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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 1,248 Documents
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FORECASTING INDONESIA COMPOSITE INDEX USING HYBRID AUTOREGRESSIVE INTEGRATED MOVING AVERAGE-DOUBLE RANDOM FOREST MODEL Ratnasari, Andika Putri; Yuli Arini, Luthfia Hanun
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0573-0584

Abstract

Modeling time series data using autoregressive integrated moving average (ARIMA) has been widely discussed. However, this has limitations in that it can only handle linear data. Machine learning is one of the alternative approaches that can solve this limitation since this method can handle nonlinear cases. Double random forest (DRF) is considered a supervised learning method that can solve regression problems. This research provides a novel hybrid forecasting framework combining ARIMA and DRF, designed to model both linear and nonlinear behaviors, and provide more accurate predictions for volatile financial data like the Indonesia Composite Index (ICI). Previous studies have not examined the performance of the hybrid ARIMA-DRF model. In this study, the performance of ARIMA, DRF, and the hybrid ARIMA-DRF models is compared using ICI data obtained from Bank Indonesia’s website. ICI has nonstationary and nonlinear characteristics. This made the ICI data suitable to be modeled using the hybrid ARIMA-DRF model. The comparison results indicate that the hybrid ARIMA-DRF model outperforms the independent ARIMA and DRF models, with a value of its mean absolute percentage error is 4.17%. Therefore, forecasting the future value of ICI data was done by using a hybrid ARIMA-DRF model with forecasting periods from October 2023 to September 2024. The forecasting results show that ICI values fluctuate over the forecasting periods, hence the authority might use the pattern to predict the ICI behaviors and take further decisions. While the forecasting results offer valuable insights for decision-making, this study has limitations as it does not incorporate external macroeconomic variables that may influence ICI behavior.
SEIRS MATHEMATICAL MODEL FOR ANALYZING THE SPREAD AND PERSISTENCE OF GADGET ADDICTION IN ELEMENTARY SCHOOL CHILDREN Panjaitan, Dedy Juliandri; Siregar, Annisa Fadhillah Putri; Sapta, Andy; Aprilia, Rima
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0585-0602

Abstract

Gadget addiction among elementary school-aged children has become a serious concern, especially with the increasing screen time that potentially disrupts learning focus, social interaction, and emotional development. Despite various efforts to control gadget usage, many schools and parents struggle to monitor and predict addiction trends effectively. This gap highlights the need for a structured approach to analyze and predict the spread of gadget addiction. Therefore, this study aims to model the dynamics of gadget addiction using the SEIRS (Susceptible-Exposed-Infected-Recovered-Susceptible) mathematical model. Data were collected through questionnaires to categorize individuals into susceptible (S), exposed (E), addicted (I), and recovered (R) groups. The model was numerically solved using the 5th-order Runge-Kutta method in MATLAB. Simulation results show a decrease in the susceptible group over time, an initial increase and eventual decline in exposed and addicted individuals, and a steady increase in the recovered group, with possible relapse into susceptibility. The analysis reveals that gadget addiction is likely to persist when the basic reproduction number exceeds a critical threshold, signifying the potential for long-term behavioral entrenchment. Sensitivity analysis indicates that the dynamics of gadget addiction are strongly influenced by the rate of peer interaction and the speed at which exposure leads to addiction, whereas higher recovery rates play a significant role in reducing its prevalence. The numerical analysis contributes by offering a reliable and accurate method for simulating real-world addiction patterns. This model provides a quantitative basis for designing more effective intervention strategies. However, this study is limited by the absence of real-time observational data and relies on parameter estimation from survey-based responses.
MODELING AND FORECASTING MORTALITY RATES DURING THE COVID-19 PANDEMIC USING THE SECOND ADAPTED NOLFI MODEL AND AUTO ARIMA Martinasari, Made Diyah Putri; Romantica, Krishna Prafidya; Gentari, Putu Tika Dinda
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0603-0618

Abstract

Modeling and forecasting mortality rates have been widely performed using various approaches. One such approach is the Second Adapted Nolfi model, which is one of three adaptations derived from the Nolfi and Generalized Nolfi models. Unfortunately, its application remains limited compared to widely used models like Lee-Carter and Cairns-Blake-Dowd. Previous studies on this model have shown satisfactory performance, particularly in residual analysis. However, those studies were conducted before the COVID-19 pandemic, and no study has yet applied it in the pandemic or post-pandemic periods. Although the pandemic may appear less relevant in 2025, the absence of such studies highlights the importance of further investigation into the model’s performance under extreme demographic conditions. This study addresses that gap by evaluating the Second Adapted Nolfi model using data from the Human Mortality Database (HMD) for the United States, the United Kingdom, and Italy. The model was applied to data up to 2019, and Auto-ARIMA was used to forecast from 2020 onward. The modeling results indicate that the logarithmic mortality curves align with established patterns, such as high rates at age 0, a decline through childhood, a sharp increase in early adulthood, and a continued rise into old age. The results also show that HMD mortality rates exceed the forecasted values for individuals aged 80 and above, suggesting increased elderly mortality during the pandemic. Three error metrics were used, yielding RMSE values from 0.01 to 0.18, MAE from 0.004 to 0.07, and MAPE from 28 to 286. Although Italy had the highest MAPE, the United States and the United Kingdom also showed notable errors. These findings reveal both the pandemic’s demographic impact and limitations of the model in capturing sudden shocks. Future studies may enhance this model through new adaptations, further comparison with other models, or alternative smoothing techniques to develop more robust mortality forecasts.
COMPARISON OF ARIMA, EXPONENTIAL SMOOTHING, AND CHEN-SINGH FUZZY MODELS FOR INFLATION FORECASTING IN ASEAN COUNTRIES Septiarini, Tri Wijayanti; Kharis, Selly Anastassia Amellia; Jayanegara, Anuraga; Abdulmana, Sahidan
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0619-0636

Abstract

This study aims to (i) develop predictive models using statistical and fuzzy approaches, and (ii) evaluate their forecasting performance. The data were obtained from www.investing.com for the period 1961 to 2017 and focus on five ASEAN countries: Indonesia, Malaysia, the Philippines, Singapore, and Thailand. The statistical models used are Autoregressive Integrated Moving Average (ARIMA) and Exponential Smoothing, while the fuzzy approaches include Chen and Singh fuzzy time series models. The dataset was divided into training and test sets in a 75%-25% proportion. ARIMA models capture trends and autocorrelations in time series data, while Exponential Smoothing uses exponentially weighted averages. Fuzzy models are designed to handle uncertainty and linguistic patterns in data. The results show that Singh’s fuzzy model yields the lowest error for Indonesia, while exponential smoothing and Chen fuzzy time series model demonstrate the same lowest error for Malaysia. For the Philippines, exponential smoothing is most accurate, whereas ARIMA and Singh fuzzy time series achieve the smallest error for Singapore. For Thailand, exponential smoothing and ARIMA perform equally well. However, the robustness of the forecasting model cannot be determined from either statistical or fuzzy methods, highlighting the challenge in determining the most robust model for inflation in the ASEAN region. The 75%-25% data split may also limit the generalizability of the findings. This study contributes a rare cross-country comparison of statistical and fuzzy forecasting methods in the ASEAN context. It highlights the importance of model selection based on country-specific inflation behavior and provides insights for improving forecasting strategies in macroeconomic applications.
INTEGRATED STATISTICAL MODELLING OF IRON EXCEEDANCE RISK: A MONTE CARLO, LOGISTIC REGRESSION, RANDOM FOREST, AND SOBOL ANALYSIS APPROACH Chaal, Rachid El; Dalhi, Hamid; Darbal, Otmane; Aboutafail, Moulay Othman
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0637-0656

Abstract

The quality of water resources in the Inaouen watershed, northern Morocco, is increasingly threatened by metal contamination, particularly iron (Fe). This study implements an integrated statistical framework to assess the risk of exceeding regulatory iron concentration thresholds. After preprocessing local physico-chemical data, a binary indicator variable was constructed to flag exceedances of the critical 30 µg/L threshold. Iron concentrations were modeled using log-normal and Weibull distributions, with a Monte Carlo simulation (n = 10,000) based on the log-normal law estimating exceedance probabilities across multiple thresholds (30, 50, 100 µg/L), revealing an 18% risk at 30 µg/L. Predictive modeling via logistic regression and random forest analysis identified calcium (Ca) as the dominant driver of iron exceedances, a finding corroborated by Sobol sensitivity analysis (S1 index = 0.74), with bicarbonate (HCO₃⁻) emerging as a secondary factor (S1 = 0.10). These results demonstrate the power of combining distribution fitting, machine learning, and global sensitivity analysis to effectively quantify and interpret iron contamination risks in vulnerable watersheds such as Inaouen. The proposed methodology offers a robust decision-support tool for sustainable water resource management and public health protection.
A NOVEL PUBLIC-KEY CRYPTOGRAPHY SCHEME UTILIZING SKEW CIRCULANT MATRICES WITH GENERALIZED ALTERNATING FIBONACCI Handoyo, Sapto Mukti; Guritman, Sugi; Jaharuddin, Jaharuddin
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0657-0672

Abstract

Circulant and skew circulant matrices play a significant role in various applications, especially in cryptography. Their determinants and inverses can be used in the decryption process. In classical cryptography, the Hill cipher is known to be susceptible to known-plaintext attacks and requires matrix-based key transmission. This study introduces a new public-key cryptography scheme that combines the Hill cipher with the ElGamal technique, utilizing skew circulant matrices with generalized alternating Fibonacci numbers. These numbers provide a pattern that simplifies the explicit formulas of the determinant and inverse of the matrices. The proposed scheme is the first of its kind to use these matrices and numbers for public-key cryptography. Explicit formulas for the determinant and inverse of these matrices are derived using elementary row and column operations. The proposed scheme is resistant to the discrete logarithm problem, known-plaintext, and brute-force attacks and requires only the transmission of key parameters. The implementation of the scheme has been tested using Wolfram Mathematica. In practice, the computational time of the scheme is significantly faster than three other related schemes, with up to 500 times faster in encryption and 17 times faster in decryption.
NOWCASTING GROWTH AT RISK IN INDONESIA: APPLICATION OF MIDAS-QUANTILE REGRESSION MODEL Latifah, Turfah; Akbar, Muhammad Sjahid; Prastyo, Dedy Dwi
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0673-0690

Abstract

One of the main problems faced by policymakers in economic monitoring is the limited availability of predictive tools that can comprehensively and in real time measure economic growth risks, particularly amid financial market volatility and rapid changes in economic indicators. This study aims to nowcast Indonesian economic growth using the Growth at Risk (GaR) approach by applying the Mixed Data Sampling-Quantile Regression (MIDAS-QR) model. This approach predicts economic risks across different quantiles, capturing best- and worst-case scenarios by integrating multi-frequency indicators, namely the Financial Conditions Index (FCI), External Financial Environment Index (EFEI), and Macroeconomic Prosperity Leading Index (MPLI), summarized using Principal Component Analysis (PCA). Prediction accuracy is evaluated using Quantile Mean Absolute Error (QMAE), Quantile Root Mean Squared Error (QRMSE), and Clark-West (CW) test metrics. The analysis utilizes a dataset of Indonesia covering the period from January 2001 to March 2025, combining quarterly GDP growth data as the dependent variable and monthly predictor variables sourced from the Central Statistics Agency (BPS), Bank Indonesia, and the Indonesia Stock Exchange. The findings show that the MIDAS-QR model significantly improves the accuracy of GaR forecasting in Indonesia relative to conventional approaches. It effectively captures risk asymmetries across quantiles, minimizes predictive errors, and facilitates the timely detection of economic downturns, offering valuable insights for early action. This study highlights the strategic role of high-frequency data in enhancing forecast precision and real-time economic risk monitoring in Indonesia. The application of the MIDAS-QR model presents a valuable tool for policymakers in formulating proactive responses to global economic uncertainty and fostering resilient economic growth.
NUMERICAL SOLUTIONS OF HERMITE DIFFERENTIAL EQUATIONS USING LEGENDRE MULTIWAVELETS Devi, Meenu; Rawan, Sunil; Rawan, Sushil Chandra; Srivastava, Vineet Kishore
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0691-0710

Abstract

This paper presents a numerical method for solving Hermite differential equations (HDEs) using operational integration matrices derived from Legendre multiwavelets of linear, quadratic, and cubic orders. The proposed technique transforms HDEs into algebraic systems, enabling efficient and accurate numerical solutions. Through several illustrative examples, the method’s effectiveness is demonstrated, with Cubic Legendre Multiwavelets (CLMW) exhibiting superior accuracy in approximating exact solutions.
INTEGRATING HOUSING ENVIRONMENTAL FACTORS INTO THE SEIR MODEL FOR PULMONARY TUBERCULOSIS TRANSMISSION: A CASE STUDY IN BANJAR, INDONESIA Yulida, Yuni; Suhartono, Eko; Anggraini, Dewi; Arifin, Syamsul
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0711-0728

Abstract

Pulmonary Tuberculosis (TB) remains one of the serious public health issues in Indonesia, including in Banjar Regency. The transmission of TB is not only influenced by biological and behavioral factors but also highly depends on the characteristics of the living environment. This study aims to analyze the influence of physical environmental factors of housing on the incidence of pulmonary TB, and to integrate the analysis results into a modified SEIR model. The research was conducted using a cross-sectional observational approach involving 73 respondents from the working areas of Puskesmas Martapura 1 and Martapura 2. Data were collected through direct observation and interviews, and analyzed using binary logistic regression to identify significant variables. The significant variables were subsequently integrated into the transmission rate parameters in the SEIR model. The results show that ventilation area and room temperature have a significant impact on the incidence of pulmonary TB. Empirical findings show that the probability of pulmonary TB incidence is highest (86.68%) when both ventilation and temperature are below standard, and lowest (26.23%) when both meet the standards. Partial compliance still results in a high probability of incidence (around 60%). The SEIR model simulation with environmental scenarios shows that living conditions that do not meet ventilation area and temperature standards result in more aggressive TB transmission. Conversely, living conditions that meet both standards significantly reduce the number of infected individuals and increase the recovery rate. This research emphasizes the importance of environment-based interventions in a comprehensive TB control strategy.
OPTIMIZATION OF PARAMETERS IN MEWMV AND MEWMA CONTROL CHARTS FOR CLEAN WATER QUALITY CONTROL AT PP KRAKATAU TIRTA GRESIK Hafiyusholeh, Moh.; Khaulasari, Hani; Firmansyah, Fery; Ulinnuha, Nurissaidah
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0729-0742

Abstract

Water is a vital resource whose quality directly affects public health. In Gresik Regency, water treatment processes must be closely monitored, particularly during production. PT PP Krakatau Tirta, a key provider of clean water in the region, plays a strategic role in treating raw water from the heavily polluted Bengawan Solo River. Ensuring that the treated water consistently meets health standards is crucial, highlighting the need for an effective process. This study aims to evaluate the clean water production process and assess the process capability in maintaining the quality of water produced by PT PP Krakatau Tirta Gresik. Laboratory data on key parameters, including pH, dissolved iron, and total dissolved solids, were collected daily from November 25, 2022, to May 31, 2023. These mandatory indicators were analyzed using Multivariate Exponentially Weighted Moving Variance (MEWMV) and Moving Average (MEWMA) control charts to assess process performance. A key contribution of this research lies in optimizing smoothing parameters to enhance control chart performance. Sixteen combinations of (ω,λ) were tested for MEWMV, with the optimal configuration found at (λ = 0.4) and (ω = 0.4), indicating that process variability is statistically stable. For MEWMA, nine values of λ were evaluated, and the optimal weight (λ=0.9) was identified as optimal, yielding a stable process mean after removing two out-of-control points. PT PP Krakatau Tirta, which plays a strategic role in treating raw water from the polluted Bengawan Solo River, was selected as a case study to evaluate the effectiveness of advanced monitoring methods. The results indicate that its clean water production process is well-controlled and capable, with water quality consistently meeting health and safety standards.

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