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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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NUMERICAL AND CONVERGENCE ANALYSIS OF AN ENHANCED DAI-LIAO METHOD FOR UNCONSTRAINED OPTIMIZATION Hassan, Basim A.; Sulaiman, Ibrahim Mohammed; Subhi, Yeldez J.
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/barekengvol19iss4pp2993-3004

Abstract

Iterative algorithms play an important role in mathematical optimization, particularly in solving large-scale unconstrained optimization problems. The conjugate gradient (CG) methods are widely used due to their low memory requirements and efficiency. However, their performance highly depends on the choice of parameters that influence search directions and convergence speed. Despite their advantages, traditional CG algorithms sometimes suffer from slow convergence or poor accuracy, especially for ill-conditioned problems. The selection of conjugate gradient parameters significantly influences the performance, and there is a need to develop improved strategies to enhance solution accuracy and efficiency. This study constructs a new conjugate gradient parameter using the curvature condition to refine search directions and accelerate convergence. The proposed approach ensures a more effective balance between descent properties and numerical stability. Preliminary numerical experiments demonstrate that the proposed method outperforms classical CG variants regarding convergence rate and accuracy. The improved search directions lead to faster and more reliable optimization solutions. The newly developed conjugate gradient formula contributes to a more robust and efficient optimization. This advancement enhances the applicability of CG methods in solving complex optimization problems, paving the way for more effective computational efficiency.
INTERPOLATION METHODS ELANDT-JOHNSON TO ESTIMATE THE COMPLETE MORTALITY TABLE OF THE INDONESIAN YOUTH POPULATION BASED ON THE MORTALITY TABLE COALE-DEMENY Riningsih, Novia; Widyasari, Rina; Husein, Ismail
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/barekengvol19iss4pp3005-3018

Abstract

The growth of the productive age population has continued to increase since 1971 and looks more significant in 2020. In 2010, the youth age group (16-30 years) reached 62.343.755. The population consists of 31.244.215 men and 31.099.540 women. In 2020, the youth age group will increase to 64.470.655 people, with 32.949.184 men and 31.529.270 women. The number of male youth is greater than the number of female youth. However, in 2020, youth health conditions worsened. Many young people experience severe stress and commit suicide due to depression. This will be one of the causes of the decline in young people in Indonesia. Since the Elandt-Johnson interpolation method provides reliable estimates for adult mortality, this study aims to obtain a more accurate, complete life table for Indonesian youth by applying the Elandt-Johnson interpolation method based on the Coale-Demeny West model a-bridged life table, using secondary data from the 2010 and 2020 Population Censuses provided by Statistics Indonesia. From the research results, it is known that the number of young men who survive until the age of 30 is 94.444 and young women who survive until the age of 30 is 95.724, meaning that the number of young women who survive is higher than young men, this means that the number of deaths of young men is higher than that of young women.
LEVERAGING JAVANESE BATIK MOTIVES IN TEACHING NUMBER PATTERNS: THE PRELIMINARY PHASE IN ETHNO-REALISTIC MATHEMATICS EDUCATION APPROACH Khasanah, Binti Anisaul; Prahmana, Rully Charitas Indra; Adiputra, Sofwan; Khalil, Ibrahim Alhussain; Pepkolaj, Lekë
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/barekengvol19iss4pp3019-3032

Abstract

Traditional textiles, such as Javanese Batik in Indonesia, are not only cultural artifacts but also repositories of mathematical knowledge. While previous studies have explored the geometric transformations embedded in Batik motives, little attention has been paid to their numerical patterns and educational potential beyond geometry. Addressing this gap, the present study investigates the mathematical structures—particularly numerical patterns—and ethical values inherent in Javanese Batik motives. The novelty of this research lies in uncovering the integration of cultural heritage and mathematics through ethnomathematical analysis, which remains underexplored in existing literature. Utilizing an ethnographic approach, including literature review, documentation, and field observations, the study identifies recurring numerical patterns and embedded cultural philosophies within Batik designs. These findings reveal that Javanese Batik offers meaningful contexts not only for teaching mathematical concepts but also for fostering character education through values such as discipline, patience, and harmony. The results suggest that these motives can be transformed into culturally responsive teaching materials, particularly e-modules for learning numerical patterns. This study contributes to the broader field of mathematics education by demonstrating how local cultural artifacts can support cognitive and affective learning goals, thus offering a novel pathway for integrating mathematics with cultural and moral education.
FUZZY MULTI-OBJECTIVE OPTIMIZATION FOR THE PLACEMENT OF REVERSE VENDING MACHINE IN URBAN WASTE MANAGEMENT SYSTEM Boonmee, Chawis; Khuankaew, Nopphamart; Mongkolkittaveepol, Phavika
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/barekengvol19iss4pp3033-3046

Abstract

This study proposes a fuzzy multi-objective optimization model for strategically placing Reverse Vending Machines (RVMs) within urban waste management systems. The research follows a structured methodology comprising seven key stages. First, a conceptual model was designed to address the challenges of post-consumer waste collection. Second, a mathematical model was formulated to optimize two conflicting objectives: maximizing recyclable waste collection and minimizing transportation distances. Third, the model was reformulated using fuzzy parameters—specifically, triangular membership functions—to account for uncertainties in waste generation rates, disposal demand, and transportation costs. Fourth, data were collected from a Lampang Province, Thailand case study covering 15 communities and 17 candidate RVM locations. Fifth, the fuzzy model was solved using the Weighted Sum Method and implemented via exact optimization in LINGO software. Sixth, results were analyzed, showing that five RVMs can be optimally installed under a 5,000,000 THB budget, achieving 23,911.50 kilograms of waste collection with a minimized transportation distance of 179.90 kilometers. Sensitivity analyses on distance, budget, and objective weights revealed key trade-offs between operational efficiency and environmental performance. Finally, the study concludes with implications for policy and planning, emphasizing the potential of fuzzy optimization in enhancing real-world recycling infrastructure. The proposed framework supports data-driven, sustainable decision-making for urban waste systems. Future research may explore dynamic waste generation patterns, behavioral modeling, and the use of metaheuristic algorithms for large-scale implementation.
A STUDY OF DERIVATIONS AND LINEAR MAPPINGS ON SKEW GENERALIZED POWER SERIES MODULES Faisol, Ahmad; Fitriani, Fitriani
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/barekengvol19iss4pp3047-3058

Abstract

This paper investigates the structure of skew generalized power series modules over skew generalized power series rings, emphasizing the extension of derivations in this context. We define and study additive mappings that generalize classical derivations with respect to module homomorphisms and ring derivations. Under suitable compatibility conditions, we construct corresponding derivations on skew generalized power series modules and establish their fundamental properties. These findings contribute to a broader understanding of how derivations can be systematically extended from classical module theory to generalized algebraic frameworks.
OPTIMIZATION OF MEDAN CITY WASTE TRANSPORTATION SYSTEM USING MULTIPLE-TRIP VEHICLE ROUTING PROBLEM (MTVRP) MODEL AND SIMULATED ANNEALING Marpaung, Faridawaty; Arnita, Arnita; Dewi, Sri; Sinaga, Marlina Setia; Widyastuti, Eri
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/barekengvol19iss4pp3059-3072

Abstract

Medan generates approximately 2,000 tons of waste daily, yet only 800 tons are successfully transported to landfills, indicating significant inefficiencies in waste transportation. This study addresses the issue by applying the Vehicle Routing Problem with Multiple Trips (VRPMT) combined with the Simulated Annealing (SA) algorithm to optimize waste transport operations. The VRPMT model allows each vehicle to make multiple daily trips, enhancing fleet utilization while ensuring that all service points are visited, vehicle capacities are not exceeded, and vehicles return to the depot after each trip. The study focuses on Tegal Sari Mandala II (TSM II), Medan Denai, a densely populated neighborhood with narrow roads that require bestari pedicabs for flexible waste collection. Data includes waste collection points, vehicle capacities, transport frequencies, and operational costs. The SA algorithm begins with a random route solution, then iteratively evaluates and improves it by minimizing total distance and cost. It also avoids local optima through a controlled temperature reduction process. Results demonstrate significant improvements: total travel distance was reduced from 12,500 meters to 8,646 meters (a 30.8% reduction), and operational costs decreased from IDR 12,000 to IDR 8,946 (a 25.5% reduction). On average, each bestari pedicab completed two daily trips, maximizing capacity utilization and minimizing penalty costs. The system integrates a structured database and Google Maps API for route visualization, enhancing planning and monitoring. Overall, this approach contributes to more efficient, cost-effective, and environmentally friendly waste transportation. It supports climate action goals and provides a scalable, replicable model for sustainable urban waste management in other regions facing similar logistical challenges. However, this study has some limitations. The VRPMT model was applied only in a neighborhood with a limited vehicle type, which may reduce its generalizability to broader urban areas with more complex logistics. Also, the Simulated Annealing algorithm settings were manually tuned and not benchmarked against other metaheuristic methods. Future studies could improve the model by considering dynamic traffic conditions, integrating real-time data, or testing hybrid optimization approaches to enhance its effectiveness and adaptability.
SEIR MODELING OF TUBERCULOSIS TRANSMISSION WITH VACCINATION: ESTIMATING THE MINIMUM COVERAGE REQUIRED FOR ELIMINATION IN NORTH SUMATERA Nasution, Hamidah; Mulyono, Mulyono; Cyntia S., Maria; Ahyaningsih, Faiz; Nofertinus Zai, Fidelis
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/barekengvol19iss4pp3073-3086

Abstract

Tuberculosis (TB) remains one of the most significant public health challenges in Indonesia, particularly in North Sumatra Province, which records a relatively high prevalence rate. e–Exposed–Infectious–Recovered) A framework to analyze TB's transmission dynamics and evaluate vaccination's effectiveness as an intervention strategy. The primary objective of this research is to estimate the minimum vaccination coverage required to eliminate TB from the population. The model was built by incorporating vaccination rate parameters into the SEIR mathematical model and applied using regional epidemiological data obtained from the North Sumatra Central Bureau of Statistics. A deterministic approach is employed to simulate the system and derive the basic reproduction number ( ), which serves as an indicator of disease persistence across various levels of vaccination coverage. The results of numerical simulations performed using 4th-Order Runge Kutta indicate the existence of a critical vaccination threshold required to reduce below the one-condition that theoretically represents the possibility of disease elimination from the population. These findings provide a quantitative basis for formulating more targeted, data-driven vaccination policies. Calculations based on real-world data reveal that the current R₀ value in North Sumatra remains above one ( ), suggesting that TB continues to pose a risk of remaining endemic. Simulations were also conducted by varying the vaccination coverage while assuming a constant transmission rate, indicating that a minimum of 87.5% vaccination coverage is required to suppress R₀ below the critical threshold. This study underscores the importance of employing mathematical modeling as a decision-support tool in public health policy. The findings deepen the understanding of TB transmission dynamics and offer a robust quantitative foundation for setting vaccination targets for disease elimination in endemic areas such as North Sumatra.
TRAVELING SALESMAN PROBLEM INTEGRATED WITH FUZZY LOGIC ON TOURISM IN D.I. YOGYAKARTA Mukminin, Uskar Sabilil; Yulianti, Irma Sari; Surodjo, 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/barekengvol19iss4pp3087-3104

Abstract

The optimization of tourist travel routes has become a crucial factor in enhancing travel efficiency, reducing costs, and optimizing the overall tourist experience. This study focuses on the innovative integration of fuzzy logic with the Traveling Salesman Problem (TSP) to determine the optimal path for visiting several major tourist destinations in the Special Region of Yogyakarta, a methodological approach not previously explored in existing literature. Initially, we perform data fuzzification, followed by fuzzy inference, to obtain fuzzy outputs. These output values are subsequently used to determine the shortest route using TSP. Several algorithms are utilized, including Minimum Spanning Tree (MST) and Nearest Neighbor (NN). The results show that the Prim algorithm in MST generates the most optimal route, with a travel distance of 223.1 km and a travel time of 442 minutes. Integrating fuzzy logic into the TSP framework effectively addresses uncertainties in distance and time, offering a solid foundation for improved travel route planning.
STRUCTURAL EQUATION MODELING ANALYSIS ON POVERTY IN WEST KALIMANTAN WITH FINITE MIXTURE IN PARTIAL LEAST SQUARE APPROACH Fauzan, Muhammad; Perdana, Hendra; Satyahadewi, Neva
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/barekengvol20iss1pp0001-0016

Abstract

Poverty occurs when individuals or groups lack the necessary resources to fulfill their basic needs. In Indonesia, including West Kalimantan, poverty remains a significant issue influenced by various socio-economic factors. This study aims to identify valid and reliable indicators of poverty and classify regencies/cities in West Kalimantan using the 2023 data from the Central Statistics Agency of West Kalimantan and Indonesia. The analysis applies the Structural Equation Modeling approach with Finite Mixture in Partial Least Squares (FIMIX-PLS). From 19 observed indicators, only 12 were found valid and reliable based on measurement and structural model evaluation. The structural model reveals three significant relationships: the Economy significantly influences Poverty, Health influences Education, and Education influences the Economy. Based on the FIMIX-PLS results, the regencies/cities are segmented into four groups with distinct structural characteristics. Segment 1 reflects the influence of Health on Education, Segment 2 reflects the influence of Health on the Economy, Segment 3 highlights the influence of Economy on Poverty, and Segment 4 captures the influence of Education on the Economy. Detailed interpretations of each segment and their policy implications are presented in the conclusion. The results support the importance of tailored poverty alleviation strategies based on latent regional characteristics and validated model findings.
COMPARISON OF CLUSTERING EARTHQUAKE PRONE AREA IN SUMATRA ISLAND USING K-MEANS AND SELF-ORGANIZING MAPS Ardiyani, Faradilla; Sulandari, Winita; Susanti, Yuliana
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/barekengvol20iss1pp0017-0030

Abstract

An earthquake is a sudden vibration on the earth's surface caused by the shifting of tectonic plates. One region in Indonesia that is particularly prone to earthquakes is Sumatra Island, due to its geographical location at the convergence of two tectonic plates, namely the Indo-Australian plate, which is actively subducting beneath the Eurasian plate. While earthquakes cannot be prevented or avoided, effective disaster mitigation strategies can help minimize the impact. The purpose of this research is to classify earthquake-prone areas on Sumatra Island based on depth and magnitude, allowing for further analysis to determine the characteristics of the clustering results. The study employs two clustering methods to analyze earthquake data from 1973 to 2024: the K-means and Self-Organizing Maps (SOM) algorithm. K-means algorithm is preferred for its simplicity and efficiency in handling large datasets, and suitability for numerical earthquake data analysis. Conversely, the SOM algorithm offers more stable clustering results and preserves the topological structure of the data, making it advantageous for exploring spatial patterns. The research findings indicate that the K-means algorithm provides better grouping, achieving a Silhouette Coefficient of 0.53, compared to 0.47 for the SOM algorithm. The K-means clustering resulted in two clusters: Cluster 1 contains 1,213 members and is characterized by shallow depths (3.9 km-41 km) and larger magnitudes (5 - 8.92 ), indicating a higher risk level. In contrast, Cluster 2 includes 412 members and represents areas with greater depths (40.8 km-70 km) and smaller magnitudes (5 - 6.85 ), corresponding to a lower risk level. This research aims to support the government in its earthquake disaster mitigation efforts, especially on Sumatra Island.

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