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Axioms
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Mathematical and Statistical Methods and Their Applications, 2nd Edition
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Mathematical and Statistical Methods and Their Applications, 2nd Edition

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 30 November 2025 | Viewed by 2110

Special Issue Editor

Dr. Jiujun Zhang

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Liaoning University, Shenyang 110036, China
Interests: statistical process control; quality engineering; non-parametric
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We are currently planning a Special Issue in Axioms on “Mathematical and Statistical Methods and Their Applications”. The Issue, as follows from its title, will be dedicated to papers describing particular methodologies with a broad review of the mathematical field, including restrictions, boundaries, reasons for them to appear, comparisons to other methods, and prominent contributions with connections to new results, which should also be presented in the paper. As we truly believe that it is important to share not only our results but also the methods that we use, manuscripts must be presented in a clear form that may be understood not just by specialists in your field. This may require a brief literature review. As long as the above requirements are met, we are pleased to accept a broad variety of papers, dedicated to mathematical and statistical methods and their applications to be compiled in a collection for personal research and new fruitful collaborations.

Dr. Jiujun Zhang
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • mathematical methods
  • mathematical statistics
  • applications
  • stochastic processes

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Related Special Issue

Published Papers (4 papers)

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Research

21 pages, 1712 KiB  
Article
A Learning Path Recommendation Approach in a Fuzzy Competence Space
by Ronghai Wang, Baokun Huang and Jinjin Li
Axioms 2025, 14(6), 396; https://doi.org/10.3390/axioms14060396 - 22 May 2025
Viewed by 55
Abstract
This study proposes a learning path recommendation method based on fuzzy competence space theory. It is developed within the theoretical framework of knowledge space theory and fuzzy set theory, aiming to address the progressive nature of learners’ skill acquisition. The proposed method ensures [...] Read more.
This study proposes a learning path recommendation method based on fuzzy competence space theory. It is developed within the theoretical framework of knowledge space theory and fuzzy set theory, aiming to address the progressive nature of learners’ skill acquisition. The proposed method ensures that a learner can improve their knowledge state by increasing only one proficiency level of a skill at a time, thereby closely reflecting the incremental characteristics of real-world learning processes. Based on fuzzy skill mappings, this work systematically defines fuzzy competence states, fuzzy competence structures, and consistent fuzzy competence spaces. Then, given a consistent fuzzy competence space and a fuzzy skill mapping, the necessary and sufficient conditions for the existence of gradual and effective learning paths are proposed and proven under the disjunctive model. Finally, a gradual and effective learning path recommendation algorithm is designed, and its effectiveness is validated through simulation experiments. This method provides a theoretical foundation and algorithmic support for the development of adaptive learning systems and intelligent testing systems. Full article
(This article belongs to the Special Issue Mathematical and Statistical Methods and Their Applications, 2nd Edition)
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25 pages, 321 KiB  
Article
Analytical and Geometric Foundations and Modern Applications of Kinetic Equations and Optimal Transport
by Cécile Barbachoux and Joseph Kouneiher
Axioms 2025, 14(5), 350; https://doi.org/10.3390/axioms14050350 - 4 May 2025
Viewed by 256
Abstract
We develop a unified analytical framework that systematically connects kinetic theory, optimal transport, and entropy dissipation through the novel integration of hypocoercivity methods with geometric structures. Building upon but distinctly extending classical hypocoercivity approaches, we demonstrate how geometric control, via commutators and curvature-like [...] Read more.
We develop a unified analytical framework that systematically connects kinetic theory, optimal transport, and entropy dissipation through the novel integration of hypocoercivity methods with geometric structures. Building upon but distinctly extending classical hypocoercivity approaches, we demonstrate how geometric control, via commutators and curvature-like structures in probability spaces, resolves degeneracies inherent in kinetic operators. Centered around the Boltzmann and Fokker–Planck equations, we derive sharp exponential convergence estimates under minimal regularity assumptions, improving on prior methods by incorporating Wasserstein gradient flow techniques. Our framework is further applied to the study of hydrodynamic limits, collisional relaxation in magnetized plasmas, the Vlasov–Poisson system, and modern data-driven algorithms, highlighting the central role of entropy as both a physical and variational tool across disciplines. By bridging entropy dissipation, optimal transport, and geometric analysis, our work offers a new perspective on stability, convergence, and structure in high-dimensional kinetic models and applications. Full article
(This article belongs to the Special Issue Mathematical and Statistical Methods and Their Applications, 2nd Edition)
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30 pages, 1867 KiB  
Article
A New Hybrid Class of Distributions: Model Characteristics and Stress–Strength Reliability Studies
by Mustapha Muhammad, Jinsen Xiao, Badamasi Abba, Isyaku Muhammad and Refka Ghodhbani
Axioms 2025, 14(3), 219; https://doi.org/10.3390/axioms14030219 - 16 Mar 2025
Viewed by 345
Abstract
This study proposes a generalized family of distributions to enhance flexibility in modeling complex engineering and biomedical data. The framework unifies existing models and improves reliability analysis in both engineering and biomedical applications by capturing diverse system behaviors. We introduce a novel hybrid [...] Read more.
This study proposes a generalized family of distributions to enhance flexibility in modeling complex engineering and biomedical data. The framework unifies existing models and improves reliability analysis in both engineering and biomedical applications by capturing diverse system behaviors. We introduce a novel hybrid family of distributions that incorporates a flexible set of hybrid functions, enabling the extension of various existing distributions. Specifically, we present a three-parameter special member called the hybrid-Weibull–exponential (HWE) distribution. We derive several fundamental mathematical properties of this new family, including moments, random data generation processes, mean residual life (MRL) and its relationship with the failure rate function, and its related asymptotic behavior. Furthermore, we compute advanced information measures, such as extropy and cumulative residual entropy, and derive order statistics along with their asymptotic behaviors. Model identifiability is demonstrated numerically using the Kullback–Leibler divergence. Additionally, we perform a stress–strength (SS) reliability analysis of the HWE under two common scale parameters, supported by illustrative numerical evaluations. For parameter estimation, we adopt the maximum likelihood estimation (MLE) method in both density estimation and SS-parameter studies. The simulation results indicated that the MLE demonstrates consistency in both density and SS-parameter estimations, with the mean squared error of the MLEs decreasing as the sample size increases. Moreover, the average length of the confidence interval for the percentile and Student’s t-bootstrap for the SS-parameter becomes smaller with larger sample sizes, and the coverage probability progressively aligns with the nominal confidence level of 95%. To demonstrate the practical effectiveness of the hybrid family, we provide three real-world data applications in which the HWE distribution outperforms many existing Weibull-based models, as measured by AIC, BIC, CAIC, KS, Anderson–Darling, and Cramer–von Mises criteria. Furthermore, the HLW exhibits strong performance in SS-parameter analysis. Consequently, this hybrid family holds immense potential for modeling lifetime data and advancing reliability and survival analysis. Full article
(This article belongs to the Special Issue Mathematical and Statistical Methods and Their Applications, 2nd Edition)
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17 pages, 4615 KiB  
Article
Analysis of Bulk Queueing Model with Load Balancing and Vacation
by Subramani Palani Niranjan, Suthanthiraraj Devi Latha, Sorin Vlase and Maria Luminita Scutaru
Axioms 2025, 14(1), 18; https://doi.org/10.3390/axioms14010018 - 30 Dec 2024
Cited by 2 | Viewed by 765
Abstract
Data center architecture plays an important role in effective server management network systems. Load balancing is one such data architecture used to efficiently distribute network traffic to the server. In this paper, we incorporated the load-balancing technique used in cloud computing with power [...] Read more.
Data center architecture plays an important role in effective server management network systems. Load balancing is one such data architecture used to efficiently distribute network traffic to the server. In this paper, we incorporated the load-balancing technique used in cloud computing with power business intelligence (BI) and cloud load based on the queueing theoretic approach. This model examines a bulk arrival and batch service queueing system, incorporating server overloading and underloading based on the queue length. In a batch service system, customers are served in groups following a general bulk service rule with the server operating between the minimum value ‘a’ and the maximum value ‘b’. But in certain situations, maintaining the same extreme values of the server is difficult, and it needs to be changed according to the service request. In this paper, server load balancing is introduced for a batch service queueing model, which is the capacity of the server that can be adjusted, either increased or decreased, based upon the service request by the customer. On service completion, if the service request is not enough to start any of the services, the server will be assigned to perform a secondary job (vacation). After vacation completion based upon the service request, the server will start regular service, overload or underload. Cloud computing using power BI can be analyzed based on server load balancing. The function that determines the probability of the queue size at any given time is derived for the specified queueing model using the supplementary variable technique with the remaining time as the supplementary variable. Additionally, various system characteristics are calculated and illustrated with suitable numerical examples. Full article
(This article belongs to the Special Issue Mathematical and Statistical Methods and Their Applications, 2nd Edition)
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