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BAREKENG: Jurnal Ilmu Matematika dan Terapan
Published by Universitas Pattimura
ISSN : 19787227     EISSN : 26153017     DOI : https://search.crossref.org/?q=barekeng
Core Subject : Economy, Science, Education, Engineering,
Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation
BAREKENG: Jurnal ilmu Matematika dan Terapan is one of the scientific publication media, which publish the article related to the result of research or study in the field of Pure Mathematics and Applied Mathematics. Focus and scope of BAREKENG: Jurnal ilmu Matematika dan Terapan, as follows: - Pure Mathematics (analysis, algebra & number theory), - Applied Mathematics (Fuzzy, Artificial Neural Network, Mathematics Modeling & Simulation, Control & Optimization, Ethno-mathematics, etc.), - Statistics, - Actuarial Science, - Logic, - Geometry & Topology, - Numerical Analysis, - Mathematic Computation and - Mathematics Education. The meaning word of "BAREKENG" is one of the words from Moluccas language which means "Counting" or "Calculating". Counting is one of the main and fundamental activities in the field of Mathematics. Therefore we tried to promote the word "Barekeng" as the name of our scientific journal also to promote the culture of the Maluku Area. BAREKENG: Jurnal ilmu Matematika dan Terapan is published four (4) times a year in March, June, September and December, since 2020 and each issue consists of 15 articles. The first published since 2007 in printed version (p-ISSN: 1978-7227) and then in 2018 BAREKENG journal has published in online version (e-ISSN: 2615-3017) on website: (https://ojs3.unpatti.ac.id/index.php/barekeng/). This journal system is currently using OJS3.1.1.4 from PKP. BAREKENG: Jurnal ilmu Matematika dan Terapan has been nationally accredited at Level 3 (SINTA 3) since December 2018, based on the Direktur Jenderal Penguatan Riset dan Pengembangan, Kementerian Riset, Teknologi, dan Pendidikan Tinggi, Republik Indonesia, with Decree No. : 34 / E / KPT / 2018. In 2019, BAREKENG: Jurnal ilmu Matematika dan Terapan has been re-accredited by Direktur Jenderal Penguatan Riset dan Pengembangan, Kementerian Riset, Teknologi, dan Pendidikan Tinggi, Republik Indonesia and accredited in level 3 (SINTA 3), with Decree No.: 29 / E / KPT / 2019. BAREKENG: Jurnal ilmu Matematika dan Terapan was published by: Mathematics Department Faculty of Mathematics and Natural Sciences University of Pattimura Website: http://matematika.fmipa.unpatti.ac.id
Arjuna Subject : Matematika - Matematika Terapan
Articles 1,429 Documents
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THE EIGENVECTORS OF REDUCIBLE MATRICES OVER MIN-PLUS ALGEBRA Siswanto Siswanto; Riko Fajarudin
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp3151-3166

Abstract

The eigenvalues and the eigenvectors of a matrix are fundamental concepts in max-plus algebra, especially for square matrices. A communication graph is classified as strongly connected or not, corresponding to irreducible and reducible matrices, respectively. This study aims to develop methods for determining the eigenvectors of reducible matrices over min-plus algebra. Before determining the eigenvectors, we need to determine the eigenvalues. The methodology used is based on the Frobenius Normal Form and graph condensation to decompose the reducible matrix into spectral classes. The eigenvalues ​​can be found using the graphical method. Eigenvectors can be determined for each corresponding eigenvalue. Once the eigenvectors are known, we can find the set of eigenvectors as a map of a matrix. The main results include a characterization of eigenvector bases for each spectral class, criteria for the existence of finite eigenvectors, and an analysis of computational complexity. An isomorphic correspondence exists between min-plus algebra and max-plus algebra. Hence, the eigenvectors of reducible matrices over min-plus algebra are able to be evaluated according to a concept from eigenvectors of reducible matrices over max-plus algebra. This study is limited to min-plus algebra and does not extend to interval min-plus algebra.
MODELING AND ESTIMATING DYNAMIC CONTRACEPTIVE BEHAVIOR USING SPATIO-TEMPORAL PHYSICS-INFORMED NEURAL NETWORKS Lely Kurnia; Nor Azah Samat; Mira Meilisa
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp3167-3184

Abstract

This study develops a Spatio-Temporal Physics-Informed Neural Network (ST-PINN) framework to model contraceptive use dynamics in West Sumatra, Indonesia. Existing models often assume spatial homogeneity and time-invariant parameters, which limit their ability to reflect real-world regional disparities and temporal changes in contraceptive behavior. To address this limitation, this study proposes a hybrid modeling approach that integrates differential equation-based modeling with data-driven learning in a spatio-temporal framework. The proposed model estimates contraceptive adoption, success, and failure rates across 19 districts and cities from 2012 to 2024. This study contributes by (1) developing a spatio-temporal PINN framework for dynamic parameter estimation, (2) integrating spatial and temporal data into a mechanistic model, and (3) providing region-specific insights into contraceptive dynamics. The PINN model achieves high predictive accuracy, with RMSE values ranging from 0.04678 to 0.16132 and R² values exceeding 0.85 in several regions with stable data patterns. In contrast, the ST-PINN framework provides enhanced capability in capturing spatial heterogeneity and reveals distinct regional patterns, including consistently high adoption rates in the Mentawai Islands and notable post-2018 changes across multiple regions. However, performance variability across regions indicates the presence of unobserved local factors. These findings highlight the importance of incorporating spatial and temporal heterogeneity in demographic modeling and demonstrate the significance of the ST-PINN framework as a flexible and effective tool for capturing complex regional dynamics and supporting policy-relevant decision-making in reproductive health. Nevertheless, the absence of socio-economic and behavioral variables remains a limitation. Future research should integrate additional data sources to improve model robustness and interpretability.
ALGORITHM DESIGN OF ELGAMAL MAX-PLUS ALGEBRA FOR LETTER AND NUMBER CRYPTOGRAPHY WITH UNI-CUSTOM CIPHERTEXT Zumrotus Sya'diyah; Nur Salamah; Faradilla Alfiani
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp3185-3196

Abstract

This study focuses on the design and implementation of a prototype cryptographic algorithm using the integration of Uni-Custom ciphertext transformation and Max-Plus algebra in the ElGamal scheme. The integration is performed through a sequential process, where the Uni-Custom ciphertext transformation converts plaintext into a dynamic numeric form, and then we use the ElGamal max plus-based algorithm in the encryption process through a public-key mechanism. The primary objective of this research is to explore the feasibility and functional correctness of the proposed hybrid framework rather than to provide a complete cryptographic performance evaluation. The implementation results show that the system exhibits high computational and structural complexity. The security of the proposed system is associated with the hardness of the discrete logarithm problem in the ElGamal scheme, while additional transformation layers enhance variability and reduce pattern predictability. Experimental results show consistent reconstruction of the original message without data loss, indicating promising potential for the development of alternative cryptographic methods based on non-conventional mathematical structures.
MIXED-INTEGER QUADRATIC PROGRAMMING (MIQP) MODEL FOR THE OPTIMIZATION OF INTEGRATED FARMING SYSTEMS Lasker Pangarapan Sinaga; Rizky Habibi; Suviardi Panggabean
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp3197-3212

Abstract

This study develops a Mixed-Integer Quadratic Programming model to optimize resource allocation and profitability in integrated farming systems. The model links crop, livestock, and aquaculture components in a closed-loop framework that promotes internal resource use and reduces dependence on external inputs. Land productivity, labor, feed, fertilizer, and capital constraints are incorporated into a deterministic annual optimization model. A scenario-based case study for North Sumatra, Indonesia, is conducted using five commodities and three main resource categories. Sensitivity analysis across 243 scenarios varies price, productivity, input cost, feed cost, and capital parameters. The results show that the model identifies optimal land and labor allocations, improves permanent labor efficiency, and strengthens internal resource circulation. Profitability is most sensitive to commodity prices and productivity, while higher input and feed costs reduce system performance. Practically, the model can assist farmers, cooperatives, and local policymakers in evaluating allocation strategies and improving input efficiency. However, the study is limited by its deterministic structure, reliance on secondary data contextualized to North Sumatra, and single-year planning horizon, and it does not yet incorporate stochastic uncertainty or broader ecological and social objectives.
DIGRUNDY NUMBER OF DIRECTED STAR, BANANA TREE, FIREWORKS, AND COCONUT TREE GRAPHS Raventino Raventino; Fransiskus Fran
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp3213-3222

Abstract

A digrundy coloring of a graph is a vertex coloring in which every vertex assigned a higher color is adjacent to vertices assigned all smaller colors. The maximum number of colors that can be realized in such a coloring of an acyclic directed graph is called the digrundy number. This paper determines the digrundy numbers of several classes of acyclic directed graphs, namely directed star graphs, directed banana tree graphs, directed fireworks graphs, and directed coconut tree graphs. The analysis is based on structural properties of the graphs and combinatorial arguments derived from digrundy coloring constraints. The results show that the digrundy number of directed star graphs is under orientations where the central vertex satisfies and . For directed banana tree graphs with a specified orientation , the digrundy number is for and for . Under arbitrary orientations, directed fireworks graphs have digrundy number , while for directed coconut tree graphs , the digrundy number is bounded by These findings provide exact values of the digrundy number for the graph classes considered and highlight the role of structural constraints in governing digrundy coloring behavior.
DYNAMICAL ANALYSIS OF TWO LOAN CATEGORIES IN A BANKING SYSTEM WITH NON-PERFORMING LOANS Onik Febria Damayanti; Isnani Darti; Agus Suryanto; Nur Shofianah; Trisilowati Trisilowati
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp3223-3240

Abstract

The ability of banks to extend credit and meet their obligations to depositors can be significantly affected by the presence of non-performing loans (NPL). The intermediation process, in which deposits are transformed into loans, can be represented through a predator–prey modeling framework. In this study, we formulate and analyze a system of three nonlinear ordinary differential equations representing deposits as the prey and two categories of loans, individual loans and company loans, as predators within a single banking system. The model incorporates the effect of NPLs as factors that reduce effective loan performance and influence system interactions. The analytical results show that the system possesses five equilibrium points. The equilibrium corresponding to the absence of deposits and loans is unstable, while the remaining four equilibria are globally asymptotically stable under specific parameter conditions, particularly those related to loan growth rates and NPL levels. The stability analysis indicates that higher NPL rates tend to reduce the stability region of equilibria and may destabilize the banking system. Furthermore, numerical simulations are conducted to support and illustrate the analytical findings. These results provide insight into the long-term dynamic behavior of deposits and loans, emphasizing the role of NPLs in determining banking system stability.
VECTOR AUTOREGRESSION AND MULTIRESPONSE REGRESSION APPROACHES FOR MODELING GOLD, TIN, AND NICKEL PRICES Suliyanto Suliyanto; Dita Amelia; Gabriella Agnes Budijono; Rere Fetri Damanik
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp3241-3258

Abstract

The mining sector plays a strategic role in the global economy, especially during periods of high economic uncertainty. Between 2020 and 2024, global markets experienced severe volatility due to the COVID-19 pandemic, geopolitical tensions, energy price shocks, and monetary policy tightening. These conditions intensified price fluctuations in major mining commodities such as nickel, gold, and tin. However, limited empirical research has compared different multivariate modeling approaches for analyzing commodity price dynamics during this volatile period. This study examines the dynamic relationships between nickel, gold, and tin prices and key global factors, namely crude oil prices, the USD exchange rate, and silver prices, using monthly data from January 2020 to December 2024. The VAR model captures temporal interdependencies among variables, while the MRR model examines simultaneous relationships among multivariate response variables. The stationarity and cointegration tests show that all variables become stationary after first differencing and exhibit no long-term equilibrium relationship. The Impulse Response Function (IRF) and Variance Decomposition (VDC) analyses reveal that fluctuations in nickel, gold, and tin prices are primarily driven by their own past values, with minor cross-commodity effects. The MRR results indicate that crude oil and silver prices significantly influence metal price variations, while the USD exchange rate has the strongest overall effect. The comparison across three evaluation metrics shows that the MRR model provides better predictive performance than the VAR model. The MRR model yields higher R² than VAR, which records R² of 0.339, 0.584, and 0.529, with MAPE up to 22.42%. The results demonstrate that the MRR model consistently outperforms the VAR model, providing stronger explanatory power and higher predictive accuracy. These findings highlight the added methodological value of comparing VAR and MRR models and offer practical insights for investors, industry stakeholders, and policymakers in managing commodity price risk under volatile economic conditions.
MULTILEVEL ITEM RESPONSE THEORY MODEL USING MML-GHQ METHOD FOR HIERARCHICAL DATA Alona Dwinata; Anang Kurnia; Aji Hamim Wigena; Muhammad Nur Aidi
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp3259-3270

Abstract

Hierarchical item response data require a multilevel approach to capture the diversity of respondent abilities and item characteristics by separating variations between examinees and schools to make item parameter and ability estimates more precise. This study aims to develop a two-parameter logistic multilevel item response theory (MIRT 2PL) model, employing the maximum marginal likelihood method with Gauss-Hermite quadrature (MML-GHQ) to estimate the rank order of examinees’ abilities. This study specifically investigates the efficiency and accuracy of the MIRT 2PL model with MML-GHQ to predict the ability rankings of examinees. The research incorporates both simulated and empirical data. The simulation study generated item response data under a two-level hierarchical structure, where examinees were nested within schools. The population consisted of 50 schools, with 20–30 students per school and five items. Each examinee’s ability was modelled as a combination of school-level and individual-level effects, under two conditions of school variability: high (τ = 1.2) and low (τ = 0.6). Random samples were drawn from the population, and the sampling process was repeated 10 times to assess consistency. The analysis included estimating item parameters, variance components, and examinees’ abilities using the EAP approach. Model performance was evaluated using RMSE, Spearman correlation, and computation time. Results indicated that MML-GHQ produced accurate and consistent rank estimates, particularly under high school variability. Using PISA data, increasing the number of schools, students, and items in the empirical data yielded results consistent with the simulation study. In conclusion, the MIRT 2PL model with MML-GHQ offers an effective and efficient alternative for estimating ability rankings in hierarchical item response data.
PERFORMANCE COMPARISON OF MISSFOREST AND MICE IN HANDLING MISSING CATEGORICAL DATA Nurhidayah Nurhidayah; Kusman Sadik; Aji Hamim Wigena
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp3271-3282

Abstract

Missing data represent a common challenge in statistical modeling and can substantially reduce the performance of classification algorithms. This study examines the impact of missing values on the performance of the XGBoost model by considering different proportions of missingness (50% and 75%) and various combinations of affected variables under the Missing Completely at Random (MCAR) and Missing at Random (MAR) mechanisms. Two imputation methods, MissForest and Multiple imputation by chained equations (MICE), were compared with a baseline model without imputation. The analysis of variance revealed that the interaction between imputation method, missing data proportion, and variable combinations had a significant effect on accuracy and specificity, while sensitivity remained relatively stable across scenarios. Tukey tests confirmed that MissForest consistently outperformed the other approaches, producing the highest accuracy and specificity, especially at 50% missingness with three variables affected. Moreover, the evaluation of categorical distributions before and after imputation indicated that MissForest better preserved category balance compared to MICE. These findings highlight that the performance of imputation methods strongly depends on the characteristics of missing data. Overall, MissForest demonstrated clear superiority in handling missing categorical data, maintaining distributional integrity while enhancing the classification performance of the XGBoost model. This study advances statistical learning by giving empirical evidence and practical tips for choosing strong imputation strategies in categorical datasets. This improves the reliability of predictive modeling when data is missing.
MATHEMATICAL MODELLING AND OPTIMAL CONTROL ANALYSIS OF TRIPLE-INTERVENTION STRATEGIES FOR SCHISTOSOMIASIS MANAGEMENT IN ENDEMIC REGIONS Afolabi Ayodeji Sunday; Josiah Chukwuebuka Orji
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp3283-3306

Abstract

Schistosomiasis remains a significant public health challenge, affecting approximately 250 million people globally, particularly in endemic regions of sub-Saharan Africa. The disease is sustained through a complex transmission cycle involving freshwater, snails and human-water contact. Although Mass Drug Administration (MDA) with praziquantel remains the cornerstone of the control efforts, rapid reinfection often limits its long-term effectiveness. In this study, we develop a novel nonlinear compartmental model that couples human and snail dynamics while incorporating three time-dependent control measures: MDA, mollusciciding for snail reduction, and water-contact reduction to reduce human-water contact. We apply Pontryagin’s Maximum Principle to derive optimal strategies and simulate four intervention combinations. Our results reveal that while single or dual interventions moderately reduce transmission, the triple-intervention strategy most effectively suppresses both human and snail infections. Crucially, we extend the analysis by evaluating the cost-effectiveness of each strategy using metrics such as the IAR, ACER, and ICER. Findings indicate that the integrated approach not only maximizes health benefits but it is also economically justified, with some strategies demonstrating cost savings alongside epidemiological gains.

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