Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi is a national journal intended as a communication forum for mathematicians and other scientists from many practitioners who use mathematics in the research. Euler disseminates new research results in all areas of mathematics and their applications. Besides research articles, the journal also receives survey papers that stimulate research in mathematics and its applications. The scope of the articles published in this journal deal with a broad range of mathematics topics, including: Mathematics Applied Mathematics Statistics and Probability Applied Statistics Mathematics Education Mathematics Learning Computational Mathematics Science and Technology Computer Science Artificial Intelegence Optimization Journal Title Journal Abbreviation Frequency Publication Language DOI E-ISSN Publisher Country : Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi : Euler J. Ilm. Mat. Sains dan Teknol. : Three times a year (April, August and December) : English (preferable), Indonesia : https://doi.org/10.37905/euler : 2776-3706 : Department of Mathematics, Universitas Negeri Gorontalo : Indonesia
Please find rights and licenses in Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi. By submitting article manuscripts, the author agrees to this policy. No special documents required. 1. License The use of articles will be governed by the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC). 2. Author(s)' Warranties The author warrants that the article is original, written by the stated author(s), has not been published before, contains no unlawful statements, does not infringe the rights of others, is subject to copyright that is vested exclusively in the author, and free of any third party rights, and that any necessary written permissions to quote from other sources have been obtained by the author(s). 3. User Rights Euler: Jurnal Ilmiah Matematika, Sains dan Teknologi spirit is to disseminate articles published are as free as possible. Under the Creative Commons license, Euler permits users to copy, distribute, display, and perform the work. Users will also need to attribute authors and Euler to distributing works in the journal and other media of publications. 4. Rights of Authors Authors retain all their rights to the published works, such as (but not limited to) the following rights; Copyright and other proprietary rights relating to the article, such as patent rights, The right to use the substance of the article in own future works, including lectures and books, The right to reproduce the article for own purposes, The right to enter into separate, additional contractual arrangements for the non-exclusive distribution of the article's published version (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal (Euler). 5. Co-Authorship If the article was jointly prepared by more than one author, any authors submitting the manuscript warrants that he/she has been authorized by all co-authors to be agreed on this copyright and license notice (agreement) on their behalf, and agrees to inform his/her co-authors of the terms of this policy. Euler will not be held liable for anything that may arise due to the author(s) internal dispute. Euler will only communicate with the corresponding author. 6. Royalties Being an open accessed journal and disseminating articles for free under the Creative Commons license term mentioned, author(s) aware that Euler entitles the author(s) to no royalties or other fees.
Analisis Komparatif Random Forest dan Support Vector Machine untuk Klasifikasi Tingkat Keparahan Serangan Siber
The escalating volume and sophistication of cyberattacks on network infrastructures processing massive daily traffic have overwhelmed security teams in prioritizing incident responses rapidly and accurately, a phenomenon known as alert fatigue. This study aims to analyze and compare the performance of the Support Vector Machine (SVM) and Random Forest (RF) algorithms for classifying cyberattack severity levels (Low, Medium, and High). The study uses the public Cyber Security Attacks dataset, consisting of 40,000 network traffic records reduced to 20,000 clean entries through preprocessing and feature engineering. The methodology includes data cleaning, selecting 10 significant features using SelectKBest, standardizing numerical features, and evaluating models across three data split scenarios (70:30, 80:20, and 90:10) using a stratified splitting approach. Experimental results show that SVM consistently outperforms RF across all scenarios, with the best performance in the 80:20 split, achieving 98.92% accuracy and a weighted average F1-Score of 0.99 using hyperparameter configurations of C = 100 and gamma = 0.01. The superiority of SVM lies in its ability to model non-linear relationships and complex feature interactions in data with overlapping class boundaries. In contrast, RF exhibits an over-prediction bias toward the minority class (’Low’) due to the class_weight=’balanced’ mechanism and limitations of axis-based separation. These findings confirm that SVM with a Radial Basis Function (RBF) kernel is more suitable for cyberattack severity classification, particularly in automated incident detection systems requiring balanced precision and recall as well as reliable decision-making.
Copyright (c) 2026 Reyhanssan Islamey, Sri Winiarti, dan Imam Riadi https://creativecommons.org/licenses/by-nc/4.0
Modeling the Health Service Queuing System Using Petri Net and Max-Plus Algebra at Integrated Health Service Post (Posyandu)
This study models the health service queue system at the Integrated Health Service Post (Posyandu) in Cilegon City, Banten, using the Petri Net and Max-Plus Algebra approaches to analyze the flow of participant arrivals and completion times. The data used are observational data from Posyandu activities simulated through a discrete event model, which includes several types of participants, namely: babies not standing yet, babies standing, pregnant mothers, and family planning programs. Petri Net modeling is used to represent the relationship between service transitions, while Max-Plus Algebra is used to calculate the process cycle time based on the critical path. The results of the study showed that the categories of non-standing babies, standing babies, and pregnant women/participants in the family planning program had identical service time patterns, namely a total duration of 17 minutes 19 seconds, with the main stages including measurement, midwife intervention, and provision of additional food. Max-Plus analysis confirms that the measurement and midwife intervention stages are the critical path that determines the length of service time. This study concludes that the combination of Petri Net and Max-Plus Algebra is effective in describing the dynamics of Posyandu queues and is able to provide quantitative information needed to identify bottleneck points and the basis for improving the service flow.
Copyright (c) 2026 Syarif Abdullah, Himmatul Mursyidah, Ferdian Bangkit Wijaya, Miftahul Huda, Sri Istiyarti Uswatun Chasanah, Nadia Eka Nursafitri, Dinda Dwi Anugrah Pertiwi https://creativecommons.org/licenses/by-nc/4.0
Evaluasi Perbandingan Model XGBoost, Random Forest, LightGBM, dan Artificial Neural Network dalam Klasifikasi Kerawanan Pangan
Food insecurity remains a serious household-level issue, particularly in densely populated regions such as West Java, highlighting the need for analytical approaches capable of accurately identifying vulnerable groups. Machine learning algorithms offer the potential to improve the accuracy and precision of food insecurity classification based on survey data. This study aims to compare the predictive performance and variable importance identification of four machine learning algorithms—Random Forest, Light Gradient Boosting Machine (LightGBM), Extreme Gradient Boosting (XGBoost), and Artificial Neural Network (ANN)—in predicting household food insecurity status. The analysis employs SUSENAS 2023 data covering 26,012 households with 14 predictor variables, and food insecurity is classified using the Food Insecurity Experience Scale (FIES). Class imbalance is addressed using the Synthetic Minority Over-sampling Technique (SMOTE) within a 10-fold cross-validation framework. The results show that XGBoost achieves the highest accuracy of 71%, while Random Forest provides the best balanced accuracy under the SMOTE scenario. Moreover, all algorithms consistently identify the Wealth Index as the most influential predictor based on their respective Variable Importance measures, followed by variables related to water access and food assistance. Accordingly, XGBoost is recommended in terms of accuracy, whereas Random Forest demonstrates superior balanced accuracy and prediction stability.
Copyright (c) 2026 Mardatunnisa Isnaini, Dela Gustiara, Rizqi Annafi Muhadi, Shalshabilla Shafa, Bagus Sartono, Aulia Rizki Firdawanti, Budi Susetyo, dan Gerry Alfa Dito https://creativecommons.org/licenses/by-nc/4.0
Optimasi Penentuan Basis Risiko pada Jaringan Saham Keuangan Menggunakan Dimensi Metrik untuk Estimasi Value at Risk
This study aims to optimize systemic risk monitoring in the Indonesian financial sector network by determining the minimum risk basis using the Metric Dimension concept. The high complexity of inter-asset correlations requires a dimension reduction method that maintains structural information regarding risk exposure. Daily stock price data from 10 financial issuers (banking, insurance, and financing) for the five-year period from January 1, 2021, to December 31, 2025, were used. The data were transformed into a weighted graph through a log-return correlation matrix converted into metric distances. The resolving set (W) was determined using a greedy algorithm to identify the optimal basis. Validation was performed by analyzing the correlation between the metric coordinates of each issuer and its 95% Value at Risk (VaR). The results showed that the financial network has a metric dimension of dim(G) = 1, with ADMF.JK selected as the optimal resolving set (basis). Actuarial validation revealed a significant negative correlation (−0.5495) between the metric distance and VaR. This implies that the metric distance from the basis can linearly map the magnitude of market risk, offering an efficient strategy for investment managers to monitor portfolio stability through a single reference entity.
Annisa Hevita Gustina Kumalasari Saefulloh
Copyright (c) 2026 Annisa Hevita Gustina Kumalasari Saefulloh, Putri Isnaini Cahyaning Baiti, Erica Grace Simanjuntak, Rahmatika Zaqiatul Latifah https://creativecommons.org/licenses/by-nc/4.0
Fostering Inclusive Mathematics Learning: A Lesson Study Approach Integrating the Wordwall Digital Platform for Special Needs Students
This study investigated the integration of the Wordwall digital interactive learning platform into a Lesson Study framework to enhance mathematics instruction for students with special needs. Conducted at a Special Education School (SLB), the research explored digital tools and collaborative teacher development improved student engagement, conceptual understanding, and motivation in learning basic mathematical concepts. A group of mathematics teachers participated in lesson planning, classroom implementation, observation, and reflection, during which Wordwall was used to design interactive and accessible math activities tailored to students with diverse disabilities. Despite growing interest in inclusive education, few studies had examined how structured professional development models such as Lesson Study could be effectively integrated with digital platforms like Wordwall in special education contexts. This study addressed that gap by demonstrating that the strategic integration of these tools significantly enhanced students’ active participation and conceptual comprehension. The interactive features of Wordwall supported multisensory engagement and differentiated instruction, while the Lesson Study process facilitated sustained collaboration and adaptive teaching among educators. The findings suggest that integrating technology-enhanced learning with professional learning communities not only improved students’ outcomes, such as accuracy in basic computations, mathematical reasoning, and enthusiasm but also strengthened teachers' capacities in inclusive instructional design, reflective practice, and adaptive pedagogical strategies. These results showed insights for future research and practice, especially in developing inclusive models that digital technology and collaborative teaching to promote equity and quality in special education.
Copyright (c) 2026 Nia Wahyu Damayanti, Ali Carli https://creativecommons.org/licenses/by-nc/4.0
Spatial Planning of Mosque-Based Ablution Water Reuse Networks in Lombok Barat Using K-Means Clustering and Minimum Spanning Tree
Lombok Barat Regency, located on Lombok Island, frequently experiences water scarcity due to its semi-arid climate and prolonged dry seasons. Agricultural and plantation activities in this region rely heavily on limited freshwater resources, particularly in dryland areas. Meanwhile, mosques continuously generate relatively clean greywater from daily ablution (wudu) activities. Despite its regular availability and relatively low contamination level, this resource remains largely underutilized. This study examines the spatial planning of mosque-based wudu water collection networks in West Lombok as a potential supplementary water source for plantation and dryland irrigation. A spatial analytical framework combining K-Means clustering and the Minimum Spanning Tree (MST) algorithm was applied and implemented through an interactive RShiny application. Spatial data from 940 mosques were preprocessed and analyzed. K-Means clustering at Level 1 grouped mosques into 25 local service clusters, while Level 2 clustering aggregated these clusters into five main reservoir zones. A cost-weighted MST based on Haversine distance was then used to estimate the minimum pipeline length required to connect mosques within the proposed network configuration. The results show that the modeled network connects all 940 mosques with a minimum total pipeline length of 411,757.28 meters and could potentially collect approximately 282,000 liters of reusable wudu water per day. However, the model represents a preliminary spatial planning framework and does not include hydraulic simulations, water quality validation, treatment system design, or operational feasibility assessment.
Copyright (c) 2026 Sutanto Sutanto, Retno Tri Vulandari, Tyas Titah Nareswari https://creativecommons.org/licenses/by-nc/4.0
Analisis Kinerja Model CNN-LSTM Berbasis Optical Character Recognition untuk Ekstraksi Informasi e-KTP Berdasarkan Kategori Teks
Optical Character Recognition (OCR) technology plays an important role in automating information extraction from identity documents such as the Electronic Identity Card (e-KTP). However, recognizing long text sequences and handling complex character variations remain significant challenges. These issues can lead to high error rates. This study aims to address these limitations by exploring a deep learning–based OCR model that integrates Convolutional Neural Network (CNN), Long Short-Term Memory (LSTM), and Connectionist Temporal Classification (CTC) in an end-to-end framework without explicit character segmentation. CNN is employed to extract visual features, LSTM captures sequential dependencies, and CTC enables flexible alignment between input images and output text. The main contribution of this study lies in analysing the performance of a CNN-LSTM model with CTC in extracting e-KTP information across text categories with different complexity levels, namely Date and Place of Birth (TTL), name, and national identification number (NIK). Performance is evaluated using the Character Error Rate (CER). The results show that the model achieves the best performance on TTL with a CER of 0.84%, followed by NIK at 1.29%, and Name at 4.33% indicating higher difficulty in recognizing more complex text patterns. These findings demonstrate that model performance is influenced by text characteristics, particularly variability and sequence length. Overall, the proposed approach is effective for end-to-end e-KTP information extraction and provides insights for developing more adaptive OCR models.
Copyright (c) 2026 Fauzan Ihza Fajar, Selly Anastassia Amellia Kharis, Asmara Iriani Tarigan https://creativecommons.org/licenses/by-nc/4.0
Pemodelan Indeks Kerukunan Umat Beragama di Indonesia Menggunakan Regresi Nonparametrik Deret Fourier Berdasarkan Fungsi Basis Sinus dan Basis Cosinus
This study aims to analyze the factors suspected of influencing the Interfaith Harmony Index (IKUB) across all provinces in Indonesia and determine the best prediction model. The predictor variables suspected of influencing are the number of religious organizations, religious instructors, educational institutions, and houses of worship. The analysis was conducted using nonparametric Fourier series regression with a comparison of cosine and sine basis functions, and evaluation through MSE, RMSE, MAPE, GCV, UBR, and . The results show that the 4-oscillating cosine basis function model is the most accurate, with MSE (2.27), RMSE (1.51), MAPE (1.47), GCV (6.56), UBR (1.29×10-10)and (86.28%), compared to the sine basic function model. This model is able to flexibly represent complex nonlinear relationship patterns and variations in IKUB between provinces. These findings demonstrate a relationship between the research variables and variations in IKUB values, thus providing a basis for understanding harmony patterns and supporting data analysis for policy considerations. While the research findings are predictive, they place greater emphasis on uncovering the relationships between variables that influence interfaith harmony.
Copyright (c) 2026 Yossy Candra, Andrea Tri Dani, Wagimin Wagimin https://creativecommons.org/licenses/by-nc/4.0
Forecasting the Consumer Price Index with Holt-Winters: A Comparative Study of Ordinary Least Squares and Maximum Likelihood Estimation
The Consumer Price Index (CPI) is a crucial macroeconomic indicator reflecting regional inflationary pressures. This study aims to compare the performance of Ordinary Least Squares (OLS) and Maximum Likelihood Estimation (MLE) methods in estimating Holt-Winters model parameters for forecasting the CPI of East Nusa Tenggara (NTT) Province. Using monthly data from January 2021 to December 2025, the research evaluates two primary approaches: conventional OLS based Holt-Winters models and the MLE based Error, Trend, and Seasonal (ETS) framework. Model performance was assessed using the Mean Absolute Percentage Error (MAPE). The results demonstrate that the MLE based approach significantly outperforms OLS; the multiplicative ETS model achieved the lowest MAPE of 0.57%, proving far more accurate than the OLS based Holt-Winters models, which yielded error rates exceeding 50%. A 12-month forecast for 2026 projects NTT CPI to increase moderately from 107.38 to approximately 109.54, indicating controlled inflationary pressure. This study affirms the superiority of the MLE approach in generating precise parameters for economic data exhibiting seasonal patterns.
Copyright (c) 2026 Esra Rombeallo, Marvin Jecson Pandu https://creativecommons.org/licenses/by-nc/4.0
Optimasi Vehicle Routing Problem pada Distribusi Tabung LPG Menggunakan Metode Ant Colony Optimization
Inefficient distribution can increase operational costs; therefore, determining optimal routes is essential to support an efficient distribution process. This problem can be formulated as a Vehicle Routing Problem (VRP), which concerns optimizing vehicle routes from a depot to multiple destinations with minimum travel distance. This study aims to optimize the distribution route of LPG cylinders at PT Jaya Sari Artha by considering 12 distribution points. The method used is Ant Colony Optimization (ACO), a heuristic algorithm inspired by the foraging behavior of ants in finding the shortest path. The data used consist of actual travel distances between distribution points obtained from Google Maps. The results show that the implementation of ACO in the VRP model produces a distribution route with a total distance of 117.40 km, shorter than the company’s initial route of 134.50 km. Thus, a distance saving of 17.10 km or 12.72% was achieved. These findings indicate that the ACO method is effective in solving VRP and improving the efficiency of LPG cylinder distribution in a real-world case.
Copyright (c) 2026 Devitasari Simamora, Riri Syafitri Lubis, Sri Ulfa Rahayu https://creativecommons.org/licenses/by-nc/4.0
Numerical Investigation of Vertical Oscillations of a Buoyant Object in a Stratified Fluid
This study explores the vertical oscillation dynamics of a buoyant object in a linearly stratified fluid and assesses the accuracy of a first-order finite difference scheme used for numerical simulation. The mathematical formulation, derived from the harmonic motion equation, was solved analytically through linearization around the equilibrium position and numerically to evaluate the scheme’s stability and precision. A sensitivity analysis with respect to the time step (∆t) revealed that numerical accuracy strongly depends on temporal resolution: at ∆t = 1 s, the numerical results closely matched the analytical solution, whereas larger ∆t values caused noticeable phase errors and reduced precision. As ∆t increased, phase errors became noticeable, with discrepancies appearing more clearly at ∆t = 5 s and beyond, highlighting a trade-off between computational efficiency and precision. The model was further extended by incorporating a quadratic damping term (R), enabling the simulation of damped oscillatory motion. Results showed that the decay rate of oscillations increases proportionally with R, where higher friction coefficients (R = 0.2) lead to faster energy dissipation and stabilization compared to smaller ones (R = 0.05). These outcomes demonstrate the robustness and reliability of the proposed numerical approach in reproducing both undamped and damped oscillation behaviors. This study provides a reliable framework for simulating buoyant object oscillations in stratified fluids, though further development is needed to incorporate more complex hydrodynamic effects for enhanced predictive accuracy.
Copyright (c) 2026 Fathya Rabiatunisa, Diki Fernandi, Ikha Magdalena https://creativecommons.org/licenses/by-nc/4.0
Pemodelan Graf Berarah Berbobot untuk Optimasi Penentuan Rute Terpendek Antar Kampus Polimarin Berbasis Algoritma Dijkstra
The mobility of academicians between the two geographically separated campuses of the Indonesian Maritime State Polytechnic (Polimarin), namely Campus 1 Ungaran and Campus 2 Bendan Duwur Semarang, creates travel efficiency issues due to numerous unmeasured route alternatives. This study aims to model the inter-campus road network as a weighted directed graph and apply the Dijkstra algorithm to determine the shortest route accurately and verifiably. The research employs an applied computational approach using actual distance data obtained from Google Maps (driving mode), collected on August 22, 2024, at 09:00 WIB to represent traffic conditions at that time. The process includes node identification (strategic locations), edge formation (connecting road segments), and weight assignment based on actual distances, resulting in a graph with 9 nodes and 10 edges. The iteration process is conducted in 8 steps by evaluating the minimum accumulated weight at each stage. The results indicate that the shortest path is A → B → E → G → H → I, passing through Jl. PTP Ngobo, Jl. Diponegoro–Jl. Slamet Riyadi, Jl. Moh. Yamin–Jl. Ahmad Yani, and Jl. Gatot Subroto, with a total distance of 25.80 km out of 11 possible routes. These findings demonstrate that the Dijkstra algorithm is effective for route optimization by eliminating inefficient paths through cumulative weight evaluation. Validation is performed by comparing the algorithm’s results with Google Maps recommendations based on travel distance. However, this study is limited to static data, and further development is required through the integration of dynamic traffic data.
Copyright (c) 2026 Helena Devi Ariyani, Khoirotun Nafillah, Kirtyana Nindita, Ngatmin Ngatmin, Sri Tutie Rahayu https://creativecommons.org/licenses/by-nc/4.0
Optimasi Waktu Pengantaran Barang melalui Model Penugasan Kurir dengan Metode Hungarian Termodifikasi pada Data Tidak Seimbang
This study aims to apply the Hungarian method to the assignment problem in determining the allocation of couriers in the case of delivering goods at PT. Shopee Express Soreang Kota Parepare Hub. The Hungarian method is used to determine the optimal allocation of couriers based on the efficiency of the delivery time of goods so that the total distribution time can be minimized. In its implementation, adjustments were made to the procedures of the Hungarian method to accommodate unbalanced data conditions. Validation of assignment results is carried out using Program for Operations Management-Quantitative Methods (POM-QM) software for Windows to ensure that the solutions obtained through manual calculations match the system's computational results and actually produce optimal values. The results showed that the total average delivery time before optimization of 53.45 minutes could be reduced to 41.80 minutes after the application of the Hungarian method, resulting in a time efficiency of 11.65 minutes. Validation using POM-QM for Windows shows results consistent with manual calculations. Thus, the Hungarian method has proven to be effective in improving the efficiency of courier assignments and minimizing the delivery time of goods.
Copyright (c) 2026 Riskiani Riskiani, Zulfiqar Busrah https://creativecommons.org/licenses/by-nc/4.0
Comparative Analysis of the Capital Asset Pricing Model and Arbitrage Pricing Theory in Estimating Expected Stock Returns in the IDX BUMN20 Index
This study examines the comparative performance of the Capital Asset Pricing Model (CAPM) and Arbitrage Pricing Theory (APT) in estimating expected stock returns within the IDX BUMN20 Index. The study is motivated by the ongoing debate regarding the empirical validity of single-factor and multifactor asset pricing models, particularly in emerging markets such as Indonesia. While prior studies provide mixed evidence, limited research has focused specifically on state-owned enterprise indices, which exhibit distinct risk characteristics. Using monthly stock price data, this study estimates expected returns under both models and evaluates their performance using Mean Absolute Deviation (MAD), which measures the average deviation between estimated and realized returns. In the APT framework, factor sensitivities are estimated using a multifactor regression approach, incorporating macroeconomic variables as systematic risk factors. This allows a more detailed assessment of how multiple sources of risk influence return estimation. The results indicate that the CAPM demonstrates relatively better estimation performance, as reflected by lower MAD values compared to the APT. However, the APT provides additional insights into the role of multiple risk factors, suggesting its relevance in capturing more complex market dynamics. These findings highlight that while simpler models may perform more consistently in certain contexts, multifactor approaches remain valuable for understanding broader sources of systematic risk. The study contributes to the asset pricing literature by providing empirical evidence from the IDX BUMN20 Index and offering a more nuanced comparison between single-factor and multifactor models in an emerging market setting.
Copyright (c) 2026 Febrant Alfariz, Evy Sulistianingsih, Neva Satyahadewi https://creativecommons.org/licenses/by-nc/4.0
Stability, Sensitivity, and Bifurcation Analysis of a Rice–Pest Interaction Model
This study develops a five-dimensional mathematical model describing the interaction between rice and four major pests: rice stem borer, rat, brown planthopper, and rice bug. The existence and local stability of several equilibrium points are analyzed using linearization and the Routh–Hurwitz criterion. In addition, the global stability of the pest-free equilibrium point is established using Lyapunov’s direct method and LaSalle’s Invariance Principle. The results show that the pest-free equilibrium is globally asymptotically stable under certain threshold conditions related to the interaction and mortality parameters. Furthermore, a transcritical bifurcation is identified, which determines the transition between pest extinction and coexistence. Sensitivity analysis indicates that the rice bug parameters significantly influence the rice population, with proportional effects on the equilibrium state. Numerical simulations are performed to support the analytical results, including the dynamic behavior around the bifurcation threshold and the sensitivity of the rice population with respect to key parameters. The results highlight the importance of controlling pest interaction rates and increasing natural mortality to maintain the stability of the rice population.
Copyright (c) 2026 Tesa Nur Padilah, Iqbal Maulana https://creativecommons.org/licenses/by-nc/4.0
Pendekatan Hybrid VARIMA–ANN untuk Peramalan Multivariat Data Cuaca Bulanan di Provinsi Gorontalo
Multivariate time series forecasting is essential for understanding the interrelationships among weather parameters. This study aims to develop a multivariate forecasting model using a hybrid Vector Autoregressive Integrated Moving Average (VARIMA)–Artificial Neural Network (ANN) approach with the backpropagation algorithm, applied to weather data from Gorontalo Province over the 2015–2023 period, including air temperature, humidity, and wind speed. The data were divided into training data (2015–2021) and testing data (2022–2023). The VARIMA model was employed to capture the linear component, while the residuals from the VARIMA model were subsequently modeled using ANN to capture nonlinear patterns. The order of the VARIMA model was determined based on the smallest Akaike Information Criterion (AIC) value, while model performance was evaluated using Mean Absolute Percentage Error (MAPE). The results indicate that the best-performing model is VARIMA(5,1,1)–ANN(18,9,3), with MAPE values of 1.32% for air temperature, 20.54% for humidity, and 21.96% for wind speed. These findings suggest that the hybrid VARIMA–ANN approach provides good forecasting performance and has the potential to serve as an alternative method for multivariate weather forecasting.
Copyright (c) 2026 Nur Anggraini T. Ali, Djihad Wungguli, Isran K. Hasan https://creativecommons.org/licenses/by-nc/4.0
The Effect of PBL Integrated Education for Sustainable Development on Students' Mathematical Communication and Problem Solving Skills
This research adopted a pretest–posttest control group experimental design. The primary objective was to investigate the impact of implementing Problem-Based Learning (PBL) integrated with the Education for Sustainable Development (ESD) approach on students’ mathematical problem-solving abilities and mathematical communication skills within the context of matrix learning. The population consisted of all 11th-grade students at SMAN 8 Pontianak (N=280), with two classes selected through probability sampling as the experimental and control groups. Data were collected using essay tests, observations, and documentation, then analyzed using independent samples t-tests, Mann-Whitney tests, and effect size analyses. The findings indicated statistically significant differences between the experimental and control groups (p<0.05). Specifically, the experimental group achieved a mean post-test score 20.21% higher than the control group in problem-solving and 36.41% higher in mathematical communication. Strong effect sizes (d=1.84 and r=1.34) further demonstrate that ESD-oriented PBL substantially improved students’ competencies compared to conventional methods.
Copyright (c) 2026 Puput Puput, Ahmad Yani T, Nurfadilah Siregar, and Verminus Verminus https://creativecommons.org/licenses/by-nc/4.0
Comparative Analysis of Grey GM(1,1) and Grey Verhulst Models for Forecasting Electricity Consumption in Indonesia
Electricity energy demand in Indonesia continues to increase in line with economic development, technological advancement, and population growth. This condition necessitates appropriate energy planning to ensure a stable electricity supply. Electricity consumption forecasting is required to predict future demand and to serve as a basis for formulating sustainable energy policies. However, studies comparing different grey forecasting models for Indonesia’s electricity consumption remain limited, particularly in identifying the most suitable model for its growth characteristics. This study aims to compare the performance of two models within Grey System Theory, namely the Grey Model GM(1,1) and the Grey Verhulst model, in forecasting electricity consumption in Indonesia. The data used consist of annual electricity consumption data for the period 2000–2024, obtained from the official websites of Statistics Indonesia (BPS) and the Ministry of Energy and Mineral Resources (ESDM). The analysis stages include model construction, parameter estimation, forecasting, and accuracy evaluation using the Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE). The results indicate that the Grey Verhulst model outperforms the GM(1,1) model, with an RMSE of 10,955.97, an MAE of 9,233.64, and a MAPE of 5%, whereas the GM(1,1) model yields an RMSE of 23,562.39, an MAE of 15,151.57, and a MAPE of 9%. These results suggest that the Grey Verhulst model provides a better fit for the observed data, which exhibits nonlinear growth behavior with a tendency toward saturation. The best-performing model, namely the Grey Verhulst model, produces a forecast of electricity consumption for the year 2025 of 388,025 GWh. This result is expected to serve as a reference for national electricity policy planning.
Copyright (c) 2026 Indri Noer Khoeriyah, Mujiati Dwi Kartikasari https://creativecommons.org/licenses/by-nc/4.0
In ring theory, a derivation is an additive mapping d:R→R satisfying Leibniz’s rule. A well-known generalization of this notion is the (α,β)-derivation, defined with respect to two ring endomorphisms α and β. In this paper, we study (α,β)-derivations on the matrix ring Mₙ(R) and several of its subrings, including scalar matrices, diagonal matrices, and upper and lower triangular matrix rings. It is shown that an (α,β)-derivation on the base ring RRR induces an (α′,β′)-derivation on these matrix subrings via entrywise extension, preserving their structural properties. Furthermore, we examine certain properties of (α,β)-derivations on the direct product ring R×R. In particular, we show that the sum of two (α,β)-derivations does not necessarily form an (α,β)-derivation, which is demonstrated through a counterexample.
Copyright (c) 2026 Dania Azzahra, Fitriani Fitriani, Ahmad Faisol https://creativecommons.org/licenses/by-nc/4.0
Ethno-STEM Mobile Apps in Formal Education: A Systematic Review of Design Principles, Cultural Adaptation, and Learning Outcomes
This study presents a systematic literature review examining the development and educational impact of ethno-STEM mobile applications used in formal education. The review aims to synthesize evidence regarding three main aspects: design principles and technical features of ethno-STEM mobile apps, the integration and cultural adaptation of local knowledge, and the learning outcomes reported for students. The review followed the PRISMA 2020 framework to ensure transparency and methodological rigor in the identification, screening, and synthesis of relevant studies. Literature was retrieved from the SCOPUS database using Boolean keywords covering publications from 2016 to 2026. After a structured screening process involving document type filtering and content-based eligibility criteria, five studies were included in the final qualitative synthesis. The findings reveal that most ethno-STEM mobile applications are developed using Android platforms and instructional design frameworks such as ADDIE, emphasizing multimedia integration, interactive visualization, and guided inquiry structures. Cultural knowledge is incorporated through approaches such as ethnopedagogy, ethnomathematics, ethnoscience, and dual representation of indigenous and scientific knowledge systems. However, cultural validation processes are commonly limited to expert reviews and user evaluations rather than participatory collaboration with community knowledge holders. The reviewed studies report positive educational outcomes, including improvements in mathematical problem solving, creative thinking, scientific literacy, and student engagement. Nevertheless, most evaluations rely on short-term interventions and limited methodological rigor, with little evidence of long-term learning impacts or identity development. Overall, the findings suggest that ethno-STEM mobile applications show strong pedagogical potential but require more robust cultural validation frameworks and longitudinal evaluation to support sustainable and culturally responsive STEM learning.
Copyright (c) 2026 Indah Permatasari, Hasan S. Panigoro, Emli Rahmi https://creativecommons.org/licenses/by-nc/4.0
Dynamic Analysis of Modified Leslie-Gower the Predator-Prey Model with Fear Effect, Additional Food, and Prey Refuge
This study discusses a Leslie–Gower prey-predator model incorporating three behavioral mechanisms: the fear effect on prey, additional food for predators, and prey refuge, with predation rate of predators using the Holling II response function. The objective of this research is to analyze the system dynamics through stability analysis of equilibrium points and the bifurcation associated with the predator attack rate parameter. The analytical results indicate that the model admits five equilibrium points, namely the extinction of both populations (E1), prey extinction (E2), predator extinction (E3), and two coexistence equilibrium points (E4 and E5), where the existence of the interior equilibrium points depends on the values of the system parameters. The prey extinction equilibrium point and the coexistence equilibrium points are asymptotically stable under certain conditions. Computational validation was performed through numerical simulations. Furthermore, variations in the predator attack rate parameter reveal the presence of bistability as well as transcritical and saddle-node bifurcations that lead to changes in the stability of the equilibrium points.
Copyright (c) 2026 Hanifa Febriana Putri, Dian Savitri https://creativecommons.org/licenses/by-nc/4.0