CAUCHY: Jurnal Matematika Murni dan Aplikasi
CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI p-ISSN: 2086-0382 | e-ISSN: 2477-3344 (BRIN | ISSN Portal) CAUCHY: Jurnal Matematika Murni dan Aplikasi is an open-access, peer-reviewed journal published twice a year (May and November) by the Department of Mathematics, Faculty of Science and Technology, Universitas Islam Negeri Maulana Malik Ibrahim Malang, Indonesia. The journal is accredited at SINTA 2 by the Ministry of Research and Technology / National Agency for Research and Innovation, Republic of Indonesia (Decree No. 177/E/KPT/2024), valid from May 2023 to May 2028. CAUCHY welcomes high-quality submissions of original research articles, comprehensive literature reviews, and special-topic contributions in pure and applied mathematics. All manuscripts must be written in English and prepared using the official CAUCHY LaTeX template available on Overleaf. Aims and Scope CAUCHY publishes manuscripts that demonstrate clear mathematical novelty and methodological rigor. The journal prioritizes contributions that present new mathematical results, develop or analyze mathematical models with sound theoretical justification, or propose computational and algorithmic methods supported by rigorous mathematical analysis such as correctness, convergence, stability, complexity, or reproducibility. The scope of the journal covers, but is not limited to, the following areas: Analysis (real analysis, functional analysis, applied analysis) Algebra and number theory Geometry and topology Discrete mathematics and graph theory Optimization and operations research Probability and mathematical statistics Dynamical systems and control Mathematical modeling with rigorous formulation and validation Computational mathematics and scientific computing Fuzzy systems and uncertainty modeling Actuarial and financial mathematics Out of Scope CAUCHY maintains a strong mathematical emphasis. Manuscripts will be considered out of scope and may be desk-rejected if they primarily fall into one or more of the following categories: Application-only case studies or implementations that do not present a clear mathematical model, theoretical analysis, or mathematically justified methodology. Machine learning / data-driven papers that mainly report benchmark results or metric comparisons (e.g., accuracy, F1-score, AUC) without explicit mathematical novelty, analytical justification, or substantive methodological contribution. Routine use of standard techniques with minimal originality (e.g., applying commonly used models to a new dataset) and without a meaningful mathematical development, analysis, or insight. Software or system papers that focus on implementation details, engineering features, or interfaces without rigorous mathematical content (e.g., correctness proof, convergence/stability analysis, complexity analysis, or error bounds). Surveys or review manuscripts that are primarily narrative/tutorial, lack a systematic review protocol, provide limited critical synthesis, or do not clearly articulate research gaps and future directions. Manuscripts with insufficient rigor or transparency to support verification and reproducibility (e.g., incomplete method description, unclear assumptions, unverifiable claims). Manuscript Requirements Submitted manuscripts must be original, clearly written, and methodologically rigorous, with sufficient detail to support verification and reproducibility. All claims should be supported by logical reasoning and appropriate evidence. The recommended manuscript length is 10–16 pages, including figures, tables, and references. Literature review articles may extend up to 25 pages and should include at least 25 references, with a minimum of 80% drawn from peer-reviewed journals published within the last five years. Journal Updates 2009–2012: Cover changed from yellow to purple 2013–2015: Two-column layout adopted 2016–present: One-column layout; all submissions in English Vol. 4 No. 2 (2016): New article layout introduced Starting from Vol. 10 No. 2 (2025): New LaTeX template in use. See the template at Overleaf . Submission guidelines and detailed author instructions are available here.
Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang
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Cluster Analysis of Cities/Districts in West Kalimantan based on Stunting Response Indicators using the Calinski Harabasz Index
The stunting rate in West Kalimantan has reached 27% , mainly due to the government’s inability to prioritise regions for essential services and education, especially for adolescents and pregnant women. This study aims to explain the role of modified K-Means and CHI methods in forming optimal clusters and interpreting their conditions. Eight research variables, sourced from BPS and SIGA in 2023, were used: number of adolescents receiving counselling, informed consents, complication cases, aslokon expenditure, aslokon stock, population growth rate, population density, and life expectancy. Clustering was done by analysing the data for each variable and the characteristics of the objects using the Euclidean distance, determining the centroid values, and iterating until the results stabilised. The clusters were evaluated from one to seven to find the optimal amount using CHI. The results identified five clusters: cluster 1 (relatively poor, three objects), cluster 2 (inferior, four objects), cluster 3 (good, three objects), cluster 4 (exquisite, three objects) and cluster 5 (good, one object).
Copyright (c) 2026 Tegar Rama Priyatna, Yundari Yundari, Nur'ainul Miftahul Huda https://creativecommons.org/licenses/by-sa/4.0
Interpolation of Fire Radiative Power Based on GSTAR Model Predictions with Queen Contiguity Weights Using Ordinary Kriging
Forest fires are a persistent environmental issue in West Kalimantan, Indonesia, driven by both natural and human factors. Fire Radiative Power (FRP) serves as a vital indicator for assessing wildfire intensity and energy release. This study aims to model and predict the spatial temporal dynamics of FRP using the Generalized Space Time Autoregressive [GSTAR(1;1)] model combined with Ordinary Kriging interpolation. The dataset covers West Kalimantan from July 2024 to September 2025, comprising four attributes: observation date, longitude, latitude, and FRP value. Data filtering was applied from the national to provincial level, focusing on three regencies Sanggau, Sekadau, and Ketapang across 14 sub-districts represented by a 1.25 × 1.25 grid. The data consisted of 65 weekly observations, with 61 used for training and 4 for testing. The GSTAR(1;1) model with a spatial area-based framework achieved an optimal RMSE of 7.42 and satisfied the white noise assumption, indicating reliable performance. Predictions for October 2025 indicated relatively stable fire intensity, with a slight FRP decrease in Nanga Tayap and Sandai during the final week. Overall, the integrated GSTAR–Kriging framework effectively captured both temporal and spatial variations, supporting improved fire risk assessment and regional decision making for wildfire management in West Kalimantan.
Copyright (c) 2026 Gita Fitriyana, Nurfitri Imro'ah, Nur’ainul Miftahul Huda https://creativecommons.org/licenses/by-sa/4.0
Implementation of DBSCAN and K-MEANS++ Methods for Flood Vulnerability Cluster Mapping in East Java Province, 2024
Flood vulnerability in East Java varies across districts due to differences in hydrometeorological pressure and exposure levels. This study compares two clustering algorithms—DBSCAN and K-Means++—for identifying patterns in eleven flood-impact indicators. DBSCAN parameter selection was conducted using a k-distance graph, resulting in ε = 0.8 and MinPts = 3, which produced five clusters and three noise points. The Silhouette Index for DBSCAN was 0.3266, calculated including noise points to ensure fair evaluation against K-Means++, which obtained a Silhouette Index of 0.2453 for five clusters. The findings indicate that DBSCAN produced higher internal cohesion under the given dataset. However, the resulting clusters are not interpreted as validated flood risk zones or as physically causal patterns, due to the absence of external validation layers such as historical flood maps, hydrological data, or topographic information. The results therefore provide a methodological comparison between density-based and centroid-based clustering for flood-impact variables without making geographical or causal inferences.
Copyright (c) 2026 Zalfa Zaliana Nugrahanto, A’yunin Sofro https://creativecommons.org/licenses/by-sa/4.0
Triple-Mutation Bat Algorithm–Optimized Extreme Learning Machine for Fetal Health Classification
Fetal health assessment is essential for preventing perinatal complications, yet manual interpretation of cardiotocography (CTG) signals is prone to variability and diagnostic delays. This study introduces TMBA–ELM, a hybrid intelligent model that optimizes Extreme Learning Machine (ELM) parameters using the Triple Mutation Bat Algorithm (TMBA). The novelty of this work lies in extending TMBA—originally designed for continuous optimization—into a mixed-variable optimization framework that simultaneously tunes the hidden-node size and the activation function. This is achieved through the integrated use of Cauchy, Gaussian, and time-based mutation strategies, representing the first adaptation of TMBA for ELM parameter optimization and its first application to CTG-based fetal health classification. The model was evaluated on an imbalanced CTG dataset comprising 2,126 samples and benchmarked against BA-ELM, EMD-FA-ELM, and PSO-EM-ELM. TMBA-ELM achieved 89.23% ± 0.44% accuracy, outperforming BA-ELM (ELM models with parameters tunned by ELM) with accuracy 87.37%±0.63%, PSO-EM-ELM (Error-minimizaed-ELM parameters tunned with particle swarm optimization) with accuracy 82.76% ± 1.83%, and EMD-FA-ELM (ELM parameters tunned with firefly algorithm and data decompositioned by empirical decomposition) with accuracy 87.76% ± 1.95%. However, TMBA-ELM required 164.23 ± 12.76 seconds of computation time, which is substantially higher than BA-ELM and PSO-EM-ELM with computing time 60.9 ± 10.24 seconds and 59.69 ± 5 seconds, respectively. Overall, TMBA-ELM provides improved accuracy compared with existing ELM-based models, while its increased computational cost represents a limitation for time-constrained applications.
Copyright (c) 2026 Prabowo Wisnumurti, Syaiful Anam, Mohammad Muslikh https://creativecommons.org/licenses/by-sa/4.0
University Scheduling Optimization Using Integer Programming: A Case Study
This paper presents an Integer Linear Programming (ILP) model to construct a weekly lecture timetable for the Mathematics Study Program at HKBP Nommensen University, Pematangsiantar. The case study comprises 25 courses, three rooms (RK 11, RK 12, and LAB 1), five teaching days (Monday–Friday), and 13 time periods per day. The model enforces hard constraints on room, lecturer, and cohort non-overlap; consecutive periods according to credit load; room-type compatibility between theory and practicum sessions; and an institutional worship-time restriction on Tuesday. Lecturers’ availability is represented by a binary acceptance matrix collected at the course level, and rejected time periods are penalized in the objective. The ILP is implemented in Python using the PuLP (Python Linear Programming) library and solved with the CBC (Coin-or Branch and Cut) solver. For the real instance, the solver returns an optimal solution with objective value Z∗ = 0 (no scheduled period falls in a rejected slot) in approximately 94 seconds. The resulting timetable is conflict-free and operationally interpretable, with a weekly room-time utilization of about 31.3%. To support verification and communication to stakeholders, the paper also provides a heatmap of the acceptance matrix and a graphical timetable by room and day.
Copyright (c) 2026 Gayus Simarmata, Rajainal Saragih, Anil Hakim Syofra https://creativecommons.org/licenses/by-sa/4.0
Nasdaq Inc. Stock Price (NDAQ) Prediction Due to Trump’s Tariff Policy Using Pulse Function Intervention Analysis
Nasdaq Inc. (NDAQ) is one of the leading stock exchanges in the United States, ranking second globally after the New York Stock Exchange (NYSE) based on market capitalization. As a highly dynamic and information-sensitive market, Nasdaq Inc. stock prices respond quickly to internal corporate conditions and external macroeconomic or policy changes. One notable event affecting market stability was President Donald Trump’s import tariff policy, aimed at protecting U.S. industries from foreign competition, particularly Chinese imports. The implementation of this policy triggered significant volatility, including a sharp decline in Nasdaq Inc. stock prices on March 2, 2025. This study examines the impact of this policy on Nasdaq Inc. stock movements using the ARIMA(0,2,1) model with an intervention of order b = 0, r = 1, and s = 0. The results show that all model parameters are statistically significant and produce accurate forecasts, with a MAPE of 2.19%, an RMSE of 5.98766, and an MAE of 2.05232. These findings indicate that intervention analysis effectively captures the impact of import tariff policies on stock market dynamics and provides valuable insights for investors and policymakers in anticipating market fluctuations driven by global economic policy changes.
Copyright (c) 2026 Kimberly Maserati Siagian https://creativecommons.org/licenses/by-sa/4.0
Quadratic and Truncated Spline Structural Equation Modeling With Double Bootstrap in The Waste Management Economy
This study aims to develop and apply a semiparametric Structural Equation Modeling (SEM) approach that integrates quadratic and truncated spline estimation, enhanced with a double bootstrap resampling method. Semiparametric SEM is used to overcome the limitations of conventional SEM, particularly when data complexity and social behavior do not fully satisfy the linearity assumptions. The model was applied to analyze the public mindset and participation in waste management based on the 3R (Reduce, Reuse, Recycle) principle, focusing on the role of waste banks in optimizing the economic value of waste. The truncated spline approach enables flexible modeling of non-linear relationships among latent variables, while the quadratic term captures global curvature effects. Furthermore, the double bootstrap approach yields smaller standard errors and higher relative efficiency in parameter estimation. The simulation and empirical results demonstrate that the semiparametric SEM with double bootstrap produces higher model stability and more accurate parameter estimation compared to the single bootstrap approach. This method provides a robust analytical framework for modeling complex social phenomena, such as community-based waste management.
Copyright (c) 2026 Anggun Fadhila Rizqia, Solimun Solimun, Nurjannah Nurjannah, Kamelia Hidayat, Fachira Haneinanda Junianto https://creativecommons.org/licenses/by-sa/4.0
Sensitivity Analysis of the SIRD Model for TB-Related Life Insurance Claims in Southeast Sulawesi
Tuberculosis (TB) remains a major public health challenge in Indonesia and generates significant mortality-related risk for the life insurance sector. This study develops an integrated Susceptible–Infected–Recovered–Deceased (SIRD) model to analyze TB transmission dynamics in Southeast Sulawesi and to estimate related life insurance claims. The model is calibrated using regional TB data from 2021–2023 and validated against 2024 observations. Analytical results include equilibrium analysis and the basic reproduction number, while long-term dynamics are examined through scenario-based simulations. Epidemiological outcomes are translated into actuarial projections by converting cumulative TB-related deaths into annual incremental deaths and expected insurance claims under optimistic, baseline, and pessimistic scenarios. Parameter sensitivity is assessed using Latin Hypercube Sampling and Partial Rank Correlation Coefficients. The results show that the transmission rate is the most influential determinant of the present value of TB-related insurance claims, followed by the recovery rate, whereas TB-induced mortality has a smaller but significant effect. These findings highlight that reducing transmission and improving treatment effectiveness can simultaneously mitigate public health impacts and lower long-term insurance liabilities, demonstrating the relevance of integrating epidemiological modeling with actuarial risk assessment.
Copyright (c) 2026 Asriani Arsita Asni, Fitriyani Fitriyani, Ira Puspita https://creativecommons.org/licenses/by-sa/4.0
b-coloring Analysis on Tree Graph Families
A tree graph is a connected graph and has no circuits. Tree graphs used in this study include: broom graph, centipede graph, and Banana Tree graph. Graph coloring is the process of giving color to graph elements with the rule that neighboring elements must not have the same color, and the number of colors used must be as minimal as possible. b-coloring of a graph G is a coloring of the vertices of G such that each color class has at least one vertex adjacent to all other color classes. The b-chromatic number of a graph G is denoted by φ(G), is the largest integer k such that G has a b-coloring with k colors. The limit of b-coloring of graph G with maximum degree ∆(G) is as follows, χ(G) ≤ φ(G) ≤ ∆(G) + 1.χ(G) is the chromatic number of a graph G where χ(G) is the minimum value of the color required for proper coloring of graph G. While ∆(G) is the maximum degree of the vertices in graph G. This study uses an exploratory research type with an axiomatic deductive method and a pattern detection method. Based on this study, the results of the b-coloring analysis on the tree graph family are known. The results of this study are expected to be used as study material and the development of scientific knowledge related to b-coloring analysis on other graphs.
Copyright (c) 2026 Arika Indah Kristiana, Rafiantika Megahnia Prihandini, Lusita Risma Dana, Edy Wihardjo, Robiatul Adawiyah https://creativecommons.org/licenses/by-sa/4.0
Enhancing Spatio-Temporal PCA with FASTMCD for Climate Comfort Assessment
This study presents a robust formulation of the Spatio-Temporal Principal Component Analysis (STPCA) by integrating the Fast Minimum Covariance Determinant (FASTMCD) estimator into the spatio-temporal decomposition framework. Unlike classical STPCA—which constructs the spatio-temporal matrix from sample-based means and is therefore highly sensitive to extreme observations—the proposed STPCA–FASTMCD replaces the classical mean and scatter structure with robust estimates derived from FASTMCD. The method incorporates functional Fourier-based temporal smoothing and an inverse power–distance spatial weight matrix to better capture the underlying spatio-temporal patterns. Monthly climate data (thermal comfort, cloud cover, rainfall, and wind speed) from 24 monitoring locations in Bali during 2010–2019 are analyzed. Performance is evaluated using mean-shift analysis, eigenvalue-stability assessment, and eigenvector perturbation diagnostics. The classical STPCA produces inflated and unstable leading components, with the first eigenvalue reaching 63.36, whereas STPCA–FASTMCD reduces this value to 37.79 and yields smoother, more coherent spatial loading patterns. The robust STPC1 reveals a clear thermal–wind variability mode, enhancing the interpretability of spatial gradients relevant to climate comfort. Overall, the proposed formulation substantially improves the stability and climatic relevance of dominant spatio-temporal modes, providing a more reliable foundation for climate comfort assessment in Bali.
Copyright (c) 2026 Agus Yarcana, Henny Pramoedyo, Suci Astutik https://creativecommons.org/licenses/by-sa/4.0
Implementation of DenseNet121 Based on Convolutional Neural Network with Geometric Augmentation for Breast Cancer Histopathology Image Classification
This study evaluates the performance of the DenseNet121 architecture for binary classification of breast cancer histopathological images using the BreakHis dataset. The model employs ImageNet pre-trained weights, fine-tuning, and geometric data augmentation to improve feature learning and generalization. To obtain more reliable results, three optimization algorithms (Adam, AdamW, and RMSprop) were evaluated through repeated experiments, and performance was reported using mean and standard deviation of test metrics. The experimental results demonstrate that DenseNet121 achieves consistently high classification performance across different optimizers, with the Adam optimizer showing the most stable results. These findings indicate that DenseNet121 combined with data augmentation provides an effective and robust approach for histopathological image classification while emphasizing the importance of repeated evaluation for reliable performance assessment.
Copyright (c) 2026 Nabilah Evi Ariani https://creativecommons.org/licenses/by-sa/4.0
Management in Design-Build Projects by Construction Management Consultants: SEM-PLS and IPMA Approaches
This study investigates the factors influencing the potential audit findings in Design and Build (DB) construction projects in Indonesia, employing Structural Equation Modelling–Partial Least Squares (SEM-PLS) and Importance–Performance Map Analysis (IPMA). Data were collected from 100 respondents, including project owners, contractors, and construction management consultants. The SEM-PLS results reveal that Integrity & Compliance Culture (β = −0.169, p = 0.045) and Administrative & Financial Compliance (β = −0.193, p = 0.027) significantly reduce the probability of audit findings, while other technical factors such as planning, supervision, and team competence show no direct effect. IPMA highlights Integrity & Compliance Culture and Contract & Documentation Management as top improvement priorities. These findings demonstrate that governance and compliance dimensions are more critical than technical performance in shaping audit outcomes. Strengthening compliance culture, enhancing administrative transparency, and implementing robust contract management are therefore key strategies to minimize audit risks in DB projects. The study contributes to the applied statistics literature in construction management and offers practical insights for policymakers, contractors, and auditors aiming to achieve accountable and transparent infrastructure delivery in Indonesia.
Copyright (c) 2026 Al Kautzar, Mawardi Amin, Agus Suroso https://creativecommons.org/licenses/by-sa/4.0
BERTopic-Based Multi-Class Topic Classification on Indonesian Shopee E-commerce Reviews Using Ensemble Learning
The rapid growth of e-commerce platforms has resulted in a large volume of unstructured user reviews, creating challenges for scalable analysis. This study proposes a multi-class topic classification framework for Indonesian Shopee application reviews by integrating BERTopic-based embedding-driven topic modeling with ensemble learning. A total of 23,956 reviews are analyzed, with BERTopic applied exclusively to 19,167 training reviews to derive eight dominant topic labels, which serve as pseudo-labels for supervised classification using CatBoost and Extra Trees. Model performance is evaluated on a held-out test set under baseline and hybrid resampling settings to address severe class imbalance. The results show that hybrid resampling substantially improves balanced accuracy, particularly for CatBoost, while ROC–AUC remains consistently high, indicating robust class discrimination. Analysis of an unlabeled 2025 dataset, used solely in a deployment-style setting, reveals semantically consistent topic distributions on unseen data. Overall, the findings demonstrate that embedding-based topic modeling combined with ensemble learning provides an effective and scalable solution for multi-class topic classification in highly imbalanced e-commerce review data, with clear separation between training, evaluation, and post-deployment analysis.
Copyright (c) 2026 Kevin Alifviansyah https://creativecommons.org/licenses/by-sa/4.0
Modelling Factors Affecting the Middle Income Trap in Indonesia Using Generalized Additive Models (GAM)
Indonesia is currently facing the risk of the Middle Income Trap (MIT), a condition in which economic growth stagnates after reaching middle-income status. This study aims to identify and model socio--economic factors affecting MIT at the provincial level in Indonesia during 2020--2023. The Generalized Additive Model (GAM) is employed to capture nonlinear and heterogeneous relationships between predictors and GRDP per capita with complex patterns that conventional linear or parametric models often fail to detect. The use of GAM in this context represents a methodological contribution, as studies applying GAM for MIT analysis in Indonesia remain very limited. This research therefore introduces a novel analytical approach by demonstrating how GAM can reveal flexible functional relationships and uncover nonlinear effects that are overlooked by traditional panel regression. GRDP per capita is modeled using six predictors: life expectancy, poverty rate, informal employment share, upper secondary education completion, food insecurity prevalence, and population density. The best model is obtained using the Gaussian family with an identity link, with five predictors showing nonlinear effects and food insecurity exhibiting a negative linear influence. The selected model demonstrates strong performance, indicated by an AIC value of 2743.279 and a R^2 of 98.6%, suggesting a very high explanatory power. In addition, the model achieves good predictive accuracy, with a MAPE of 8.04%. The findings support evidence-based policies aligned with Sustainable Development Goal (SDG) 8, promoting inclusive and sustainable economic growth.
Copyright (c) 2026 Dita Amelia, Suliyanto Suliyanto, Azizah Atsariyyah Zhafira, Aulia Ramadhanti, Billy Christandy Suyono, Firqa Aqila Hizbullah https://creativecommons.org/licenses/by-sa/4.0
Transmission Dynamics of Dengue Disease Incorporating Treatment, Mass Awareness, and Wolbachia Intervention
Dengue Hemorrhagic Fever (DHF) remains a serious global public health threat, with its transmission dynamics strongly influenced by vector control strategies and human behavior. This study constructs and analyzes a mathematical model based on a system of differential equations to investigate the transmission dynamics of DHF by integrating three control strategies: treatment, public awareness, and the release of Wolbachia-infected mosquitoes. The basic reproduction number (R0) is derived using the Next Generation Matrix (NGM) method and serves as a threshold parameter for disease spread. Numerical simulations show that when R0 < 1, the system converges to the disease-free equilibrium, indicating that the disease will eventually die out. Conversely, by adjusting the parameter δ such that R0 > 1, the system becomes stable at the endemic equilibrium, implying the persistence of the disease within the population. These findings highlight the importance of controlling key parameters through integrated intervention strategies to reduce R0 below unity.
Copyright (c) 2026 Rafika Nanda Agustina, Budi Priyo Prawoto https://creativecommons.org/licenses/by-sa/4.0
Modeling the Dynamics of Tuberculosis-Diabetes Mellitus Coinfection with an Optimal Control Approach
Tuberculosis–Diabetes Mellitus (TB–DM) coinfection increases morbidity, treatment failure, and healthcare costs. This study analyzes TB–DM transmission dynamics and identifies effective prevention strategies using a ten-compartment mathematical model that distinguishes non-diabetic and diabetic populations, each classified into susceptible, latent, active, treatment, and recovered classes. Numerical analysis verifies that the disease-free equilibrium is stable when the basic reproduction number is less than one, whereas an endemic equilibrium exists when it exceeds one. Using baseline parameter values, the reproduction number is estimated as 3.592, indicating persistent TB–DM transmission. An optimal control framework is formulated to evaluate two time-dependent interventions: reducing TB transmission through case detection and contact tracing, and preventing diabetes onset in non-diabetic individuals through metabolic monitoring. Numerical simulations demonstrate that the combined implementation of both control strategies significantly reduces TB–DM incidence while minimizing intervention costs. These findings support the importance of integrated, time-varying TB–DM control programs for public health.
Copyright (c) 2026 Muna Afdi Muniroh https://creativecommons.org/licenses/by-sa/4.0
Spatial Variation of HDI in East Java: A Tricube-Based Geographically Weighted Regression–Flower Pollination Algorithm Modeling Approach
Understanding spatial disparities in human development is essential for designing equitable development policies. This study examines the spatial variation of the Human Development Index (HDI) in East Java Province using an integrated Geographically Weighted Regression–Flower Pollination Algorithm (GWR–FPA) optimized with a Tricube kernel. The integration of GWR and FPA enables simultaneous spatial weighting and bandwidth optimization using the corrected Akaike Information Criterion (AICc) as the objective function. For standard GWR, the bandwidth was selected using Cross-Validation (CV) to minimize prediction error, while for the GWR–FPA model, bandwidth optimization was performed using the Flower Pollination Algorithm (FPA) with the corrected Akaike Information Criterion (AICc) as the objective function. Three predictors were analyzed: population size (X1), literacy rate (X2), and mean years of schooling (X3). Statistical diagnostics indicated significant spatial autocorrelation and heteroskedasticity in the OLS residuals, justifying the use of a spatial modeling framework. The GWR estimates revealed strong spatial non-stationarity: X1 showed no significant local effect, whereas educational factors (X2 and X3) were significant in all 38 districts and cities. The FPA optimization enhanced bandwidth selection, resulting in improved model fit. Model comparison based on AIC and AICc showed that the GWR–FPA–Tricube model achieved the lowest values (AIC = 135.8821; AICc = 137.0045), outperforming both global OLS and standard GWR. The results highlight the dominant contribution of education-related components to the spatial decomposition of HDI variation across East Java. The optimized model provides a more accurate spatial representation of local development disparities, supporting targeted policy interventions and illustrating the effectiveness of integrating metaheuristic optimization within spatial regression.
Copyright (c) 2026 Friansyah Gani, Henny Pramoedyo, Achmad Efendi https://creativecommons.org/licenses/by-sa/4.0
Some Properties of Prime Graph of Cartesian Product of The Rings and It's Line Graph
The prime graph of the ring R, P G(R), is a graph which set of vertices consists of elements of R and two different vertices are adjacent if their product in the ring is zero. We study the prime graph of cartesian product of the rings Zp1 × Zp2 for distinct prime numbers p1 and p2. We find that some properties of P G(Zp1 × Zp2 ) such as order, size, the number of triangles, and Wiener index. Further, we construct the line graph of P G(Zp1 × Zp2 ) and calculate the order, size, and Wiener index of L(P G(Zp1 × Zp2 )).
Copyright (c) 2026 Vira Hari Krisnawati, Ayunda Faizatul Musyarrofah, Noor Hidayat, Farah Maulidya Fatimah https://creativecommons.org/licenses/by-sa/4.0
Dynamic Analysis of a Predator–Prey Model with Group Defense in Prey and Cooperative Hunting in Predators
This article discusses a single-prey and single-predator model by incorporating two behavioral mechanisms, namely group defense in prey modeled through a Holling type IV response function and cooperative hunting in predators represented by a predation rate dependent on predator density. Through system analysis, up to four equilibrium points are obtained mathematically. Among these, three equilibria are biologically feasible under typical parameter values, corresponding to total extinction, predator extinction, and coexistence states. The total extinction equilibrium is always unstable, while the stability of the predator extinction and coexistence equilibria depends on the predator attack rate. Numerical simulations in the form of phase portraits were obtained by varying the parameters related to the predator attack rate. The simulation results show various dynamic behaviors, including predator extinction, asymptotically stable coexistence between prey and predators, and bistability. Numerical continuation analysis identifies a subcritical Hopf bifurcation at α=0.4595, confirmed by a positive first Lyapunov coefficient, as well as a saddle-node at α= 0.0478 and transcritical bifurcations α=3.0505 that alter equilibrium structure and stability. These findings demonstrate how prey group defense and predator cooperation can generate bistability and abrupt transitions between extinction and coexistence, accompanied by damped oscillatory dynamics near critical parameter values.
Copyright (c) 2026 Dian Savitri https://creativecommons.org/licenses/by-sa/4.0
Sensitivity Analysis of a Tuberculosis Transmission Model with Incomplete Treatment
Tuberculosis (TB) remains a major global health concern due to its complex transmission dynamics and frequent treatment interruptions. This study utilizes a SEITR compartmental model to quantitatively analyze the spread and control of TB. The model calculates the basic reproduction number, disease-free equilibrium, and endemic equilibrium to evaluate system stability. Sensitivity analysis identifies key parameters influencing the infected population: effective contact rate, natural mortality rate, population recruitment rate, and treatment rate. Among these, the effective contact rate and natural mortality rate significantly impact disease persistence. The findings suggest that effective TB control can be achieved through early detection and isolation of infectious individuals, timely and proper treatment, improved indoor ventilation, and the consistent use of masks by active TB patients. This model-based approach offers empirical evidence to inform public health policies, highlighting critical intervention points to interrupt TB transmission and improve treatment outcomes.
Copyright (c) 2026 Joko Harianto, Diki Fernandi https://creativecommons.org/licenses/by-sa/4.0
Mathematical Modeling and Regime Dynamics of Ammonium Chloride Imports in Indonesia Using Threshold Vector Autoregressive Integrated (TVARI) Approach
Ammonium chloride plays an important role in Indonesia as a key raw material for NPK fertilizers and chemical industries. Despite its importance, domestic production remains limited, and potential supply from by-product sources has not been utilized effectively. Consequently, Indonesia depends heavily on imports sourced mainly from a single country. This situation creates vulnerabilities in industrial supply chain and highlights the need for a clearer understanding of import volume and value dynamics. This study employs a Threshold Vector Autoregressive Integrated (TVARI) model to capture nonlinear and regime-dependent adjustments in the joint dynamics of import volume and value, with import volume growth as the threshold variable. The approach's novelty lies in its ability to accommodate structural changes that cannot be adequately represented by a single linear specification. Empirical results identify two statistically distinct regimes defined by whether import growth lies below or above an estimated threshold. In the first regime, where growth is below the threshold, short-run dynamics are primarily driven by changes in import value, indicating price-related adjustments. In the second regime, import volume exhibits stronger responses, reflecting quantity adjustments associated with supply-side conditions. These findings demonstrate that linear models are insufficient to capture asymmetric adjustment mechanisms in import behavior. By providing a formal mathematical description of regime-dependent dynamics, this study contributes to a deeper understanding of Indonesia’s industrial import structure and offers insights for data-informed supply chain planning. The results support policy discussions related to Sustainable Development Goals 8 (economic stability), 9 (industry resilience), and 12 (responsible consumption and production).
Copyright (c) 2026 Carissa Egytia Widiantoro, Restu Arisanti, Gumgum Darmawan https://creativecommons.org/licenses/by-sa/4.0
ResNet-50 and ResNeXt-50 for Multiclass Classification of Chronic Wound Images under Gaussian Blur
Chronic wound image classification is important for supporting the assessment of conditions such as diabetic foot ulcers (DFU) and pressure ulcers (PU). While convolutional neural network (CNN)--based approaches have shown promising results, most previous studies focus on binary classification and rarely evaluate robustness in multiclass chronic wound scenarios. This study investigates multiclass classification of chronic wound images, distinguishing DFU, PU, and Normal Skin, using ResNet-50 and ResNeXt-50 architectures. A total of 2,146 publicly available images were stratified at the image level into training (70%), validation (15%), and test (15%) sets. Both models were trained under an identical configuration using data augmentation and class-weighted loss. On clean test images, ResNet-50 and ResNeXt-50 achieved strong and comparable performance, with accuracies of 0.9877 and 0.9938 and macro-averaged F1-scores of 0.9866 and 0.9928, respectively. Robustness was evaluated by applying Gaussian blur at the inference stage to simulate image defocus. Under stronger blur ((σ = 2.0), ResNeXt-50 maintained higher performance (accuracy 0.9723, macro-F1 0.9679) than ResNet-50 (accuracy 0.9200, macro-F1 0.9123). These results highlight the contribution of this study in evaluating robustness to blur in multiclass chronic wound image classification, while emphasizing that robustness is limited to resistance against image blur or defocus.
Copyright (c) 2026 Reynaldi Ikbar Surya Andhika https://creativecommons.org/licenses/by-sa/4.0
Spatial Analysis of Child Violence Victims in West Java in 2024 Using Geographically Weighted Negative Binomial Regression
Violence against children remains a critical issue in Indonesia, with West Java consistently reporting high numbers of reported child violence victims. This study examines socioeconomic factors associated with the count of reported child violence victims across 27 districts and cities in West Java in 2024, using secondary administrative data obtained from Open Data Jabar. The explanatory variables include poverty rate (X1), average years of schooling (X2), number of divorce cases (X3, Labor Force Participation Rate (X4), and Open Unemployment Rate (X5). Diagnostic tests indicate the presence of spatial heterogeneity and overdispersion, supporting the application of a Geographically Weighted Negative Binomial Regression (GWNBR) model with a child population offset. Model performance comparison based on in-sample fit criteria shows that the GWNBR model provides superior fit (deviance = 42.94, AICc = 99.87) compared to the global Negative Binomial Regression model (deviance = 48.27, AIC = 105.63). The GWNBR results reveal substantial spatial variation: average years of schooling (X2) is statistically significant across all 27 regions, while the number of divorce cases (X3) is significant in 23 regions. Poverty rate (X1) shows localized significance in 16 regions. Labor force participation rate (X4) and unemployment rate (X5) each exhibit significance in 6 regions, though with distinct spatial patterns. These findings highlight geographically varying risk structures that cannot be adequately captured by global models and underscore the importance of spatially adaptive modeling for informing region-specific child protection policies. Although the analysis relies on reported administrative data that may not fully represent the true underlying prevalence of child violence, the results provide valuable spatial insights relevant to policy development aligned with SDG 3, SDG 4, and SDG 16.
Copyright (c) 2026 Suliyanto Suliyanto, Dita Amelia, Lisa Amanda Putri, Aurellia Calista Anggakusuma https://creativecommons.org/licenses/by-sa/4.0
Numerical Pricing of European Stock Options Using Black-Scholes Interval Model
This study presents the numerical implementation of the Black-Scholes interval model for determining the price of European call options under parameter uncertainty. Unlike the classic Black-Scholes model, which assumes fixed volatility and risk-free interest rates, this study represents both parameters as limited intervals constructed based on historical data. Daily stock closing prices obtained from Yahoo Finance and risk-free interest rate data from the Federal Reserve Bank of St. Louis were used to define the parameter ranges. The interval Black-Scholes model was discretized in the asset price and time domains and solved numerically by formulating an optimization problem that minimizes the residual error of the interval partial differential equation with terminal payoff constraints. The numerical solution produces lower and upper bounds for option prices in the specified domain. Simulation results show that classic Black-Scholes option prices lie within the calculated interval price bounds, demonstrating numerical consistency between the deterministic and interval formulations. This study provides a structured numerical case study showing how the Black-Scholes interval model can be implemented to generate option price bounds under bounded parameter uncertainty.
Copyright (c) 2026 Muhammad Iqbal Aditama, Rudianto Artiono https://creativecommons.org/licenses/by-sa/4.0
Stability Analysis of a Three-Trophic Rice Ecosystem with Holling Type II and Crowley--Martin Responses
This study examines three-trophic-level ecological dynamics in rice field ecosystems involving rice as the producer, brown planthoppers Nilaparvata lugens as herbivores, and Pardosa sp. as top predators. Population interactions were modeled using logistic growth for rice and two response functions: the Holling type II response for planthopper predation on rice, and the Crowley--Martin response for Pardosa sp. predation on planthoppers to capture predator interference. The resulting model was formulated as a system of nonlinear differential equations. Analytically, four equilibrium points were obtained: total population extinction, extinction of planthoppers and Pardosa sp., extinction of Pardosa sp., and coexistence of all three species. Local stability analysis at each equilibrium point was conducted using the Jacobian matrix and the Routh--Hurwitz criterion. Numerical simulations were performed for several parameter combinations by varying planthopper growth efficiency and Pardosa sp. predation intensity. Parameter values are obtained from relevant literature where available, and the remaining parameters are considered reasonable biological assumptions for exploring the dynamics of the system qualitatively. The simulation results were consistent with the theoretical analysis and showed that small changes in biological parameters could shift the system from stable coexistence to near extinction of the planthopper population. Ecologically, the model demonstrates that rice field ecosystem balance is strongly influenced by the interaction between planthopper reproductive capacity and the predatory strength of Pardosa sp., providing theoretical insights that may support the development of sustainable planthopper pest management strategies.
Systematic Literature Review of GPS-based Multi-Objective Environmentally Friendly Shortest Path with a Proposed Lexicographic Framework
Environmentally friendly path planning has become an important topic in transportation research as concerns about carbon emissions continue to grow. This study presents a Systematic Literature Review (SLR) and bibliometric analysis to identify the state of the art in green shortest path optimization. Using the PRISMA guideline, the study analyzes 20 articles selected from Scopus, ScienceDirect, and Dimensions databases published between 2021 and 2025. Results indicate that the field is dominated by metaheuristic and AI-based approaches, while deterministic methods with explicit objective prioritization remain underutilized. Bibliometric visualization identifies traffic congestion and carbon emission policies as major research clusters, yet few studies integrate these with real-time GPS data in developing countries. Based on these findings, this paper proposes a conceptual framework for a GPS-based Lexicographic Multi-Objective Optimization model. The proposed framework prioritizes carbon emission minimization as the primary objective, followed by travel time, offering a transparent decision-making tool for sustainable urban transportation.
Copyright (c) 2026 Thania Nur Salsabila, Diah Chaerani, Herlina Napitupulu https://creativecommons.org/licenses/by-sa/4.0
Hybrid Otsu Morphological Pre-processing for EfficientNetB4 Based Acute Lymphoblastic Leukemia Classification
Image quality plays a crucial role in improving the performance of image-based classification models, particularly when raw images exhibit noise, uneven illumination, and unclear object boundaries. This study proposes a hybrid segmentation approach to enhance object separation by reducing background interference and refining object contours. The method combines Otsu thresholding for initial object–background separation with elliptical morphological operations to improve region consistency and boundary definition. The segmented grayscale images are replicated into three channels and resized to 224×224 pixels before being used as input to an EfficientNetB4-based classification model optimized with the AdamW optimizer and fine-tuning. Experimental results under identical data splits, training settings, and fine-tuning protocols show that the proposed segmentation-based method achieves a final test accuracy of 97%, outperforming the baseline model trained on raw images (95% test accuracy) using the same EfficientNetB4-AdamW configuration. These results demonstrate that incorporating segmentation in the preprocessing stage effectively enhances discriminative feature learning and improves overall classification performance.
Copyright (c) 2026 Maretta Mia Audina, Sugiyarto Surono, Aris Thobirin, and Goh Khang Wen https://creativecommons.org/licenses/by-sa/4.0
Approximation Properties on a Set Based on Equivalence Relations and Dominance Relations
An equivalence relation on a set forms equivalence classes so that the concept of approximation is formed on that set (rough set). The concept of approximation on a set is developing very rapidly. Some papers replace the equivalence relation with other relations, one of which is the dominance relation. The symmetry property of the equivalence relation is replaced by the anti-symmetry property so that a dominance relation is formed. This paper reviews several papers related to approximation on a set $w.r.t$ equivalence and dominance relations by describing the approximation properties that hold in both relations in terms of the concept of 3 types of approximation on a set. This paper also provides the approximation properties that hold in the equivalence relation but do not hold in the dominance relations in terms of the concept of 3 types of approximation on a set. The main contribution of this paper is showing that the relationship between the concept of 3 types of approximation on a set $w.r.t$ the equivalence relation and the dominance relation.
Copyright (c) 2026 Dian Winda Setyawati, Soleha Soleha, Rinurwati Rinurwati https://creativecommons.org/licenses/by-sa/4.0
Application of the Saint-Venant Model for Simulation of the Kapuas River Flow Using the Finite Difference Method
The Kapuas River plays an essential role in transportation, fisheries, tourism, and natural drainage in Pontianak, where river geometry and downstream tidal effects shape its flow conditions. These tidal forces produce variations in discharge and water level over space and time, which can exceed the river’s capacity and cause flooding. This study simulates the dynamics of discharge and water level along the Kapuas Kecil River segment. Researchers developed a mathematical flow model using the Saint-Venant framework, based on mass and momentum conservation principles. This study numerically solved the equations using a finite difference approach with a forward-time and central-space scheme. Researchers collected river width and depth data along a 5 km stretch from Pontianak Utara to Jungkat. The study presents simulation results as spatial and temporal profiles of water level and discharge. The results of this study show that water discharge increases along the channel, while water levels generally decrease over time in the direction of flow. These results provide insights into tidal-influenced river flows in urban environments and can support flood-related analysis and management efforts.
Copyright (c) 2026 Dian Eka Ratnasari, Meliana Pasaribu, Meliana Pasaribu, Yudhi Yudhi, Yudhi Yudhi https://creativecommons.org/licenses/by-sa/4.0
From Risk-Neutral to Risk-Sensitive Reinforcement Learning: Actor–Critic vs REINFORCE with Tail-Based Risk Measures
his study investigates the application of \emph{risk-sensitive reinforcement learning} on heavy-tailed return series by comparing two primary algorithms: REINFORCE with baseline (REINFORCE-BL) and episodic batched actor--critic (A2C-B). Initial exploratory analysis reveals an asymmetric return distribution with numerous extreme \emph{outliers}, rendering variance-based risk measures inadequate and motivating the integration of tail-based risk measures—specifically Value at Risk (VaR), Conditional Value at Risk (CVaR), and Entropic Value at Risk (EVaR)—into the RL objective function. This study constructs a simple portfolio environment with discrete actions (market entry, market exit, and \emph{hold}) and trains both algorithms under four scenarios: risk-neutral, VaR, CVaR, and EVaR. Experimental results demonstrate that A2C-B consistently outperforms REINFORCE-BL across all scenarios, exhibiting higher average long-term rewards, faster convergence rates, and more stable \emph{learning curves}. While VaR and CVaR penalties significantly reduce rewards and increase learning volatility for REINFORCE-BL, A2C-B experiences only moderate reward reductions while maintaining stability. In the EVaR scenario, both algorithms yield high rewards, yet A2C-B retains a slight advantage in terms of stability. These findings indicate that in environments with heavy-tailed returns, employing coherent risk measures (particularly CVaR and EVaR) within an actor--critic framework offers a more compelling trade-off between tail risk control and average performance, serving as a viable \emph{baseline} for the development of risk-sensitive RL in finance and actuarial science.
Copyright (c) 2026 Adhitya Ronnie Effendie https://creativecommons.org/licenses/by-sa/4.0
Stage-Structured Predator Model with Prey Protection: Application to Rice Plants–Leptocorisa oratorius
This study investigates a stage-structured predator–prey model consisting of prey, juvenile predators, and adult predators. The prey population follows logistic growth, while predation is described using a Holling type I functional response. Prey protection is incorporated through a protection parameter (1-m), representing the proportion of prey that successfully avoid predation by reducing the predation rate of adult predators. The model is analyzed by determining equilibrium points and examining their existence and stability. The results show four equilibrium points: total population extinction, prey-only equilibrium, juvenile predator extinction, and coexistence equilibrium. Predator extinction occurs when predation efficiency and predator reproduction are insufficient to compensate for predator mortality, whereas coexistence occurs when predation and conversion rates exceed mortality thresholds. Numerical simulations support the analytical results and demonstrate that increasing prey protection reduces predation pressure and may lead to predator decline, while appropriate predation efficiency promotes stable coexistence. These findings highlight the ecological importance of prey defense mechanisms in predator–prey interactions, particularly in rice–Leptocorisa oratorius.
Copyright (c) 2026 Dian Savitri, Safirah Rahmah https://creativecommons.org/licenses/by-sa/4.0
Box Fractal as an Iterated Function System in Fractal Interpolation for Determining the Approximate Value of Demand Data
A common problem in inventory planning is the uncertainty of the demand. One technique for determining the demand approximation value is the fractal interpolation. The aim of this study is to develop a fractal interpolation technique with an Fractal Interpolated Function constructed by the affine function that forms the Box Fractal shape. The development results are applied to interpolate rice demand data based on prices at a rice milling factory. Mean Absolute Percentage Error (MAPE) is used to measure the accuracy of interpolation results. For the nth iteration, the number of boxes formed are 5n and 4×5n pairs of points. Based on the rice demand data at one of the factories, the best MAPE was obtained at the 6th Iteration, which is 7.1596% within very good category. Based on the data used, the affine function that forms the Box Fractal as an Fractal Interpolated Function can be used in the fractal interpolation technique.
Copyright (c) 2026 Eka Susanti, Oki Dwipurwani, Dian Cahyawati Sukanda, Novi Rustiana Dewi, Husnul Khotimah, Wahyuni Apria Ningsih https://creativecommons.org/licenses/by-sa/4.0
Stability Analysis and Invasion Thresholds in a Rosenzweig--MacArthur Model with Prey Immigration and Cooperative Hunting
Predator--prey systems with multiple interacting ecological mechanisms require integrated modeling approaches for realistic analysis. This study develops a unified Rosenzweig--MacArthur model incorporating both continuous prey immigration and cooperative hunting among predators to analyze how these combined mechanisms affect equilibrium existence, stability, and transient dynamics. Analytical methods derive explicit invasion thresholds and local stability conditions through eigenvalue analysis, while numerical simulations with biologically plausible parameters compare two dynamical regimes: baseline conditions produce stable-node convergence, whereas high-efficiency conditions yield stable-spiral oscillations. Results show that immigration elevates prey density above invasion thresholds, enabling predator persistence, while increased cooperation intensity transitions the system from monotonic to oscillatory convergence. The integrated framework demonstrates how bottom-up (immigration) and top-down (cooperation) processes interact to shape predator--prey dynamics, providing testable predictions for ecosystems where both mechanisms operate simultaneously and establishing a foundation for more complex ecological modeling.
Copyright (c) 2026 Dian Savitri, Naufal Daffa Faustin https://creativecommons.org/licenses/by-sa/4.0
Sentiment Analysis of the 2022 Fuel Price Hike Using the Naïve Bayes Classifier
This study examines public opinion towards Indonesia’s 2022 fuel price hike using social media analytics and assesses the pace of a supervised machine learning classifier for policy-oriented sentiment analysis. The research aimed to answer the following two questions (1) What was the prevailing public sentiment articulated on Twitter after fuel pricing announcement? and (2) How well is a Naïve Bayes classifier able to classify sentiment polarity in this domain? We employed a quantitative cross-sectional design utilizing Twitter data obtained from 3–4 September 2022 via the hashtags #hargabbm and #bbmnaik. Ultimately, after preprocessing, there were 1,867 unique tweets out of the 2,003 retrieved ones. Training data consisted of a total of 489 manually labeled tweets, and 1,378 for testing. Tokenization and TF–IDF weighting were performed on text data, while the sentiment classification was done using Gaussian Naïve Bayes model and evaluated through confusion matrix metrics. The results suggest that public sentiment was overwhelmingly negative during the analysis period and that the classifier reached an accuracy of 94.89% with a precision of 73.40%, recall of 100%, and F1-score of 84.66. These findings show that probabilistic text classification offers newsworthy evidence about whether the public unanimously supports economically sensitive policies (or not), with voltage and salience meaningfully specified.
Copyright (c) 2026 Alia Lestari, Muhammad Hajarul Aswad, Subekti Masri https://creativecommons.org/licenses/by-sa/4.0
Complex-Valued Neural Networks with Adaptive Frequency Attention for Image Denoising
Image denoising encompasses various noise types; in this work, we focus specifically on periodic interference, which introduces coherent frequency-domain artifacts that are challenging to remove using conventional real-valued convolutional neural networks (CNNs). This paper introduces a Complex-Valued Neural Network with Adaptive Frequency Attention (CVNN-AFA) tailored to periodic noise removal, integrating complex-domain feature propagation with explicit radial frequency-band modulation. The proposed architecture employs complex convolutions, complex batch normalization, and ModReLU activations to jointly model amplitude and phase information. An Adaptive Frequency Attention (AFA) module operates in the Fourier domain and partitions the spectrum into low-, mid-, and high-frequency radial bands using distance-based masks, enabling adaptive band-wise reweighting aligned with interference characteristics. Experiments on the BSDS500 dataset augmented with synthetic periodic noise evaluate both low-noise and moderate-to-high noise regimes under matched training budgets and strong real-valued frequency-aware baselines. Results indicate that CVNN-AFA achieves competitive performance overall and provides consistent, moderate improvements in low-amplitude settings, while the real-valued frequency-aware baseline remains more robust under extreme corruption levels. Qualitative and spectral analyses suggest that the proposed approach offers incremental attenuation of periodic components while maintaining comparable detail preservation. These findings are specific to the controlled periodic noise scenarios evaluated in this study.
Copyright (c) 2026 Marjono Marjono, Avin Maulana, Anggi Gustiningsih Hapsani https://creativecommons.org/licenses/by-sa/4.0
Evaluating Hierarchical Pathfinding A* (HPA*) for Multi‑Order Routing in a Small Warehouse Layout
Hierarchical Pathfinding A* (HPA*) is a hierarchical search framework that partitions grid‑based environments into clusters to reduce computational time while preserving a near-optimal path. The warehouse layout features cross-aisle connectivity, and multi-order optimization is performed using the HPA* algorithm, which integrates travel times with multi-rack picking times to the objective cost function. We simulate by assigning 30 random orders, with a total of 10641 items stored in the warehouse and 10 item types. The travel time is calculated assuming a picker has a constant speed of 1.2 m/s along edges, the picking time is proportional to the number of items picked per rack, and a small warehouse layout. Estimated cycle times of the orders (travel plus picking time) range from 114.4 to 349.9 seconds using the HPA* optimization, with a mean of 232.0 seconds. From the optimization results, orders require an average of 5.2 rack visits, ensuring that the picker travels more than two racks per order. The HPA* reduces the original low‑level graph (50 nodes and 61 edges, including base and stage station) to a graph with 22 nodes and 17 edges, enabling faster route computation while preserving observed cycle‑time patterns when combined with picking-time durations. Compared to A*, given the layout and orders, HPA* demonstrates an efficient warehouse path‑planning method that reduces search computation while maintaining near‑optimal routing performance.
Copyright (c) 2026 Ig. Prasetya Dwi Wibawa, Meta Kallista, Ramdhan Nugraha, Heni Widayani, Harish Chandra Bhandari, Angga Rusdinar https://creativecommons.org/licenses/by-sa/4.0
Stability and Bifurcation of a 3D Eco Epidemiological Predator Prey Model with Pesticide
Eco--epidemiological predator--prey models provide an important mathematical framework for understanding the interaction between disease transmission, predation, and human intervention in ecological systems. This study investigates a three--dimensional deterministic model incorporating saturated disease incidence, Holling type II predation, and pesticide application. Analytical techniques are employed to determine the existence and local stability of biologically feasible equilibrium points, while numerical simulations using a fourth--order Runge--Kutta method illustrate the dynamical behavior of the system under different parameter regimes. The analysis reveals the possibility of disease--free, predator--free, and interior coexistence equilibria, as well as bistability depending on parameter values and initial conditions. Bifurcation analysis identifies critical thresholds in disease transmission and predator conversion efficiency that govern transitions between predator persistence and extinction. These findings provide theoretical insights for integrated pest management strategies by emphasizing the balance between chemical control and ecological stability.
Temporary Immunity in a Fractional-Order SEIR Model: Stability Analysis
Infectious disease has become a serious problem over the past few years. At the same time, research on disease dynamics keeps advancing, especially on diseases caused by viruses. One concept that has been used in epidemic models is fractional calculus, or more specifically, fractional differential equations. This paper discusses the analytical properties of a fractional-order SEIR model, which are then verified by numerical simulations. Analytical results have shown that the global asymptotic stability of disease-free equilibrium is achieved when the basic reproduction number is equal to or less than 1, while endemic equilibrium is globally asymptotically stable when the value is greater than 1. Simulation results from Explicit Fractional Order Runge-Kutta (EFORK) method are confirmed to be in agreement with the basic properties provided by the analysis. The results also illustrate the impact of fractional-order and recovery rate on temporary immunity, which indicates that smaller fractional-orders converge faster compared to larger orders.
Copyright (c) 2026 Muhammad Iqbal, Mohammad Januar Ismail Burhan, Adam Adam https://creativecommons.org/licenses/by-sa/4.0
Stability Analysis of Conventional and E-Cigarette Smokers Behavior Model with Saturation Effects
Smoking behavior is a harmful habit that poses serious health risks and has been regarded as a lifestyle by certain segments of society, regardless of age, gender, or social status. This study develops and analyzes a mathematical model of smoking behavior that classifies between conventional smokers and e-cigarette smokers, incorporates interaction with lung cancer patients, and considers the saturation effect on potential smokers as the number of smokers in the population increases. The method is determining assumptions to create a compartment diagram and construct the model. This model has four equilibrium points. The results show that when R01 < 1, R02 < 1, the smoker-free equilibrium point is asymptotically stable. When R01 < 1, R02 > 1, the endemic equilibrium point of e-cigarette smokers becomes stable. When R01 > 1 and R02 < 1, the endemic equilibrium point of conventional smokers becomes stable. Meanwhile, when R01 > 1 and R02 > 1, the endemic equilibrium point of coexistence of conventional and e-cigarette smokers becomes stable. Numerical simulations show that the intensity of smoking transmission affects the dynamics of the system. The lower the transmission rate by conventional and e-cigarette smokers, the faster the transition to a smoker-free population. The saturation effect plays a role in limiting excessive contact between potential smokers and smokers.
Copyright (c) 2026 Budi Priyo Prawoto, Binti Mu'alafi Suryantini https://creativecommons.org/licenses/by-sa/4.0
Comparison of ARIMA, Random Forest, and Hybrid ARIMA-Random Forest Models in Forecasting Indonesian Crude Oil Prices
The price of Indonesian crude oil (ICP) is highly volatile due to fluctuations in global demand, energy policies, and geopolitical tensions, making accurate forecasting challenging. This study compares three forecasting models: ARIMA, Random Forest, and Hybrid ARIMA–Random Forest. The models are evaluated using Time-Series Cross-Validation (TSCV) with MAPE, sMAPE, and RMSE as performance metrics. The results indicate that the Hybrid ARIMA–Random Forest model achieves the lowest MAPE and sMAPE, while Random Forest attains the lowest RMSE, and ARIMA exhibits the highest forecast errors. Diebold–Mariano (DM) tests confirm that ARIMA’s predictive accuracy is significantly lower than both machine-learning-based models, whereas no significant difference is found between Random Forest and the hybrid model. Out-of-sample forecasts for January–June 2026 show relatively stable price movements within 59–63 USD per barrel, with short-term fluctuations reflected in wide prediction intervals. These findings suggest that Indonesian crude oil prices contain both linear and non-linear components, which are effectively captured by the hybrid approach. Overall, the Hybrid ARIMA–Random Forest model provides the most accurate forecasts in percentage-based metrics, offering a robust and reliable tool for policymakers, investors, and market participants navigating volatile oil markets.
Copyright (c) 2026 Yeni Rahkmawati, Selvi Annisa, Hardianti Hafid, Nuramaliyah Nuramaliyah https://creativecommons.org/licenses/by-sa/4.0
Clustering for Mapping Food Insecurity in the Land of Papua: A Five-Year Multiyear Analysis with Spatial Interpretation (2020-2024)
Food insecurity in the Land of Papua remains a critical issue due to extreme geographical conditions, limited infrastructure, and unstable food distribution systems. This study aims to map food vulnerability across 42 districts/cities in Papua using insufficient food consumption data from 2020 to 2024. Clustering was performed using five methods—Single Linkage, Complete Linkage, Ward, K-Means, and Gaussian Mixture Model (GMM)—and evaluated using three validation indices: Silhouette, Davies–Bouldin Index (DBI), and Calinski–Harabasz Index (CHI). To obtain a balanced and comprehensive model selection, a Performance-Based Weighting (PBW) framework was applied. In this framework, the DBI was first transformed to ensure a consistent higher-is-better orientation, and all validation indices were normalized to the [0,1] range prior to computing variance-based weights. This normalization step mitigates potential scale dominance, particularly from the unbounded CHI metric, ensuring proportional contribution from each validation criterion in the aggregated score. Although individual validation indices exhibited varying optimal values of k, the integrated PBW evaluation consistently identifies the two-cluster configuration as the most stable and interpretable overall structure. Specifically, Complete Linkage with k = 2 achieved the highest combined PBW score (0.8658), reflecting strong cluster separation and consistency across validation measures. Spatial interpretation of the resulting clusters reveals that the first cluster predominantly consists of high-risk mountainous districts with persistently elevated levels of food consumption inadequacy, particularly during 2021–2022, while the second cluster represents coastal and urban regions with comparatively lower and improving prevalence in 2023–2024. These findings provide a multiyear clustering perspective with geographic insight into regional disparities in food insecurity across Papua. Overall, this study presents a data-driven and reproducible multiyear clustering framework that integrates multiple validation criteria to enhance robustness in model selection and support evidence-based regional policy formulation.
Copyright (c) 2026 Ishak Semuel Beno https://creativecommons.org/licenses/by-sa/4.0
Deterministic Modeling of HIV–Malaria Co-Infection and Sensitivity Analysis in Papua
HIV and malaria co-infection poses a significant public health challenge in Papua, Indonesia, where high HIV prevalence overlaps with persistent malaria endemicity. Their biological interaction worsens clinical outcomes and complicates transmission. This study develops a deterministic mathematical model using nonlinear differential equations to describe HIV--malaria co-infection dynamics, tailored to Papua's epidemiology. The model includes coupled human and vector compartments and is analyzed through disease-free and endemic equilibria. The basic reproduction number $R_0$ is derived using the next-generation matrix method and its sensitivity is assessed using normalized forward sensitivity indices to identify key parameters affecting transmission. The results show that the HIV transmission rate ($\beta_H$), the mosquito bite rate ($b_M$), and the malaria transmission from humans to mosquitoes ($\beta_V$) increase the most strongly $R_0$, while the progression of HIV to AIDS ($\alpha_1$), malaria-induced mortality ($\delta_M$), and vector mortality ($\mu_V$) reduce it. Numerical simulations based on realistic initial conditions for Papua indicate that the system reaches a stable equilibrium when interventions target the most sensitive parameters. These findings provide a mathematical foundation for integrated control strategies, emphasizing reduced human--vector contact, suppression of HIV transmission, and effective vector control. The model enriches biomathematics research on co-infection dynamics and supports evidence-based policymaking for managing dual epidemics in regions like Papua.
Copyright (c) 2026 Vina Lusiana https://creativecommons.org/licenses/by-sa/4.0
Compare Bede-Gal Between dH Differentiability of Set Valued Functions
This paper presents a comparative study between the Bede--Gal differentiability and the dH-differentiability for set-valued functions whose values belong to the family of nonempty compact convex subsets of $\mathbb{R}^n$. The Bede--Gal derivative, originally introduced for fuzzy and interval-valued functions, is redefined for the set-valued framework and analyzed through its metric properties. Meanwhile, the dH-derivative is formulated in terms of the Pompeiu-Hausdorff metric, allowing differentiability without requiring the existence of the Hukuhara or generalized Hukuhara difference. We establish several results clarifying the relationship between these two concepts, including sufficient conditions under which a function that is Bede-Gal differentiable is also dH-differentiable, and conversely. Illustrative examples are provided to demonstrate cases where one type of differentiability exists while the other fails. The comparison emphasizes that dH-differentiability provides a broader and more flexible framework, extending the applicability of the differential calculus in set-valued analysis.
Copyright (c) 2026 Wildan Bagus Wicaksono https://creativecommons.org/licenses/by-sa/4.0
Dynamics of Predator-Prey Model with Holling Type II Involving Predator Stage-Structured and Cannibalism
Predator–prey models with nonlinear functional responses provide a robust framework for understanding population regulation and oscillatory dynamics. This study analyzes a three-dimensional predator–prey model incorporating Holling type II functional responses, explicit predator stage structure, and cannibalism. The primary objective is to investigate how adult predation, maturation, and cannibalism parameters influence equilibrium stability and the emergence of oscillations through Hopf bifurcation. Analytical results establish the existence and local stability of a positive coexistence equilibrium. For a biologically relevant parameter set, numerical simulations demonstrate that trajectories converge to the coexistence equilibrium (59.9078, 23.9092, 56.0552). This state is locally asymptotically stable, as the real parts of all Jacobian eigenvalues are negative. Numerical continuation methods are employed to detect Hopf bifurcations induced by key parameters. Two Hopf points are identified for the adult predation rate at 0.4211 and 8.7725, while the maturation rate induces bifurcations at 0.2661 and 0.5271. Additionally, the cannibalism parameter triggers a Hopf bifurcation at 0.1835, initiating periodic population oscillations. These results demonstrate that maturation and cannibalism define distinct instability thresholds, jointly governing the transition from stable coexistence to sustained oscillatory dynamics in stage-structured systems
Copyright (c) 2026 Dian Savitri, Sela Tri Indah Sari https://creativecommons.org/licenses/by-sa/4.0
Comparison Of Methods For Handling Imbalanced Datasets In Improving Classification Algorithm Performance
Data availability in large observations and dimensions is known as big data. There are several problems in processing big data, such as imbalanced datasets. In classification modeling, an imbalanced dataset is a common challenge. Data class predictions are more likely to be accurate in the majority class data and inaccurate in the minority class, resulting from the problem of imbalanced data. The data-level, the algorithm-level, and the ensemble method approach are the solutions that have been extensively researched. Some methods with a data-level approach are SMOTE, Undersampling, and Oversampling. The algorithm-level method is NWKNN. And then, the ensemble approach is UnderBagging, RUSBoosting, SMOTEBoost, and SMOTEBagging. The goal of this study is to determine the best method for handling each case of the imbalanced dataset. There are three cases of imbalance, namely mild, moderate, and extreme. A simulation study was conducted for each imbalanced case to evaluate the accuracy of each method. Based on the AUC value, the SMOTEBagging method is the best for mild imbalance cases with an AUC value of 0.9581. For moderate imbalance cases, the SMOTEBagging method is the best method, with an AUC value of 0.9033. Meanwhile, for extreme imbalance cases, the UnderBagging method provides the best performance.
Copyright (c) 2026 Winalia Agwil, Dyah Setyo Rini, Dian Agustina, Ahmad Famuji https://creativecommons.org/licenses/by-sa/4.0
A Review of Pompeiu-Hausdorff Metric Differentiability and Its Relation to Generalized Hukuhara Differentiability
The Pompeiu-Hausdorff distance/Pompeiu-Hausdorff metric is a concept in analysis that measures the distance between two subsets of a metric space, one of its important applications being the Hausdorff metric differentiability of set-valued functions . This article reviews the definition and properties of Pompeiu-Hausdorff distance differentiability on the space of compact and convex subsets of the Euclidean space with dimension n. We also present concepts about the generalized Hukuhara difference and its differentiability. By studying both topics, we discuss the established relationship between Pompeiu-Hausdorff metric differentiability and generalized Hukuhara differentiability
Copyright (c) 2026 William Surya Putra https://creativecommons.org/licenses/by-sa/4.0
Step-Stress Accelerated Life Testing with Type II Censoring and Exponential Distribution for Solar-Powered Lighting Systems
This study addresses the reliability assessment of solar-powered lighting systems using a partial step-stress accelerated life testing (ALT) model with Type-II censoring. The research aims to estimate the mean failure time and quantify the acceleration effect due to elevated stress. Secondary data from an experiment involving 31 lighting devices were analyzed. Initially, devices were tested at a normal temperature (293 K) until 16 failures occurred. Subsequently, the stress was increased to 353 K, and testing continued until all units failed or were censored. Under the assumption of an exponential lifetime distribution and a linear accelerated failure-time model, the maximum likelihood estimation (MLE) method was applied for parameter inference. The results show that the estimated mean failure time under normal conditions is approximately 711.6 hours, which reduces to about 38.7 hours under accelerated stress, yielding an acceleration factor of 18.354. Furthermore, a 95% confidence interval for the mean failure time under normal conditions is between 460.2 and 1245 hours. The reliability and percentile life at various stress levels were also derived. This research provides a practical statistical framework for evaluating the reliability of solar-powered lighting devices, offering a more efficient alternative to conventional life testing methods.
Copyright (c) 2026 ardi kurniawan, Vanisia Suci Ananda, Yovita Karin Kalista https://creativecommons.org/licenses/by-sa/4.0
Numerical Pricing of Discrete-Dividend European Options: An Empirical Case Study
This applied quantitative study implements Simpson's 1/3 numerical integration to systematically evaluate the pricing of discrete-dividend-adjusted European options. Using an anonymized technology stock, XYZ Tech Corp., as an empirical case study, this research pursues two primary objectives: validating the computational convergence of the numerical algorithm against the exact Black-Scholes analytical benchmark using Relative Error, and analyzing the model's empirical pricing deviation against real market observations across various moneyness zones. Computational tests demonstrate that the Simpson's 1/3 method, which is theoretically bounded by a fourth-order truncation error, achieves optimal and rapid convergence. By establishing the grid partition at N = 200, the algorithm successfully suppresses the relative error strictly below a 0.001% threshold compared to the analytical solution, while executing efficiently in under 0.005 seconds. Empirically, while the theoretical model exhibits high accuracy for In-The-Money (ITM) options with minimal deviation, it consistently reveals a significant overvaluation bias for Out-Of-The-Money (OTM) Call contracts, whereas OTM Put valuations exhibit a structurally different deviation pattern. This valuation asymmetry suggests a potential limitation of the constant historical volatility assumption, which appears inadequate to fully capture the implied volatility skew and shifting risk perceptions prevalent in actual market microstructures.
Copyright (c) 2026 Muhammad Gibran Elgiffary https://creativecommons.org/licenses/by-sa/4.0
Latent Household Food Security in Raja Ampat Marine Protected Areas: A Binary CFA Approach
This study examines household food security in four marine protected areas in Raja Ampat using repeated cross-sectional household survey data. Data were collected between 2010 to 2024, grouped into five monitoring periods. This study aims to provide a measurement framework for household food security as a latent construct based on binary indicators representing dimensions of food access and to estimate latent household food security scores in the four analyzed areas. In addition to applying confirmatory factor analysis to new empirical data, this study also presents a systematic estimation framework for measuring the latent construct using binary household indicators in repeated cross-sectoral survey data. The framework includes indicator threshold estimation, tetrachoric correlation estimation, parameter estimation using the robust diagonally weighted least squares method, and derivation of latent scores based on posterior expectations using the Gauss–Hermite quadrature approach. The analysis results indicate that the one-factor model provides acceptable fit and adequate construct reliability across the analyzed area-period groups. Estimates of factor loadings and thresholds provide information on the relative contribution and severity of each indicator in representing variations in household food access conditions. Overall, the goodness-of-fit indices indicate that the one-factor structure provides a reasonable representation of the relationships among the observed indicators under the fitted measurement model.
Copyright (c) 2026 indah ratih anggriyani https://creativecommons.org/licenses/by-sa/4.0
Short- and Long-Run Relationships Between Observed and Model 1 Output Rainfall Data in Majalengka Regency
This study examines the short-run and long-run relationships between observed monthly rainfall and CMIP6 climate model projections in Majalengka Regency, Indonesia. Monthly rainfall observations from the BMKG Kertajati Meteorological Station are analyzed using the Autoregressive Distributed Lag (ARDL) framework, which enables simultaneous assessment of short-term dynamics and long-term equilibrium relationships. Stationarity and cointegration are evaluated using the Augmented Dickey–Fuller test and ARDL bounds testing, respectively, while model performance is assessed through out-of-sample validation for the period 2015–2017 under three CMIP6 emission scenarios: SSP1-2.6, SSP2-4.5, and SSP5-8.5. The results indicate a positive and statistically significant short-run relationship between observed rainfall and CMIP6 projections across all scenarios, suggesting that climate models capture local scale monthly rainfall variability reasonably well. In contrast, the long-run relationship is weak and negative, highlighting limitations in representing long-term local rainfall dynamics. Model performance is highest under the low-emission SSP1-2.6 scenario and decreases under higher-emission scenarios. These findings suggest that CMIP6 outputs are more reliable for short-term rainfall analysis than for long-term local assessments without bias correction or downscaling.
Copyright (c) 2026 Sri Nurdiati, Mohamad Khoirun Najib, Fathia Rahmaisty https://creativecommons.org/licenses/by-sa/4.0
Modification of Norms on the Sequence Space ℓp
In this article, we explore sequence spaces by introducing a newly defined norm. We construct the Orlicz sequence space and demonstrate that the norm in this space is equivalent to the norm in the ℓp space. As a result, the fundamental properties of the ℓp space are carried over to the Orlicz sequence space through the equivalence of norms. One significant implication of this result is that Hölder's inequality, which holds in ℓp spaces, can also be applied to the Orlicz sequence space with different positive constants.
Copyright (c) 2026 Rikha Syahda Salsabilla, mochammad Idris https://creativecommons.org/licenses/by-sa/4.0
On A-Distance (Anti)magic Labeling of Prime Graph over the Ring Zn
Let G = (V, E) be a simple graph with n vertices, and let A be an abelian group of order n. Let f: V(G) → A be a bijection, and define the weight of a vertex x by w(x) = Σy ∈ N(x) f(y), where N(x) denotes the open neighborhood of x. We call f an A-distance magic labeling if all vertex weights are equal, and an A-distance antimagic labeling if the weights of distinct vertices are pairwise different. The prime graph of a commutative ring R is the simple graph with vertex set R in which two vertices x and y are adjacent if and only if xRy = {0}. In this paper, we investigate the existence of A-distance magic and A-distance antimagic labelings of the prime graph over the ring Zn for several values of n.
Copyright (c) 2026 Muhammad Husnul Khuluq https://creativecommons.org/licenses/by-sa/4.0
Comparison Of Vector Autoregressive and Multiresponse Fourier Series for Cryptocurrency Prediction Post-Bitcoin Halving 2024
This study examines cryptocurrency price modeling after the 2024 Bitcoin halving by comparing two multivariate forecasting methods: the Vector Autoregressive (VAR) model and the cosine-based Multiresponse Fourier Series Estimator. The research aligns with SDGs 8 on Decent Work and Economic Growth, as accurate forecasting in digital asset markets can support financial stability and informed investment decisions. The novelty of this study lies in applying a Fourier-based multiresponse model for post-halving cryptocurrency prediction, an approach that remains limited in existing literature. The dataset consists of daily prices of Bitcoin, Ethereum, and Litecoin from April 2024 to August 2025 (t=480), obtained from investing.com, with 90% for data training and 10% for data testing. Prior to modeling, the Bartlett test produced p-value 0.000<α, indicating significant correlations among cryptocurrencies, thereby validating the use of simultaneous multivariate analysis. The results show that the Fourier Series Estimator with five oscillation parameters (k=5) provides superior predictive accuracy, achieving a MAPE of 3.768%, compared to the VAR model’s MAPE of 8.503%. These findings demonstrate that the Fourier estimator more effectively captures cyclical and nonlinear patterns in digital assets and offers valuable contributions to financial statistics, providing practical insights for investors and policymakers in the highly volatile cryptocurrency market.
Copyright (c) 2026 Dita Amelia, Rizky Dwi Kurnia Rahayu, Bimo Okta Syahputra https://creativecommons.org/licenses/by-sa/4.0
A Damped Hessian-Free Newton--Conjugate Gradient Method for Weighted Multiclass Neural Classification
This study presents a deterministic damped Hessian-free Newton--CG method for weighted multiclass neural classification. The method is built from a weighted categorical cross-entropy objective, a damped local quadratic model, and a matrix-free curvature representation through Hessian--vector products. The search direction is computed by an inexact conjugate gradient solve, while Armijo backtracking and adaptive damping are used to improve stability. The method is implemented for the classification of academic predicate categories using preprocessed student data with mixed categorical and numerical features. Its numerical behavior is compared with SGD with momentum, RMSProp, and Adam under the same loss, initialization, and network architecture. The proposed method is computationally feasible, attains the best overall weighted test-set performance among the compared methods, and exhibits a distinct optimization trajectory driven by curvature-informed updates. These results show that a damped Hessian-free formulation provides a mathematically transparent, reproducible, and practically competitive framework for second-order optimization in multiclass neural classification.
Copyright (c) 2026 Andy Irawan, Zainal Abidin, Mohammad Jamhuri https://creativecommons.org/licenses/by-sa/4.0
Analysis of Color Space Transformations on MobileNetV2 Performance for Image Classification
This study analyzes the effect of color space transformation on the performance of MobileNetV2 for rice leaf disease classification using RGB, HSV, CIELab, and their combinations. The RGB color space is used as the baseline representation, while HSV and CIELab are applied to provide alternative representations of color information. In addition, a dual-stream architecture is employed to combine different color spaces for feature extraction. The results show that the choice of color space influences classification performance. In the single color-space scenario, RGB achieves the highest accuracy of 91.42%, while in the combined scenario, the RGB+CIELab model achieves the best performance with an accuracy of 97.00%. These findings suggest that the use of multiple color spaces can provide richer feature representations and may improve classification performance. Furthermore, the results indicate that optimizing input representation plays an important role in improving model performance, particularly when using lightweight architectures such as MobileNetV2. This study shows that color space transformation can improve classification performance in the rice leaf disease dataset used in this study.
Copyright (c) 2026 Sherlyn Vironica, Sugiyarto Surono, Aris Thobirin https://creativecommons.org/licenses/by-sa/4.0
Option Pricing Using Modification of Black Scholes Merton Model with GJR-GARCH
Option pricing is an important topic in modern finance as it plays a role in investment strategy and risk management. The Black-Scholes-Merton (BSM) model introduced in 1973 has become the standard in option pricing, but the assumption of constant volatility and symmetry makes this model often less suitable for volatile and asymmetric market conditions. This study aims to modify the BSM by incorporating volatility estimated through the Glosten-Jagannathan-Runkle GARCH (GJR-GARCH) model, and compare its performance with the Fractional Black-Scholes-Merton (FBSM) model. The data used is the daily closing price of Apple Inc. shares for the period January 7, 2022 to March 7, 2025 obtained from Yahoo Finance. The research procedure includes stationarity test using Augmented Dickey-Fuller (ADF), ARIMA identification, heteroscedasticity testing, and volatility estimation with GJR-GARCH (1,1) model. European call option prices are estimated by BSM and FBSM using both historical volatility and GJR-GARCH volatility. The results show that the FBSM model with GJR-GARCH (1,1) volatility provides the most accurate estimation with a Mean Absolute Percentage Error (MAPE) of 4.08%. In contrast, the BSM with historical volatility yields a MAPE of 17.25%. These findings confirm that the integration of FBSM with GJR-GARCH volatility is more realistic and reliable in option pricing under dynamic and asymmetric market conditions.
Copyright (c) 2026 Fatimah Oktaviani, Emy Siswanah https://creativecommons.org/licenses/by-sa/4.0
Haversine-Based Geographically Weighted Panel Regression of Human Development in Gorontalo (2016–2025)
Spatial disparities in human development indicate that socioeconomic factors may influence development outcomes differently across locations. This study aims to analyze spatially varying relationships between the Human Development Index and its key determinants in districts and cities in Gorontalo Province, Indonesia, during the period 2016--2025. The analysis uses balanced panel data and models human development as a function of mean years of schooling, life expectancy at birth, and real per capita expenditure. A geographically weighted panel regression approach is applied, with spatial relationships modeled using great-circle distances and an adaptive kernel weighting scheme, while a fixed-effects panel model serves as the global reference. The results reveal a clear spatial heterogeneity in the effects of the explanatory variables, where education consistently shows the strongest positive influence on human development in all regions, followed by health conditions. Economic expenditure exhibits a weaker and spatially varying effect and is not influential in the provincial capital. These findings underscore the importance of accounting for spatial heterogeneity in regional development analyses and support the formulation of place-based human development policies tailored to local conditions.
Copyright (c) 2026 Debora Dwi Kurniawati, Henny Pramoedyo, Suci Astutik, Friansyah Gani https://creativecommons.org/licenses/by-sa/4.0
ARIMA–GGJR–GARCH Modeling of Asymmetric Conditional Volatility in Wind Speed Time Series
Volatility modeling plays a crucial role in time-series forecasting, particularly for wind speed, where variability and asymmetric responses to shocks are commonly observed. Accurate wind speed forecasting can help mitigate potential risks associated with extreme or uncontrolled wind events. While the Autoregressive Integrated Moving Average (ARIMA) model is widely used to model the conditional mean of time series, it does not capture time-varying volatility or asymmetric effects. To address this limitation, we combine ARIMA with Generalized Autoregressive Conditional Heteroskedasticity (GARCH) and asymmetric extensions, including the Glosten–Jagannathan–Runkle GARCH (GJR-GARCH) and its generalized form (GGJR-GARCH). This framework allows simultaneous modeling of the conditional mean and conditional variance, accommodating heteroscedasticity and leverage effects in wind speed data. The empirical results indicate that negative shocks exert a stronger impact on conditional volatility than positive shocks, confirming the presence of asymmetry. Based on forecasting performance evaluation, the ARIMA(2,0,1)–GGJR-GARCH(1,1) specification provides the most accurate predictions among the competing models.
Copyright (c) 2026 Nurhayati Nurhayati, Andi Fitriawati https://creativecommons.org/licenses/by-sa/4.0
A Simulation Study On The Robustness Of Bayesian Structural Equation Modeling Under Small Samples, Heavy Tails, and Collinearity
Bayesian Structural Equation Modeling (BSEM) is increasingly used in health and social research, yet its operating characteristics under district-level constraints remain under-documented when three difficulties co-occur: small sample sizes, heavy-tailed errors, and strong correlations among exogenous constructs. We evaluate BSEM robustness using a Monte Carlo simulation with a fixed full-mediation SEM comprising four latent variables (two exogenous constructs, a mediator, and an outcome) and three reflective indicators per construct. A balanced 2×2×2 design varies sample size (n ∈ {22, 75}), error family (Normal vs. Student-t with ν = 5, variance-matched), and exogenous correlation (ρ ∈ {0.30, 0.80}). For each scenario, R = 50 independent datasets are generated and fitted using MCMC (Stan/NUTS via blavaan). We summarize global fit via posterior predictive p-values (PPP), sampling quality via \hat{R} and effective sample size (ESS), and sampler diagnostics including divergent transitions, alongside parameter recovery via Monte Carlo bias, RMSE, and 95% credible-interval coverage for structural paths, mediated effects, and ρ. Across conditions, increasing n improves both parameter recovery and sampling behavior. The most fragile settings occur when n = 22 and ρ is high, where the parallel paths X1→M and X2→M become weakly identified and heavy-tailed errors can further degrade precision. These results provide practical guidance for applying BSEM to district-level studies with limited sample sizes.
Copyright (c) 2026 Agustina Susi Susanti Parung, Ani Budi Astuti, Rahma Fitriani https://creativecommons.org/licenses/by-sa/4.0
Modeling Airplane Passenger Volatility during the COVID-19 Crisis: a SARIMA and Intervention Analysis
The COVID-19 pandemic in early 2020 had a severe impact on air traffic at Indonesia’s Soekarno-Hatta International Airport, which is among the busiest in the world. This caused a sharp decline in passenger numbers in April 2020, resulting in significant data fluctuations that required statistical intervention. Therefore, to forecast passenger numbers during these fluctuating trends, this study used the SARIMA and Step Function Intervention analysis. The results showed that the Step Function Intervention model was more accurate than SARIMA in predicting the number of passengers at the domestic departure terminal. Based on data for the period between January 2006 and June 2024, the step function intervention model produced MAD, MSE, RMSE, and MAPE values that are smaller than the SARIMA model. The best model, SARIMA Intervention (2,1,0)(1,1,1)12 b = 0, s = 3, r = 1, fulfilled the white noise and normality assumptions with a MAD accuracy value of 82381.85 and MAPE of 9.62%. In addition, the Step Function Intervention Method further reduced the MAPE value by up to 6.93%.
Copyright (c) 2026 Nur Faizin, Achmad Fauzan https://creativecommons.org/licenses/by-sa/4.0
Coronary Heart Disease Risk Prediction under Class Imbalance Using XGBoost with SHAP-Based Interpretation
Coronary heart disease (CHD) risk prediction is challenging because clinical data are heterogeneous and the response variable is imbalanced. This study develops an interpretable predictive framework for CHD risk using Extreme Gradient Boosting (XGBoost), median imputation, IQR-based winsorization, standardization, the Synthetic Minority Over-sampling Technique (SMOTE), bootstrap-based uncertainty assessment, and Shapley Additive Explanations (SHAP). The learning problem is formulated within a regularized empirical risk minimization framework, so the model is viewed as a statistical estimator rather than merely an algorithmic classifier. To avoid information leakage, train–test splitting is performed before any resampling, and SMOTE is applied only to the training data. The primary analysis is fixed a priori at an 80:20 stratified split, whereas 60:40 and 70:30 splits are treated as sensitivity analyses rather than model-selection devices. In the primary analysis, the model attains accuracy of 79.36%, precision of 27.88%, recall of 22.48%, F1-score of 24.89%, and ROC–AUC of 0.6502. The 95% bootstrap confidence interval for ROC–AUC is [0.6017, 0.6981]. SHAP analysis in probability space identifies age , cigsPerDay , male , heartRate , and sysBP as the most influential predictors. These results show that the proposed framework is mathematically well-structured and interpretable, but that its out-of-sample discrimination on this dataset is moderate rather than high.
Copyright (c) 2026 Siti Amiroch https://creativecommons.org/licenses/by-sa/4.0
Higher-Order Numerical Solution of the KdV-BBM Equation: A Comparative Analysis of Temporal Integration Schemes in the Method of Lines Framework
This study investigates the numerical simulation of solitary wave propagation governed by the KdV-BBM equation using a robust Method of Lines (MOL) framework. The governing nonlinear equation is transformed into a system of ordinary differential equations through spatial discretization, and the performance of three temporal integration schemes is evaluated: the first-order Euler method, the fourth-order Runge-Kutta (RK-4), and the fifth-order iRK-5 method. Quantitative analysis using Mean Absolute Error (MAE) for various time steps (Δt = 0.2, 0.1, 0.05, and 0.01) reveals that the iRK-5 scheme provides enhanced temporal precision, achieving error magnitudes as low as 10−6 and consistently aligning with the exact traveling-wave solution. Notably, the iRK-5 method demonstrates greater algorithmic efficiency, achieving an accuracy level of 4.55 × 10−6 at a coarser time step of Δt = 0.1, whereas the RK-4 scheme requires a finer time step of Δt = 0.05 to reach the same precision. Both high-order methods eventually reach a spatial error floor where further temporal refinement yields no significant reduction in MAE, emphasizing that high-order temporal integration, particularly the iRK-5 scheme, is essential for preserving the physical integrity of complex nonlinear wave phenomena while maintaining optimal computational effort.
Copyright (c) 2026 Dita Ardiana, Ummu Habibah, Trisilowati -, Rahifa Binti Ranom https://creativecommons.org/licenses/by-sa/4.0
Total Edge Irregularity Strength of Cycle Snake Graphs
Let G be a simple undirected graph with vertex and edge sets. A total labeling that assigns integers from 1 to k to the union of the vertex and edge sets is called a k-total labeling. The weight of an edge uv, denoted by w(uv), is defined as the sum of the labels of the two vertices u, v, and the label of edge uv itself. A k-total labeling is called an edge irregular total k-labeling of G if the weights of all distinct edges are different. The minimum k for which every edge of G has a distinct weight is called the total edge irregularity strength of G, denoted by tes(G). A cycle snake graph CSm,n is obtained from the path graph Pn with n + 1 vertices and n edges by replacing each edge with a cycle graph Cm, where m ≥ 3 and n ≥ 2. In this paper, we study the graphs CS3,n and CSm,n and determine their total edge irregularity strength. The case m = 3 is considered separately because the structure of CS3,n gives a different representation of the vertex and edge sets than for m ≥ 4, requiring a different labeling construction.
Copyright (c) 2026 Stenly Pranata https://creativecommons.org/licenses/by-sa/4.0
The Charactherization Criterion of g-quasi-Frobenius Lie Algebra Corresponding to Inner Derivation
The structure of a g-quasi-Frobenius Lie Algebra can be realized as a quasi-Frobenius Lie Algebra modules over a Lie Algebra g. This research discusses a special condition of the g-quasi-Frobenius Lie Algebra, namely when g acts on its self. This condition supports the construction of an inner derivation on g. The criterion investigated is the characterization of the g-quasi-Frobenius Lie Algebra in relation to the inner derivation. The result obtained is a criterion: a g-quasi-Frobenius Lie Algebra can be constructed on g itself if and only if the inner derivation is zero. Furthermore, several concrete examples are provided to test this criterion.
Copyright (c) 2026 Muhammad Arief Budiman, Edi Kurniadi, Sukono Sukono https://creativecommons.org/licenses/by-sa/4.0
Sentiment Analysis of Indonesia’s Free Nutritious Meal Program on X Using SVM and Random Forest
The Free Nutritious Meal (Makan Bergizi Gratis/MBG) Program was introduced to address stunting in Indonesia, yet its implementation has sparked diverse public debate. This study aims to map public perception on social media X and compare the performance of Support Vector Machine (SVM) and Random Forest algorithms in sentiment classification. Utilizing a large-scale dataset of 7,452 tweets collected via stratified random sampling from January to October 2025, this research applies TF-IDF feature extraction and SMOTE data balancing. The analysis reveals that positive sentiment dominates at 47.62%, while negative sentiment accounts for 39.8\%, and neutral for 12.57%. In model comparison, SVM without SMOTE achieved the best performance with 80.66% accuracy and an F1-Score of 79.79%, outperforming Random Forest, which only reached a maximum accuracy of 72.23% after SMOTE application. These findings provide an objective overview of MBG policy acceptance and methodological insights into the effectiveness of SVM in handling high-dimensional text data.
Copyright (c) 2026 Ferdy Aliansyah Hasyim, Talenta Parfaibya Mahenindra, Lilis Sriwahyuni, Alika Azka Shapira, Wigawijayanti Wigawijayanti, Nadhifa Zahra Ghaisani, Mirlan Sujana, Sri Nurdiati, Mohamad Khoirun Najib https://creativecommons.org/licenses/by-sa/4.0
Spectral Analysis of a Cyclic Tank Mixing System
In this paper, we study a cyclic mixing tank system consisting of n identical tanks arranged in a closed-loop configuration, each operating under constant volume with equal inflow and outflow rates. The model is further generalized to an m-layer structure, where each layer comprises n circularly interconnected tanks. Based on mass balance principles, the concentration dynamics are formulated as a linear system of first-order ordinary differential equations. By exploiting the structured form of the system matrix, we derive an explicit analytical solution and obtain a closed-form characterization of its spectrum. We show that the eigenvalues of the system are explicitly given by λk,j = α(-2 + e2πi(k-1)/n), which inherently guarantees the decay of all modes. In particular, the solution exhibits a polynomial-exponential form associated with the multilayer cyclic tank. We also establish that the system is exponentially stable under conditions ensuring decay of all modes. Finally, we present numerical simulations to validate the analytical results and to illustrate the transient dynamics of the multilayer system.
Copyright (c) 2026 Pebrudal Zanu, Sri Wahyu, Muhammad Januar Ismail Burhan https://creativecommons.org/licenses/by-sa/4.0
Local Stability and Bifurcation Analysis of a Mangrove Detritus Small-Fish Model with Dynamic Harvesting Effort under a Beddington-DeAngelis Functional Response
This study develops a three-dimensional mangrove detritus small fish model with a dynamics harvesting effort governed by a threshold rule and a Beddington DeAngelis functional response. The main objective is to understand how adaptive harvesting and consumer interference shape long-term dynamics and stability. Equilibrium points are derived and their local stability is examined using the Jacobian matrix and eigenvalue-based criteria, supported by numerical simulations. Bifurcation analysis with respect to the threshold parameter is performed using numerical continuation to detect qualitative transitions in system behavior. The results show the existence of biologically feasible coexistence equilibria with active harvesting, including a stable branch and an unstable branch. A Hopf bifurcation is detected at approximately a = 6.6159, confirming the emergence of sustained oscillations limit cycles in fish density and harvesting effort, while a fold limit point occurs near a = 22.001, indicating changes in equilibrium structure. Moreover, simulation scenarios demonstrate that reducing environmental capacity and increasing fish mortality can drive the system toward a no-effort equilibrium where harvesting collapses. These findings highlight the threshold parameter as a key control factor that can switch the system between stable harvesting, effort extinction, and oscillatory harvesting regimes.
Copyright (c) 2026 Dian Savitri, Donna Kurniasih https://creativecommons.org/licenses/by-sa/4.0
Spatial Regression Analysis using Queen Contiguity Weight Matrix and PCA Dimensionality Reduction
Conventional linear regression often falls short in poverty analysis, as it fails to account for spatial interdependence between neighboring regions and frequently encounters multicollinearity among socioeconomic variables. This study investigates the presence and nature of spatial effects in poverty data across regencies and cities in Central Java Province, Indonesia, and assesses the performance of an enhanced spatial regression model. We employ a Spatial Autoregressive Model (SAR) integrated with a queen contiguity spatial weight matrix and apply Principal Component Analysis (PCA) to reduce dimensionality and mitigate multicollinearity. The results demonstrate a strong model fit, with a pseudo R2 of 0.94311, and reveal a statistically significant negative spatial lag coefficient (ρ = -0.2039, p-value = 0.04420), indicating that areas of lower poverty are often surrounded by higher poverty neighbors. This integrated approach provides a more accurate framework for spatial poverty mapping, offering actionable insights for designing regionally targeted development policies.
Copyright (c) 2026 Joko Purwadi, Iliana Dewinta https://creativecommons.org/licenses/by-sa/4.0
β-Duality of the Sequence Space ℓpL and a Geometric Realization via Wulff Shapes
In the present paper, we investigate the structural and geometric properties of the non-absolute type sequence space ℓpλ. Our primary novel contribution lies in demonstrating that the natural norm on its β-dual coincides with the dual norm of ℓpλ. We then investigate geometric properties of the space and prove that ℓpλ inherits uniform convexity and uniform smoothness from the classical space ℓp for 1 < p < ∞, while these properties fail in the case p = 1. Finally, by considering finite-dimensional truncations, we interpret the dual norm geometrically through the Wulff construction. This yields a visualization of the norm unit sphere as a Wulff shape and shows that geometric features of the resulting shape reflect the convexity and smoothness properties of the underlying sequence space.
Copyright (c) 2026 Adrian Taruna Barus https://creativecommons.org/licenses/by-sa/4.0
Let R be a commutative ring and let Z(R) denotes the set of zero-divisors of R. The triple total graph of R, denoted by TT(R), is a simple graph whose vertex set is R∖{0}. Two distinct vertices v1 and v2 are adjacent in TT(R) if and only if v1+v2∉Z(R) and there exists v3∈R∖{0}, with v3≠v1 and v3≠v2, such that v1+v3∉Z(R), v2+v3∉Z(R), and v1+v2+v3∈Z(R). In this paper, we investigate the structural properties of the graph TT(Zn). We show that if n is even with n > 2, then TT(Zn) is an empty graph. When n is prime with 2 < n < 11, the graph TT(Zn) is disconnected. In contrast, for prime integers n≥ 11, the graph becomes connected with diam(TT(Zn))=2 and gr(TT(Zn))=3. Moreover, each vertex has degree n−5, implying that the graph is (n−5)-regular and consequently both Eulerian and Hamiltonian. These results illustrate how the arithmetic nature of n determines the global structure of the triple total graph.
Copyright (c) 2026 Vika Yugi Kurniawan, Syaifudin Zyuhri, Santoso Budi Wiyono https://creativecommons.org/licenses/by-sa/4.0
Stability Analysis of a Predator-Prey Model with Disease in Prey, Predator Harvesting, and Internal Migration of Susceptible Prey in a Closed Ecosystem
This study develops and analyzes a mathematical model of a predator-prey system incorporating three simultaneous ecological factors: disease in the prey population, harvesting of the predator, and internal migration of healthy prey within a closed ecosystem. The prey population is divided into two compartments healthy prey and infected prey where disease transmission follows the law of mass action. The predator population is subject to a constant harvesting rate representing external pressure such as hunting or capture. Internal migration of healthy prey is modeled as a density-dependent flux governed by a migration parameter m, which drives the redistribution of healthy prey across spatial patches without allowing permanent emigration from the system. The model is formulated as a system of three autonomous ordinary differential equations. Six equilibrium points are identified, representing a range of ecological scenarios from total extinction to full coexistence of all populations. The local stability of each equilibrium point is analyzed by linearization via the Jacobian matrix, and stability conditions are derived in terms of the model parameters, including the application of the Routh–Hurwitz criterion for the coexistence equilibrium. A key finding is that the migration parameter m does not alter the location of equilibrium points but directly influences the eigenvalues of the Jacobian, thereby affecting the rate at which the system recovers from perturbations. Numerical simulations are conducted to verify and illustrate the analytical results. This work extends the model of Mansur et al. [1] by introducing an internal spatial dimension, offering a more ecologically realistic framework for understanding population dynamics in ecosystems where disease, harvesting, and migration co-occur
Copyright (c) 2026 Dian Savitri, Muhammad Thariq Firmansyah https://creativecommons.org/licenses/by-sa/4.0
Minor-Eigenvalue Spectral Analysis in Intuitionistic Fuzzy Soft Sets for Multicriteria Decision Making
Multi-criteria decision making (MCDM) under uncertain data requires a framework capable of capturing ambiguity and non-linear interactions among criteria. This study develops an Intuitionistic Fuzzy Soft Set (IFSS)-based MCDM model using spectral analysis of aggregation matrices constructed with the Einstein operator. Unlike approaches that rely mainly on global eigenvalues, the proposed method utilizes dominant eigenvalues of principal minors to capture local structural variations among alternatives. The method is validated using subdistrict-level economic facility data from Lamongan Regency. The results produce spectral scores ranging from 0.0683 to 2.0000, with Bluluk obtaining the lowest score and Lamongan obtaining the highest score. Several alternatives with comparable global structural characteristics also exhibit distinct minor-eigenvalue responses, indicating that the proposed approach can reveal local structural variations that may not be reflected in global spectral analysis. These findings suggest that minor-eigenvalue-based spectral analysis provides an alternative local perspective for distinguishing alternatives within the IFSS framework. The proposed framework contributes theoretically to IFSS-based spectral modeling and practically supports decision-makers in prioritizing subdistrict development based on local structural characteristics.
Copyright (c) 2026 Silfiatis Sabila Azra Shofa, Siti Amiroch, Awawin Mustana Rohmah https://creativecommons.org/licenses/by-sa/4.0
Qualitative and Numerical Analysis of an SVEIR Model for HIV-HBV Co-Infection
The dynamics of HIV-HBV co-infection present significant epidemiological challenges, particularly in resource-limited areas. This study employs the SVEIR mathematical model to explore the transmission and control of HIV-HBV co-infection in Kupang City, Indonesia. Using the Next Generation Matrix method, the basic reproduction number (R0) was estimated at 1.36, indicating persistent disease transmission without effective intervention. Sensitivity analyses identified HBV vaccination coverage and treatment accessibility as critical parameters significantly influencing infection dynamics. Numerical simulations validated the theoretical model, demonstrating that increased vaccination rates and enhanced antiviral therapy access substantially reduce co-infection prevalence. Furthermore, equilibrium analyses revealed that effective interventions capable of lowering R0 below unity could transition the system from persistent endemicity toward disease elimination. These results emphasize the necessity of integrated intervention strategies, including expanded HBV vaccination, improved antiviral therapy access, and comprehensive community education to mitigate HIV-HBV co-infection. Future research should address existing limitations, incorporating behavioral and socioeconomic determinants to enhance model accuracy and applicability.
Copyright (c) 2026 Maria Lobo https://creativecommons.org/licenses/by-sa/4.0
Comparison of Extreme Value Logistic and Copula Approaches for Bivariate Extreme Value in Pekanbaru
Global climate change has intensified extreme weather events in tropical regions, increasing heat-related risks in Pekanbaru City. This study aims to analyze the joint behavior of extreme maximum temperature and humidity using a multivariate extreme value framework. Daily data from 2014–2024 were processed using a seasonal block maxima approach, resulting in 24 seasonal extreme observations. The marginal distributions follow a Weibull-type Generalized Extreme Value (GEV) distribution, indicating bounded extreme values. Dependence analysis indicates a weak association, where the Joe copula converges to the independence case, while the Frank copula yields the lowest AIC value among the fitted copula models. However, the difference in AIC values is small and should be interpreted cautiously. Joint return period analysis indicates that joint exceedance of seasonal block maxima is relatively infrequent (approximately 100 years), whereas single-variable exceedances occur more frequently (approximately 5.2 years). These return period estimates are exploratory and subject to uncertainty due to the limited sample size. Overall, the results suggest a weak dependence structure between the variables, and the findings should be interpreted cautiously in the context of climate-related risk assessment.
Copyright (c) 2026 Fadilla Afsari, A'yunin Sofro https://creativecommons.org/licenses/by-sa/4.0
Risk Analysis of Shallot Farm Income Using D-vine Copula-Based Monte Carlo Simulation
Shallot farm income is highly uncertain due to fluctuations in yields, prices, and production costs, which are interdependent and significantly correlated. This study evaluates income risk by modeling the dependence structure among the variables that constitute income, while addressing data limitations. Two approaches are employed. First, a parametric approach models income as a univariate variable under the assumption of a normal distribution, ignoring dependence among its components. Second, a multivariate simulation approach utilizes a D-vine copula, combined with Monte Carlo simulation, to capture the dependence among income components and generate synthetic observations that better represent tail behavior. Risk is measured using Value-at-Risk (VaR) and Expected Shortfall (ES) based on 32 observations of average shallot farm income per harvest season over the period 2014–2024, and the results are compared with empirical estimates. Due to limited data, the empirical approach produces relatively coarse estimates, particularly in the tail region. The normal distribution approach yields higher and smoother estimates, indicating a higher level of risk. In contrast, the D-vine copula approach provides lower estimates than the normal distribution. These differences indicate that each method offers a distinct perspective on income risk.
Copyright (c) 2026 Fatimah Fuzzaroh, Berlian Setiawaty, I Gusti Putu Purnaba https://creativecommons.org/licenses/by-sa/4.0
Application of Reich-Perov α-Contractive Mapping in Vector Valued Metric Space
This paper presents two new applications of a fixed point theorem for Reich–Perov α-contractive mappings in vector-valued metric spaces. As a new application, we first demon-strate the existence and uniqueness of a solution to the vector valued Volterra-Fredholm integral equation system. By constructing suitable integral operators, we show that they satisfy the α-contractive Reich-Perov condition. The second application concerns the determination of the fixed point for discrete recursive systems with coupled components, for which the existence of a unique solution is established.
Copyright (c) 2026 Sunarsini Sunarsini, Mahmud Yunus, Subiono Subiono https://creativecommons.org/licenses/by-sa/4.0