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Jurnal Matematika
Published by Universitas Udayana
ISSN : 16931394     EISSN : 26550016     DOI : https://doi.org/10.24843/JMAT
Core Subject : Education,
Mathematics
This journal encompasses original research articles, review articles, and case studies, including those in Mathematics and Its Application. Scope of Journal: Analysis, algebra, topology, graph, approach of numerical simulation, also known as numerical analysis, optimum controls, queuing issues, optimization, finance, biomatematics, industrial mathematics, financial mathematics, and others.
Arjuna Subject : Matematika - Matematika (Lain-Lain)
Articles 13 Documents
 1   2 
Kontrol Optimal untuk Model SIR Campak dengan Imunisasi Menggunakan Prinsip Minimum Pontryagin Dhea Wasila Rahmi; Elyin Fitrawati; Amilia Ulul Azmi; Bulqis Nebulla Syechah; Tri Maryono Rusadi
Jurnal Matematika Vol. 16 No. 1 (2026)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Science, Udayana University Gedung UKM, Ruang UKM 8 Lt 1, Kampus Bukit Jimbaran, Badung-Bali.

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/JMAT.2026.v16.i01.p197

Abstract

Measles is a contagious disease that continues to affect a significant portion of the population, particularly infants and children. The disease can be prevented through immunization programs, including both basic and booster immunizations, which are part of government public health initiatives. This study aims to reduce the spread of measles while minimizing immunization costs by incorporating a control variable into the SIR (Susceptible–Infected–Recovered) model of disease transmission. The method employed is Pontryagin’s Minimum Principle to determine the optimal immunization strategy that is both effective and cost-efficient. The results indicate that the inclusion of an immunization control in the model significantly decreases the susceptible population and reduces the growth rate of the infected compartment. Furthermore, the recovered population increases more rapidly compared to the model without control. The proportion of the immunized population demonstrates that a more optimal control strategy leads to greater effectiveness in suppressing disease transmission. Therefore, the application of optimal control in the SIR model provides a valuable mathematical framework to support immunization policies for measles prevention and control.
Hotelling’s T² Control Chart for Monitoring Correlated Wine Quality in Small-Scale Production Alfred Ayo Ayenigba; Deborah Ayomide Adegboye; Dorcas Omobola Folarin; James Serumun Ivande
Jurnal Matematika Vol. 16 No. 1 (2026)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Science, Udayana University Gedung UKM, Ruang UKM 8 Lt 1, Kampus Bukit Jimbaran, Badung-Bali.

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/JMAT.2026.v16.i01.p198

Abstract

This research papers investigates the use of Hotelling's T² control charts for monitoring correlated quality features in a small-scale wine production process with small samples. Analysis of physicochemical data obtained from 50 red wine samples (fixed acidity, volatile acidity, alcohol content, residual sugar) for multivariate process stability demonstration and comparison made to standard univariate Shewhart charts. The correlation analysis exhibited significant relationships, including a relatively high, positive correlation between alcohol and residual sugar (r = 0.668) and a moderate negative correlation of fixed and volatile acidity (r = -0.435). Hotelling’s T² charts reveal four out-of-control samples, while univariate charts only detect two, failing to recognise coordinated multivariate deviations. The T² chart signals a 40 action detection with no monitoring of univariate charts by signals under the coordinated 1.5sigma shift simulated. The sample-to-variable ratio of 12.5:1 supported robust covariance estimation. The results show that Hotelling's T² has greater sensitivity to joint process deviations, provides control of inflated family-wise error rates, and gives actionable diagnostic information. This framework provides small wine producers with a practical and data-based approach for enhancing product consistency and enabling early detection of multivariate deviations, even with limited production data.
Convergence Analysis of Function Approximation: From Classical Polynomials to Neural Networks Ekhlas Annon Mousa
Jurnal Matematika Vol. 16 No. 1 (2026)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Science, Udayana University Gedung UKM, Ruang UKM 8 Lt 1, Kampus Bukit Jimbaran, Badung-Bali.

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/JMAT.2026.v16.i01.p199

Abstract

Function approximation lies at the boundary between classical analysis and modern computing, although the literature tends to consider its classical and modern branches as independent. In this paper, we propose that polynomial neural networks with a single hidden layer, methods, and Hilbert space projections are not only identical but also share a fundamental structure that can be explicitly expressed. We revisit Weiserstrasse and Bernstein's probabilistic construction theories, develop a Hilbert space projection framework, and investigate numerical problems such as node positioning and least-squares stability. All these lines converge in a discussion of Sybenko's theory of total approximation, which can be read as a classical result rather than a break from it. Numerical experiments on the Fourier square wave reconstruction and the Fourier square wave reconstruction are accompanied by theoretical development on . There is an error and stability at which the paper concludes. The analysis can be applied to all three approximation models.

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