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Redaksi BAREKENG: Jurnal ilmu matematika dan terapan, Ex. UT Building, 2nd Floor, Mathematic Department, Faculty of Mathematics and Natural Sciences, University of Pattimura Jln. Ir. M. Putuhena, Kampus Unpatti, Poka - Ambon 97233, Provinsi Maluku, Indonesia Website: https://ojs3.unpatti.ac.id/index.php/barekeng/ Contact us : +62 85243358669 (Yopi) e-mail: barekeng.math@yahoo.com
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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 1,309 Documents
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MARKETING GAMES AND SENSITIVITY ANALYSIS FOR ANY NUMBER OF COMPANIES Amir, Almira; Simanjuntak, Ruth Mayasari; Suzana, Yenny; Lubis, Riri Syafitri; Syarah, Fatmah; Fajriana, Fajriana; Zahedi, Zahedi
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp0927-0940

Abstract

In the business world, advertising plays a crucial role in shaping market dynamics. This study analyzes advertising competition among companies by calculating the optimal profits for two to four competitors and postulating a general formula for a larger number of companies. Sensitivity analysis is employed to observe how changes in advertising parameters affect profits. The simulation results indicate that in the case of four companies, the optimal spending (Xopt) ranges from 137246 to 191288, while the optimal profit (Popt) ranges from 38693.1 to 92702. The sensitivity analysis shows that companies with higher advertising effectiveness achieve greater profits, whereas those with lower effectiveness tend to experience reductions in both allocation and profit. With the aid of Maple and Excel, this research extends previous advertising competition models by providing a comprehensive framework for optimizing advertising budgets in oligopolistic markets.
FIXED POINT THEOREMS FOR MULTIVALUED MAPPINGS IN MODULAR B-METRIC SPACES Hartono, Hartono; Harini, Lusi; Hayati, Afifah; Mas'ud, Syamsudin; Yusri, Thesa Adi Saputra; Karyati, Karyati; Saptaningtyas, Fitriana Yuli
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp0941-0954

Abstract

This paper explores multivalued mappings in modular b-metric spaces, with particular emphasis on contraction-type mappings. It introduces the concept of a Hausdorff distance adapted to this setting and investigates fixed point theorems associated with these mappings. The existence of fixed points is established under the assumptions that the space is complete, the considered subset is closed, and the modular -metric satisfies the -condition. These results not only extend classical fixed point theory but also provide a theorem that guarantees the existence of solutions to integral equations, with potential applications in mathematical modeling.
FORECASTING THE INFLATION RATE IN INDONESIA USING ARIMA-GARCH MODEL Saifudin, Toha; Suliyanto, Suliyanto; Afifa, Fitriana Nur; Arrofah, Aini Divayanti; Fauzi, Doni Muhammad; Pratama, Fachriza Yosa; Adyatma, Isryad Yoga
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp0955-0970

Abstract

Inflation is a key economic indicator that affects purchasing power, economic growth, and financial stability. Accurate forecasting is essential for policymakers to implement effective monetary and fiscal policies. However, traditional models like ARIMA (Autoregressive Integrated Moving Average) mainly capture general trends and often fail to address inflation volatility. This study enhances inflation forecasting accuracy by applying the ARIMA-GARCH hybrid model, which combines trend estimation with volatility modelling. Focusing on Indonesia’s inflation patterns using recent data, it addresses a gap in existing research. This type of research uses quantitative methods, and the data were obtained from the official website of Bank Indonesia. The dataset consists of 240 monthly Indonesian inflation data points spanning from September 2004 to August 2024. The ARIMA (0,1,1)-GARCH (2,0) model is used to analyze inflation trends and volatility dynamics. The model evaluation shows strong predictive performance, with a Mean Absolute Percentage Error (MAPE) of 2.73% and Root Mean Squared Error (RMSE) of 0.74 for training data. Testing data results in a MAPE of 18.95% and RMSE of 0.702, which remains within an acceptable range. These findings highlight the importance of incorporating volatility modelling in inflation forecasting to enhance economic decision-making. A reliable forecast mitigates economic uncertainty, thereby providing a stronger foundation for achieving long-term economic growth. This study contributes by demonstrating the practical application of ARIMA-GARCH in Indonesia’s inflation modelling, providing valuable insights for policymakers in managing inflation-related risks.
SOME CHEMICAL TOPOLOGICAL INDICES FOR THE COPRIME GRAPH OF THE INTEGERS MODULO GROUP Elfiyanti, Gustina; Sari, Mutia Nofita; Wisnu Wardhana, I Gede Adhitya; Candra, Ade; Semil Ismail, Ghazali
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp0971-0980

Abstract

This paper delves into the exploration of the coprime graph of a finite group G, a graph with vertices representing all group elements. Vertices x and y are considered adjacent in ΓG if their orders are relatively prime. Specifically, our focus lies in determining essential topological indices: the first Zagreb index, the second Zagreb index, and the Wiener index of the coprime graph associated with the group of integers modulo n. The groups under consideration in this study are those of integers modulo n, where n takes the form of prime power and multiplication of two prime powers, with p and q representing distinct prime numbers and r and s representing natural numbers. This investigation aims to provide a comprehensive understanding of the structural and numerical properties of the coprime graph within the context of finite groups, shedding light on the intricate relationships between group elements and their algebraic properties.
HETEROGENEOUS GRAPH NEURAL NETWORKS FOR STOCK PRICE PREDICTION: MODELING TEMPORAL AND CROSS-STOCK DEPENDENCIES Bukhori, Hilmi Aziz; Aruchunan, Elayaraja; Anam, Syaiful; Bukhori, Saiful; Maulana, Avin
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp0981-1000

Abstract

Stock price prediction remains a challenging task due to the complex interplay of temporal trends and relational dependencies within financial markets. This study proposes the GNN-LSTM Hybrid model, a novel framework that integrates Graph Neural Networks (GNNs) with Long Short-Term Memory (LSTM) units to simultaneously capture heterogeneous graph structures and temporal dynamics in stock data, leveraging GNNs to model relational dependencies and LSTMs to address long-term temporal patterns, with graph construction based on stock correlation and temporal edge features. Using a dataset covering 1,270 trading days from March 2015 to April 2020, we evaluate the model against traditional methods (ARIMA, LSTM) and modern graph-based approaches (T-GCN, GAT, Transformer-TS, Base GraphSAGE, SAGE-IS). The GNN-LSTM Hybrid achieves superior performance, with a Mean Absolute Error (MAE) of 0.740 (±0.13), Root Mean Squared Error (RMSE) of 1.100 (±0.21), Mean Absolute Percentage Error (MAPE) of 4.92% (±1.16), and Directional Accuracy (DA) of 67.0% (±2.7), and significantly outperforms all baselines, as confirmed by paired t-tests (p < 0.05). Hyperparameter analysis reveals that a configuration of 6 GNN layers and a hidden dimension size of 128 optimizes predictive accuracy, balancing computational efficiency (training time: 16.0 ± 0.7 s) and performance. Validation across 100 training epochs further confirms the model’s robust convergence across all metrics. With an inference time of 20.0 ± 1.0 ms, which is competitive compared to baselines like ARIMA (23.5 ± 1.1 ms) and GAT (20.5 ± 1.0 ms), the GNN-LSTM Hybrid demonstrates strong potential for practical financial forecasting, offering a scalable and accurate solution for capturing the multifaceted dynamics of stock markets, with implications for real-time applications and broader economic modeling.
WHOLE LIFE INSURANCE UTILIZING THE COMMISSIONERS METHOD AND THE VASICEK INTEREST RATE MODEL FOR PREMIUM RESERVE ANALYSIS Romantica, Krishna Prafidya; Johan, Arsyelina Husni; Jayanegara, Anuraga; Leo, Jason Filbert
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1001-1018

Abstract

Premium reserves play a vital role in ensuring that insurance firms can meet their future obligations to policyholders. Traditional fixed-rate approaches often fail to reflect market volatility, leading to potential misestimations. This study addresses this gap by integrating the Commissioners Method with the Vasicek stochastic interest rate model to evaluate premium reserves for whole life insurance. The research hypothesizes that the Vasicek model provides more realistic reserve estimates than fixed-rate models, that payment frequency and behavioral preferences significantly affect reserve levels, and that gender-specific mortality impacts reserve adequacy. Using BI-7D-RR interest rate data from 2019–2024, Vasicek parameters were calibrated and applied to reserve calculations. A sensitivity analysis was conducted by varying the model’s mean reversion, volatility, and long-term mean parameters. The results confirm that Vasicek-based reserves are more robust and realistic than fixed-rate estimates. Incorporating a DARA utility function adds behavioral realism, while payment frequency strongly influences reserve accumulation. Gender-specific mortality produces systematically higher reserves for male policyholders. Sensitivity analysis highlights the model’s robustness, with reserves responding predictably to parameter changes. This research contributes theoretically by linking stochastic modeling, demographics, and behavioral economics, while providing practical guidance for insurers to strengthen reserve adequacy and financial resilience under uncertainty.
OPTIMIZING LANDSLIDE SUSCEPTIBILITY MAPPING IN CENTRAL SULAWESI WITH RECURSIVE FEATURE ELIMINATION AND RANDOM FOREST ALGORITHM Siregar, Indra Rivaldi; Djuraidah, Anik; Soleh, Agus Mohamad
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1019-1034

Abstract

Landslides are among the most destructive natural hazards, causing severe casualties, economic losses, and environmental degradation. Central Sulawesi, characterized by active tectonics such as the Palu-Koro fault, is highly susceptible to landslides, as tragically demonstrated in 2018. Therefore, developing accurate landslide susceptibility maps is essential to support comprehensive landslide mitigation efforts in this region. While machine learning, particularly Random Forest (RF), has proven highly effective for landslide modeling, previous studies around Palu have often overlooked model simplification through feature selection and hyperparameter optimization. This study proposes an integrated approach combining RF with Recursive Feature Elimination (RFE) to reduce model complexity and enhance predictive accuracy. This research utilizes 498 landslide events with fifteen conditions, including topography, environment, geology, and anthropogenic influences. The RFE-RF model achieves superior classification performance, with accuracy, balanced accuracy, and F1-scores exceeding 0.81, outperforming the RF without RFE and Logistic Regression baselines. These findings underscore the urgent need to integrate feature selection methods such as RFE into landslide modeling frameworks to improve predictive accuracy. High accuracy enables government authorities and stakeholders to develop more targeted and effective mitigation priorities. Spatial analysis indicates that Donggala, Palu, and Sigi are the most critical areas requiring prioritized mitigation, with over 9% of their territories classified as highly susceptible. Feature importance analysis reveals that elevation, slope, and land cover are the most influential factors. This study suggests that mitigation efforts should focus on the hills and mountainous areas on both sides of the Palu Valley, with recommended strategies emphasizing land cover management practices, such as reforestation, to enhance slope stability and reduce landslide risk.
OPTIMAL CRYPTOCURRENCY PORTFOLIO CONSTRUCTION USING GARCH-BASED MONTE CARLO SIMULATION Staenly, Staenly; Irsan, Maria Yus Trinity; Ginting, Josep
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1035-1046

Abstract

This study investigates the construction of an optimal cryptocurrency portfolio comprising Ethereum and Solana using a GARCH-based Monte Carlo simulation framework. Asset volatilities were modelled individually through GARCH (1,1) processes, while asset correlations were captured using standardized residuals and Cholesky decomposition. Simulation results over 180- and 360-day horizons showed that the optimized portfolio achieved slightly higher cumulative growth factors and better upside capture compared to an equal-weighted benchmark, particularly during volatile market phases. In out-of-sample testing, the return-to-risk optimized portfolio delivered a total return of 34% over six months, compared to 33% for the equal-weighted strategy, while maintaining a higher return-to-risk ratio (0.06 versus 0.05) and lower volatility (3% versus 4%). Over a one-year period, both portfolios converged closely, with the equal-weighted strategy achieving a slightly higher total return of 45% compared to 43% for the optimized portfolio. These findings suggest that GARCH-based optimization can enhance portfolio resilience and risk-adjusted returns, although its realized return advantage may diminish in synchronized market conditions.
REVEALING THE STICKY FLOOR EFFECT OF THE GENDER WAGE GAP IN INDONESIA BY USING AN UNCONDITIONAL QUANTILE REGRESSION WITH RIF-OLS APPROACH Rahmah, Aisyah ‘Azizah Nur; Sofa, Wahyuni Andriana
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1047-1060

Abstract

Gender inequality persists as an ongoing challenge, particularly evident in the persistent wage gap which often stems from entrenched societal perceptions that restrict women into subordinate roles. This study aims to investigate factors influencing wage gap and its explained and unexplained contributor. Many studies in Indonesia only measure gender wage gap at one average point. Each point of the wage distribution has different characteristics, so the gender pay gap at one average point cannot be assumed to apply to the entire wage distribution. This study uses a more up-to-date method to examine wage differences between gender. Besides, the use of the internet as part of digitalization is crucial as a factor that has not been widely explored in other researches. Using data from Sakernas February 2023, this study employs UQR with RIF-OLS estimation and Blinder-Oaxaca decomposition. The results show that regional status, secondary education, work experience, internet use, working hours, and union membership affect the wages of both male and female workers across quantiles. Blinder-Oaxaca decomposition shows that women receive 12.25 to 69.37 percent lower wages than men, and the pattern varies across different wage group, confirming a sticky floor effect. Furthermore, education, regional status, marital status, training, internet use, activity status, and union membership are proven to narrow the gap. The differences in worker characteristics by gender affect wage disparities, and the government is expected to address the widening gap, especially at the bottom of the wage distribution.
MATHEMATICAL ANALYSIS OF QC-MDPC STRUCTURES IN BIKE V5.2 POST-QUANTUM KEY ENCAPSULATION SCHEME Rosa, Rosa; Carita, Sa'aadah Sajjana; Adiati, Nadia Paramita Retno; Rosdiana, Sri
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1061-1076

Abstract

The security of the BIKE scheme depends on a complex mathematical structure built upon QC-MDPC codes. This scheme is constructed using the Niederreiter framework and the application of transformation. Its security is based on the complexity of two main mathematical problems: the QCSD Problem and the QCCF Problem. The BIKE v5.2 scheme is the latest version of this scheme. This study aims to mathematically analyze the characteristics forming the BIKE v5.2, focusing on QC-MDPC codes, the Niederreiter framework, and the transformation, as well as the QCSD and QCCF problems. The method used in this study is a systematic literature review combined with theoretical analysis. The study highlights how the interplay of these three components forms a rational and resilient design. Although the BIKE v5.2 scheme was not selected for standardization by NIST, it is still capable of producing an efficient, secure, and relevant KEM for post-quantum cryptography. Through mathematical analysis of the QC-MDPC construction, the formulation of the complex computational problems QCCF and QCSD, and the rational design of the Niederreiter framework with the transformation, this study demonstrates that BIKE has a strong security foundation and resistance to both classical and quantum attacks.

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