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Mathematics
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Mathematical Modelling and Applied Statistics
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Mathematical Modelling and Applied Statistics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D1: Probability and Statistics".

Deadline for manuscript submissions: 31 July 2026 | Viewed by 4080

Special Issue Editor

Dr. Helena Sofia Rodrigues

E-Mail Website
Guest Editor
1. Applied Digital Transformation Laboratory (ADiT-Lab), Polytechnic Institute of Viana do Castelo, Viana do Castelo, Portugal
2. Center for Research & Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, Aveiro, Portugal
Interests: optimal control; nonlinear optimization; mathematical modelling; biomathematics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The Special Issue is dedicated to advancing research at the intersection of mathematical theory and practical applications across various scientific and engineering disciplines. It serves as a platform for the dissemination of innovative methodologies, theoretical advancements, and real-world applications of mathematical modeling and statistical analysis. We welcome high-quality original research, review articles, and case studies that contribute to the development, validation, and application of mathematical and statistical techniques in diverse fields such as physics, engineering, biology, economics, finance, social sciences, and data science.

Dr. Helena Sofia Rodrigues
Guest Editor

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Keywords

  • mathematical modeling
  • applied statistics
  • interdisciplinary applications

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Published Papers (3 papers)

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Research

39 pages, 1089 KB  
Article
Generalized Kinematic Modeling of Wheeled Mobile Robots: A Unified Framework for Heterogeneous Architectures
by Jesús Said Pantoja-García, Alejandro Rodríguez-Molina, Miguel Gabriel Villarreal-Cervantes, Andrés Abraham Palma-Huerta, Mario Aldape-Pérez and Jacobo Sandoval-Gutiérrez
Mathematics 2026, 14(3), 415; https://doi.org/10.3390/math14030415 - 25 Jan 2026
Cited by 1 | Viewed by 1080
Abstract
The increasing heterogeneity of wheeled mobile robot (WMR) architectures, including differential-drive, Ackermann, omnidirectional, and reconfigurable platforms, poses a major challenge for defining a unified, scalable kinematic representation. Most existing formulations are tailored to specific mechanical layouts, limiting analytical coherence, cross-platform interoperability, and the [...] Read more.
The increasing heterogeneity of wheeled mobile robot (WMR) architectures, including differential-drive, Ackermann, omnidirectional, and reconfigurable platforms, poses a major challenge for defining a unified, scalable kinematic representation. Most existing formulations are tailored to specific mechanical layouts, limiting analytical coherence, cross-platform interoperability, and the systematic reuse of modeling, odometry, and motion-related algorithms. This work introduces a generalized kinematic modeling framework that provides a mathematically consistent formulation applicable to arbitrary WMR configurations. Wheel–ground velocity relationships and non-holonomic constraints are expressed through a concise vector formulation that maps wheel motions to chassis velocities, ensuring consistency with established models while remaining independent of the underlying mechanical structure. A parameterized wheel descriptor encodes all relevant geometric and kinematic properties, enabling the modular assembly of complete robot models by aggregating wheel-level relations. The framework is evaluated through numerical simulations on four structurally distinct platforms: differential-drive, Ackermann, three-wheel omnidirectional (3, 0), and 4WD. Results show that the proposed formulation accurately reproduces the expected kinematic behavior across these fundamentally different architectures and provides a coherent and consistent representation of their motion. The unified representation further provides a common kinematic backbone that is directly compatible with odometry, motion-control, and simulation pipelines, facilitating the systematic retargeting of algorithms across heterogeneous robot platforms without architecture-specific reformulation. Additional simulation studies under realistic physics-based conditions show that the proposed formulation preserves coherent kinematic behavior during complex trajectory execution and supports the explicit incorporation of geometric imperfections, such as wheel mounting misalignments, when such parameters are available. By consolidating traditionally separate derivations into a single coherent formulation, this work establishes a rigorous, scalable, and architecture-agnostic foundation for unified kinematic modeling of wheeled mobile robots, with particular relevance for modular, reconfigurable, and cross-architecture robotic systems. Full article
(This article belongs to the Special Issue Mathematical Modelling and Applied Statistics)
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19 pages, 560 KB  
Article
Modeling PM2.5 Pollution Using a Truncated Positive Student’s-t Distribution: A Case Study in Chile
by Héctor J. Gómez, Karol I. Santoro, Diego I. Gallardo, Paola E. Leal and Tiago M. Magalhães
Mathematics 2025, 13(23), 3838; https://doi.org/10.3390/math13233838 - 30 Nov 2025
Viewed by 466
Abstract
This study revisits a recently proposed member of the truncated positive family of distributions, referred to as the positively truncated Student’s-t distribution. The distribution retains the structure of the classical Student’s-t distribution while explicitly incorporating a kurtosis parameter, yielding a flexible three-parameter formulation [...] Read more.
This study revisits a recently proposed member of the truncated positive family of distributions, referred to as the positively truncated Student’s-t distribution. The distribution retains the structure of the classical Student’s-t distribution while explicitly incorporating a kurtosis parameter, yielding a flexible three-parameter formulation that governs location, scale, and tail behavior. A closed-form quantile function is derived, allowing a novel reparameterization based on the pth quantile and thereby facilitating integration into quantile regression models. The analytical tractability of the quantile function also enables efficient random number generation via the inverse transform method, which supports a comprehensive simulation study demonstrating the strong performance of the proposed estimators, particularly for the degrees-of-freedom parameter. The entire methodology is implemented in the tpn package for the R software. Finally, two real-data applications involving PM2.5 measurements—one without covariates and another with covariates—highlight the model’s robustness and its ability to capture heavy-tailed behavior. Full article
(This article belongs to the Special Issue Mathematical Modelling and Applied Statistics)
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24 pages, 7349 KB  
Article
Return Level Prediction with a New Mixture Extreme Value Model
by Emrah Altun, Hana N. Alqifari and Kadir Söyler
Mathematics 2025, 13(17), 2705; https://doi.org/10.3390/math13172705 - 22 Aug 2025
Viewed by 1222
Abstract
The generalized Pareto distribution is frequently used for modeling extreme values above an appropriate threshold level. Since the process of determining the appropriate threshold value is difficult, a mixture of extreme value models rises to prominence. In this study, mixture extreme value models [...] Read more.
The generalized Pareto distribution is frequently used for modeling extreme values above an appropriate threshold level. Since the process of determining the appropriate threshold value is difficult, a mixture of extreme value models rises to prominence. In this study, mixture extreme value models based on exponentiated Pareto distribution are proposed. The Weibull, gamma, and log-normal models are used as bulk densities. The parameter estimates of the proposed models are obtained using the maximum likelihood approach. Two different approaches based on maximization of the log-likelihood and Kolmogorov–Smirnov p-value are used to determine the appropriate threshold value. The effectiveness of these methods is compared using simulation studies. The proposed models are compared with other mixture models through an application study on earthquake data. The GammaEP web application is developed to ensure the reproducibility of the results and the usability of the proposed model. Full article
(This article belongs to the Special Issue Mathematical Modelling and Applied Statistics)
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