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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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APPLICATION OF THE PRINCIPAL COMPONENT ANALYSIS-VECTOR AUTOREGRESSIVE INTEGRATED (PCA-VARI) MODEL TO FORECASTING ECONOMIC GROWTH IN INDONESIA Al Madani, Aulia Rahman; Najwa, Sandrina; Ruchjana, Budi Nurani
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/barekengvol19iss4pp2301-2316

Abstract

Indonesia's economic growth has undergone significant fluctuations in recent years, driven by global shocks such as the 2020 COVID-19 pandemic, the 2013 taper tantrum, and the 2022 global energy crisis. These events underscore the urgent need for more accurate and robust forecasting models to support economic stability and policymaking. This study applies the Principal Component Analysis-Vector Autoregressive Integrated (PCA-VARI) model to forecast economic growth in Indonesia. PCA reduces seven economic variables into two principal components for ten years (2012-2022). The results show that the first component (PC1) shows the highest correlation with the variables of Money Supply, BI Rate, and Foreign Exchange Reserves, which reflect monetary policy and financial stability. Meanwhile, the second component (PC2) is highly correlated to the GDP Index, Exchange Rate, and Inflation variables, which reflect macroeconomic conditions. VARI, as a non-stationary multivariate time series model, is used to model the relationship between these components, with the third-order lag selected as the optimal lag based on the Akaike Information Criterion (AIC), Hannan-Quinn Criterion (HQ), and Final Prediction Error (FPE) values. The results show that the PCA-VARI(3) model is able to provide highly accurate forecasting with a MAPE of 1.21% for PC1 and 1.34% for PC2, and has met all the necessary model assumptions.
DYNAMIC ANALYSIS OF THE MATHEMATICAL MODEL FOR STUNTING WITH NUTRITION AND EDUCATION INTERVENTIONS Sabran, La Ode; Annur, Lathifah; Ratu Laura, Athisa
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/barekengvol19iss4pp2317-2334

Abstract

This study presents a mathematical model that analyzes the impact of nutrition and education interventions on stunting prevalence. Nutritional interventions are carried out on toddlers indicated to be stunted and toddlers who are healthy but susceptible to stunting. Meanwhile, education is given to the toddler's mother compartment. The model categorizes the toddler population into four compartments: susceptible, stunting-indicated, permanently stunted, and non-stunted. Similarly, the maternal population is categorized into three compartments: susceptible mothers, mothers exhibiting poor parenting practices, and educated mothers. The model's equilibrium point comprises two distinct states: a stable stunting-free equilibrium point when the basic reproduction number (R0) is less than one and a stable stunting-endemic equilibrium point when R0 is more significant than one. Sensitivity analysis reveals that the parameters that significantly influence the reduction or increase in stunting cases are the rate of nutritional intervention for children and the intensity of education for mothers. Numerical simulations demonstrate that implementing nutritional intervention activities and continuous education programs can effectively eliminate stunting cases in the population. The simulation results show a high number of stunting cases, reaching 161,566 cases in the population, due to poor education and poor nutritional interventions. In contrast, education programs and effective nutritional interventions eliminate stunting from the population. However, it takes longer.
HYBRID ARIMA–ANN MODEL FOR AIR QUALITY INDEX PREDICTION IN DKI JAKARTA Windasari, Wahyuni; Pradani, Augistri Putri
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/barekengvol19iss4pp2335-2346

Abstract

Air pollution is a threat to all countries, including Indonesia. One area in Indonesia with poor air quality is DKI Jakarta. One step to minimize the decline in air quality in an area is to predict the air quality index in the future. In this study, a hybrid ARIMA-ANN analysis was conducted, combining the ARIMA method and Artificial Neural Networks to model air quality in DKI Jakarta. The time series data of the air quality index sourced from the DKI Jakarta Environmental Service during January 19-30, 2023, which was observed every hour with a total of 288 data. The results of the study showed that the SAE and RMSE of the ARIMA model were 94.135 and 1.157, respectively, while the SAE and RMSE values ​​of the hybrid ARIMA-ANN model were 61.094 and 1.15. The results of the study showed that the hybrid ARIMA-ANN model had a higher accuracy value compared to the single ARIMA model in describing DKI Jakarta air quality data. This study has limitations in that determining the network architecture in the ANN model is still done by trial and error, so it takes a relatively longer time.
MODELING DEMOCRACY INDEX IN INDONESIA WITH MULTIVARIATE ADAPTIVE REGRESSION SPLINE APPROACH Saifudin, Toha; Suliyanto, Suliyanto; Nugraha, Galuh Cahya; Valida, Hanny; Nahar, Muhammad Hafidzuddin; Fortunata, Regina
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/barekengvol19iss4pp2347-2358

Abstract

Democracy is a system of government where citizens participate in political decision-making through freely elected representatives. To measure the quality of democracy in Indonesia, the Indonesian Democracy Index (IDI) is used as a composite indicator reflecting various aspects of political freedoms, civil liberties, and governance. The IDI score declined from 6.71 in 2022 to 6.53 in 2023, the lowest in 14 years, indicating disruption in Indonesia’s democracy. Therefore, it is necessary to identify the root causes of the disruption in Indonesia’s democracy through several indicators. This study analyzes the relationship between predictor variables, including socio-economic and development indicators, and IDI using the Multivariate Adaptive Regression Spline (MARS) approach. This study uses the MARS method by considering six predictor variables, namely the Human Development Index (HDI), Gender Empowerment Index (GEI), Information and Communication Technology Development Index (ICT-DI), Press Freedom Index (PFI), Poverty Depth Index (PDI), and High School Completion Rate (HSCR). The data used is secondary data from 34 Indonesian provinces in 2023 obtained from the Statistics Indonesia-BPS. The results showed that the best model was obtained with a combination of BF = 12, MI = 3, and MO = 1 resulting in a GCV value of 11.27 and R2 of 80%. MARS model interpretation identifies the significant influence of social and economic indicators on IDI and is able to explain 80% of data variability. The significance test shows that all predictor variables significantly affect the IDI, with the highest level of importance on the ICT-DI variable. Therefore, improving ICT-DI in each province needs to be a major concern as a strategic step to improve the democracy index in Indonesia and support the achievement of Sustainable Development Goal 16 on peace, justice, and strong institutions.
APPLICATION OF BACKPROPAGATION FOR FORECASTING OPEN UNEMPLOYMENT IN MAKASSAR CITY Syam, Rahmat; Sidjara, Sahlan; Abdullah, Adib Roisilmi
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/barekengvol19iss4pp2359-2376

Abstract

Based on data from the Statistics Bureau of South Sulawesi Province, the open unemployment rate in Makassar City has remained consistently high over the past ten years, averaging 11.41%. This highlights a persistent labor market issue and positions Makassar as the leading contributor to the open unemployment rate in the province. To support effective policymaking and early intervention strategies, it is essential to forecast future unemployment trends based on historical data. Therefore, this study aims to forecast the open unemployment rate in Makassar City over the next five years using a machine learning approach. Among the available forecasting methods, the Backpropagation Artificial Neural Network (ANN) was selected due to its proven ability to model complex, non-linear relationships often found in socio-economic data. ANN is particularly effective in handling temporal dynamics without assuming linearity or stationarity, unlike traditional statistical models. In this study, the forecasting process involved data normalization, scenario-based data partitioning, ANN architecture design, and model training and testing. The model with the best performance consisted of 11 neurons in the input layer, 55 neurons in the hidden layer, and 1 neuron in the output layer, using 80% of the data for training and 20% for testing. This configuration yielded a forecasting accuracy of 91.896%, with a MAPE of 8.131% and an MSE of 0.003. The denormalized results forecast a steady decline in the open unemployment rate from 9.078% in 2023 to 7.248% in 2027, indicating a positive trend in employment. Nevertheless, it is important to acknowledge the limitations of forecasting models and the potential influence of external factors that may affect actual outcomes.
THE RAINBOW VERTEX-CONNECTION NUMBERS OF WHEEL-SHIELD GRAPHS Palupi, Ratnaning; Salman, A. N. M.
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/barekengvol19iss4pp2377-2390

Abstract

Let be a nontrivial simple connected graph, be an edge of and be an integer greater than or equal to . A path of order , denoted by , is a graph whose vertices can be labelled such that . A -shield graph is a graph obtained by and copies of such that the edge of -th embedded to -th edge of by embedding to and to . A path in a vertex-colored graph is said to be rainbow-vertex path if every internal vertex in the path has different color. A vertex-colored graph is said to be rainbow-vertex connected if for every pair of vertices there exists a rainbow-vertex path connecting them. The rainbow- vertex connection number of , denoted by , is the minimum colors needed to make rainbow-vertex connected. In this paper, we determine the rainbow-vertex connection numbers of of wheel-shield graphs , specifically finding that the number ranges from to depending on the order of the wheel.
THE UTILIZATION OF TRANSITION MATRIX IN BONUS-MALUS SCHEME FOR DETERMINING MOTOR VEHICLE INSURANCE PREMIUMS Miasary, Seftina Diyah; Isnawati, Ayus Riana; Marmu'asyifa, Hana Zhafira
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/barekengvol19iss4pp2391-2404

Abstract

Motor vehicle usage in Indonesia ranks among the highest globally, reaching approximately 141,992,573 units. The growing variety and number of automobiles contribute significantly to traffic congestion and heightened risks to public safety. Given the inherent dangers associated with motorized transportation, including auto theft and accidents, efforts to shift these risks to insurance companies have become crucial. The fundamental idea of insurance is to establish a pool in which policyholders can manage their risk, with premiums determined by the amount of risk that each participant adds to the group. Actuaries in the field of motor vehicle insurance must generate a reasonable premium rate utilizing a variety of methodologies, including the Bonus-Malus approach. The latter, a widely utilized approach, classifies policyholders based on their claims history, incentivizing safe driving. Examining the internal dynamics of the Bonus-Malus system necessitates studying mathematics, particularly algebra, and the use of linear algebra in transition matrices is critical in anticipating changes in bonus-malus rates over time. This research is a quantitative descriptive analysis that explores the implementation of the Bonus-Malus system using a transition matrix framework. It aims to investigate the collaboration of algebra and actuarial science in a real-world application of the Bonus-Malus scheme for motor vehicle insurance, focusing on the use of the transition matrix in premium computation, utilizing secondary data from PT. Jasa Raharja Kota Semarang for the years 2021–2022. The transition matrix analysis shows that Model 2 allows for smoother class transition, lowers the possibility of high-risk class recurrence, and provides more consistent premium adjustments. This demonstrates the model's ability to create a balanced incentive structure while interpreting claim trends. Furthermore, Model 2 has a greater expected value of Loimaranta efficiency than Model 1, supporting findings that added status improves Bonus-Malus system efficiency.
COMPARISON ANALYSIS OF CLAYTON, GUMBEL, AND FRANK COPULA FOR MODELING THE DEPENDENCE BETWEEN BBCA CLOSING PRICE AND INDONESIA MACROECONOMIC FACTORS Hanin, Noerul; Satyahadewi, Neva; Sulistianingsih, Evy
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/barekengvol19iss4pp2405-2418

Abstract

PT. Bank Central Asia Tbk is a company in Indonesia with the biggest market capitalization. These advantages attract investors to buy PT. Bank Central Asia Tbk (BBCA) shares. However, fluctuating share prices can lead to both gains and losses, where these are not entirely caused by the company’s finances, but also by the country’s macroeconomic conditions. Therefore, this study aims to examine the dependency between BBCA closing price and macroeconomic indicators, which are limited on only three macroeconomic variables, consists of inflation, interest, and USD-IDR exchange rate. This study compares the Clayton, Gumbel, and Frank copula to analyze the dependence characteristics between two non-normally distributed variables based on the highest log-likelihood value. The data used are monthly data from 2021 to 2023, consists of inflation and interest rate from Bank Indonesia website, USD-IDR exchange rate from Satu Data Kementerian Perdagangan website, alongside BBCA closing price from yahoo finance website. Based on the analysis, the best copula models to describe the relationship between each macroeconomic factor (inflation, interest, exchange rate) and BBCA closing price respectively is Clayton copula with parameter 2.042, Frank copula with parameter 10.3, and Frank copula with parameter 5.891. These findings indicate that inflation shows a strong dependence with BBCA closing price when both variables are low, while exchange rate and interest rate exhibit strong dependence with BBCA closing price when these variables are high. It provides valuable insights into the asymmetric relationships between macroeconomic conditions and stock prices, offering practical relevance for investors and policymakers.
MODELLING AND NUMERICAL ANALYSIS FOR CRACK PROPAGATION IN COMBINING CONCRETE WITH 25% FEATHER SHELL POWDER USING FINITE ELEMENT METHOD Nasution, Marah Doly; Syahputra, Muhammad Romi; Rambe, Isnaini Halimah
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/barekengvol19iss4pp2419-2430

Abstract

This study explores the application of the Extended Finite Element Method (XFEM) for modeling fracture behavior, utilizing COMSOL Multiphysics 5.6 to simulate a homogeneous concrete medium without embedded reinforcement. The computational model incorporates key parameters such as stress ratio (Young’s modulus of 137.9 MPa), lateral strain from axial loading (Poisson’s ratio of 0.17), concrete density of 2.4 g/cm³, and a crack growth rate governed by Paris’ law. The simulation results show a maximum stress intensity factor ( ) of 66.2 and a failure point occurring after approximately 22,568 load cycles. A mixture comprising 25% clamshell ash and lime was used as a sustainable cement substitute, achieving a maximum compressive strength of 20.53 MPa—meeting the structural concrete standard. These findings contribute to enhancing predictive fracture models and promoting sustainable material innovation in civil engineering.
PRIME LABELING OF AMALGAMATION OF FLOWER GRAPHS Rahmadani, Desi; Aldiansyah, Ardi; Pratiwi, Dina; Yunus, Mahmuddin; Kusumasari, Vita
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/barekengvol19iss4pp2431-2442

Abstract

Graph labeling is the assigning of labels represented by integers or symbols to graph elements, edges and/or vertices (or both) of a graph. Consider a simple graph with a vertex-set and an edge-set . The order of graph , denoted by , is the number of vertices on . The prime labeling is a bijective function , such that the labels of any two adjacent vertices in G are relatively prime or , for every two adjacent vertices and in . If a graph can be labeled with prime labeling, then the graph can be said to be a prime graph. A flower graph is a graph formed by helm graph by connecting its pendant vertices (the vertices have degree one) to the central vertex of , such a flower graph is denoted as In this research, we employ constructive and analytical methods to investigate prime labelings on specific graph classes. Definitions, lemmas, and theorems are developed as the main results in this research. The amalgamation is a graph formed by taking all by taking all the and identifying their fixed vertices . If , then we write with . In previous research, it has been shown that the flower graphs , for are prime graphs. Continuing the research, we prove that two classes of amalgamation of flower graphs are prime graphs.

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