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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 1,429 Documents
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A MATHEMATICAL APPROACH OF DUAL CHANNEL SUPPLY CHAIN BY CONSIDERING, CUSTOMER LOYALITY, CORPORATE SOCIAL RESPONSIBILITY, AND DELIVERY TIME Bhecti Purwaningsih; Ririn Setiyowati; Nughthoh Arfawi Khurdi
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp3307-3322

Abstract

Rapid technological advancement has fundamentally transformed consumer purchasing behavior, leading to the widespread adoption of online shopping channels. In this context, timely product delivery has become a critical determinant of customer satisfaction and loyalty in dual-channel markets. At the same time, growing environmental concerns have increased the importance of integrating Corporate Social Responsibility into supply chain decision-making. Motivated by these developments, this study develops a dual-channel supply chain model that simultaneously incorporates customer loyalty, delivery-time sensitivity, and Corporate Social Responsibility. The novelty of the study lies in its integrated analysis of these three factors within two distinct payment schemes, namely real-time payment and prepaid systems, under both decentralized and centralized decision-making structures. Optimal decisions are derived analytically and numerically to determine the pricing and operational strategies that maximize system profits in each setting. Furthermore, sensitivity analysis is conducted to examine how customer loyalty, delivery-time sensitivity, and Corporate Social Responsibility elasticity affect the decision variables and profitability of the supply chain. The results show that increases in customer loyalty and Corporate Social Responsibility elasticity enhance overall system profit. In addition, Corporate Social Responsibility elasticity influences most decision variables, except the wholesale price, manufacturer demand, and retailer demand. These findings provide new insights into the role of payment mechanisms and sustainability-oriented strategies in improving the performance of dual-channel supply chains.
MODIFYING MIXED MODEL NEURAL NETWORKS FOR UNIT-LEVEL PROPORTION SMALL AREA ESTIMATION Ade Riyawan; Muhammad Nur Aidi; Budi Susetyo; Anang Kurnia
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp3323-3340

Abstract

This paper develops a Small Area Estimation Mixed Model Neural Network (SAE-MNN) for unit-level estimation of area-level proportions under clustered binary responses. The method is motivated by a limitation of conventional generalized linear mixed model (GLMM)-based small area estimation, namely the linear specification of the fixed-effects component on the latent scale, which may be inadequate when auxiliary variables exhibit nonlinear effects and higher-order interactions. The proposed model replaces the linear predictor with a neural-network-based nonlinear function while retaining area-level random effects within a likelihood-based mixed-model framework. Thus, SAE-MNN combines nonlinear function approximation with the borrowing-strength mechanism required for coherent small area inference. The method is evaluated through a controlled simulation study and a real-data application. The simulation study considers four scenarios generated by combining two predictor structures (linear and interaction-based nonlinear) with two levels of between-area heterogeneity (small and large), and compares SAE-MNN with a conventional GLMM and a standard deep neural network (DNN). SAE-MNN performs robustly across all scenarios and is especially effective when nonlinear interaction and substantial area-level heterogeneity coexist. In the most complex scenario, SAE-MNN attains the lowest median RRMSE (8.389%), compared with 11.474% for GLMM and 18.826% for DNN, while maintaining empirical coverage between 0.89 and 0.94. In the real-data application, using KSA segment-level harvest proportions to estimate subdistrict-level monthly harvest proportions, SAE-MNN shows the closest overall agreement with the direct estimator, reproduces the main temporal pattern more faithfully than GLMM, and yields moderate shrinkage without excessive smoothing. Overall, the results indicate that SAE-MNN provides a principled compromise between the rigidity of GLMM and the purely predictive character of DNN, thereby extending hybrid small area estimation methodology to binary and proportional outcomes in data-rich settings with nonlinear auxiliary information and area-level heterogeneity.
THREEFOLD HIERARCHICAL SMALL AREA ESTIMATION MODEL FOR ESTIMATING PREVALENCE OF STUNTING IN WEST NUSA TENGGARA Logananta Puja Kusuma; Kusman Sadik; Anang Kurnia
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp3341-3354

Abstract

Stunting is a condition of growth failure in toddlers due to chronic malnutrition, becoming an issue in various regions of Indonesia. West Nusa Tenggara Province has one of Indonesia's highest stunting prevalence rates, calculated at 29.8% in 2024, which is more than twice the national target of 14%. Appropriate and efficient policy-making for stunting reduction requires reliable estimates for small areas like districts. This study aims to produce more reliable district-level estimates of stunting prevalence for districts level area, while direct estimation from the Survei Kesehatan Indonesia (SKI) is unreliable due to limited sample size. This research develops a threefold hierarchical Bayesian (HB) Small Area Estimation (SAE) model based on the Poisson-Gamma distribution to model the number of stunted toddlers as discrete count data with overdispersion. The proposed model incorporates auxiliary variables from official sources and includes three hierarchical random effects representing district, regency/municipality, and grouped regency/municipality levels based on geographical structure. The results show that the threefold HB SAE model achieves convergent parameter estimates and provides more stable and precise district-level stunting prevalence estimates compared to direct estimators. The multilevel model performs better than one random effect model as reflected by the lower LOOIC. The findings also suggest that districts in Sumbawa Island, particularly in the eastern part and areas located farther from regency/municipality capitals, tend to have higher stunting prevalence. However, this study is limited by the assumption of independence among area-level random effects and restricted availability of auxiliary variables. This study contributes methodologically by extending Poisson-based SAE literature through the application of a threefold HB framework in stunting estimation and provides district-level stunting statistics that support evidence-based policymaking and targeted interventions aligned with SDG Target 2.2.
REDUCING BIAS IN PREDICTING POVERTY PERCENTAGE AT THE VILLAGE LEVEL IN BENGKULU CITY USING SMALL AREA ESTIMATION Etis Sunandi; Pepi Novianti; Nurul Hidayati; Anggun Permatasari; Alya Saputri; Lutfiah Firlian; Indah Srilita Asmuyana
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp3355-3370

Abstract

Analysis of poverty rates at the small area level, especially at the village level, often faces obstacles due to limited sample sizes. As a result, the use of direct estimates has large variances, making them less reliable. One solution to this problem is to use the Small Area Estimation (SAE) method. This study aims to apply the Beta-Binomial Small Area Estimation (SAE-BB-APHL) model by utilizing a second-order Laplace approach to estimate fixed effects that were fixed in the previous model, namely SAE-BB-HL. The SAE-BB-APHL model was applied to the case of poverty rates in each village in Bengkulu City. The results show a decrease in Mean Squared Error (MSE) in estimating the poverty rate when using SAE-BB-APHL compared to direct estimation and SAE-BB-HL. The MSE values produced by the direct estimation method in several villages were 0.20638 in village 1, 0.04865 in village 2, and 0.04865 in village 46. Meanwhile, the SAE-BB-APHL method successfully reduced the MSE to 0.00524 in village 1, 0.00493 in village 2, and 0.00630 village 46. In addition, the MSE in SAE-BB-APHL is also smaller than SAE-BB-HL as evidenced in Table 3. This decrease in MSE indicates that bias is reduced by using the SAE-BB-APHL method. Therefore, this approach can be a superior alternative in poverty analysis at the village level. More accurate estimation results are expected to assist the government in designing more targeted poverty alleviation policies.
SPATIO-TEMPORAL MODELING OF SEMI-HETEROSKEDASTIC RAINFALL DATA USING A GSTAR-GARCH FRAMEWORK Nurhayati Nurhayati; Muhammad Rozzaq Hamidi; Utriweni Mukhaiyar; Kurnia Novita Sari
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp3371-3390

Abstract

Rainfall often varies across time and space, with sudden and irregular changes that are difficult to capture. These variations are commonly linked to residual heteroskedasticity and spatial dependence, both of which can reduce the accuracy of statistical modeling when ignored. This study considers a semi-heteroskedastic setting, where residuals at one location remain stable while those at another show varying variance. To accommodate this mixed structure, we construct a covariance matrix that reflects both conditions. A hybrid model is then proposed by combining the Generalized Space-Time Autoregressive (GSTAR) framework with the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) process. The GARCH component is used because it generalizes ARCH through a more flexible lag structure, allowing for better representation of volatility persistence and long-term fluctuations. The approach is applied to monthly average rainfall data retrieved from the NASA POWER database for two sites in Tasikmalaya Regency, Indonesia, which differ in distributional patterns and variability. The results show that the GSTAR-GARCH model can effectively capture spatial and temporal dependencies as well as volatility dynamics, performing consistently in both estimation and validation stages.
BASIC-STATE ANALYSIS OF NANOFLUID BIOCONVECTION WITH GYROTACTIC MICROORGANISMS UNDER ZERO-NANOPARTICLE FLUX BOUNDARY CONDITION Ming Hui Lim; Yian Yian Lok; Syakila Ahmad; Norshafira Ramli; Anuar Ishak
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp3391-3404

Abstract

This study presents an analysis of the basic state of nanofluid bioconvection in a horizontal finite-depth layer containing gyrotactic microorganisms. To enhance the physical realism of the system, zero-nanoparticle flux boundary conditions are incorporated for the nanoparticle fraction. The basic-state solution refers to a simplified, time-independent configuration that serves as the reference or background state for analysing perturbations in stability analysis. In this case, the quiescent flow has zero velocity, while other state variables - such as temperature, nanoparticle concentration, and microorganism density - vary only in the vertical direction. The resulting system of ordinary differential equations is solved to obtain analytical solutions while the effects of key parameters on the steady-state profiles are investigated. The results show that the swimming strength parameter mainly influences microorganism accumulation near the upper boundary. Both the swimming strength parameter and the bioconvection Rayleigh number have only a limited effect on the pressure profile. In contrast, the thermal Rayleigh number and modified diffusivity ratio produce the most noticeable pressure variations, indicating that thermal and thermophoretic effects play the dominant role in shaping the basic-state pressure distribution. Overall, the pressure profile remains nearly linear. The findings provide insight into the role of zero-nanoparticle flux boundary conditions in finite-depth nanofluid bioconvection systems.
HEAT AND MASS TRANSFER ANALYSIS ON MHD GO-AG-CUO-AL2O3/EG NANOFLUID FLOW PAST SHRINKING SHEET Nooraini Zainuddin; Nur Syahirah Wahid; Iskandar Waini; Nor Ain Azeany Mohd Nasir; Norihan Md Arifin; Norli Abdullah
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp3405-3424

Abstract

This study discovers the mass and heat transfer characteristics of a magnetohydrodynamic GO-Ag-CuO-Al₂O₃/EG nanofluid streaming past a shrinking sheet under the force of various physical effects. The Powell-Eyring fluid model is engaged to account for the effect of a magnetic field, a stagnation point, viscous dissipation, radiation, Joule heating, and suction. Through similarity transformations, the governing partial differential equations are reduced to a system of ordinary differential equations, which are then resolved numerically using the bvp4c solver in MATLAB. The results affirmed that raising the heat transfer complements the thermal boundary layer, whereas reductions in the skin friction coefficient contribute to a reduction in drag force. Moreover, the velocity profile rises because of the shrinking effect, while the temperature profile decreases. The enhanced thermal conductivity provided by the quaternary nanoparticle suspension (GO-Ag-CuO-Al₂O₃) suggests that this fluid can maintain lower surface temperatures under high-heat flux conditions compared to mono or hybrid nanofluids. Consequently, these characteristics are particularly advantageous for electronic device cooling and heat exchangers in renewable energy systems where rapid heat dissipation is critical. Furthermore, the observed reduction in drag force under the influence of the magnetic field provides a theoretical basis for optimizing energy efficiency in magnetohydrodynamic pumps and metallurgical processing. These findings offer specific design parameters for boosting thermal management in industrial applications involving tetra-hybrid nanofluids.
COMBINATION OF CONTENT VALIDITY INDEX AND FUZZY DELPHI FOR EXPERT VALIDATION OF A THREE-TIER MATHEMATICS LEARNING DIFFICULTIES DIAGNOSTIC ASSESSMENT Khaerun Nisa; Iva Sarifah; Riyadi Riyadi
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp3425-3438

Abstract

The persistent challenges in identifying mathematics learning difficulties require diagnostic instruments that are not only valid but also capable of accurately capturing students’ conceptual understanding, reasoning, and confidence. This study aims to compare the Content Validity Index (CVI) and the Fuzzy Delphi Method (FDM) in expert validation of a three-tier diagnostic assessment for mathematics learning difficulties. Theoretically, the study integrates classical content validation theory with fuzzy logic-based expert consensus analysis to strengthen the methodological rigor of instrument development. The research involved five doctoral-level experts who evaluated 21 diagnostic items. The CVI results yielded an excellent S-CVI/Ave value of 0.97, indicating high content validity, while the FDM results confirmed 20 of 21 items met the validity thresholds (d ≤ 0.2, consensus ≥ 75%, A ≥ 0.5). A key finding shows that the CVI provides clear numerical validation, whereas the FDM captures linguistic uncertainty and confidence variations among experts, producing a more comprehensive validation outcome. The integration of both methods offers a robust framework for expert validation that enhances interpretive depth and accuracy. This study contributes to the field of mathematics education by presenting a validated, reliable, and pedagogically meaningful diagnostic instrument for identifying students’ misconceptions and reasoning patterns.
SMART INDOOR NAVIGATION FOR MOBILE ROBOTS: A HARMONIC POTENTIAL-BASED APPROACH WITH ACCELERATED OVER-RELAXATION ITERATIVE METHOD A'Qilah Ahmad Dahalan; Rupal Srivastava; Ruzanna Mat Jusoh; Azali Saudi; Jumat Sulaiman
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp3439-3458

Abstract

Path planning for autonomous mobile robots remains a critical challenge, particularly in environments with obstacles and constraints. Efficient navigation requires a robust algorithm capable of generating smooth, collision-free trajectories while ensuring computational efficiency. This study addresses the problem of indoor mobile robot navigation by leveraging harmonic potential fields, a solution derived from Laplace’s equation, to formulate an effective path-planning strategy. Conventional numerical methods for solving Laplace’s equation, such as Successive Over-Relaxation and Accelerated Over-Relaxation, often require extensive computational resources, especially in large-scale environments. To overcome this limitation, this research introduces an improved iterative approach, the Explicit Decoupled Group Modified Accelerated Over-Relaxation (EDGMAOR) method, which enhances computational efficiency and convergence speed. The EDGMAOR method incorporates a half-sweep block approach, significantly reducing the number of computations required per iteration while maintaining accuracy. To validate the effectiveness of the proposed method, simulations were conducted in a static, enclosed environment with various configurations of obstacles. Different starting and goal positions were tested to assess the efficiency, accuracy, and computational cost of the generated paths. The results indicate that the EDGMAOR method outperforms conventional approaches by achieving faster convergence rates and reduced computational time, demonstrating its suitability for real-time robot pathfinding applications. Furthermore, the study highlights that with greater obstacles proliferation, the EDGMAOR method maintains its efficiency, as obstacle regions are automatically excluded from unnecessary computations. This characteristic makes the method particularly useful for complex indoor environments where real-time processing is crucial. In conclusion, this research establishes EDGMAOR as a practical and effective solution for solving mobile robot path-planning problems, providing a balance between computational speed, accuracy, and robustness. The findings contribute to the ongoing advancements in autonomous robotics and artificial intelligence-driven navigation systems, with potential applications in industrial automation, smart transportation, and defence sectors.
INVESTIGATION ON TOPOLOGICAL INDICES OF LINE GRAPH BASED ON SUBDIVISION APPROACH FOR ABID-WAHEED GRAPH Mohamad Nazri Husin; Kee Yeong Chua
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp3459-3472

Abstract

In chemical graph theory, there is the study of Quantitative Structure Property Relationships (QSPR) and Quantitative Structure Activity Relationships (QSAR) that uses topological in dices which are numerical measures for the structures of molecular graphs. These topological indices are also able to predict the physico-chemical properties of chemical compounds such as boiling points, enthalpy of vaporization and stability. This paper aims to generalize the Randić index, geometric-arithmetic index, atom-bond connectivity index, first Zagreb index and second Zagreb index for a line graph of Abid-Waheed graph and a line graph of subdivision graph of Abid-Waheed graph. An analysis and comparison of the topological indices studied are also computed and shown. This study successfully generalized and compared several topological indices for Abid-Waheed Graph.

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