data acquisition method and detection algorithm designed in this paper effectively enhance the efficiency of defect detection permanent magnetic ferrite magnet rotors.
]]>Mathematics doi: 10.3390/math12070954
Authors: Yingxue Zhang Jinbao Chen Meng Chen Chuanzhi Chen Zeyu Zhang Xiaokang Deng
For the formation and obstacle avoidance challenges of UAVs (unmanned aerial vehicles) in complex scenarios, this paper proposes an improved collaborative strategy based on APF (artificial potential field). This strategy combines graph theory, the Leader–Follower method, and APF. Firstly, we used graph theory to design formation topology and dynamically adjust the distances between UAVs in real time. Secondly, we introduced APF to avoid obstacles in complicated environments. This algorithm innovatively integrates the Leader–Follower formation method. The design of this attractive field is replaced by the leader’s attraction to the followers, overcoming the problem of unreachable targets in APF. Meanwhile, the introduced Leader–Follower mode reduces information exchange within the swarm, realizing a more efficient “few controlling many” paradigm. Afterwards, we incorporated rotational force to assist the swarm in breaking free from local minima. Ultimately, the stability of the integrated formation strategy was demonstrated using Lyapunov functions. The feasibility and effectiveness of the proposed strategy were validated across multiple platforms.
]]>Mathematics doi: 10.3390/math12070956
Authors: Kailin Xie Jianfei Yin Hengyong Yu Hong Fu Ying Chu
Developing effective trend estimators is the main method to solve the online portfolio selection problem. Although the existing portfolio strategies have demonstrated good performance through the development of various trend estimators, it is still challenging to determine in advance which estimator will yield the maximum final cumulative wealth in online portfolio selection tasks. This paper studies an online ensemble approach for online portfolio selection by leveraging the strengths of multiple trend estimators. Specifically, a return-based loss function and a cross-entropy-based loss function are first designed to evaluate the adaptiveness of different trend estimators in a financial environment. On this basis, a passive aggressive ensemble model is proposed to weigh these trend estimators within a unit simplex according to their adaptiveness. Extensive experiments are conducted on benchmark datasets from various real-world stock markets to evaluate their performance. The results show that the proposed strategy achieves state-of-the-art performance, including efficiency and cumulative return.
]]>Mathematics doi: 10.3390/math12070955
Authors: Cun Wang Zupeng Zhou Jingjing Wang
Component failures can lead to performance degradation or even failure in multi-agent systems, thus necessitating the development of fault diagnosis methods. Addressing the distributed fault diagnosis problem in a class of partial differential multi-agent systems with actuators, a fault estimator is designed under the introduction of virtual faults to the agents. A P-type iterative learning control protocol is formulated based on the residual signals, aiming to adjust the introduced virtual faults. Through rigorous mathematical analysis utilizing contraction mapping and the Bellman–Gronwall lemma, sufficient conditions for the convergence of this protocol are derived. The results indicate that the learning protocol ensures the tracking of virtual faults to actual faults, thereby facilitating fault diagnosis for the systems. Finally, the effectiveness of the learning protocol is validated through numerical simulation.
]]>Mathematics doi: 10.3390/math12070953
Authors: Qiong Pang Xijian Hu
The Semi-variable Coefficient Spatial Lag Model (SVC-SLM) not only addresses the “dimension disaster” associated with the Varying Coefficient Spatial Lag Model(VC-SLM), but also overcomes the non-linear problem of the variable coefficient, and fully explores the hidden information of the model. In this paper, INLA is firstly used to estimate the parameters of (SVC-SLM) by using B-spline to deal with the non-parametric terms, and the comparative experimental results show that the INLA algorithm is much better than MCMCINLA in terms of both time efficiency and estimation accuracy. For the problem of identifying the constant coefficient terms in the SVC-SLM, the bootstrap test is given based on the residuals. Taking the PM2.5 data of 31 provinces in mainland China from 2015 to 2020 as an empirical example, parametric, non-parametric, and semi-parametric perspectives establish three models of Spatial Lag Model (SLM), VC-SLM, SVC-SLM, which explore the relationship between the covariate factors and the level of urbanization as well as their impacts on the concentration of PM2.5 in the context of increasing urbanization; among the three models, the SVC-SLM has the smallest values of DIC and WAIC, indicating that the SVC-SLM is optimal.
]]>Mathematics doi: 10.3390/math12070951
Authors: Zhongzhe Ouyang Lu Wang Alzheimer’s Disease Neuroimaging Initiative Alzheimer’s Disease Neuroimaging Initiative
When integrating data from multiple sources, a common challenge is block-wise missing. Most existing methods address this issue only in cross-sectional studies. In this paper, we propose a method for variable selection when combining datasets from multiple sources in longitudinal studies. To account for block-wise missing in covariates, we impute the missing values multiple times based on combinations of samples from different missing pattern and predictors from different data sources. We then use these imputed data to construct estimating equations, and aggregate the information across subjects and sources with the generalized method of moments. We employ the smoothly clipped absolute deviation penalty in variable selection and use the extended Bayesian Information Criterion criteria for tuning parameter selection. We establish the asymptotic properties of the proposed estimator, and demonstrate the superior performance of the proposed method through numerical experiments. Furthermore, we apply the proposed method in the Alzheimer’s Disease Neuroimaging Initiative study to identify sensitive early-stage biomarkers of Alzheimer’s Disease, which is crucial for early disease detection and personalized treatment.
]]>Mathematics doi: 10.3390/math12070952
Authors: Lemnaouar Zedam Hamza Boughambouz Bernard De Baets
Recently, we have introduced and studied all possible four-point compositions (one degree of freedom) and five-point compositions (two degrees of freedom) of ternary relations in analogy with the usual composition of binary relations. In this paper, we introduce and study new types of compositions of ternary relations inspired by the compositions of binary relations introduced by Bandler and Kohout (BK-compositions, for short). Moreover, we pay particular attention to the link between BK-compositions and the traces of binary relations and use it as source of inspiration to introduce traces of ternary relations. Moreover, we show that these new notions of BK-compositions and traces are useful tools to solve some relational equations in an unknown ternary relation.
]]>Mathematics doi: 10.3390/math12070950
Authors: Nevena Čolić Pavle Milošević Ivana Dragović Miljan S. Ćeranić
The interpretability and explainability of machine learning (ML) approaches play a key role in the trustworthiness of ML models in various applications. The objective of this paper is to incorporate a logic-based reasoning in the ML model that is not only accurate but also interpretable and easily applied. More precisely, we propose a hybrid IBA-VNS approach based on interpolative Boolean algebra (IBA) and variable neighborhood search (VNS). IBA is chosen over traditional multi-valued and/or fuzzy logic techniques due to its consistency in preserving all Boolean axioms. The VNS heuristic is used for model training, i.e., determining the optimal logical aggregation function within the IBA framework for solving observed prediction problems. Obtained logic aggregation functions are easy to understand and may provide additional insight to the decision-maker. The proposed approach does not require any domain knowledge and is applicable in various domains. IBA-VNS is evaluated on several standard datasets. Further, IBA-VNS is applied to the real-world problem of predicting hospital length of stay (LOS), showing exceptional results in terms of interpretability and accuracy. In fact, the dataset is collected from the LabSerb program regarding colorectal surgeries in the period 2015–2023. The proposed approach extracted knowledge regarding the problem, i.e., the causal relations between the patient’s health condition and LOS, along with achieving an MAE of 1.144 days.
]]>Mathematics doi: 10.3390/math12070949
Authors: Juan Yu Kailong Xiong Cheng Hu
The asymptotic synchronization of quaternion-valued delayed neural networks with impulses and inertia is studied in this article. Firstly, a convergence result on piecewise differentiable functions is developed, which is a generalization of the Barbalat lemma and provides a powerful tool for the convergence analysis of discontinuous systems. To achieve synchronization, a constant gain-based control scheme and an adaptive gain-based control strategy are directly proposed for response quaternion-valued models. In the convergence analysis, a direct analysis method is developed to discuss the synchronization without using the separation technique or reduced-order transformation. In particular, some Lyapunov functionals, composed of the state variables and their derivatives, are directly constructed and some synchronization criteria represented by matrix inequalities are obtained based on quaternion theory. Some numerical results are shown to further confirm the theoretical analysis.
]]>Mathematics doi: 10.3390/math12070948
Authors: Haonan Tan Le Wang Dong Zhu Jianyu Deng
In order to cope with ever-evolving and increasing cyber threats, intrusion detection systems have become a crucial component of cyber security. Compared with signature-based intrusion detection methods, anomaly-based methods typically employ machine learning techniques to train detection models and possess the capability to discover unknown attacks. However, intrusion detection methods face the challenge of low detection rates for minority class attacks due to imbalanced data distributions. Traditional intrusion detection algorithms address this issue by resampling or generating synthetic data. Additionally, reinforcement learning, as a machine learning method that interacts with the environment to obtain feedback and improve performance, is gradually being considered for application in the field of intrusion detection. This paper proposes a reinforcement-learning-based intrusion detection method that innovatively uses adaptive sample distribution dual-experience replay to enhance a reinforcement learning algorithm, aiming to effectively address the issue of imbalanced sample distribution. We have also developed a reinforcement learning environment specifically designed for intrusion detection tasks. Experimental results demonstrate that the proposed model achieves favorable performance on the NSL-KDD, AWID, and CICIoT2023 datasets, effectively dealing with imbalanced data and showing better classification performance in detecting minority attacks.
]]>Mathematics doi: 10.3390/math12070947
Authors: Shichang Xiao Pan Peng Peng Zheng Zigao Wu
The half-open multi-depot vehicle routing problem (HOMDVRP) is a typical decision optimization problem in the field of collaborative logistics that considers resource sharing. This study aims to develop an effective meta-heuristic algorithm for solving the HOMDVRP. Firstly, a mixed-integer programming model of HOMDVRP is established to minimize the total travel distance of the vehicles. After that, a novel hybrid adaptive simulated annealing and tempering algorithm (HASATA) is proposed based on the features of HOMDVRP. The proposed algorithm combines the strengths of the simulated annealing algorithm and the large-neighborhood search algorithm to balance the algorithm’s searching capabilities in both breadth and depth. Meanwhile, an adaptive Markov chain length mechanism and a tempering mechanism are designed to improve the algorithm’s computational efficiency and convergence ability. Finally, simulation experiments are conducted to verify the effectiveness of the proposed model and the computational performance of the proposed algorithm. Four comparison algorithms are selected and analyzed using 24 groups of problem instances. The comparison results show that the proposed HASATA can solve the HOMDVRP more efficiently and obtain a solution with better optimization performance and satisfactory stability.
]]>Mathematics doi: 10.3390/math12070946
Authors: Mashadi Yuliana Safitri Sukono Igif Gimin Prihanto Muhamad Deni Johansyah Moch Panji Agung Saputra
Trapezoidal positive/negative fuzzy numbers have no single definition; instead, various authors define them in relation to different concepts. This means that arithmetic operations for trapezoidal fuzzy numbers also differ. For the operations of addition, subtraction, and scalar multiplication, there are not many differences; for multiplication, however, there are many differences. In general, multiplication is divided into various cases. For the inverse operation, there is not much to define; in general, for any trapezoidal fuzzy number u~, u~⊗1u~=i~=(1,1,0,0) does not necessarily apply. As a result of the different arithmetic operations for multiplication and division employed by various authors, several researchers have tackled the same problem and reached different solutions, meaning that the application will also produce different results. To date, many authors have proposed various alternatives for the algebra of the trapezoidal fuzzy number. In this paper, using the parametric form approach to trapezoidal fuzzy numbers, an alternative to multiplication with only one formula is constructed for various cases. Furthermore, based on the definition of multiplication for any trapezoidal fuzzy number, u~ is constructed 1u~ so that u~⊗1u~=i~=(1,1,0,0). Based on these conditions, we show that various properties that apply to real numbers also apply to any trapezoidal fuzzy number. Furthermore, we modify the elementary row operational steps for the trapezoidal fuzzy number matrix, which can be used to determine the inverse of a trapezoidal fuzzy number matrix with the order m×m. We also give the steps and examples necessary to determine the general inverse for a trapezoidal fuzzy number matrix of the order m×n with m ≠n. This ability to easily determine the inverse and general inverse of a trapezoidal fuzzy number matrix has a number of applications, such as solving fully trapezoidal fuzzy number linear systems and fuzzy transportation problems, especially in applications in fields outside of mathematics; for example, the application of triangular fuzzy numbers in medical problems is a topic currently receiving a significant amount of attention.
]]>Mathematics doi: 10.3390/math12070945
Authors: Shuai Sang Lu Li
Long Short-Term Memory (LSTM) is an effective method for stock price prediction. However, due to the nonlinear and highly random nature of stock price fluctuations over time, LSTM exhibits poor stability and is prone to overfitting, resulting in low prediction accuracy. To address this issue, this paper proposes a novel variant of LSTM that couples the forget gate and input gate in the LSTM structure, and adds a “simple” forget gate to the long-term cell state. In order to enhance the generalization ability and robustness of the variant LSTM, the paper introduces an attention mechanism and combines it with the variant LSTM, presenting the Attention Mechanism Variant LSTM (AMV-LSTM) model along with the corresponding backpropagation algorithm. The parameters in AMV-LSTM are updated using the Adam gradient descent method. Experimental results demonstrate that the variant LSTM alleviates the instability and overfitting issues of LSTM, effectively improving prediction accuracy. AMV-LSTM further enhances accuracy compared to the variant LSTM, and compared to AM-LSTM, it exhibits superior generalization ability, accuracy, and convergence capability.
]]>Mathematics doi: 10.3390/math12070944
Authors: Fu-Hsing Wang Cheng-Ju Hsu
An edge coloring of a graph G results in G being rainbow connected when every pair of vertices is linked by a rainbow path. Such a path is defined as one where each edge possesses a distinct color. A rainbow coloring refers to an edge coloring that guarantees the rainbow connectedness of G. The rainbow connection number of G represents the smallest quantity of colors required to achieve rainbow connectedness under a rainbow coloring scheme. Wang and Hsu (ICICM 2019: 75–79) provided upper bounds on the size of the rainbow connection numbers in WK-recursive networks WKd,t and WK-recursive pyramids WKPd,n. In this paper, we revise their results and determine the exact values of the rainbow connection numbers of WKd,2 for d=3 and 4. The rainbow connection numbers of WKd,2 are bounded between 4 and ⌊d2⌋+2 for d>4. In addition to our previous findings, we further investigate and determine upper bounds for the size of the rainbow connection numbers of WKPd,n. This involves analyzing various aspects of the graph structure and exploring potential limitations on the rainbow connection numbers. By establishing these upper bounds, we gain deeper insights into the potential range and constraints of the rainbow connection numbers within the given context.
]]>Mathematics doi: 10.3390/math12070943
Authors: Giovanni Fusco Monica Motta
We consider a constrained optimal control problem and an extension of it, in which the set of strict-sense trajectories is enlarged. Extension is a common procedure in optimal control used to derive necessary and sufficient optimality conditions for the original problem from the extended one, which usually admits a minimizer and has a more regular structure. However, this procedure fails if the two problems have different infima. Therefore, it is relevant to identify such situations. Following on from earlier work by Warga but adopting perturbation techniques developed in nonsmooth analysis, we investigate the relation between the occurrence of an infimum gap and the abnormality of necessary conditions. For the notion of a local minimizer based on control distance and an extension, including the impulsive one, we prove that (i) a local extended minimizer that is not a local minimizer of the original problem, and (ii) a local strict-sense minimizer that is not a local minimizer of the extended problem both satisfy the extended maximum principle in abnormal form. The main novelty is result (ii), as until now, it has only been shown that a strict-sense minimizer that is not an extended minimizer is abnormal for an ‘averaged version’ of the maximum principle.
]]>Mathematics doi: 10.3390/math12070942
Authors: Yunfeng Ji Wei Li Gang Wang
In this paper, we investigate the consensus control problem of Euler–Lagrange systems which can be used to describe the motion of various mechanical systems such as manipulators and quadcopters. We focus on consensus control strategies, which are important for achieving coordinated behavior in multi-agent systems. The paper considers the key challenges posed by random communication delays and packet losses that are increasingly common in networked control systems. In addition, it is assumed that each system receives information from neighboring agents intermittently. Addressing these challenges is critical to ensure the reliability and efficiency of such systems in real-world applications. Communication delay is time-varying and can be very large, but should be smaller than some bounded constant. To decrease the frequency of control input updates, we implement an event-triggered scheme that regulates the controller’s updates for each agent. Specifically, it does not update control inputs at traditional fixed intervals, but responds to predefined conditions and introduces a dynamic consensus item to handle information irregularities caused by communication delays and intermittent information exchange. The consensus can be achieved if the communication graph of agents contains a spanning tree with the desired velocity as the root node. That is, all Euler–Lagrange systems need to obtain the desired velocity, directly or indirectly (via neighbors), to reach consensus. We establish that the Zeno behavior can be avoided, ensuring a positive minimum duration between successive event-triggered instances. Finally, we provide simulation results to show the performance of our proposed algorithm.
]]>Mathematics doi: 10.3390/math12070941
Authors: Reinhard Schlickeiser Martin Kröger
The susceptible–infected–recovered–vaccinated–deceased (SIRVD) epidemic compartment model extends the SIR model to include the effects of vaccination campaigns and time-dependent fatality rates on epidemic outbreaks. It encompasses the SIR, SIRV, SIRD, and SI models as special cases, with individual time-dependent rates governing transitions between different fractions. We investigate a special class of exact solutions and accurate analytical approximations for the SIRVD and SIRD compartment models. While the SIRVD and SIRD equations pose complex integro-differential equations for the rate of new infections and the fractions as a function of time, a simpler approach considers determining equations for the sum of ratios for given variations. This approach enables us to derive fully exact analytical solutions for the SIRVD and SIRD models. For nonlinear models with a high-dimensional parameter space, such as the SIRVD and SIRD models, analytical solutions, exact or accurately approximative, are of high importance and interest, not only as suitable benchmarks for numerical codes, but especially as they allow us to understand the critical behavior of epidemic outbursts as well as the decisive role of certain parameters. In the second part of our study, we apply a recently developed analytical approximation for the SIR and SIRV models to the more general SIRVD model. This approximation offers accurate analytical expressions for epidemic quantities, such as the rate of new infections and the fraction of infected persons, particularly when the cumulative fraction of infections is small. The distinction between recovered and deceased individuals in the SIRVD model affects the calculation of the death rate, which is proportional to the infected fraction in the SIRVD/SIRD cases but often proportional to the rate of new infections in many SIR models using an a posteriori approach. We demonstrate that the temporal dependence of the infected fraction and the rate of new infections differs when considering the effects of vaccinations and when the real-time dependence of fatality and recovery rates diverge. These differences are highlighted for stationary ratios and gradually decreasing fatality rates. The case of stationary ratios allows one to construct a new powerful diagnostics method to extract analytically all SIRVD model parameters from measured COVID-19 data of a completed pandemic wave.
]]>Mathematics doi: 10.3390/math12070940
Authors: Haoteng Tang Siyuan Dai Eric M. Zou Guodong Liu Ryan Ahearn Ryan Krafty Michel Modo Liang Zhan
The hippocampus is a crucial brain structure involved in memory formation, spatial navigation, emotional regulation, and learning. An accurate MRI image segmentation of the human hippocampus plays an important role in multiple neuro-imaging research and clinical practice, such as diagnosing neurological diseases and guiding surgical interventions. While most hippocampus segmentation studies focus on using T1-weighted or T2-weighted MRI scans, we explore the use of diffusion-weighted MRI (dMRI), which offers unique insights into the microstructural properties of the hippocampus. Particularly, we utilize various anisotropy measures derived from diffusion MRI (dMRI), including fractional anisotropy, mean diffusivity, axial diffusivity, and radial diffusivity, for a multi-contrast deep learning approach to hippocampus segmentation. To exploit the unique benefits offered by various contrasts in dMRI images for accurate hippocampus segmentation, we introduce an innovative multimodal deep learning architecture integrating cross-attention mechanisms. Our proposed framework comprises a multi-head encoder designed to transform each contrast of dMRI images into distinct latent spaces, generating separate image feature maps. Subsequently, we employ a gated cross-attention unit following the encoder, which facilitates the creation of attention maps between every pair of image contrasts. These attention maps serve to enrich the feature maps, thereby enhancing their effectiveness for the segmentation task. In the final stage, a decoder is employed to produce segmentation predictions utilizing the attention-enhanced feature maps. The experimental outcomes demonstrate the efficacy of our framework in hippocampus segmentation and highlight the benefits of using multi-contrast images over single-contrast images in diffusion MRI image segmentation.
]]>Mathematics doi: 10.3390/math12070939
Authors: Sergey N. Mergelyan
Preface by Hovik A [...]
]]>Mathematics doi: 10.3390/math12070938
Authors: J. Alberto Conejero Andrei Velichko Òscar Garibo-i-Orts Yuriy Izotov Viet-Thanh Pham
The classification of time series using machine learning (ML) analysis and entropy-based features is an urgent task for the study of nonlinear signals in the fields of finance, biology and medicine, including EEG analysis and Brain–Computer Interfacing. As several entropy measures exist, the problem is assessing the effectiveness of entropies used as features for the ML classification of nonlinear dynamics of time series. We propose a method, called global efficiency (GEFMCC), for assessing the effectiveness of entropy features using several chaotic mappings. GEFMCC is a fitness function for optimizing the type and parameters of entropies for time series classification problems. We analyze fuzzy entropy (FuzzyEn) and neural network entropy (NNetEn) for four discrete mappings, the logistic map, the sine map, the Planck map, and the two-memristor-based map, with a base length time series of 300 elements. FuzzyEn has greater GEFMCC in the classification task compared to NNetEn. However, NNetEn classification efficiency is higher than FuzzyEn for some local areas of the time series dynamics. The results of using horizontal visibility graphs (HVG) instead of the raw time series demonstrate the GEFMCC decrease after HVG time series transformation. However, the GEFMCC increases after applying the HVG for some local areas of time series dynamics. The scientific community can use the results to explore the efficiency of the entropy-based classification of time series in “The Entropy Universe”. An implementation of the algorithms in Python is presented.
]]>Mathematics doi: 10.3390/math12070936
Authors: Larisa Beilina Vitoriano Ruas
In this paper, we address the approximation of the coupling problem for the wave equation and Maxwell’s equations of electromagnetism in the time domain in terms of electric field by means of a nodal linear finite element discretization in space, combined with a classical explicit finite difference scheme for time discretization. Our study applies to a particular case where the dielectric permittivity has a constant value outside a subdomain, whose closure does not intersect the boundary of the domain where the problem is defined. Inside this subdomain, Maxwell’s equations hold. Outside this subdomain, the wave equation holds, which may correspond to Maxwell’s equations with a constant permittivity under certain conditions. We consider as a model the case of first-order absorbing boundary conditions. First-order error estimates are proven in the sense of two norms involving first-order time and space derivatives under reasonable assumptions, among which lies a CFL condition for hyperbolic equations. The theoretical estimates are validated by numerical computations, which also show that the scheme is globally of the second order in the maximum norm in time and in the least-squares norm in space.
]]>Mathematics doi: 10.3390/math12070937
Authors: Muhamad Nur Rohman Jeng-Rong Ho Chin-Te Lin Pi-Cheng Tung Chih-Kuang Lin
This study focused on the efficacy of employing a pulsed fiber laser in the curved cutting of thin, non-oriented electrical steel sheets. Experiments were conducted in paraffinic oil by adjusting the input process parameters, including laser power, pulse frequency, cutting speed, and curvature radius. The multiple output quality metrics included kerf width, inner and outer heat-affected zones, and re-welded portions. Analyses of the Random Forest Method and Response Surface Method indicated that laser pulse frequency was the most important variable affecting the cut quality, followed by laser power, curvature radius, and cutting speed. To improve cut quality, an innovative artificial intelligence (AI) approach incorporating a deep neural network (DNN) model and a modified equilibrium optimizer (M-EO) was proposed. Initially, the DNN model established correlations between input parameters and cut quality aspects, followed by M-EO pinpointing optimal cut qualities. Such an approach successfully identified an optimal set of laser process parameters, even beyond the specified process window from the initial experiments on curved cuts, resulting in significant enhancements confirmed by validation experiments. A comparative analysis showcased the developed models’ superior performance over prior studies. Notably, while the models were initially developed based on the results from curved cuts, they proved adaptable and capable of yielding comparable outcomes for straight cuts as well.
]]>Mathematics doi: 10.3390/math12070935
Authors: Igor Litvinchev Andreas Fischer Tetyana Romanova Petro Stetsyuk
Packing irregular objects composed by generalized spheres is considered. A generalized sphere is defined by an arbitrary norm. For three classes of packing problems, balance, homothetic and sparse packing, the corresponding new (generalized) models are formulated. Non-overlapping and containment conditions for irregular objects composed by generalized spheres are presented. It is demonstrated that these formulations can be stated for any norm. Different geometrical shapes can be treated in the same way by simply selecting a suitable norm. The approach is applied to generalized spheres defined by Lp norms and their compositions. Numerical solutions of small problem instances obtained by the global solver BARON are provided for two-dimensional objects composed by spheres defined in Lp norms to demonstrate the potential of the approach for a wide range of engineering optimization problems.
]]>Mathematics doi: 10.3390/math12070934
Authors: Abdulaziz Almalaq Saleh Albadran Mohamed A. Mohamed
The authors wish to make the following corrections to this paper [...]
]]>Mathematics doi: 10.3390/math12070933
Authors: Alessandro Ramponi Maria Elisabetta Tessitore
In this paper, we introduce an approach to the management of infectious disease diffusion through the formulation of a controlled compartmental SVIR (susceptible–vaccinated–infected–recovered) model. We consider a cost functional encompassing three distinct yet interconnected dimensions: the social cost, the disease cost, and the vaccination cost. The proposed model addresses the pressing need for optimized strategies in disease containment, incorporating both social control measures and vaccination campaigns. Through the utilization of advanced control theory, we identify optimal control strategies that mitigate disease proliferation while considering the inherent trade-offs among social interventions and vaccination efforts. Finally, we present the results from a simulation-based study employing a numerical implementation of the optimally controlled system through the forward–backward sweep algorithm. The baseline model considered incorporates parameters representative of typical values observed during the recent pandemic outbreak.
]]>Mathematics doi: 10.3390/math12070932
Authors: Aneesh S. Deogan Roeland Dilz Diego Caratelli
Fractional derivative operators are finding applications in a wide variety of fields with their ability to better model certain phenomena exhibiting spatial and temporal nonlocality. One area in which these operators are applicable is in the field of electromagnetism, thereby modelling transient wave propagation in complex media. To apply fractional derivative operators to electromagnetic problems, the operator must adhere to certain principles, like the trigonometric functions invariance property. The Grünwald–Letnikov and Marchaud fractional derivative operators comply with these principles and therefore could be applied. The fractional derivative arises when modelling frequency-dispersive dielectric media. The time-domain convolution integral in the relation between the electric displacement and the polarisation density, containing an empirical extension of the Debye model, is approximated directly. A common approach is to recursively update the convolution integral by approximating the time series by a truncated sum of decaying exponentials, with the coefficients found through means of optimisation or fitting. The finite-difference time-domain schemes using this approach have shown to be more computationally efficient compared to other approaches using auxiliary differential equation methods.
]]>Mathematics doi: 10.3390/math12070931
Authors: Xiangyun Xie Haihui Wang Yu Liu
In this paper, we investigate the Besov space and the Besov capacity and obtain several important capacitary inequalities in a strictly local Dirichlet space, which satisfies the doubling condition and the weak Bakry–Émery condition. It is worth noting that the capacitary inequalities in this paper are proved if the Dirichlet space supports the weak (1,2)-Poincaré inequality, which is weaker than the weak (1,1)-Poincaré inequality investigated in the previous references. Moreover, we first consider the strong subadditivity and its equality condition for the Besov capacity in metric space.
]]>Mathematics doi: 10.3390/math12070930
Authors: Xinhua Gao Song Liu Shan Jiang Dennis Yu Yong Peng Xianting Ma Wenting Lin
To optimize the evacuation process of rail transit passenger flows, the influence of the feeder bus network on bus demand is pivotal. This study first examines the transportation mode preferences of rail transit station passengers and addresses the feeder bus network’s optimization challenge within a three-dimensional framework, incorporating an elastic mechanism. Consequently, a strategic planning model is developed. Subsequently, a multi-objective optimization model is constructed to simultaneously increase passenger numbers and decrease both travel time costs and bus operational expenses. Due to the NP-hard nature of this optimization problem, we introduce an enhanced non-dominated sorting genetic algorithm, INSGA-II. This algorithm integrates innovative encoding and decoding rules, adaptive parameter adjustment strategies, and a combination of crowding distance and distribution entropy mechanisms alongside an external elite archive strategy to enhance population convergence and local search capabilities. The efficacy of the proposed model and algorithm is corroborated through simulations employing standard test functions and instances. The results demonstrate that the INSGA-II algorithm closely approximates the true Pareto front, attaining Pareto optimal solutions that are uniformly distributed. Additionally, an increase in the fleet size correlates with greater passenger volumes and higher operational costs, yet it substantially lowers the average travel cost per customer. An optimal fleet size of 11 vehicles is identified. Moreover, expanding feeder bus routes enhances passenger counts by 18.03%, raises operational costs by 32.33%, and cuts passenger travel time expenses by 21.23%. These findings necessitate revisions to the bus timetable. Therefore, for a bus network with elastic demand, it is essential to holistically optimize the actual passenger flow demand, fleet size, bus schedules, and departure frequencies.
]]>Mathematics doi: 10.3390/math12060929
Authors: Antonio Sabbatella Andrea Ponti Ilaria Giordani Antonio Candelieri Francesco Archetti
Prompt optimization is a crucial task for improving the performance of large language models for downstream tasks. In this paper, a prompt is a sequence of n-grams selected from a vocabulary. Consequently, the aim is to select the optimal prompt concerning a certain performance metric. Prompt optimization can be considered as a combinatorial optimization problem, with the number of possible prompts (i.e., the combinatorial search space) given by the size of the vocabulary (i.e., all the possible n-grams) raised to the power of the length of the prompt. Exhaustive search is impractical; thus, an efficient search strategy is needed. We propose a Bayesian Optimization method performed over a continuous relaxation of the combinatorial search space. Bayesian Optimization is the dominant approach in black-box optimization for its sample efficiency, along with its modular structure and versatility. We use BoTorch, a library for Bayesian Optimization research built on top of PyTorch. Specifically, we focus on Hard Prompt Tuning, which directly searches for an optimal prompt to be added to the text input without requiring access to the Large Language Model, using it as a black-box (such as for GPT-4 which is available as a Model as a Service). Albeit preliminary and based on “vanilla” Bayesian Optimization algorithms, our experiments with RoBERTa as a large language model, on six benchmark datasets, show good performances when compared against other state-of-the-art black-box prompt optimization methods and enable an analysis of the trade-off between the size of the search space, accuracy, and wall-clock time.
]]>Mathematics doi: 10.3390/math12060928
Authors: Weifang Yan Linlin Wang Min Zhang
In this paper, the singularly perturbed modified Gardner equation is considered. Firstly, for the unperturbed equation, under certain parameter conditions, we obtain the exact expressions of kink wave solution and antikink wave solution by using the bifurcation method of dynamical systems. Then, the persistence of the kink and antikink wave solutions of the perturbed modified Gardner equation is studied by exploiting the geometric singular perturbation theory and the Melnikov function method. When the perturbation parameter is sufficiently small, we obtain the sufficient conditions to guarantee the existence of kink and antikink wave solutions.
]]>Mathematics doi: 10.3390/math12060925
Authors: Mario A. Sánchez Juan C. Maya Farid Chejne Brennan Pecha Adriana M. Quinchía-Figueroa
This study introduces a novel particle model for biomass fast pyrolysis, incorporating an anisotropic cylindrical particle to address mass and energy transport coupled with aerosol ejection, which previous models have overlooked. The main contribution lies in developing a model that considers aerosol generation in anisotropic cylindrical particles for the first time, addressing bubbling dynamics and bursting within the liquid phase. The population balance equation describes bubble dynamics and aerosol formation, capturing phenomena like nucleation, growth, coalescence, and bursting. The model employs the method of moments with bubble volume as an internal variable, substantially reducing computational costs by eliminating dependence on this variable. Results highlight the significant impact of anisotropy and particle size on aerosol ejection: smaller, less elongated particles experience faster heating, quicker conversion, and the increased accumulation of the liquid intermediate phase. Specifically, 1 mm diameter particles yield higher concentrations of metaplast and bio-oil aerosols, exceeding 15%, compared to concentrations below 11% for 3 mm particles. This model provides insights into aerosol structure (volume, surface area), aiding in understanding aerosol reactivity at the reactor scale.
]]>Mathematics doi: 10.3390/math12060927
Authors: Wen-Xiu Ma
The aim of this paper is to analyze a specific fourth-order matrix spectral problem involving four potentials and two free nonzero parameters and construct an associated integrable hierarchy of bi-Hamiltonian equations within the zero curvature formulation. A hereditary recursion operator is explicitly computed, and the corresponding bi-Hamiltonian formulation is established by the so-called trace identity, showing the Liouville integrability of the obtained hierarchy. Two illustrative examples are novel generalized combined nonlinear Schrödinger equations and modified Korteweg–de Vries equations with four components and two adjustable parameters.
]]>Mathematics doi: 10.3390/math12060926
Authors: Ahmad Al-Buenain Mohamed Haouari Jithu Reji Jacob
Mega sports events generate significant media coverage and have a considerable economic impact on the host cities. Organizing such events is a complex task that requires extensive planning. The success of these events hinges on the attendees’ satisfaction. Therefore, accurately predicting the number of fans from each country is essential for the organizers to optimize planning and ensure a positive experience. This study aims to introduce a new application for machine learning in order to accurately predict the number of attendees. The model is developed using attendance data from the FIFA World Cup (FWC) Russia 2018 to forecast the FWC Qatar 2022 attendance. Stochastic gradient descent (SGD) was found to be the top-performing algorithm, achieving an R2 metric of 0.633 in an Auto-Sklearn experiment that considered a total of 2523 models. After a thorough analysis of the result, it was found that team qualification has the highest impact on attendance. Other factors such as distance, number of expatriates in the host country, and socio-geopolitical factors have a considerable influence on visitor counts. Although the model produces good results, with ML it is always recommended to have more data inputs. Therefore, using previous tournament data has the potential to increase the accuracy of the results.
]]>Mathematics doi: 10.3390/math12060924
Authors: Dina Abuzaid Samer Al-Ghour Monia Naghi
In this paper, we present a novel family of soft sets named “soft ωδ-open sets”. We find that this class constitutes a soft topology that lies strictly between the soft topologies of soft δ-open sets and soft ω0-open sets. Also, we introduce certain sufficient conditions for the equivalence between this new soft topology and several existing soft topologies. Moreover, we verify several relationships that contain soft covering properties, such as soft compactness and soft Lindelofness, which are related to this new soft topology. Furthermore, in terms of the soft interior operator in certain soft topologies, we define four classes of soft sets. Via them, we obtain new decomposition theorems for soft δ-openness and soft θ-openness, and we characterize the soft topological spaces that have the soft “semi-regularization property”. In addition, via soft ωδ-open sets, we introduce and investigate a new class of soft functions named “soft ωδ-continuous functions”. Finally, we look into the connections between the newly proposed soft concepts and their counterparts in classical topological spaces.
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