Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
1.9
Journals
Axioms
Special Issues
Mathematical and Statistical Methods and Their Applications, 2nd Edition
share announcement

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 1670

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

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue policies can be found here.

Related Special Issue

Published Papers (3 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

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
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)
►▼ Show Figures

Graphical abstract

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 307
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)
►▼ Show Figures

Figure 1

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 1 | Viewed by 727
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)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-3
Back to TopTop