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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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NIL DERIVATIONS AND d-IDEALS ON POLYNOMIAL RINGS Mursyidah, Ditha Lathifatul; Fitriani, Fitriani; Utami, Bernadhita Herindri Samodera; Faisol, Ahmad
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/barekengvol20iss1pp0325-0334

Abstract

Let be a ring. An additive mapping is called derivation if satisfies Leibniz's rule, i.e., for every In a special case, for each there exists a positive integer which depends on such that , then is called as a nil derivation on . The concept of - ideal which is an ideal that remains stable under the derivation operation . This research presents a systematic construction of nil derivations on polynomial rings and investigates their corresponding nilpotency indices. Unlike prior studies that often treat derivations in abstract terms, this work emphasizes explicit constructions, offering concrete examples and techniques for generating such derivations. A key focus is the relationship between nil derivations and general nilpotent derivations, including an analysis of their linear combinations. Furthermore, the study provides new insights into the behavior of nil derivations in the context of d-ideals, shedding light on their structural properties within ring theory. To enhance understanding, each theoretical development is supported by illustrative examples, reinforcing the applicability and significance of the results.
COMPARATIVE ANALYSIS OF BCBIMAX AND PLAID BICLUSTERING ALGORITHM FOR PATTERN RECOGNITION IN INDONESIA FOOD SECURITY Sumertajaya, I Made; Hikmah, Nur; Afendi, Farit Mochamad
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/barekengvol20iss1pp0335-0346

Abstract

Biclustering is an unsupervised learning algorithm that simultaneously groups rows and columns in a data matrix. Unlike conventional clustering, which evaluates objects across all variables independently, biclustering identifies subsets of objects and variables that share similar patterns—revealing localized structures within complex datasets. This study applies the BCBimax and Plaid algorithms to examine food security patterns across 34 Indonesian provinces. The indicators cover three key dimensions: availability, accessibility, and utilization of food. The algorithms are evaluated using the Jaccard Index, Mean Squared Residue (MSR), and the number of provinces effectively clustered. Results show that BCBimax, using a binarization threshold based on the median value, generates eight biclusters covering 58.8% of provinces. Meanwhile, the Plaid algorithm, applying constant column model parameters, produces six biclusters with 55.88% coverage, including overlapping memberships. Overall, BCBimax demonstrates superior performance, as indicated by a lower average MSR value (0.035) compared to Plaid (0.209). The Jaccard Index similarity score of 14.61% suggests that the biclusters formed by each method are significantly distinct. Both approaches indicate that the majority of Indonesian regions exhibit low to moderate food security characteristics.
FLOOD REINSURANCE PREMIUM PRICING BASED ON THE STANDARD DEVIATION PRINCIPLE WITH POT-BASED THRESHOLDS FOR MORTALITY AND PROPERTY DAMAGE RISKS Anggriawan, Vanessa; Permana, Ferry Jaya; Yong, Benny
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/barekengvol20iss1pp0347-0366

Abstract

Disasters that occur in Indonesia lead to financial loss. One approach to mitigating the financial impact is through the utilization of natural disaster insurance. Although natural disasters occur with a relatively small frequency, the associated losses are substantial. Insurance companies need to carefully consider the characteristics of natural disaster data, as these events can lead to significant claims and potentially result in the bankruptcy of insurance companies. Insurance companies can reduce the risk of bankruptcy by transferring some risk to reinsurance companies. In this paper, the disaster reinsurance premium is determined by considering both the mortality and economic risks using the peaks over threshold (POT) model under the standard deviation principle. The Poisson, generalized Pareto, and lognormal distributions are used to determine the premium, with parameters estimated using the maximum likelihood method. A simulation analysis is conducted using synthetic data generated with RStudio software, which includes the frequency of floods per year over 20 years, as well as the number of deaths and the number of houses damaged in each flood event. The threshold is determined using the percentage method, where 10% of the data is considered extreme values. The POT model is applied to various retention cases. The simulation results show that the risk of the number of damaged houses has a greater impact on the premium amount that the insurance company must pay to the reinsurance company than the risk of the number of deaths. Additionally, cases with retention values below the threshold result in the highest reinsurance premiums, while cases with retention values above the threshold result in the lowest reinsurance premiums. This paper also shows that the reinsurance premium changes almost linearly with the increase in the extreme value percentage. This study is among the first to apply the peaks over threshold model in combination with multiple distributions for reinsurance premium estimation in the Indonesian context. The findings provide new insights into the sensitivity of reinsurance premiums to damage thresholds and retention levels, offering a practical tool for insurers in disaster-prone regions.
PERFORMANCE EVALUATION OF SEASONAL ARIMA-SVR AND SEASONAL ARIMAX-SVR HYBRID METHODS ON FORECASTING PADDY PRODUCTION Risnawati, I'lmisukma; Afendi, Farit Mochamad; Sumertajaya, I Made
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/barekengvol20iss1pp0367-0380

Abstract

This study explores advances in forecasting time series data by combining linear and non-linear models. Traditional methods such as ARIMA and its variant ARIMAX are effective for linear data but have limitations when dealing with non-linearity. Support Vector Regression (SVR), a non-linear method, complements these weaknesses. Hybrid models such as ARIMA-SVR and ARIMAX-SVR synergize ARIMA or ARIMAX for linear components and SVR for non-linear components, improving accuracy. The purpose of this study is to evaluate the performance of hybrid ARIMA-SVR and ARIMAX-SVR methods on Indonesian paddy production data. The data analyzed is national-level data per sub-round (i.e., three sub-rounds per year) from sub-round 1 (January-April) of 1992 to sub-round 3 (September-December) of 2024, obtained from the Indonesian Central Statistics Agency and the Indonesian Ministry of Agriculture.Forecasting accuracy is measured using Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE). The results show that the best model is the Seasonal ARIMAX (1,1,1)(0,1,1)[3]-SVR ( 0.05) hybrid model, with the smallest RMSE and MAPE values of 0.304 and 1.473%. The addition of the harvested area variable and the ASF dummy improved the accuracy of the ARIMAX model prediction, while the application of SVR to ARIMAX residuals successfully captured previously undetected linear patterns. Based on these considerations, the Seasonal ARIMAX(1,1,1)(0,1,1)[3]-SVR ( 0.05) hybrid model was selected as the model with the best performance.
COMPANY VALUATION AND PORTFOLIO ANALYSIS BASED ON K-MEANS CLUSTERING IN KOMPAS 100 STOCKS INDEX Fajriyah, Rohmatul; Tjen, Yoel Christopher
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/barekengvol20iss1pp0381-0396

Abstract

The capital market plays a vital role in investment, providing a platform for trading long-term financial instruments. Indonesia’s capital market has shown significant growth in recent years. This study aims not only to find stock clusters but to show that grouping stocks based on similar valuation characteristics can serve as a solid foundation for constructing superior-performing portfolios. The Kompas 100 index is used because it represents the most liquid and fundamentally stocks in Indonesia. The k-means clustering method is employed, and the number of clusters is determined using the elbow method. This approach resulted in four clusters, with the cluster identified as containing stocks with low PER, PBV, and PSR, representing the “best” portfolio each year based on valuation. Portfolios were formed from these clusters and compared to benchmark portfolios in Indonesia and globally. Global portfolios used as benchmarks include VSMPX, FXAIX, and SAM Equity. Over five years (2018–2022), the cluster-based portfolios outperformed Indonesian and global benchmarks in 2018, 2021, and 2022, while slightly underperforming global portfolios in 2019 and 2020 but still exceeding Indonesian benchmarks. This confirms that clustering techniques can deliver strong performance compared to conventional methods. A limitation of this study is that it focuses only on return performance without analyzing risk-adjusted returns, which future research should address.
MODELING AND SEGMENTATION OF FACTORS AFFECTING HUMAN DEVELOPMENT IN ISLANDS OF JAVA USING FIMIX PLS METHOD WITH MEDIATION EFFECT Az Zuhro, Muhammad Rosyid Ridho; Kurniawan, Ardi; Amelia, Dita; Syahzaqi, Idrus
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/barekengvol20iss1pp0397-0412

Abstract

Human development is a key indicator used to assess the quality of a country's human resources. Although Indonesia's HDI has experienced a significant increase of 75.02 in 2024, inequality is still a pressing issue, especially in terms of gender representation in the workforce. This study aims to identify the influence of poverty, economic, health, employment and education factors on human development in Java Island by considering gender equality as a mediating variable. The data used in the study is limited to 119 districts/cities in Java Island and sourced from BPS publications, the Health Office and the Education Office. The novelty of this study lies in the use of the Finite Mixture Partial Least Square (FIMIX-PLS) approach with mediation effects which is rarely applied in human development research in Indonesia, as well as allowing the identification of latent population heterogeneity and region-based segmentation. The results of this method reveal two distinct district/city segments in Java, with Segment 1 dominated by the variables in this study that have significant direct and indirect effects through the mediation of gender equality on human development, while Segment 2 has characteristics that emphasize the effect of gender equality. Given these differences in characteristics, it is important that contextual and regional segmentation-based development policies are designed by local and central governments. Statistical segmentation approaches such as FIMIX-PLS make a significant contribution to more targeted policy making. By changing the type of intervention according to specific problems, the government can allocate resources more effectively. This supports the achievement of SDG-10 in reducing inequality.
BAYESIAN ESTIMATION OF THE SCALE PARAMETER OF THE WEIBULL DISTRIBUTION USING THE LINEX AND ITS APPLICATION TO STROKE PATIENT DATA Rahmanita, Tentri Ryan; Kurniawan, Ardi; Ana, Elly; Sediono, Sediono; Amelia, Dita
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/barekengvol20iss1pp0413-0426

Abstract

Survival analysis is used to study the timing of an event, such as recovery or death, in the context of medical data. One of the diseases that many people suffer from is stroke. Based on the survey results, the number of stroke sufferers in Indonesia reached 8.3% of 1000 people in Indonesia continues to increase every year, especially among the elderly. The research conducted aims to model the estimation of the type III censored Weibull distribution parameters with the Bayesian Linear Exponential Loss Function (LINEX) method. This study uses secondary data on stroke patients in the period January-November 2024 with a sample of 62 patients at the Haji Surabaya Regional General Hospital. Weibull distribution model with Bayesian approach using Linear Exponential Loss Function (LINEX) was applied to estimate the distribution parameters and survival function. The estimation results show that the parameter α is 6.32342 with an average hospitalization time of 5.9151646 days. MSE value is 0.000270555, which indicates that the estimation model is more accurate in predicting data for the length of hospitalization for stroke patients at the Haji Surabaya Regional General Hospital. The probability value of the survival function of stroke patients who have been hospitalized on the 5th day shows a probability of 82.4% so that no further hospitalization is needed, which indicates that the patient's health condition is improving. In addition, the hazard function analysis shows that the longer a patient is hospitalized, the greater the risk of the patient not recovering.
ENHANCING LQ45 STOCK PRICE FORECASTING USING LSTM MODEL Sinaga, Marlina Setia; Iskandar, Said; Manullang, Sudianto; Arnita, Arnita; Marpaung, Faridawaty; Buulolo, Fatizanolo
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/barekengvol20iss1pp0427-0438

Abstract

Stocks listed in the LQ45 index represent companies with high liquidity, large market capitalization, and strong fundamentals, making them pivotal to the movements of the Indonesian capital market. This study selects eight LQ45-listed stocks from the energy and mining sectors, as well as the banking sector. Historical data spanning a 10-year period from February 28, 2015, to February 28, 2025. This research aims to mitigate the impact of stock market dynamics, a significant challenge for investor decision-making. The Long Short-Term Memory (LSTM) method was employed to forecast stock prices using four variables: opening, highest, lowest, and closing prices. The LSTM architecture was chosen because its gated memory cells can effectively capture long‑term dependencies and nonlinear patterns in financial time series, thereby aligning with the research objective of minimizing forecasting error under volatile market conditions. Evaluation results using the Mean Absolute Percentage Error (MAPE) showed prediction errors below 2.5%, indicating relatively low forecasting error. Root Mean Squared Error (RMSE) values varied depending on stock price volatility. Companies exhibiting higher stock prices, such as Indo Tambangraya Megah Tbk (ITMG), demonstrate larger RMSE values. For opening prices, predictive accuracy was notably strong, with MAPE values consistently below 1.26%. This suggests that opening prices, influenced by pre-market sentiment and historical data, are more stable and easier to predict compared to other price variables.
HYBRIDIZING HENSEL’S LEMMA, FUNDAMENTAL THEOREM OF ARITHMETIC, AND CHINESE REMAINDER THEOREM FOR SOLVING POLYNOMIAL CONGRUENCES Oktaviansyah, Eka; Kurniadi, Edi; Kusuma, Dianne Amor
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/barekengvol20iss1pp0853-0864

Abstract

Polynomial congruence can be solved by applying Hensel’s Lemma. However, Hensel’s Lemma itself does not apply to solving generalized polynomial congruences. The purpose of this research is to determine the recursive formula for the solution of polynomial congruence modulo prime numbers and to construct a general solution algorithm of polynomial congruence modulo arbitrary positive integers. Unlike previous studies, this research proposes the recursive hybrid algorithm combining Hensel’s Lemma, the Fundamental Theorem of Arithmetic, and the Chinese Remainder Theorem, highlighting the originality of the approach in extending its application beyond prime power moduli. The result of this research is the form of a recursive formula for the solution of polynomial congruence modulo prime numbers and the algorithm for solving polynomial congruence modulo arbitrary positive integers using the combination of Hensel’s Lemma, Fundamental Theorem of Arithmetic, and Chinese Remainder Theorem. The results of this research contribute to the development of mathematical methods, especially in the field of number theory. However, the applicability of the recursive formula is limited to cases where the conditions of Hensel’s Lemma are satisfied, that is, when a solution of the polynomial modulo a prime is such that the polynomial equals zero while its derivative does not equal zero modulo the same prime. Extending the method to situations where this condition fails remains a subject for future research.
CLUSTER ANALYSIS OF MULTIVARIATE PANEL DATA ON DATA CONTAINING OUTLIERS Kapiluka, Kristuisno Martsuyanto; Wijayanto, Hari; Fitrianto, Anwar
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/barekengvol20iss1pp0439-0452

Abstract

One clustering method for panel data is K-Means Longitudinal (KML), which considers only a single trajectory per subject over time. To address this limitation, KML was extended into K-Means Longitudinal 3D (KML3D), which enables clustering of joint or multivariate longitudinal data by considering multiple trajectories measured simultaneously for each subject. Both KML and KML3D provide new insights into clustering panel data using a non-hierarchical K-means approach. Hereinafter, this method is referred to as KML3D K-Means. KML3D K-Means implements the K-Means algorithm, specifically designed to cluster trajectories in panel data, and uses the mean as the clustering centroid. In practice, the K-Means algorithm is less effective in clustering data with outliers. This issue can be overcome by KML3D K-Medoids, a method based on KML3D that uses the median as the centroid. This study aims to determine cluster analysis for multivariate panel data on data containing outliers with KML3D K-Means and KML3D K-Medoids. Both methods are applied to panel data of social and welfare statistical data from 34 provinces observed for 8 years (2016 – 2023). The comparison of methods is based on the Calinski–Harabasz index. The results of the study show that KML3D K-Medoids has a Calinski-Harabasz index that is higher than KML3D K-Means in clustering multivariate panel data with outliers. The analysis identified three optimal clusters (k = 3) based on the Calinski–Harabasz (CH) index, which can be categorized as the “more prosperous”, “moderately prosperous”, and “less prosperous” groups. The growth rate analysis reveals disparities in development trajectories across clusters, with cluster 3 showing the most consistent improvements, cluster 1 moderate progress, and cluster 2 lagging in key social and welfare indicators.

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