CAUCHY: Jurnal Matematika Murni dan Aplikasi
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.
Articles
476 Documents
<![CDATA[Hybrid Otsu Morphological Pre-processing for EfficientNetB4 Based Acute Lymphoblastic Leukemia Classification ]]>
<![CDATA[Audina, Maretta Mia]]>;
<![CDATA[Surono, Sugiyarto]]>;
<![CDATA[Thobirin, Aris]]>;
<![CDATA[Wen, Goh Khang]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/cauchy.v11i1.40730
<![CDATA[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.]]>
<![CDATA[Application of Mixture of Weibull and Pareto (IV) Distribution to Health and Environmental Data ]]>
<![CDATA[Adeniji, Tolulope Olubunmi]]>;
<![CDATA[Odeyemi, Akinwumi Sunday]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/cauchy.v10i2.31431
<![CDATA[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. ]]>
<![CDATA[Spatial Analysis of Child Violence in West Java Using a Geographically Weighted Negative Binomial Regression Approach ]]>
<![CDATA[Suliyanto, Suliyanto]]>;
<![CDATA[Amelia, Dita]]>;
<![CDATA[Putri, Lisa Amanda]]>;
<![CDATA[Anggakusuma, Aurellia Calista]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/cauchy.v11i1.40390
<![CDATA[Kekerasan terhadap anak tetap menjadi isu kritis di Indonesia, dengan Jawa Barat secara konsisten melaporkan jumlah kasus yang tinggi. Studi ini meneliti faktor-faktor sosioekonomi yang memengaruhi jumlah kasus kekerasan terhadap anak di 27 kabupaten dan kota, dengan fokus pada tingkat kemiskinan, rata-rata tahun sekolah, tingkat perceraian, Tingkat Partisipasi Angkatan Kerja (PFPR), dan Tingkat Pengangguran Terbuka (OUR). Tes diagnostik mengidentifikasi heterogenitas spasial dan overdispersi, yang mendukung penggunaan model Regresi Binomial Negatif Berbobot Geografis (GWNBR). Model GWNBR mengungguli model Poisson dan Binomial Negatif global, yang ditunjukkan oleh nilai Akaike Information Criterion (AIC) terendah sebesar 193,23, yang menunjukkan kemampuannya untuk menangani data hitungan spasial yang overdispersi. Hasil penelitian mengungkapkan variasi spasial yang substansial dalam pengaruh faktor-faktor sosioekonomi. Rata-rata tahun sekolah dan tingkat perceraian signifikan di sebagian besar wilayah, sementara Kota Bandung adalah satu-satunya wilayah di mana kelima prediktor tersebut signifikan. Temuan ini menunjukkan struktur risiko yang bervariasi secara geografis yang tidak dapat ditangkap oleh model global. Studi ini menyoroti pentingnya pemodelan adaptif spasial dalam analisis sosial dan demografis serta menyarankan agar karakteristik spesifik wilayah dipertimbangkan dalam perumusan kebijakan. Temuan ini mendukung strategi perlindungan anak yang terarah dan selaras dengan SDG 3, SDG 4, dan SDG 16.]]>
<![CDATA[Dynamic Analysis of a Predator–Prey Model with Group Defense in Prey and Cooperative Hunting in Predators ]]>
<![CDATA[Meladelvia, Nabilah]]>;
<![CDATA[Savitri, Dian]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/cauchy.v11i1.40210
<![CDATA[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, three critical points were obtained, namely the total extinction point, the predator extinction point, and the interior point that describes the coexistence of both species. The total extinction point is always unstable, while the other two critical points are conditionally stable depending on the predator attack rate parameter. Numerical simulations in the form of phase portraits were obtained by varying the parameters related to the predator attack rate. The simulation results show double stability (bistability) when α = 3, where the system can lead to predator extinction or stable coexistence depending on the initial population conditions. Furthermore, numerical continuation was performed to track changes in equilibrium point stability. The results show a Hopf bifurcation at α = 0.4595, marked by a change in the stability of the interior point, a limit point bifurcation (saddle-node) at α = 0.0478 due to the merging of two interior equilibrium points, and a transcritical bifurcation at α = 3.0505, which shows an exchange of stability between equilibrium points.]]>
<![CDATA[Numerical Pricing of European Stock Options Using Black-Scholes Interval Model ]]>
<![CDATA[Aditama, Muhammad Iqbal]]>;
<![CDATA[Artiono, Rudianto]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/cauchy.v11i1.40272
<![CDATA[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]]>
<![CDATA[Sensitivity Analysis of a Tuberculosis Transmission Model with Incomplete Treatment ]]>
<![CDATA[Harianto, Joko]]>;
<![CDATA[Fernandi, Diki]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/cauchy.v11i1.36325
<![CDATA[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.]]>
<![CDATA[Stability Analysis of a Three-Trophic Rice Ecosystem with Holling II and Crowley–Martin Responses ]]>
<![CDATA[Nisa', Anastasya Choirun]]>;
<![CDATA[Savitri, Dian]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/cauchy.v11i1.40204
<![CDATA[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. spiders 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 predatorinterference. 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 threespecies. Local stability analysis at each equilibrium point was conducted using the Jacobian matrix and the Routh–Hurwitz criterion. Numerical simulations were performed for severalparameter combinations by varying planthopper growth efficiency and Pardosa sp. predation intensity. 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 planthopperreproductive capacity and the predatory strength of Pardosa sp., providing a theoretical basisfor sustainable planthopper pest control strategies.]]>
<![CDATA[Mathematical Modeling and Regime Dynamics of Ammonium Chloride Imports in Indonesia Using Threshold Vector Autoregressive Integrated (TVARI) Approach ]]>
<![CDATA[Widiantoro, Carissa Egytia]]>;
<![CDATA[Arisanti, Restu]]>;
<![CDATA[Darmawan, Gumgum]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/cauchy.v11i1.40052
<![CDATA[Ammonium chloride plays an important role in Indonesia as a key raw material for Nitrogen, phosphorus, and potassium (NPK) fertilizers and various chemical industries. Despite its importance, domestic production remains limited, and the potential supply from by-product sources has not been utilized in a meaningful way. As a result, Indonesia depends heavily on imports that come mainly from a single country. This situation creates vulnerabilities in the industrial supply chain and highlights the need for a clearer understanding of how import volume and import value behave over time. This study offers a mathematical model that examines the joint movement of these two variables by using the Threshold Vector Autoregressive Integrated approach, commonly known as TVARI. The novelty of the study lies in its use of a nonlinear threshold structure to show how the system shifts between different market conditions. The model reveals that import behavior changes across regimes. When import growth is low, movements are shaped mostly by changes in import value. When growth becomes higher, the pattern reflects the stronger influence of supply conditions. A single linear model cannot fully explain these shifts. By presenting a mathematical description of these regime movements, the study enhances the understanding of the underlying dynamics of Indonesia’s industrial imports. The insights support data informed decisions in supply chain planning and relate to Sustainable Development Goal 9 (industry resilience) and Sustainable Development Goal 12 (efficient and responsible use of raw materials). Goal 8 of the Sustainable Development Agenda, which is to encourage stable and sustainable economic activity, is likewise aligned with the enhanced comprehension of market behavior.]]>
<![CDATA[Stability Analysis and Invasion Thresholds in a Rosenzweig--MacArthur Model with Prey Immigration and Cooperative Hunting ]]>
<![CDATA[Faustin, Naufal Daffa]]>;
<![CDATA[Savitri, Dian]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/cauchy.v11i1.40677
<![CDATA[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.]]>
<![CDATA[Temporary Immunity in a Fractional-Order SEIR Model: Stability Analysis ]]>
<![CDATA[Iqbal, Muhammad]]>;
<![CDATA[Burhan, Mohammad Januar Ismail]]>;
<![CDATA[Adam, Adam]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/cauchy.v11i1.40849
<![CDATA[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.]]>
