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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 1,248 Documents
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COMPARISON OF THE VOLATILITY OF GARCH FAMILY MODEL IN THE CRYPTOCURRENCY MARKET: SYMMETRY VERSUS ASYMMETRY Pasaribu, Asysta Amalia; Sa'adah, Aminatus
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss4pp2571-2582

Abstract

Cryptocurrencies can be considered an individual asset class due to their distinct risk/return characteristics and low correlation with other asset classes. Volatility is an important measure in financial markets, risk management, and making investment decisions. Different volatility models are beneficial tools to use for various volatility models. The purpose of this study is to compare the accuracy of various volatility models, including GARCH, EGARCH, and GJR-GARCH. This study applies these volatility models to the Bitcoin, Ethereum, and Litecoin return data in the period January 1st, 2020, to December 31st, 2024. The performance of these models is based on the smallest AIC value for each model. The results of the study indicate that the GARCH (1,1) is the most suitable model for Bitcoin, Litecoin, and Ethereum returns.
DUAL RECIPROCITY BOUNDARY ELEMENT METHOD FOR SOLVING TIME-DEPENDENT WATER INFILTRATION PROBLEMS IN IMPERMEABLE CHANNEL IRRIGATION SYSTEMS Irene, Yanne; Manaqib, Muhammad; Alamsyah, Mochammad Rafli; Wijaya, Madona Yunita
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss4pp2583-2596

Abstract

The mathematical model of water infiltration in a furrow irrigation channel with an impermeable layer in homogeneous soil is formulated as a Boundary Value Problem (BVP) with the Modified Helmholtz Equation as the governing equation and mixed boundary conditions. The purpose of this study is to solve the infiltration problem using the Dual Reciprocity Boundary Element Method (DRBEM). The results show that the highest values of suction potential and water content are located beneath the permeable channel, while the lowest values are found at the soil surface outside the channel and beneath the impermeable layer. The values of suction potential and water content increase over time t and converge, indicating stability in the infiltration process. These findings align well with real-world scenarios, demonstrating that the developed mathematical model and its numerical solution using DRBEM accurately illustrate the time-dependent water infiltration process in impermeable furrow irrigation channels.
TRUNCATED SPLINE SEMIPARAMETRIC REGRESSION TO HANDLE MIXED PATTERN DATA IN MODELING THE RICE PRODUCTION IN EAST JAVA PROVINCE Handajani, Sri Sulistijowati; Pratiwi, Hasih; Respatiwulan, Respatiwulan; Susanti, Yuliana; Nirwana, Muhammad Bayu; Nareswari, Lintang Pramesti
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss4pp2597-2608

Abstract

Climate change can affect rice production through changes in temperature, precipitation patterns, extreme weather events, and atmospheric carbon dioxide levels. A statistical model can be used to understand the correlation between rice production and factors that affect it. The existence of some patterns that are formed from independent variables and others that do not show data patterns due to volatility in weather element data makes semiparametric regression modeling more appropriate. In forming a parametric model, the data pattern needs to be regular to make the model more precise. Irregular data patterns are more appropriately modeled with nonparametric regression models. The existence of several patterns formed from independent variables to their dependent variables, and several others, does not show a particular pattern due to the volatility in climate data, making truncated spline semiparametric regression modeling more appropriate to use. This research aims to model rice production in several regions in East Java Province in 2022 using a semiparametric regression model. The data used were from the Meteorology, Climatology, and Geophysics Agency and the Central Statistics Agency for East Java Province in 2022. The response variable is the rice production (tons) in 2022 in Tuban, Gresik, Nganjuk, Malang, Banyuwangi, and Pasuruan Regency (Y). The predictor variables are paddy harvested area (hectares), average temperature (℃), humidity (percent), and rainfall (mm). The semi-parametric spline truncated regression model is obtained by combining the parametric and non-parametric models based on truncated splines. The analysis showed a spline truncated semiparametric regression model with a combination of knot points (3,3,1) with a minimum GCV value of 12,642,272. The variables significantly affecting rice production were rice harvest area, temperature, air humidity, and rainfall, with an adjusted value of 98.522%.
INTEGRATION OF DAVIES-BOULDIN INDEX VALIDATION AND MEAN-VARIANCE EFFICIENT PORTFOLIO IN K-MEANS++ CLUSTERING FOR OPTIMIZATION OF THE LQ45 STOCK PORTFOLIO Dhandio, David Jordy; Sulistianingsih, Evy; Satyahadewi, Neva
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss4pp2609-2620

Abstract

Stock investment involves allocating funds to get returns based on the associated risks. In stock investments, returns and risks exhibit a linear correlation, meaning higher expected returns come with higher risks. Risk in stock investments can be minimized by forming portfolios using a cluster analysis approach, where the groups of stocks generated from the analysis represent the resulting portfolios. This research aims to form an optimal stock portfolio using K-Means++ Clustering, validated by the Davies Bouldin Index (DBI), the weighting of stocks in a portfolio using the Mean-Variance Efficient Portfolio (MVEP), and evaluated based on the Sharpe Index. The data used include stocks indexed in LQ45 from February 2020 to August 2024, stock closing prices from August 1, 2023, to August 1, 2024, company financial ratios as of June 2024, and the average Bank Indonesia interest rate from August 2023 to August 2024. Based on the financial ratios, K-Means++ Clustering and DBI validation identified three optimal clusters. Clusters 1 and 2, consisting of single stocks, cannot be directly utilized as portfolios due to the requirement for diversification. Each cluster’s stocks with the highest expected return were selected to form a new portfolio. According to the MVEP analysis, the investment proportion f each stock in portfolio 1 is 44.10% (BBCA.JK), 15.40% (BBNI.JK), 2.89% (BMRI.JK), 15.02% (CPIN.JK), and 22.60% (PGAS.JK). In portfolio 2, the weights are 27.68% (BBTN.JK), 36.00% (ADRO.JK), and 36.33% (BMRI.JK). Based on the Sharpe Index, portfolio 2 achieved the highest value (0.048404) compared to portfolio 1 (0.034465), indicating that portfolio 2 shows a better risk-adjusted return than portfolio 1.
THE LINEARITY OF THE EXPECTED VALUE OF A FUZZY VARIABLE Kencono, Uvi Dwian; Indarsih, Indarsih -
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss4pp2621-2632

Abstract

In this research, we introduce a novel credibility measure defined as a non-empty set satisfying the axioms of normality, monotonicity, self-duality, and maximality. Based on this credibility measure, a credibility space is constructed, upon which a fuzzy variable can be defined. Similar to fuzzy numbers, fuzzy variables are characterized by membership functions. The membership function of this fuzzy variable is directly derived from the credibility measure. Subsequently, by integrating the credibility measure, the expected value of the fuzzy variable is obtained. The linearity property of fuzzy expected value on fuzzy variables will be proven. This linearity property is highly useful in solving various problems involving fuzzy variables. Therefore, the proposed credibility measure provides a new framework in fuzzy variable theory. This credibility measure not only offers a more formal approach to measuring uncertainty but also opens up possibilities for the development of more complex and applicable fuzzy models.
CLUSTERING WITH SKATER METHODS AND UTILIZATION OF LISA ON UNEMPLOYMENT RATE Abdila, Naufal Shela; Fitriani, Rahma; Pratama, Muhamad Liswansyah
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss4pp2633-2646

Abstract

Spatial cluster analysis is an analysis used to identify a spatial pattern or geographical grouping of data. One method that can be used in spatial cluster analysis is Spatial Cluster Analysis by Tree Edge Removal (SKATER). This research aims to analyze the spatial pattern of the Unemployment Rate in East Java by utilizing the SKATER method. The clustering results are then used to create a weighting matrix, which is used to find local spatial autocorrelation values ​​using the Local Indicators of Spatial Association (LISA) index. The data is taken from BPS East Java with variables including unemployment rate, education level, minimum wage, Human Development Index, and population density. The results show that this approach is able to identify significant local spatial patterns. However, the selection of the number of clusters and input variables proved to be very influential on the results, so care needs to be taken.
PREDICTION OF NATURAL GAS PRICES ON THE NEW YORK MERCANTILE EXCHANGE BASED ON A PULSE FUNCTION INTERVENTION ANALYSIS APPROACH Sediono, Sediono; Saifudin, Toha; Dewanti, Maria Setya; Azis, Aurelia Islami
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss4pp2647-2660

Abstract

Natural gas is a key energy commodity with significant global economic impact, and its pricing is influenced by factors like weather, energy policies, geopolitics, and supply-demand balance. The Russia-Ukraine conflict disrupted Russia’s gas exports, causing price volatility and affecting global markets, including Indonesia. This has heightened the need for accurate price prediction to support policy and investment decisions. Previous studies show ARIMA-GARCH models predict well but need pulse function intervention for sudden shocks. This study aims to apply pulse function intervention analysis, which captures the immediate effects of external events on time-series data, to improve the precision of natural gas price forecasts, aiding government and industry decision-makers. The optimal intervention model for predicting natural gas prices on the New York Mercantile Exchange is the Probabilistic ARIMA (0,2,1) with a pulse function intervention order of b=0, r=2, and s=0. Using this model with the pulse function intervention approach yields consistent fluctuation patterns over time and achieves a MAPE value of 12.2586%, indicating that the model provides good predictive accuracy.
NUMERICAL ANALYSIS OF BLOOD VESSEL CONSTRICTION DUE TO ATHEROSCLEROSIS DISEASE USING FINITE VOLUME METHOD Fatahillah, Arif; Mubarokah, Umi; Megahnia Prihandini, Rafiantika; Wihardjo, Edy; Adawiyah, Robiatul; Hussen, Saddam; Monalisa, Lioni Anka
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss4pp2661-2678

Abstract

Atherosclerosis is a leading cause of coronary heart disease. This study analyses how elliptically shaped stenoses alter blood-flow velocity in coronary arteries. The governing equations are discretised with the finite-volume method, coupling pressure and velocity through the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm and accelerating convergence with the Successive Over-Relaxation (SOR) technique. A weighted Gauss–Seidel iteration whose over-relaxation factor ( in this work) damps low-frequency error modes, cutting the number of iterations needed for residuals to fall below 10⁻⁴ by roughly 40 % compared with the standard Gauss–Seidel scheme. Simulations of 30 %, 50 %, and 70 % constrictions were carried out in MATLAB R2013a and ANSYS Fluent. Quantitative and qualitative cross-validation of the two software packages confirmed consistent velocity and pressure fields, though minor discrepancies arose from differing numerical schemes and model assumptions, underscoring the need for experimental verification. The highest centre-line velocity occurred at 70 % stenosis—0.72075 m/s in MATLAB versus 0.90 m/s in Fluent—while the lowest was recorded at 30 %. Velocity–pressure profiles showed that increasing inlet velocity or degree of narrowing elevates velocity but decreases pressure, with the largest drop (11492.4 Pa in MATLAB; 11747.32 Pa in Fluent) again at 70% stenosis. Study limitations include modelling blood as a Newtonian fluid and idealising arterial geometry; future work should incorporate non-Newtonian rheology and patient-specific shapes to enhance physiological accuracy.
THE EFFECT OF SAMPLE SIZE ON THE STABILITY OF XGBOOST MODEL PERFORMANCE IN PREDICTING STUDENT STUDY PERIOD Damar Sakti, Muhammad Lintang; Jailani, Jailani; Retnawati, Heri; Hidayati, Kana; Waryanto, Nur Hadi; Ibrahim, Zulfa Safina; Khoirunnisa, Asma’; Satiranandi Wibowo, Firdaus Amruzain; Berlian, Miftah Okta; Batubara, Angella Ananta
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss4pp2679-2692

Abstract

Student success can be defined based on the period of study taken until graduation from college. Machine learning can be used to predict the factors that are thought to influence student success. To achieve optimal machine learning model performance, attention is needed on the sample size. This study aims to determine the effect of student sample size on the stability of model performance to predict student success. This research is quantitative. The data used is student data from a university in Yogyakarta from 2014 to 2019, totaling 19061 students. The target variable is the student study period in months, while the predictor variables are college entrance pathways, GPA from semester 1 to semester 6, and family socioeconomic conditions based on the father’s and mother’s income. This research uses the XGBoost model with the best hyperparameters and the bootstrap approach. Bootstrapping was performed on the original data by sampling twenty different sample sizes: 250, 500, 750, 1000, 1250, 1500, 1750, 2000, 2250, 2500, 2750, 3000, 3250, 3500, 3750, 4000, 4250, 4500, 4750, and 5000. The resulting bootstrap samples were replicated ten times. Model performance evaluation uses the Root Mean Square Error (RMSE) value. The result of this research is the XGBoost model with the best hyperparameters, obtained through the training data division scheme of 90% and testing data of 10%, which has the smallest RMSE value of 8.318. The model uses the best hyperparameters: n_estimators of 75, max_depth of 8, min_child_weight of 5, eta of 0.07, gamma of 0.2, subsample of 0.8, and colsample_bylevel of 1. The XGBoost model with optimal hyperparameters demonstrates peak performance stability at a sample size of 1750 students, as evidenced by consistent RMSE values across 10 bootstrap replications, confirming that this data quantity provides the ideal balance between prediction accuracy and stability for estimating study duration.
DISTRIBUTION MODEL OF HUMAN DEVELOPMENT INDEX IN PAPUA PROVINCE BASED ON REGIONAL CLUSTERING Wororomi, Jonathan K.; Sroyer, Alvian M.; Morin, Henderina; Reba, Felix; Beno, Ishak S.; Wambrauw, Oscar O. O.
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss4pp2693-2708

Abstract

Modeling the distribution of Human Development Index (HDI) components is essential to uncover underlying disparities and guide targeted policy interventions. This study aims to analyze HDI data, focusing on the average length of schooling across 26 districts in Papua Province from 2010 to 2023, to identify the most suitable probability distribution model. Using the k-means clustering method, two main groups were identified based on the average length of schooling. Cluster 1 includes 11 districts with a Weibull distribution, characterized by a scale parameter of 8.9931 and a shape parameter of 16.1272, indicating significant variation in education duration. Cluster 2 consists of 15 districts with a scale parameter of 3.73006 and a shape parameter of 8.07662, showing a distribution with a long tail and greater variability. This study provides insights into the distribution patterns of education duration in Papua, which could aid policymakers in making more targeted decisions and allocating resources efficiently. The findings also highlight regional disparities and the need for specific educational interventions. These results are valuable for government entities, NGOs, researchers, and international donors interested in improving educational outcomes in underdeveloped areas. However, the analysis is limited by the scope of available data and the assumption of homogeneity within clusters.

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