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CAUCHY: Jurnal Matematika Murni dan Aplikasi
Published by Universitas Islam Negeri Maulana Malik Ibrahim Malang
ISSN : 20860382     EISSN : 24773344     DOI : 10.18860
Core Subject : Education,
Mathematics
Jurnal CAUCHY secara berkala terbit dua (2) kali dalam setahun. Redaksi menerima tulisan ilmiah hasil penelitian, kajian kepustakaan, analisis dan pemecahan permasalahan di bidang Matematika (Aljabar, Analisis, Statistika, Komputasi, dan Terapan). Naskah yang diterima akan dikilas (review) oleh Mitra Bestari (reviewer) untuk dinilai substansi kelayakan naskah. Redaksi berhak mengedit naskah sejauh tidak mengubah substansi inti, hal ini dimaksudkan untuk keseragaman format dan gaya penulisan.
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Articles 476 Documents
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Application of the Saint-Venant Model for Simulation of the Kapuas River Flow Using the Finite Difference Method Ratnasari, Dian Eka; Pasaribu, Meliana; Yudhi, Yudhi
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.38622

Abstract

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.
Sentiment Analysis of the 2022 Fuel Price Hike Using the Naïve Bayes Classifier Lestari, Alia; Aswad, Muhammad Hajarul; Masri, Subekti
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.36473

Abstract

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.
Stability Analysis of Conventional and E-Cigarette Smokers Behavior Model with Saturation Effects Suryantini, Binti Mu'alafi; Prawoto, Budi Priyo
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.40109

Abstract

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.
From Risk-Neutral to Risk-Sensitive Reinforcement Learning: Actor–Critic vs REINFORCE with Tail-Based Risk Measures Lestia, Aprida Siska; Effendie, Adhitya Ronnie; Tantrawan, Made; Azrarsyah, Muhammad Rafli
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.40309

Abstract

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.
Complex-Valued Neural Networks with Adaptive Frequency Attention for Image Denoising Marjono, Marjono; Maulana, Avin; Hapsani, Anggi Gustiningsih
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.36851

Abstract

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.
Comparison of ARIMA, Random Forest, and Hybrid ARIMA-Random Forest Models in Forecasting Indonesian Crude Oil Prices Rahkmawati, Yeni; Annisa, Selvi; Hafid, Hardianti; Nuramaliyah, Nuramaliyah; Safitri, Emeylia
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.36540

Abstract

The price of Indonesian crude oil is highly volatile due to global demand fluctuations, energy policies, and geopolitical tensions, making accurate forecasting challenging. This study compares three forecasting models: ARIMA, Random Forest, and Hybrid ARIMA--Random Forest, to identify the most accurate approach. Model performance was evaluated using Time-Series Cross-Validation (TSCV) and metrics including Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE), and Root Mean Squared Error (RMSE). The results indicate that the Random Forest model, tuned with \texttt{mtry = 1} and \texttt{ntree = 200}, outperformed both ARIMA and Hybrid ARIMA--Random Forest, achieving the lowest MAPE, MAE, and RMSE values. This suggests that Indonesian crude oil prices during the study period are predominantly non-linear, and Random Forest alone effectively captures these dynamics. Forecasts based on this model indicate a short-term increase in prices from 61.10 USD/Barrel in December 2025 to 64.29 USD/Barrel in March 2026, followed by a slight decline and modest recovery by June 2026. Overall, Random Forest provides a reliable and accurate tool for forecasting Indonesian crude oil prices, offering valuable insights for policymakers, investors, and market participants navigating volatile oil markets.
Stage-Structured Predator Model with Prey Protection: Application to Rice Plants–Leptocorisa oratorius Rahmah, Safira; Savitri, Dian
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.40733

Abstract

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.
Evaluating Hierarchical Pathfinding A* (HPA*) for Multi‑Order Routing in a Small Warehouse Layout Wibawa, Ig. Prasetya Dwi; Kallista, Meta; Nugraha, Ramdhan; Widayani, Heni; Bhandari, Harish Chandra; Rusdinar, Angga
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.39659

Abstract

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.
Clustering for Mapping Food Insecurity in the Land of Papua: A Five-Year Multiyear Analysis with Spatial Interpretation (2020-2024) Beno, Ishak Semuel; Sroyer, Alvian M; Reba, Felix; Kmurawak, Remuz M. B.; Tama, Antonius A. P.
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.40366

Abstract

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.
Box Fractal as an Iterated Function System in Fractal Interpolation for Determining the Approximate Value of Demand Data Susanti, Eka; Dwipurwani, Oki; Cahyawati, Dian; Dewi, Novi Rustiana; Khotimah, Husnul; Ningsih, Wahyuni Apria
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.38905

Abstract

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.

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