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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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SYMBOLIC COMPUTATION APPROACH TO REDUCE ROUNDING ERRORS IN NUMERICAL OPERATIONS USING RYACAS Anom Yudistira, I Gusti Agung; Ivanky Saputra, Kie Van
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/barekengvol20iss1pp0743-0754

Abstract

Computational operations on computers produce only approximations due to the limitations of numerical representation, finite precision arithmetic, and hardware constraints. For simple calculations, these errors are usually negligible. However, in a sequence of numerical computations, they can propagate and accumulate, leading to significant inaccuracies and becoming a critical issue, where small errors can have substantial consequences. R, like other programming languages designed for numerical computations, is not immune to precision errors. One approach to this issue is to preserve exact values throughout calculations. In R, there are several packages, such as Ryacas and Ryacas0 enable symbolic computation, which allow true values to be maintained during operations. In this paper, we propose an application of computational techniques that effectively eliminates precision errors arising from numerical calculations. We developed a user-defined function for solving linear systems using Gauss-Jordan row elementary operations. We first developed a function to solve linear systems without using the Ryacas package, named OBE.R, and another function with the same purpose but now using Ryacas, named yac-OBE.R. These two functions are compared, and as expected, the latter eliminates numerical precision errors; hence, the accuracy is one hundred percent improved. Additionally, this study is limited to solving linear systems with a unique solution and does not discuss cases with multiple solutions or no solution. Also, symbolic computation as implemented via Ryacas typically requires more processing time.
COMPARISON OF COPULA FAMILY (GAUSSIAN, ARCHIMEDEAN, AND REGRESSION) IN A CASE STUDY OF COMPOSITE STOCK PRICE INDEX ON INDONESIA STOCK EXCHANGE Darwis, Darwis; Sartono, Bagus; Yuliani, Leny
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/barekengvol20iss1pp0755-0768

Abstract

Stocks are one of the most popular financial market instruments. On the other hand, stocks are an investment instrument that is widely chosen by investors because stocks are able to provide attractive profit levels. Investment is an effort to postpone consumption in the present. Comparing copula families is crucial for selecting the model that best fits the observed data dependency structure. This helps produce more accurate analysis and more meaningful interpretations. This study analyzes different types of copula relationships using the Tau Kendall method, applying it to the movement of the Composite Stock Price Index (IHSG) on the Indonesia Stock Exchange (IDX). The data used are secondary monthly data of IHSG as a response variable, while the explanatory variables are inflation (%), exchange rate (Rp/USD), and interest rate (%) in 2010-2014. The results show the pattern of the relationship between IHSG and its macroeconomic factors on the IDX using copula parameter estimation with the Tau Kendall approach, with the largest log-likelihood fitting results showing a relationship pattern following the Gumbel copula, namely IHSG with inflation, interest rates with IHSG following the Clayton copula, and exchange rates following the Frank copula. Meanwhile, using the regression copula has better interpretation results compared to the Gaussian and Archimedean copula, with an MAPE value of 0.122 with a correlation of 70.63%.
THE APPLICATION OF FUZZY LOGIC IN CLUSTERING PROVINCES BASED ON SOCIAL WELFARE, ECONOMIC STATUS, AND HEALTHCARE FACILITIES Muhammad, Hubbi; Fatimah, Iik Nurul
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/barekengvol20iss1pp0769-0784

Abstract

Assessing the quality of life across provinces in Indonesia requires a comprehensive evaluation of multiple socio-economic indicators. This study applies Fuzzy Inference Systems (FIS), specifically the Mamdani and Sugeno models, to cluster Indonesian provinces based on five key parameters: Gross Regional Domestic Product (GRDP), crime rate, open unemployment rate, the number of senior high schools, and the number of hospitals. These indicators collectively represent economic status, public safety, employment conditions, educational infrastructure, and healthcare access, fundamental components of social well-being. The use of fuzzy logic allows for nuanced modeling of complex and uncertain data, accommodating both quantitative and qualitative dimensions. Data were obtained from the Indonesian Central Bureau of Statistics and processed using MATLAB’s fuzzy logic toolbox. The results show consistent clustering outputs from both FIS approaches, with most provinces falling within the mid-level cluster. The findings highlight regional disparities that can inform targeted development policies. Moreover, while the ecological dimension was not directly modeled, it is recognized as an underlying factor influencing the observed socio-economic patterns. This framework provides a flexible and adaptable method for future studies incorporating environmental variables to support sustainable regional development.
COMPARISON OF XGBOOST AND RANDOM FOREST METHODS IN PREDICTING AIR POLLUTION LEVELS Pulih Asih, Akas Yekti; Yudianto, Firman; Triwinanto, Puguh; Sinatriya Marjianto, Rachman; Herlambang, Teguh; Arof, Hamzah
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/barekengvol20iss1pp0785-0796

Abstract

Air is one of the elements needed by living things, including humans, to survive. The air quality in an area also affects the health and quality of human life and its surrounding environment. However, with the current phenomenon, the influence of the increasing number and mobility of humans actually degrades air quality, caused by the pollutants produced. For further impacts, poor air quality can reduce human life expectancy. Big cities in Indonesia, such as Surabaya, also experience the same thing due to the lack of public awareness of air pollution. The biggest contributors to air pollution are motor vehicles and industrial activities that emit carbon monoxide (CO), nitrogen oxides (NO), ozone (O3), and other particles (PM10). This condition is addressed by the Surabaya City Government by installing air condition measuring devices at points considered prone to pollution. This device works to measure urban air conditions daily and provides data that can be utilized to establish strategic policies. By utilizing the data, in this research, we implemented two prediction methods from machine learning technology, namely XG Boost and Random Forest. In accordance with the objective of this research, both methods will be compared for accuracy in predicting air pollution levels in Surabaya based on Ozon (O3) substance within the period of January 1, 2020, to December 31, 2020. Both of them have a similarity in that they implement tree-ensemble based, which are appropriate for handling non-linear data. The XG Boost method managed to achieve the best error value of 0.0510, and the Random Forest method reached the best error value of 0.0468.
APPLICATION OF COOPERATIVE GAME THEORY: SOLVING THE PROBLEM OF TRAVELING BETWEEN FIVE CITIES IN JAVA Ariyanto, Muhammad Aditya Tri; Setiawan, Rubono
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/barekengvol20iss1pp0797-0814

Abstract

Intercity travel between Surabaya, Madiun, Surakarta, Semarang, Cirebon, and Jakarta is increasingly facilitated by integrated infrastructure such as toll roads, railways, and airports. Among travelers, forming informal coalitions with others heading in the same direction has become a practical way to reduce individual travel expenses. This study aims to analyze the cost-efficiency of coalition-based intercity travel compared to solo travel, utilizing cooperative game theory to determine fair contribution values among travelers. This study aims to analyze the cost-efficiency of coalition-based intercity travel compared to solo travel, utilizing cooperative game theory to determine fair contribution values among travelers. A case study was conducted in an urban setting involving individuals who travel intercity using various transportation modes. Data were collected through semi-structured interviews. The study applied the Shapley value method within cooperative game theory to model and evaluate each participant’s contribution in a travel coalition. An algorithm was developed to calculate Shapley values for different coalition scenarios. Initial expenditures were: Player A (IDR 210,000), B (IDR 240,000), C (IDR 60,000), D (IDR 400,000), and E (IDR 165,000). First calculation (5-player coalition): A spent IDR 122,750, B IDR 147,750, C IDR 77,750, D IDR -52,250, and E IDR 104,000. Player C opted out, as joining the coalition would cost more than traveling individually (IDR 60,000). Second calculation (4-player coalition): A spent IDR 113,750, B IDR 133,750, D IDR 53,750, and E IDR 98,750. The study’s findings are based on a small sample with specific subject criteria and cannot be generalized to broader intercity travel scenarios. This research demonstrates the practical application of game theory—specifically the Shapley value—in modeling travel coalitions and optimizing cost distribution, offering insights for policy makers and transport planners in collaborative travel schemes.
POISSON MIXED MODELS WITH A BOOSTING APPROACH FOR THE ANALYSIS OF COUNT DATA Wulandari, Ita; Notodiputro, Khairil Anwar; Sartono, Bagus; Fitrianto, Anwar; Kurnia, Anang
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/barekengvol20iss1pp0815-0828

Abstract

Boosting is a powerful technique for enhancing predictive accuracy by iteratively reweighting observations, and is particularly effective in high-dimensional settings and for variable selection. While previous studies have demonstrated the advantages of integrating boosting with generalized linear mixed models (GLMMs) for binary outcomes, its application to count data within hierarchical frameworks remains limited. This study addresses that gap by extending boosting methods to count data through the development of a boosted Poisson mixed model (bPMM), a novel approach for small area estimation and variable selection in complex survey designs. The proposed model is applied to fertility data in the Indonesian provinces of Bali and East Nusa Tenggara, where the response variable is the number of live births and the predictors include twenty-eight socio-demographic covariates. Using the Akaike Information Criterion (AIC) for model selection, three significant variables were identified in Bali (Model 1), and one in East Nusa Tenggara (Model 2). The results demonstrate that bPMM not only improves variable selection in high-dimensional settings but also accommodates hierarchical structure in count data.
ESTIMATING MODULARITY BOUNDS FOR HOMOPHILIC SCALE-FREE NETWORKS Shergin, Vadim; Udovenko, Serhii; Miroshnychenko, Tetiana; Chala, Larysa; Dorokhov, Oleksandr
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/barekengvol20iss1pp0829-0840

Abstract

The problem of estimating the modularity boundaries for networks that are both homophilic and scale-free is considered. The key property of homophilic networks is the tendency of nodes to link with similar nodes, i.e., belonging to the same community. Thus, homophily is a natural mechanism for community formation, i.e., network structuring. One of the measures of network structuring is modularity. In homophilic networks, not only can the distribution of node degrees be scale-free, but also the distribution of community sizes. In this case, communities can differ significantly in size, which leads to narrowing the achievable modularity boundaries. Estimates of the modularity boundaries of networks of the considered class are obtained. Mathematically strict estimates contain non-elementary functions, which complicates the practical application of such estimates. Approximate estimates with high (0.005) accuracy for the most characteristic values of network parameters are obtained.
ISLAMIC MORTGAGE FINANCING: DETERMINATION OF AN OPTIMAL NISBAH OF PROFIT-SHARING SCHEME UNDER MUSHARAKAH MUTANAQISAH CONTRACT Kamilah, Wulan Nurul; Sumarti, Novriana; Sidarto, Kuntjoro Adji
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/barekengvol20iss1pp0841-0852

Abstract

In an Islamic investment using a profit-sharing scheme, one of the important issues to be determined is the optimal value of nisbah, so that all the parties are fairly treated. This study aims to determine the optimal constant nisbah for an Islamic home financing under musharakah mutanaqisah (MMQ) contract, to ensure a fair arrangement for both parties: the Islamic Bank (IB) and the customer. Under MMQ, the model combines partnership (Musharakah) and a leasing agreement, with gradual ownership transfer from the IB to the customers using an installment payment. For describing its dynamic, the customer’s income is assumed to follow the Geometric Brownian Motion (GMB), and the defined objective function is solved using the simulated data of payments of rental fee and ownership installment. Based on the simulation results, it will show that the middle value of a parameter of the defined objective function as a biased portion, with , is not always chosen. The objective function, which shows a parabolic plot trend, can be interpreted as a fair situation between the IB and the customer. With the selected α value, the maximum objective function value will be sought. The determined nisbah can inform policy decisions in Islamic financial institutions.

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