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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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MULTIPLE STATE MODEL FOR PREMIUM CALCULATION OF THE ELDERLY LONG-TERM CARE INSURANCE Aini, Nadhira Fajri; Ruhiyat, Ruhiyat; Erliana, Windiani
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/barekengvol19iss4pp2443-2454

Abstract

As Indonesia enters an ageing population phase—with 12% of its population categorized as elderly—the need for financial protection in later life is increasingly urgent. The elderly population faces declining economic productivity, increased health risks, and a growing need for long-term care support. To address this, the present study develops an actuarial framework for calculating net annual premiums for elderly long-term care (LTC) insurance using the equivalence principle and a five-state multiple state model. Unlike previous research that focused on critical illness insurance, the proposed model reflects elderly care needs more realistically by incorporates transitions into and out of dependency where the elderly need assistance to perform daily activities. The results show that premiums rise significantly with later enrollment ages due to higher dependency and mortality risks along with shorter contribution periods. Furthermore, cash flow simulations based on 500 life table iterations demonstrate that LTC insurance can remain financially sustainable when accurately priced and supported by stable investment returns. This study offers a novel actuarial approach to developing sustainable LTC insurance products for Indonesia’s ageing population.
CERTAIN INDEXES OF UNIT GRAPH IN INTEGER MODULO RINGS WITH SPECIFIC ORDERS Lestari, Sahin Two; Albaracin, Jimboy R.; Wisnu Wardhana, I Gede Adhitya
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/barekengvol19iss4pp2455-2466

Abstract

Topological indices quantify structural properties of graphs and find wide applications in chemistry, physics, and network analysis. This study investigates several key indices—namely the Harary Index, Wiener Index, Randić Index, Schultz Index, and the Zagreb Indices—within the context of unit graphs derived from the ring of integers modulo. General formulas for these indices are established, demonstrating how they reflect the combinatorial and algebraic characteristics of unit graphs. Each index captures distinct structural aspects: the Wiener Index evaluates global connectivity and correlates with molecular stability and boiling points; the Randić Index highlights molecular branching relevant to enzyme activity; the Harary Index models electronic interactions through distance reciprocals; and the Zagreb Indices and Schultz Index provide insights into bonding properties and molecular interactions. By linking these indices to unit graphs, this work reinforces the synergy between graph theory and algebra, offering a systematic framework to interpret algebraic structures through graph-based invariants. The results not only contribute to theoretical understanding but also suggest potential applications in modeling chemical compounds and complex networks, paving the way for further exploration of topological indices in other algebraically defined graphs.
BIRESPONSE SPLINE TRUNCATED NONPARAMETRIC REGRESSION MODELING FOR LONGITUDINAL DATA ON MONTHLY STOCK PRICES OF THREE PRIVATE BANKS IN INDONESIA Pahlepi, Reza; Sriliana, Idhia; Agwil, Winalia; Oktarina, Cinta Rizki
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/barekengvol19iss4pp2467-2480

Abstract

This study investigates the application of a truncated spline nonparametric regression model for biresponse analysis of longitudinal data, focusing on modeling monthly stock prices specifically opening and closing prices of three private banks in Indonesia: Bank Mayapada, Bank Mega, and Bank Sinar Mas. The data used in this research are secondary data sourced from the website Id.Investing.com and monthly financial statement publications of three private banks in Indonesia. Longitudinal data, combining cross-sectional and time-series dimensions, are utilized to capture trends and patterns not detectable in traditional cross-sectional analysis. The truncated spline method is selected for its adaptability to nonlinear relationships and abrupt data behavior changes. The model incorporates three predictor variables traded stock volume, total assets, and total liabilities and evaluates their influence on stock prices. Assumptions of longitudinal data are validated using the Ljung-Box autocorrelation test, Bartlett’s sphericity test, and Pearson correlation. Results confirm significant within-subject correlations, independence between subjects, and strong interdependence between response variables. The optimal configuration is determined using Generalized Cross Validation (GCV), with up to three knots considered for segmentation. Weighted Least Squares (WLS) is employed for parameter estimation, accounting for within-subject correlations. Model evaluation based on Mean Absolute Percentage Error (MAPE) indicates high accuracy, with all MAPE values below 5%. The highest MAPE value is 4.41% for the closing price of Bank Mayapada, while the lowest is 2.65% for the opening price of the same bank. The segmentation analysis reveals that traded stock volume and total assets positively influence stock prices, while total liabilities exhibit a predominantly negative impact. The model is limited to internal financial indicators and does not include external macroeconomic factors such as interest rates or inflation. This study is the first to apply a biresponse truncated spline nonparametric regression approach to analyze stock prices of private banks in Indonesia by simultaneously modeling both opening and closing prices, providing a flexible and effective method for capturing complex patterns in longitudinal financial data.
ETHNOMATHEMATICS IN ARCHITECTURE: EXPLORING GEOMETRY AND PATTERNS IN THE WE TENRI OLLE TOMB Naufal, Muhammad Ammar; Ja'faruddin, Ja'faruddin; Satrina, Satrina; Latif, Lhenny Ardillah; Novianti, Gita Eka; Risaldi, Risaldi; Muhammad, Fadhel; Hassan, Muhammad Nasiru
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/barekengvol19iss4pp2481-2494

Abstract

This study explores the application of ethnomathematics in the We Tenri Olle Tomb, located in Pancana Village, Barru Regency, South Sulawesi. The study aims to identify mathematical concepts, particularly geometry, embedded within the tomb’s architectural elements. Using a qualitative descriptive method, data were collected through direct observation and literature review. The results show that the tomb's design reflects the application of planar geometry concepts, such as rectangular walls, and spatial geometry, such as a semi-spherical dome. Geometric transformations, including reflections on walls, translations in floral patterns, and rotations in window designs, were also identified. The tomb design embodies the dynamic cultural acculturation between the local Bugis culture and European colonial influences while symbolizing the diplomatic relationship between the Tanete Kingdom and the Netherlands. This study contributes to ethnomathematics by connecting cultural heritage with mathematical concepts and providing insights for developing culture-based mathematics education to enhance students’ understanding of geometry and appreciation for local traditions.
STRATEGY FOR ELIMINATING NEGLECTED TROPICAL DISEASES THROUGH INDIVIDUAL AND AREA ASPECTS USING THE HIERARCHICAL LOGISTIC REGRESSION METHOD Oktora, Siskarossa Ika; Matualage, Dariani; Amalia Pasaribu, Asysta; Fitriyani Sahamony, Nur; Kurnia, Anang
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/barekengvol19iss4pp2495-2506

Abstract

Filariasis is one of the Neglected Tropical Diseases (NTDs) that is often associated with poverty and marginalized community groups. Papua is the province with the highest number of chronic filariasis cases and has the largest number of endemic districts/municipalities compared to other provinces in Indonesia. Papua is also the province with the highest poverty rate in Indonesia. To support the government's filariasis elimination program, this study aims to determine variables that influence the incidence of filariasis in Papua at the individual and area levels. This study uses 2018 Indonesia Basic Health Research data from the Ministry of Health and regional data from BPS-Statistics Indonesia. The results using Hierarchical Binary Logistic Regression concluded that defecation behavior in latrines, prevention behavior against mosquito bites, participation in mass preventive drug administration, number of poor people, and number of health workers have a significant effect on the incidence of filariasis. In contrast, the variables age, gender, type of work, and level of education do not have a significant effect.
OPTIMIZING BI-OBJECTIVE MULTIPLE TRAVELING SALESMEN ROUTES FOR DISASTER RELIEF LOGISTICS USING GENETIC ALGORITHM Sihombing, Amos Hatoguan; Herdiana, Ratna; Pratama, Jovian Dian
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/barekengvol19iss4pp2507-2520

Abstract

Handling natural disasters such as floods requires efficient logistics distribution to minimize the negative impact on victims. Distribution route optimization becomes very important in this process. This paper applies a metaheuristic method using Genetic Algorithm to the Bi-objective Multiple Traveling Salesman Problem (BMTSP) to obtain a solution that minimizes the distance and time to deliver disaster relief logistics. Multiple vehicles are used in this study to represent delivery agents with two main objectives, namely minimizing total distance and travel time. Genetic Algorithm is applied by considering these two main objectives through the process of selection, crossover, mutation, and produces an effective Pareto solution. The results indicate that applying the Genetic Algorithm to the Bi-Objective Multiple Traveling Salesman Problem yields more efficient delivery routes—reducing both distance and time—compared to the Nearest Neighbor Algorithm. The simulation and testing in this study utilize data on distances and travel times among Central Java Regional Disaster Management Agency offices in 19 regencies—including a central depot—located in flood-prone areas of Central Java Province. The scenario involves two vehicles with identical load capacities.
THE TRIPLE IDENTITY GRAPH OF THE RING Z_n Kurniawan, Vika Yugi; Ekasiwi, Chessa Fanny; Wiyono, Santoso Budi
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/barekengvol19iss4pp2521-2530

Abstract

Let be a commutative ring with identity and is an identity element of . The triple identity graph of the ring , represented by ), is an undirected simple graph with the vertex set . In , two different vertices and is called adjacent if there is an element such that and . The triple identity graph of the ring of integers modulo , represented by , is the subject of this study. We obtain several results regarding the properties of the graph , which are summarized as follows. The graph is a connected graph if and only if is prime and . If is connected, then diam and gr. Furthermore, is a Hamiltonian graph if is a prime number and .
IMPROVING SUPPORT VECTOR MACHINE PERFORMANCE WITH BINARY GAUSSIAN IMPROVED WHALE OPTIMIZATION ALGORITHM: A CASE STUDY ON DIABETES DATA Fajri, Haidar Ahmad; Ardiyansa, Safrizal Ardana; Anam, Syaiful; Maharani, Natasha Clarrisa; Julianto, Eric
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/barekengvol19iss4pp2531-2542

Abstract

Diabetes mellitus is a chronic condition with high blood sugar that can cause severe organ damage, affecting all ages globally. Early diagnosis is crucial for improving patients' quality of life, and machine learning offers a promising approach. The Support Vector Machine (SVM) is effective for classification, but feature selection is essential to enhance the relevance of features. The Whale Optimization Algorithm (WOA) is an optimal method for global feature selection, but it has a drawback-premature convergence, which can lead to suboptimal results. This issue should be addressed by modifying mutation operations, convergence factors, and population initialization, resulting in Binary Gaussian IWOA (BGIWOA). This research focuses on feature selection using BGIWOA, comparing it with Variance Inflation Factor (VIF) using SVM. The result show that BGIWOA is better than VIF and the best configuration BGIWOA’s parameter is with linear kernel. This configuration produces the best accuracy of 95.00%. BGIWOA-SVM demonstrates better accuracy with stable consistency compared to VIF-SVM. The best SVM model achieves average accuracy of 95.62% for training data and 95.58% for validation data, with an accuracy of 93.85% for the test data. This model also yields an average precision of 94.00%, a recall of 91.00%, and an -score of 92.00%. The model was also better than SVM without optimization, which only achieved a training accuracy of 84.25% and a testing accuracy of 81.30%. This model can assist in diagnosing diabetes with accurate and consistent predictions for new data. The results are specific to the diabetes dataset used in this research, so further testing on other binary datasets is necessary to confirm the model's effectiveness and generalizability across different domains and types of data.
AN EXAMINATION OF THE GREEN STOCK PORTFOLIO IN CONNECTION WITH THE 2024 INDONESIAN REPUBLIC PRESIDENTIAL GENERAL ELECTION Sulistianingsih, Evy; Martha, Shantika; Andani, Wirda; Agustono, Hendri; Pebriyandi, Rifki; Gunawan, Risky; Maharani, Cinta Priscillia
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/barekengvol19iss4pp2543-2556

Abstract

The presidential election of the Republic of Indonesia occurs on a frequency of once every five years. The present work investigated the impact of the 2024 Presidential Election on the performance of the optimal stock portfolio constructed by K-Means Clustering during the first phase of stock selection. Subsequently, the portfolio will be evaluated using two distinct approaches, namely Mean Absolute Deviation (MAD) and Mean-Variance Efficient Portfolio (MVEP). Both techniques were employed to construct several portfolios throughout three time periods: before the Presidential Election (13 August 2023 to 13 February 2024) and after the Presidential Election (15 February to 15 April 2024 and 20 April 2024 to 20 May 2024). This was done by implementing a mechanism to manage the allocation of shares in order to optimize the portfolio. The analyzed data is historical data on daily green stock closing prices indexed on the SRI-KEHATI index. A portfolio was constructed and subsequently evaluated for its performance using the Sharpe Index. The findings of this study suggest that the upcoming 2024 general election for the presidency of the Republic of Indonesia had a favorable impact on the Indonesian capital market, particularly for stocks that are indexed by SRI-KEHATI. This criterion was proposed based on the observation that the average Sharpe ratio index for Period II and Period III exceeds the average Sharpe ratio index for Period I (prior to the election day). The most optimal portfolio examined in this study was the MVEP portfolio, mostly composed of assets in the primary consumer products industry, with a Sharpe ratio of 0.53586. Furthermore, the performance of portfolios in period III (after the election result release) was far superior to that of other portfolios examined in previous periods.
MODELING POVERTY IN WEST JAVA PROVINCE USING NEGATIVE BINOMIAL REGRESSION WITH PENALIZED SMOOTHLY CLIPPED ABSOLUTE DEVIATION Santi, Vera Maya; Baihaqi, Aulia; Siregar, Dania
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/barekengvol19iss4pp2557-2570

Abstract

The number of poor people is an example of discrete or count data. One commonly used regression model for count responses is the Negative Binomial regression. Regression modeling with many predictor variables results in the problem of multicollinearity. This condition causes the parameter estimator to become unstable. One method to overcome this problem is to use the penalty function to optimize the selection of predictor variables. This study aims to analyze the factors influencing the number of poor people in West Java Province using Negative Binomial regression with the Smoothly Clipped Absolute Deviation (SCAD) penalty function. The research data was sourced from the Central Bureau of Statistics in 2022, covering 27 districts/cities in West Java Province with 21 predictor variables. The method applied selects variables and estimates parameters simultaneously in the Negative Binomial regression model. Based on the AIC value, it was found that the Negative Binomial penalized SCAD model (AIC = 628.12) had better performance than the Negative Binomial regression model (AIC = 634.34). The Negative Binomial penalized SCAD regression model yielded five significant predictor variables with value of 92.8%. This model is simpler than the Negative Binomial regression model with six predictor variables. The regional minimum wage, number of cooperatives, percentage of the population who have health insurance, the pure college enrollment rate, and non-food expenditure are important variables as factors affecting the number of poor people in West Java Province.

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