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Asymptotics of the Least Trimmed Squares Estimator
A Causal Evaluation of the UK’s Mini-Budget Policy on Stock Market
Elimination Algorithms for Skew Polynomials with Applications in Cybersecurity
A Projection-Type Implicit Algorithm for Finding a Common Solution for Fixed Point Problems and Variational Inequality Problems

Journal Description

Mathematics

Mathematics is a peer-reviewed, open access journal which provides an advanced forum for studies related to mathematics, and is published semimonthly online by MDPI. The European Society for Fuzzy Logic and Technology (EUSFLAT) and International Society for the Study of Information (IS4SI) are affiliated with Mathematics and their members receive a discount on article processing charges.

Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
High Visibility: indexed within Scopus, SCIE (Web of Science), RePEc, and other databases.
Journal Rank: JCR - Q1 (Mathematics) / CiteScore - Q1 (General Mathematics )
Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 18.3 days after submission; acceptance to publication is undertaken in 1.9 days (median values for papers published in this journal in the second half of 2024).
Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
Sections: published in 13 topical sections.
Companion journals for Mathematics include: Foundations, Analytics, International Journal of Topology, Geometry and Logics.

Impact Factor: 2.3 (2023); 5-Year Impact Factor: 2.2 (2023)

Imprint Information Journal Flyer Open Access ISSN: 2227-7390

Latest Articles

24 pages, 983 KiB

Open AccessArticle

MeTa Learning-Based Optimization of Unsupervised Domain Adaptation Deep Networks

by Hsiau-Wen Lin, Trang-Thi Ho, Ching-Ting Tu, Hwei-Jen Lin and Chen-Hsiang Yu

Mathematics 2025, 13(2), 226; https://doi.org/10.3390/math13020226 - 10 Jan 2025

This paper introduces a novel unsupervised domain adaptation (UDA) method, MeTa Discriminative Class-Wise MMD (MCWMMD), which combines meta-learning with a Class-Wise Maximum Mean Discrepancy (MMD) approach to enhance domain adaptation. Traditional MMD methods align overall distributions but struggle with class-wise alignment, reducing feature [...] Read more.

This paper introduces a novel unsupervised domain adaptation (UDA) method, MeTa Discriminative Class-Wise MMD (MCWMMD), which combines meta-learning with a Class-Wise Maximum Mean Discrepancy (MMD) approach to enhance domain adaptation. Traditional MMD methods align overall distributions but struggle with class-wise alignment, reducing feature distinguishability. MCWMMD incorporates a meta-module to dynamically learn a deep kernel for MMD, improving alignment accuracy and model adaptability. This meta-learning technique enhances the model’s ability to generalize across tasks by ensuring domain-invariant and class-discriminative feature representations. Despite the complexity of the method, including the need for meta-module training, it presents a significant advancement in UDA. Future work will explore scalability in diverse real-world scenarios and further optimize the meta-learning framework. MCWMMD offers a promising solution to the persistent challenge of domain adaptation, paving the way for more adaptable and generalizable deep learning models. Full article

(This article belongs to the Special Issue Advances in Intelligent Computing, Machine Learning and Pattern Recognition)

19 pages, 1741 KiB

Open AccessArticle

A Dual-Path Neural Network for High-Impedance Fault Detection

by Keqing Ning, Lin Ye, Wei Song, Wei Guo, Guanyuan Li, Xiang Yin and Mingze Zhang

Mathematics 2025, 13(2), 225; https://doi.org/10.3390/math13020225 - 10 Jan 2025

High-impedance fault detection poses significant challenges for distribution network maintenance and operation. We propose a dual-path neural network for high-impedance fault detection. To enhance feature extraction, we use a Gramian Angular Field algorithm to transform 1D zero-sequence voltage signals into 2D images. Our [...] Read more.

High-impedance fault detection poses significant challenges for distribution network maintenance and operation. We propose a dual-path neural network for high-impedance fault detection. To enhance feature extraction, we use a Gramian Angular Field algorithm to transform 1D zero-sequence voltage signals into 2D images. Our dual-branch network simultaneously processes both representations: the CNN extracts spatial features from the transformed images, while the GRU captures temporal features from the raw signals. To optimize model performance, we integrate the Crested Porcupine Optimizer (CPO) algorithm for the adaptive optimization of key network hyperparameters. The experimental results demonstrate that our method achieves a 99.70% recognition accuracy on a dataset comprising high-impedance faults, capacitor switching, and load connections. Furthermore, it maintains robust performance under various test conditions, including different noise levels and network topology changes. Full article

(This article belongs to the Special Issue Complex Process Modeling and Control Based on AI Technology)

20 pages, 973 KiB

Open AccessArticle

A Distributed Energy-Throughput Efficient Cross-Layer Framework Using Hybrid Optimization Algorithm

by Pratap Singh, Nitin Mittal, Vikas Mittal, Tapankumar Trivedi, Ashish Singh, Szymon Łukasik and Rohit Salgotra

Mathematics 2025, 13(2), 224; https://doi.org/10.3390/math13020224 - 10 Jan 2025

Magnetic induction (MI)-operated wireless sensor networks (WSNs), due to their similar performance in air, underwater, and underground mediums, are rapidly emerging networks that offer a wide range of applications, including mine prevention, power grid maintenance, underground pipeline monitoring, and upstream oil monitoring. MI-based [...] Read more.

Magnetic induction (MI)-operated wireless sensor networks (WSNs), due to their similar performance in air, underwater, and underground mediums, are rapidly emerging networks that offer a wide range of applications, including mine prevention, power grid maintenance, underground pipeline monitoring, and upstream oil monitoring. MI-based wireless underground sensor networks (WUSNs), utilizing small antenna coils, offer a viable solution by providing consistent channel conditions. The cross-layer protocols address the specific challenges of WUSNs, leading to improved network performance and enhanced operational capabilities in real-world applications. This work proposes a distributed cross-layer solution, leveraging the hybrid marine predator naked mole rat algorithm (MPNMRA) for MI-operated WUSNs. The solution, called DECMN (distributed energy-throughput efficient cross-layer network using MPNMRA), is designed to optimize the MI communication channels, MI relay coils (MI waveguide), and MI waveguide with 3D coils to fulfill quality of service (QoS) parameters, while achieving energy savings and throughput gains. DECMN utilizes the interactions between various layers to develop cross-layer protocols based on MPNMRA. Simulation results demonstrate the effectiveness of DECMN, offering energy savings, increased throughput, and reliable transmissions within the performance limits. Full article

(This article belongs to the Special Issue Advances in Artificial Intelligence: Models, Optimization, and Machine Learning, 3rd Edition)

52 pages, 871 KiB

Open AccessReview

Series and Connections Among Central Factorial Numbers, Stirling Numbers, Inverse of Vandermonde Matrix, and Normalized Remainders of Maclaurin Series Expansions ^†

by Feng Qi

Mathematics 2025, 13(2), 223; https://doi.org/10.3390/math13020223 - 10 Jan 2025

This paper presents an extensive investigation into several interrelated topics in mathematical analysis and number theory. The author revisits and builds upon known results regarding the Maclaurin power series expansions for a variety of functions and their normalized remainders, explores connections among central [...] Read more.

This paper presents an extensive investigation into several interrelated topics in mathematical analysis and number theory. The author revisits and builds upon known results regarding the Maclaurin power series expansions for a variety of functions and their normalized remainders, explores connections among central factorial numbers, the Stirling numbers, and specific matrix inverses, and derives several closed-form formulas and inequalities. Additionally, this paper reveals new insights into the properties of these mathematical objects, including logarithmic convexity, explicit expressions for certain quantities, and identities involving the Bell polynomials of the second kind. Full article

(This article belongs to the Section Difference and Differential Equations)

19 pages, 308 KiB

Open AccessArticle

Global Well-Posedness and Determining Nodes of Non-Autonomous Navier–Stokes Equations with Infinite Delay on Bounded Domains

by Huanzhi Ge and Feng Du

Mathematics 2025, 13(2), 222; https://doi.org/10.3390/math13020222 - 10 Jan 2025

The asymptotic behavior of solutions to nonlinear partial differential equations is an important tool for studying their long-term behavior. However, when studying the asymptotic behavior of solutions to nonlinear partial differential equations with delay, the delay factor

u (t + θ)

[...] Read more.

The asymptotic behavior of solutions to nonlinear partial differential equations is an important tool for studying their long-term behavior. However, when studying the asymptotic behavior of solutions to nonlinear partial differential equations with delay, the delay factor

u (t + θ)

in the delay term may lead to oscillations, hysteresis effects, and other phenomena in the solution, which increases the difficulty of studying the well-posedness and asymptotic behavior of the solution. This study investigates the global well-posedness and asymptotic behavior of solutions to the non-autonomous Navier–Stokes equations incorporating infinite delays. To establish global well-posedness, we first construct several suitable function spaces and then prove them using the Galekin approximation method. Then, by accurately estimating the number of determining nodes, we reveal the asymptotic behavior of the solution. The results indicate that the long-term behavior of a strong solution can be determined by its values at a finite number of nodes. Full article

(This article belongs to the Special Issue Advances in Study of Time-Delay Systems and Their Applications, 2nd Edition)

20 pages, 2612 KiB

Open AccessArticle

Extracting Implicit User Preferences in Conversational Recommender Systems Using Large Language Models

by Woo-Seok Kim, Seongho Lim, Gun-Woo Kim and Sang-Min Choi

Mathematics 2025, 13(2), 221; https://doi.org/10.3390/math13020221 - 10 Jan 2025

Conversational recommender systems (CRSs) have garnered increasing attention for their ability to provide personalized recommendations through natural language interactions. Although large language models (LLMs) have shown potential in recommendation systems owing to their superior language understanding and reasoning capabilities, extracting and utilizing implicit [...] Read more.

Conversational recommender systems (CRSs) have garnered increasing attention for their ability to provide personalized recommendations through natural language interactions. Although large language models (LLMs) have shown potential in recommendation systems owing to their superior language understanding and reasoning capabilities, extracting and utilizing implicit user preferences from conversations remains a formidable challenge. This paper proposes a method that leverages LLMs to extract implicit preferences and explicitly incorporate them into the recommendation process. Initially, LLMs identify implicit user preferences from conversations, which are then refined into fine-grained numerical values using a BERT-based multi-label classifier to enhance recommendation precision. The proposed approach is validated through experiments on three comprehensive datasets: the Reddit Movie Dataset (8413 dialogues), Inspired (825 dialogues), and ReDial (2311 dialogues). Results show that our approach considerably outperforms traditional CRS methods, achieving a 23.3% improvement in Recall@20 on the ReDial dataset and a 7.2% average improvement in recommendation accuracy across all datasets with GPT-3.5-turbo and GPT-4. These findings highlight the potential of using LLMs to extract and utilize implicit conversational information, effectively enhancing the quality of recommendations in CRSs. Full article

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16 pages, 6616 KiB

Open AccessArticle

On the Fractional Dynamics of Kinks in Sine-Gordon Models

by Tassos Bountis, Julia Cantisán, Jesús Cuevas-Maraver, Jorge Eduardo Macías-Díaz and Panayotis G. Kevrekidis

Mathematics 2025, 13(2), 220; https://doi.org/10.3390/math13020220 - 10 Jan 2025

In the present work, we explored the dynamics of single kinks, kink–anti-kink pairs and bound states in the prototypical fractional Klein–Gordon example of the sine-Gordon equation. In particular, we modified the order

β

of the temporal derivative to that of a Caputo fractional [...] Read more.

In the present work, we explored the dynamics of single kinks, kink–anti-kink pairs and bound states in the prototypical fractional Klein–Gordon example of the sine-Gordon equation. In particular, we modified the order

β

of the temporal derivative to that of a Caputo fractional type and found that, for

1 < β < 2

, this imposes a dissipative dynamical behavior on the coherent structures. We also examined the variation of a fractional Riesz order

α

on the spatial derivative. Here, depending on whether this order was below or above the harmonic value

α = 2

, we found, respectively, monotonically attracting kinks, or non-monotonic and potentially attracting or repelling kinks, with a saddle equilibrium separating the two. Finally, we also explored the interplay of the two derivatives, when both Caputo temporal and Riesz spatial derivatives are involved. Full article

(This article belongs to the Special Issue Chaos Theory and Complexity)

23 pages, 13392 KiB

Open AccessArticle

Incorporation of Histogram Intersection and Semantic Information into Non-Negative Local Laplacian Sparse Coding for Image Classification

by Ying Shi, Yuan Wan, Xinjian Wang and Huanhuan Li

Mathematics 2025, 13(2), 219; https://doi.org/10.3390/math13020219 - 10 Jan 2025

Traditional sparse coding has proven to be an effective method for image feature representation in recent years, yielding promising results in image classification. However, it faces several challenges, such as sensitivity to feature variations, code instability, and inadequate distance measures. Additionally, image representation [...] Read more.

Traditional sparse coding has proven to be an effective method for image feature representation in recent years, yielding promising results in image classification. However, it faces several challenges, such as sensitivity to feature variations, code instability, and inadequate distance measures. Additionally, image representation and classification often operate independently, potentially resulting in the loss of semantic relationships. To address these issues, a new method is proposed, called Histogram intersection and Semantic information-based Non-negativity Local Laplacian Sparse Coding (HS-NLLSC) for image classification. This method integrates Non-negativity and Locality into Laplacian Sparse Coding (NLLSC) optimisation, enhancing coding stability and ensuring that similar features are encoded into similar codewords. In addition, histogram intersection is introduced to redefine the distance between feature vectors and codebooks, effectively preserving their similarity. By comprehensively considering both the processes of image representation and classification, more semantic information is retained, thereby leading to a more effective image representation. Finally, a multi-class linear Support Vector Machine (SVM) is employed for image classification. Experimental results on four standard and three maritime image datasets demonstrate superior performance compared to the previous six algorithms. Specifically, the classification accuracy of our approach improved by 5% to 19% compared to the previous six methods. This research provides valuable insights for various stakeholders in selecting the most suitable method for specific circumstances. Full article

(This article belongs to the Special Issue Optimization Models and Algorithms in Data Science)

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22 pages, 1200 KiB

Open AccessArticle

Interaction Between Two Rigid Hydrophobic Spheres Oscillating in an Infinite Brinkman–Stokes Fluid

by Azza M. Algatheem, Hala H. Taha and Shreen El-Sapa

Mathematics 2025, 13(2), 218; https://doi.org/10.3390/math13020218 - 10 Jan 2025

This study investigates the dynamics of two oscillating rigid spheres moving through an infinite porous medium saturated with Stokes fluid flow, addressing the problem of how fluid properties, permeability, frequency, and slip length influence the system. The objective is to model the interactions [...] Read more.

This study investigates the dynamics of two oscillating rigid spheres moving through an infinite porous medium saturated with Stokes fluid flow, addressing the problem of how fluid properties, permeability, frequency, and slip length influence the system. The objective is to model the interactions between the spheres, which differ in size and velocity as they move along the axis connecting their centers while applying slip boundary conditions to their surfaces. We derive the governing field equations using a semi-analytical method and solve the resulting system of equations numerically through a collocation technique. Our novel quantitative results include insights into the drag force coefficients for both in-phase and out-of-phase oscillations of each hydrophobic sphere, considering parameters such as diameter ratio, permeability, frequency, velocity ratios, slip lengths, and the distances between the spheres. Notably, when the spheres are sufficiently far apart, the normalized drag force coefficients behave as if each sphere is moving independently. Additionally, we present streamlines that illustrate the interactions between the spheres across a range of parameters, highlighting the novelty of our findings. A purely viscous medium and no-slip conditions are used to validate the numerical approach and results. Full article

(This article belongs to the Section Computational and Applied Mathematics)

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15 pages, 2358 KiB

Open AccessArticle

Bifurcations and Exact Solutions of the Coupled Nonlinear Generalized Zakharov Equations with Anti-Cubic Nonlinearity: Dynamical System Approach

by Jie Song, Feng Li and Mingji Zhang

Mathematics 2025, 13(2), 217; https://doi.org/10.3390/math13020217 - 10 Jan 2025

We consider the exact traveling wave solutions for the coupled nonlinear generalized Zakharov equations. By employing the method of dynamical systems, we are able to obtain bifurcations of the phase portraits of the corresponding planar dynamical system under various parameter conditions. Based on [...] Read more.

We consider the exact traveling wave solutions for the coupled nonlinear generalized Zakharov equations. By employing the method of dynamical systems, we are able to obtain bifurcations of the phase portraits of the corresponding planar dynamical system under various parameter conditions. Based on different level curves, we derive all possible exact explicit parametric representations of bounded solutions, which include pseudo-periodic peakon, pseudo-peakon, smooth periodic wave solutions, solitary solutions, kink wave solution and the compacton solution family. Full article

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22 pages, 797 KiB

Open AccessArticle

Digital Twin-Empowered Robotic Arm Control: An Integrated PPO and Fuzzy PID Approach

by Yuhao Cen, Jianjue Deng, Ye Chen, Haoxian Liu, Zetao Zhong, Bo Fan, Le Chang and Li Jiang

Mathematics 2025, 13(2), 216; https://doi.org/10.3390/math13020216 - 10 Jan 2025

With rapid advancements in digital twin technology within the Industrial Internet of Things, integrating digital twins with industrial robotic arms presents a promising direction. This integration promotes the remote operation and intelligence of industrial control processes. However, the control and error management of [...] Read more.

With rapid advancements in digital twin technology within the Industrial Internet of Things, integrating digital twins with industrial robotic arms presents a promising direction. This integration promotes the remote operation and intelligence of industrial control processes. However, the control and error management of robotic arms in digital twin systems pose challenges. In this paper, we present a digital twin-empowered robotic arm system and propose a control policy using deep reinforcement learning, specifically the proximal policy optimization approach. The construction and functionality of each subsystem within the digital twin-empowered robotic arm control system are detailed. To address errors caused by mechanical structure and virtual–real mapping in the digital twin, an integrated proximal policy optimization and fuzzy PID approach is proposed. Experimental results demonstrate that proximal policy optimization is adaptable to virtual–real mapping errors, while the fuzzy PID method corrects physical errors quickly and accurately. The robotic arm can reach the target point using this integrated approach. Overall, error management problems in digital systems have been well addressed, and our scheme can provide an accurate and adaptive control strategy for the robotic arm. Full article

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26 pages, 1404 KiB

Open AccessFeature PaperArticle

Research on Three-Dimensional Extension of Barzilai-Borwein-like Method

by Tianji Wang and Qingdao Huang

Mathematics 2025, 13(2), 215; https://doi.org/10.3390/math13020215 - 10 Jan 2025

The Barzilai-Borwein (BB) method usually uses BB stepsize for iteration so as to eliminate the line search step in the steepest descent method. In this paper, we modify the BB stepsize and extend it to solve the optimization problems of three-dimensional quadratic functions. [...] Read more.

The Barzilai-Borwein (BB) method usually uses BB stepsize for iteration so as to eliminate the line search step in the steepest descent method. In this paper, we modify the BB stepsize and extend it to solve the optimization problems of three-dimensional quadratic functions. The discussion is divided into two cases. Firstly, we study the case where the coefficient matrix of the quadratic term of quadratic function is a special third-order diagonal matrix and prove that using the new modified stepsize, this case is R-superlinearly convergent. In addition to that, we extend it to n-dimensional case and prove the rate of convergence is R-linear. Secondly, we analyze that the coefficient matrix of the quadratic term of quadratic function is a third-order asymmetric matrix, that is, when the matrix has a double characteristic root and prove the global convergence of this case. The results of numerical experiments show that the modified method is effective for the above two cases. Full article

(This article belongs to the Section Computational and Applied Mathematics)

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22 pages, 2061 KiB

Open AccessArticle

An Adaptive Large Neighborhood Search for a Green Vehicle Routing Problem with Depot Sharing

by Zixuan Wu, Ping Lou, Jianmin Hu, Yuhang Zeng and Chuannian Fan

Mathematics 2025, 13(2), 214; https://doi.org/10.3390/math13020214 - 10 Jan 2025

In urban logistics distribution, vehicle carbon emissions during the distribution process significantly contribute to environmental pollution. While developing green logistics is critical for the sustainable growth of the logistics industry, existing studies often overlook the potential benefits of depot sharing among enterprises. By [...] Read more.

In urban logistics distribution, vehicle carbon emissions during the distribution process significantly contribute to environmental pollution. While developing green logistics is critical for the sustainable growth of the logistics industry, existing studies often overlook the potential benefits of depot sharing among enterprises. By enabling depots belonging to different enterprises to be shared, it would shorten the distance traveled by vehicles returning to depots and reduce carbon emissions. And it would also reduce the number of depots being built. Therefore, a green vehicle routing problem with depot sharing is presented in the paper. To solve this problem, an improved adaptive large neighborhood search algorithm is presented, in which the Split strategy and two new operators are proposed to enhance solution quality and computational efficiency. Extensive numerical experiments are conducted on instances of varying scales to evaluate this algorithm, and also demonstrate its effectiveness and efficiency. Furthermore, the experimental results demonstrate that depot sharing significantly reduces carbon emissions, achieving an average optimization rate of 10.1% across all instances compared to returning to the original depot. Full article

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14 pages, 283 KiB

Open AccessArticle

Convergence Speed of Bermudan, Randomized Bermudan, and Canadian Options

by Guillaume Leduc

Mathematics 2025, 13(2), 213; https://doi.org/10.3390/math13020213 - 10 Jan 2025

American options have long received considerable attention in the literature, with numerous publications dedicated to their pricing. Bermudan and randomized Bermudan options are broadly used to estimate their prices efficiently. Notably, the penalty method yields option prices that coincide with those of randomized [...] Read more.

American options have long received considerable attention in the literature, with numerous publications dedicated to their pricing. Bermudan and randomized Bermudan options are broadly used to estimate their prices efficiently. Notably, the penalty method yields option prices that coincide with those of randomized Bermudan options. However, theoretical results regarding the speed of convergence of these approximations to the American option price remain scarce. In this paper, we address this gap by establishing a general result on the convergence speed of Bermudan and randomized Bermudan option prices to their American limits. We prove that for convex payoff functions, the convergence speed is linear; that is, of order

1 / n

, where n denotes the number of exercisable opportunities in the Bermudan case and serves as the intensity parameter of the underlying Poisson process in the randomized Bermudan case. Our framework is quite general, encompassing Lévy models, stochastic volatility models, and nearly any risk-neutral model that can be incorporated within a strong Markov framework. We extend our analysis to Canadian options, showing under mild conditions a convergence rate of

1 / \sqrt{n}

to their American limits. To our knowledge, this is the first study addressing the speed of convergence in Canadian option pricing. Full article

(This article belongs to the Special Issue Financial Mathematics and Financial Engineering)

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13 pages, 309 KiB

Open AccessFeature PaperArticle

The Cyclically Resolvable Steiner Triple Systems of Order 57

by Svetlana Topalova and Stela Zhelezova

Mathematics 2025, 13(2), 212; https://doi.org/10.3390/math13020212 - 10 Jan 2025

A resolution of a Steiner triple system of order v (STS(v)) is point-cyclic if it has an automorphism permuting the points in one cycle. An STS(v) is cyclically resolvable if it has at least one point-cyclic resolution. Cyclically resolvable [...] Read more.

A resolution of a Steiner triple system of order v (STS(v)) is point-cyclic if it has an automorphism permuting the points in one cycle. An STS(v) is cyclically resolvable if it has at least one point-cyclic resolution. Cyclically resolvable STS(v)s have important applications in Coding Theory. They have been classified up to

v = 45

and before the present work

v = 57

was the first open case. There are 2,353,310 cyclic STS(57)s. We establish that 155,966 of them are cyclically resolvable yielding 3,638,984 point-cyclic resolutions which we classify with respect to their automorphism groups and to the availability of some configurations. Full article

(This article belongs to the Section Mathematics and Computer Science)

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8 pages, 227 KiB

Open AccessFeature PaperArticle

Error Correction for Check Digit Systems over p-Groups and Applications to DNA Sequences

by Louis Beaugris

Mathematics 2025, 13(2), 211; https://doi.org/10.3390/math13020211 - 10 Jan 2025

Statistical analysis shows that the most common errors in the transmission of information consist of single errors and transposition errors. Error detection and correction methods are often desired, particularly when the accuracy of information is of crucial importance. Inspired by a check digit [...] Read more.

Statistical analysis shows that the most common errors in the transmission of information consist of single errors and transposition errors. Error detection and correction methods are often desired, particularly when the accuracy of information is of crucial importance. Inspired by a check digit system constructed from the companion matrix of a primitive polynomial over the integers

Z_{p}

and that focused on error detection, this work develops error-correction formulas for single errors and transposition errors for that check digit scheme. We also propose an application to DNA sequences. Full article

18 pages, 561 KiB

Open AccessArticle

Exploring the Structure of Possibility Multi-Fuzzy Soft Ordered Semigroups Through Interior Ideals

by Sana Habib, Kashif Habib, Violeta Leoreanu-Fotea and Faiz Muhammad Khan

Mathematics 2025, 13(2), 210; https://doi.org/10.3390/math13020210 - 9 Jan 2025

This paper aims to introduce a novel idea of possibility multi-fuzzy soft ordered semigroups for ideals and interior ideals. Various results, formulated as theorems based on these concepts, are presented and further validated with suitable examples. This paper also explores the broad applicability [...] Read more.

This paper aims to introduce a novel idea of possibility multi-fuzzy soft ordered semigroups for ideals and interior ideals. Various results, formulated as theorems based on these concepts, are presented and further validated with suitable examples. This paper also explores the broad applicability of possibility multi-fuzzy soft ordered semigroups in solving modern decision-making problems. Furthermore, this paper explores various classes of ordered semigroups, such as simple, regular, and intra-regular, using this innovative method. Based on these concepts, some important conclusions are drawn with supporting examples. Moreover, it defines the possibility of multi-fuzzy soft ideals for semiprime ordered semigroups. Full article

(This article belongs to the Special Issue Fuzzy Logic and Soft Computing—In Memory of Lotfi A. Zadeh)

14 pages, 839 KiB

Open AccessArticle

Multi-Dimensional Markov Chains of M/G/1 Type

by Valeriy Naumov and Konstantin Samouylov

Mathematics 2025, 13(2), 209; https://doi.org/10.3390/math13020209 - 9 Jan 2025

We consider an irreducible discrete-time Markov process with states represented as (k, i) where k is an M-dimensional vector with non-negative integer entries, and i indicates the state (phase) of the external environment. The number n of phases may [...] Read more.

We consider an irreducible discrete-time Markov process with states represented as (k, i) where k is an M-dimensional vector with non-negative integer entries, and i indicates the state (phase) of the external environment. The number n of phases may be either finite or infinite. One-step transitions of the process from a state (k, i) are limited to states (n, j) such that n ≥ k−1, where 1 represents the vector of all 1s. We assume that for a vector k ≥ 1, the one-step transition probability from a state (k, i) to a state (n, j) may depend on i, j, and n −k, but not on the specific values of k and n. This process can be classified as a Markov chain of M/G/1 type, where the minimum entry of the vector n defines the level of a state (n, j). It is shown that the first passage distribution matrix of such a process, also known as the matrix G, can be expressed through a family of nonnegative square matrices of order n, which is a solution to a system of nonlinear matrix equations. Full article

(This article belongs to the Special Issue Queue and Stochastic Models for Operations Research, 3rd Edition)

29 pages, 878 KiB

Open AccessReview

Persistent Topological Laplacians—A Survey

by Xiaoqi Wei and Guo-Wei Wei

Mathematics 2025, 13(2), 208; https://doi.org/10.3390/math13020208 - 9 Jan 2025

Persistent topological Laplacians constitute a new class of tools in topological data analysis (TDA). They are motivated by the necessity to address challenges encountered in persistent homology when handling complex data. These Laplacians combine multiscale analysis with topological techniques to characterize the topological [...] Read more.

Persistent topological Laplacians constitute a new class of tools in topological data analysis (TDA). They are motivated by the necessity to address challenges encountered in persistent homology when handling complex data. These Laplacians combine multiscale analysis with topological techniques to characterize the topological and geometrical features of functions and data. Their kernels fully retrieve the topological invariants of corresponding persistent homology, while their non-harmonic spectra provide supplementary information. Persistent topological Laplacians have demonstrated superior performance over persistent homology in the analysis of large-scale protein engineering datasets. In this survey, we offer a pedagogical review of persistent topological Laplacians formulated in various mathematical settings, including simplicial complexes, path complexes, flag complexes, digraphs, hypergraphs, hyperdigraphs, cellular sheaves, and N-chain complexes. Full article

(This article belongs to the Section Algebra, Geometry and Topology)

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38 pages, 4670 KiB

Open AccessFeature PaperArticle

Exploring the Performance of Some Efficient Explicit Numerical Methods with Good Stability Properties for Huxley’s Equation

by Husniddin Khayrullaev, Issa Omle and Endre Kovács

Mathematics 2025, 13(2), 207; https://doi.org/10.3390/math13020207 - 9 Jan 2025

Four explicit numerical schemes are collected, which are stable and efficient for the diffusion equation. Using these diffusion solvers, several new methods are constructed for the nonlinear Huxley’s equation. Then, based on many successive numerical case studies in one and two space dimensions, [...] Read more.

Four explicit numerical schemes are collected, which are stable and efficient for the diffusion equation. Using these diffusion solvers, several new methods are constructed for the nonlinear Huxley’s equation. Then, based on many successive numerical case studies in one and two space dimensions, the least performing methods are gradually dropped out to keep only the best ones. During the tests, not only one but all the relevant time step sizes are considered, and for them, running-time measurements are performed. A major aspect is computational efficiency, which means that an acceptable solution is produced in the shortest possible time. Parameter sweeps are executed for the coefficient of the nonlinear term, the stiffness ratio, and the length of the examined time interval as well. We obtained that usually, the leapfrog–hopscotch method with Strang-type operator-splitting is the most efficient and reliable, but the method based on the Dufort–Frankel scheme can also be very efficient. Full article

(This article belongs to the Section Computational and Applied Mathematics)

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Research on Blockchain Technology for Peer-to-Peer (P2P) Energy Trading Topic Editors: Pierre-Martin Tardif, Brahim El Bhiri, Bilal Abu-Salih, Kenji Tanaka
Deadline: 28 February 2025

Topic in Electricity, Energies, Mathematics, Sustainability, Symmetry

Intelligent Control in Smart Energy Systems Topic Editors: Eduard Petlenkov, Larbi Chrifi-Alaoui
Deadline: 10 March 2025

Topic in Drones, Electronics, Energies, JMSE, Mathematics

Cooperative Localization, Optimization and Control of Networked Autonomous Systems: Theories, Analysis Tools and Applications Topic Editors: Xu Fang, Chao Deng, Shankar A. Deka, Jitao Li, Heling Yuan
Deadline: 31 March 2025

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16–19 May 2025 The 5th International Conference on Symmetry

15–16 October 2025 The 1st International Electronic Conference on Games (IECGA 2025)

21–23 March 2025 The 5th International Conference on Applied Mathematics, Modelling and Intelligent Computing (CAMMIC 2025)

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Special Issue in Mathematics

Mathematics, Cryptography, Secret Sharing, Information Hiding and Their Applications Guest Editors: Peng Li, Xuehu Yan
Deadline: 10 January 2025

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Recent Developments in Image Analysis and Applications Guest Editor: Guojun Liao
Deadline: 10 January 2025

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Application of Survival Analysis in Economics, Finance and Insurance Guest Editor: David Zapletal
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Robust Optimization in Federated Learning for Industrial IoT: Mathematical Foundations Guest Editors: Chunjiong Zhang, Tao Xie
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