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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.
Arjuna Subject : -
Articles 501 Documents
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Hybrid Otsu Morphological Pre-processing for EfficientNetB4 Based Acute Lymphoblastic Leukemia Classification Audina, Maretta Mia; Surono, Sugiyarto; Thobirin, Aris; Wen, Goh Khang
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.v11i1.40730

Abstract

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.
Application of Mixture of Weibull and Pareto (IV) Distribution to Health and Environmental Data Adeniji, Tolulope Olubunmi; Odeyemi, Akinwumi Sunday
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): 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.v10i2.31431

Abstract

Weibull and Pareto distributions are widely used in several areas, including lifetime data modelling and reliability analysis. In real-life practice, these distributions may not capture the various distributional properties of certain datasets. The use of finite mixture models enhanced the performances of these distributions in adaptability and accuracy. This study focused on the Mixture Weibull Pareto (IV) distribution proposed by [1], which has been used in modelling insurance claims, and it showed superior performance as compared with other distributions. The current study applied this distribution to health and environmental datasets. The result showed that the Mixture Weibull Pareto (IV) distribution performed better than other distributions, using Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and Kolmogorov-Smirnov test (KS test) for the significance of the distribution. 
Spatial Analysis of Child Violence Victims in West Java in 2024 Using Geographically Weighted Negative Binomial Regression Suliyanto, Suliyanto; Amelia, Dita; Putri, Lisa Amanda; Anggakusuma, Aurellia Calista
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.v11i1.40390

Abstract

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.
Dynamic Analysis of a Predator–Prey Model with Group Defense in Prey and Cooperative Hunting in Predators Meladelvia, Nabilah; 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.v11i1.40210

Abstract

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.
Numerical Pricing of European Stock Options Using Black-Scholes Interval Model Aditama, Muhammad Iqbal; Artiono, Rudianto
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.v11i1.40272

Abstract

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.
Sensitivity Analysis of a Tuberculosis Transmission Model with Incomplete Treatment Harianto, Joko; Fernandi, Diki
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.v11i1.36325

Abstract

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.
Stability Analysis of a Three-Trophic Rice Ecosystem with Holling Type II and Crowley--Martin Responses Nisa', Anastasya Choirun; 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.v11i1.40204

Abstract

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.
Mathematical Modeling and Regime Dynamics of Ammonium Chloride Imports in Indonesia Using Threshold Vector Autoregressive Integrated (TVARI) Approach Widiantoro, Carissa Egytia; Arisanti, Restu; Darmawan, Gumgum
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.v11i1.40052

Abstract

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).
Stability Analysis and Invasion Thresholds in a Rosenzweig--MacArthur Model with Prey Immigration and Cooperative Hunting Faustin, Naufal Daffa; 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.v11i1.40677

Abstract

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.
Temporary Immunity in a Fractional-Order SEIR Model: Stability Analysis Iqbal, Muhammad; Burhan, Mohammad Januar Ismail; Adam, Adam
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.v11i1.40849

Abstract

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.

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