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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 1,369 Documents
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A MATHEMATICAL MODEL OF DIPHTHERIA TRANSMISSION DYNAMICS WITH HETEROGENEOUS SUSCEPTIBILITY Mohamad Tafrikan; Fatmawati Fatmawati; Windarto Windarto; Chinwendu E. Madubueze
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 3 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss3pp1967-1984

Abstract

Despite the availability of vaccines, diphtheria continues to pose a public health risk in Indonesia due to uneven vaccination coverage across regions. Previous models have not distinguished between highly susceptible (unvaccinated) and susceptible (vaccinated) populations, nor have they been calibrated with actual Indonesian epidemiological data. To address this gap, this study develops a five-compartment diphtheria transmission model: Highly susceptible (unvaccinated)-Susceptible (vaccinated)-Exposed-Infectious-Recovered (S_1 S_2 EIR), which incorporates two levels of susceptibility based on vaccination status, using empirical diphtheria case data in Indonesia from 2012 to 2023. The analysis begins by proving the positivity, boundedness, and uniqueness of solutions, followed by the calculation of the basic reproduction number using the Next-Generation Matrix method. The analysis shows that the disease-free equilibrium (DFE) is locally and globally asymptotically stable when R₀<1, while the endemic equilibrium (EE) is globally stable when R₀>1. Simulations indicate that the interaction parameter for the unvaccinated group η₁, strongly accelerates epidemic growth, leading to a higher and earlier infection peak, whereas increased vaccination coverage and recovery rates effectively suppress transmission. This model can be used because the Mean Absolute Percentage Error (MAPE) between the data and the model solution for diphtheria cases in Indonesia is 8.77%. These results highlight the importance of interventions focused on highly susceptible groups to prevent more severe outbreaks. Therefore, this study is significant in strengthening the theoretical understanding of diphtheria transmission, while also providing data-driven insights as recommendations for policymakers to implement effective and efficient outbreak control measures.
MIXED-EFFECT MODELS WITH RESTRICTED MAXIMUM LIKELIHOOD (REML), BOOT-STRAPPED REML AND BAYESIAN INFERENCE IN APPLICATION OF GAPMINDER DATA Asysta Amalia Pasaribu; Kusman Sadik; Anang Kurnia
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 3 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss3pp1985-1998

Abstract

Mixed effects model combines fixed effects and random effects, allowing for the analysis of data with both fixed and random variations. This modeling approach is widely utilized across various fields. In R, the lme4 package is commonly employed to estimate mixed effects models using Restricted Maximum Likelihood (REML). There are several methods for estimating model parameters, including Bayesian inference, which has gained prominence with ongoing research advancements. Bayesian inference using Markov Chain Monte Carlo (MCMC) is among the most widely used Bayesian methods. Bayesian inference leverages probabilistic distributions to estimate parameters.to understand the general overview of life expectancy, serving as an indicator of survival time across different continents in the Gapminder dataset, it's essential to identify relevant variables after computing mixed effects predictions using Maximum Likelihood and REML estimation. This involves predicting life expectancy by integrating both random and fixed effects, determining relevant variables after estimating the Mixed Effects Model using REML Bootstrap estimation, and identifying influential variables after estimating the Mixed Effects Model using Bayesian MCMC inference. The methods employed include REML, Bootstrapped-REML, and Bayesian MCMC. The results indicate that all inference methods can be utilized to estimate parameters, with all predictor variables influencing life expectancy, except for the population variable. Further research is recommended to utilize data with more complex predictor variables.
LAPLACE TRANSFORMATION AND MITTAG-LEFFLER FUNCTION FOR THE SOLUTION OF DAMPED OSCILLATOR EQUATION WITH FRACTIONAL ORDER Gusrian Putra; Meysi Supmawati; Lutfi Mardianto
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 3 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss3pp1999-2008

Abstract

Fractional calculus has emerged as an active area of research due to its ability to model complex dynamical systems with memory effects and anomalous diffusion. In particular, the Mittag–Leffler function plays a fundamental role in solving fractional differential equations. This study aims to derive the analytical solution of the Linear Fractionally Damped Oscillator using the Laplace transform and the Mittag–Leffler function, where the derivative is of Caputo type with order 0<α<1. We further extend the analysis to both homogeneous and nonhomogeneous models, the latter corresponding to the presence of an external forcing term. The results indicate that the oscillatory behavior exhibits algebraic decay and eventual convergence due to damping or dissipation effects. The decay rate is directly influenced by the asymptotic properties of the Mittag–Leffler function, which depend on the fractional order α. These findings provide a deeper understanding of fractional-order damped oscillatory systems and offer a more generalized framework for analyzing dissipative processes in engineering, physics, and control systems.
MULTIVARIATE ROBUST MONITORING OF PLASTIC WASTE QUALITY USING PCA-BAYESIAN MEWMA CONTROL CHART Agis Wahyu Lestari; Ani Budi Astuti; Suci Astutik
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 3 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss3pp2009-2026

Abstract

Quality control is essential for ensuring manufacturing processes consistently meet predefined specifications and for minimizing the risks caused by process deviations. The MEWMA control chart is widely used for detecting small shifts in multivariate processes which does not require strict multivariate normality but the performance can be compromised when data contain outliers or high multicollinearity that commonly found in plastic waste processing. This study proposes a robust monitoring approach by integrating PCA to address multicollinearity, Bayesian estimation to improve parameter robustness. The four charts examined in this study are PCA-Bayesian MEWMA (SELF), PCA-Bayesian MEWMA (MSELF), PCA-Bayesian MEWMA (KLF), and PCA-MEWMA using Bootstrap control limit as comparison. These charts are evaluated across 324 simulated scenarios, varying in collinearity levels (0.2, 0.6, 0.95), sample sizes (10, 20, 30), outlier proportions (5%, 10%, 15%), and smoothing parameters (λ = 0.2, 0.5, 0.8). Performance is measured using Average Run Length (ARL), Standard Deviation of Run Length (SDRL), Median Run Length (MRL), and False Alarm Rate (FAR). Results indicate that the PCA-Bayesian MEWMA outperformed PCA-MEWMA using Bootstrap control limit. PCA-Bayesian MEWMA (SELF) excelled under clean data condition, whereas PCA-Bayesian (MSELF) provided stable detection under high correlation, moderate-to-high outlier contamination, and larger smoothing parameters, achieving an average ARL of 3.44, an SDRL of 0.58, an MRL of 3.46, and FAR of 0.03, making it well-suited for monitoring complex industrial plastic waste processes and demonstrating its effectiveness for robust quality monitoring in production.
A STUDY ON THE APPLICABILITY OF TRAPEZOIDAL FUZZY AHP WITH FEATURE SELECTION: THE CASE OF SKSS SCHOLARSHIP RECIPIENTS AT BAZNAS EAST JAVA Syamil Waris Dien Muhammad; Abdulloh Hamid; Hani Khaulasari; Dian Candra Rini Novitasari; Moh Hafiyusholeh
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 3 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss3pp2027-2044

Abstract

The One Family One Graduate (SKSS) scholarship program, managed by BAZNAS East Java, aims to alleviate the financial burden of higher education for underprivileged communities. However, the absence of clearly defined weights for each selection criterion may lead to unfairness in the selection process. This study aims to determine the objective weights of each criterion and to rank prospective scholarship recipients using the Trapezoidal Fuzzy AHP approach. The data were obtained from 78 scholarship applicants for the 2024 SKSS period and from questionnaires completed by three expert respondents (expert judgment). Feature selection was conducted to identify the most relevant criteria, resulting in 13 selected variables are tuition fee per semester (K₁), father's latest education level (K₂), father's income (K₃), mother's latest education level (K₄), mother's income (K₅), house size (K₆), amount of family installments (K₇), number of parental dependents (K₈), income of working family members (K₉), type of transportation used to campus (K₁₀), distance from home to campus (K₁₁), monthly allowance (K₁₂), and monthly income if the student is working (K₁₃). The results show that the criterion with the highest weight is tuition fee per semester (0.139142), while the lowest is Type of transportation to campus (0.059970). The highest priority subject is Subject 74 (S_74) with a total weight of 0.7964, whereas Subject 23 (S_23) ranks lowest with a total weight of 0.7723. These findings are expected to enhance the objectivity and fairness of the SKSS scholarship selection process.
FORECASTING SEA LEVEL CHANGES USING HYBRID ARIMA-RADIAL BASIS FUNCTION NEURAL NETWORK METHODS Soehardjoepri Djoepri; Ulil Azmi; Prilyandari Dina Saputri; Moch. Taufik Hakiki; Denisha A. E. Ananda; Roslinazairimah Zakaria
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 3 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss3pp2045-2062

Abstract

Understanding sea level variability is crucial for ensuring the safety of tourists, particularly in marine tourism areas like Marina Ancol Beach in North Jakarta. Climate change has led to rising sea levels, significantly impacting coastal regions. Accurate predictions of sea level are essential for anticipating tidal flooding, which occurs when seawater inundates these areas. Short-term sea level fluctuations are influenced by both linear tidal patterns and nonlinear local effects, making accurate forecasting challenging when using a single modeling approach. This study proposes a hybrid forecasting method that combines the Autoregressive Integrated Moving Average (ARIMA) model to capture linear temporal structures and a Radial Basis Function Neural Network (RBFNN) to model nonlinear patterns present in the residuals. Hourly sea level data consisting of 17,520 observations collected from January 2021 to December 2022 were analyzed. The proposed hybrid ARIMA–RBFNN model achieved a Mean Absolute Percentage Error (MAPE) of 2.74%, slightly outperforming the ARIMA model, which yielded a MAPE of 2.76%. The model provides accurate 24-hour sea level forecasts for Marina Ancol Beach, offering timely information that can support local authorities in anticipating and mitigating tidal flooding events.
THE EXPLICIT FORMULAS OF PARAMETRIZATION OF COADJOINT ORBITS OF THE HEISENBERG LIE GROUP Muhammad Zaky Zachary; Edi Kurniadi; Sisilia Sylviani
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 3 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss3pp2063-2074

Abstract

This research focuses on the Heisenberg Lie group. The aim is to determine the coadjoint orbits and their parametrizations. The method used in this research involves constructing the parametrization of coadjoint orbit for Heisenberg Lie group corresponding to the Heisenberg Lie algebra of dimension 2n+1. Furthermore, the obtained results are specialized to the cases of n=1, 2, and 3 which correspond to the Heisenberg Lie algebras of dimensions 3, 5, and 7. The main results are the explicit formulas of coadjoint orbits for the Heisenberg Lie group H_1, H_2, and H_3 which are expressed by the equations (〖Ad〗^* H_1 ) l_(α,β,γ)={l_(α^',β^',γ^' ):α^',β^',γ^'∈R}, (〖Ad〗^* H_2 ) l_(α,β,γ)={l_(α^',β^',γ^' ):α^',β^'∈R^2,γ^'∈R}, and (〖Ad〗^* H_3 ) l_(α,β,γ)={l_(α^',β^',γ^' ):α^',β^'∈R^3,γ^'∈R}. In addition, their associated parametrizations are given by the explicit formulas ψ(γZ^*,u)=∑_(i=1)^n▒(u_i X_i^*+u_(n+i) Y_i^* ) +γZ^* for n=1, 2, and 3. As a further study, various types of Lie groups can be explored to determine coadjoint orbits and their parametrization. Two Lie groups that are interesting to investigate further regarding their coadjoint orbits and parametrization are the diamond and Jacobi groups.
SOME PROPERTIES OF N-INTEGRAL ON SET-VALUED FUNCTIONS Corina Karim; Cornelia Yosefine Halim
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 3 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss3pp2075-2084

Abstract

The Upper and Lower N-integrals were introduced in 2019 based on the concept of δ-fine partitions, which also underlies the Henstock–Kurzweil integral. While the integration of set-valued functions was initially developed through measure-theoretic approaches, later studies extended the Henstock–Kurzweil integral to the set-valued setting and compared it with measure-based integrals. In this paper, we study the N-integral for set-valued functions within this framework. We prove that the N-integral satisfies fundamental properties such as boundedness and linearity, and we establish conditions under which it coincides with the Henstock–Kurzweil integral. Our results extend and complement several earlier results on the integration of set-valued functions and Henstock–Kurzweil-type integrals.
DEVELOPMENT STUDY OF GLMM-GEE-TREE REGRESSION MODELLING FOR BETA DISTRIBUTION RESPONSE DATA (IMPLICATIONS OF GINI RATIO MODELING IN INDONESIA, 2018-2024) Pardomuan Robinson Sihombing; Erfiani Erfiani; Khairil Anwar Notodiputro; Anang Kurnia
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 3 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss3pp2085-2098

Abstract

Economic inequality remains one of the most persistent challenges faced by Indonesia as a developing country. Previous studies have predominantly employed conventional models such as Ordinary Least Squares (OLS) or Panel Least Squares. However, these models are often inappropriate, as they fail to account for the bounded nature of inequality indices such as the Gini ratio, which ranges between 0 and 1. Beta regression offers a more appropriate alternative. In the context of panel data, Generalized Linear Mixed Models (GLMM) and Generalized Estimating Equations (GEE) are commonly used to handle correlated data; however, their integration with nonlinear models for longitudinal Beta-distributed responses remains limited. This study proposes a novel GLMM-GEE-Tree modeling approach for Beta-distributed response data. The proposed model combines GLMM (to capture individual random effects), GEE (to handle temporal correlation and provide robust marginal estimates), and Regression Trees (to address nonlinear relationships and complex interactions). The aim is to simultaneously tackle the challenges of proportional responses, panel structure, random effects, correlation, and nonlinearity. Empirical validation uses Gini ratio data from 34 Indonesian provinces spanning 2018 to 2024. The findings reveal that in this empirical data, the GLMM-GEE-Tree model outperforms alternative models, achieving an R² of 0.472 and a QIC of 13.435 and yielding the lowest AIC and BIC values.
BETA REGRESSION MODELING ON POVERTY DATA IN INDONESIA 2019 - 2022 Muhammad Arib Alwansyah; Sigit Nugroho; Ramya Rachmawati
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 3 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss3pp2099-2116

Abstract

The Central Statistics Agency (BPS) reported that the percentage of poor people in Indonesia increased from 2019 to 2021, reaching 10.14 percent. This condition highlights the need for an analytical approach capable of accurately modeling percentage data that are naturally bounded between 0 and 1. This study introduces a new approach by applying the Beta regression model to analyze the factors influencing poverty levels across Indonesian provinces. The novelty of this research lies in the application of the Beta regression model to panel data on poverty, which remains rarely explored in empirical studies on Indonesia’s socio-economic indicators. The model was chosen because it provides more efficient and unbiased parameter estimates than the ordinary least squares (OLS) method, especially when the dependent variable exhibits asymmetry and heteroskedasticity. Parameter estimation was conducted using the Maximum Likelihood Estimation (MLE) method with the Newton–Raphson iterative algorithm to ensure convergence and estimation efficiency. The data used in this study are provincial-level poverty data sourced from official publications by the BPS. The analysis results indicate that the model meets the model suitability criteria for 2019 and 2020. Factors that significantly influenced the percentage of poor people in both years included the percentage of the population with health insurance and the literacy rate. Meanwhile, in 2021 and 2022, factors that significantly influenced the percentage of the poor population included the average years of schooling, the percentage of the population with health insurance, and the literacy rate. This study contributes to the field of applied statistics by demonstrating that the Beta regression model offers a novel and robust alternative for analyzing bounded and asymmetric socio-economic data. Furthermore, it provides new empirical insights into the statistical modeling of poverty in Indonesia, offering a methodological advancement over traditional regression approaches.

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