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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 476 Documents
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Stability and Bifurcation of a 3D Eco Epidemiological Predator Prey Model with Pesticide Savitri, Aqiila Ollyana; 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.v11i1.40676

Abstract

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.
Approximation Properties on a Set Based on Equivalence Relations and Dominance Relations Setyawati, Dian Winda; Soleha, Soleha; Rinurwati, Rinurwati
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.v11i1.40603

Abstract

 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.
Deterministic Modeling of HIV–Malaria Co-Infection and Sensitivity Analysis in Papua Lusiana, Vina; Fanny, Diva Hardiestya; Syazali, Muhammad
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.v11i1.40964

Abstract

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.
Step-Stress Accelerated Life Testing with Type II Censoring and Exponential Distribution for Solar-Powered Lighting Systems Kurniawan, Ardi; Ananda, Vanisia Suci; Kalista, Yovita Karin
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.v11i1.41076

Abstract

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.
On A-Distance (Anti)magic Labeling of Prime Graph over the Ring Zn Khuluq, Muhammad Husnul
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.v11i1.41237

Abstract

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.
Compare Bede-Gal Between dH Differentiability of Set Valued Functions Wicaksono, Wildan Bagus; Muslikh, Mohamad
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.v11i1.38181

Abstract

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.
Numerical Pricing of Discrete-Dividend European Options: An Empirical Case Study Elgiffary, Muhammad Gibran; 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.v11i1.40995

Abstract

Studi kuantitatif terapan ini menerapkan integrasi numerik Simpson 1/3 untuk secara sistematis menerbitkan penetapan harga opsi Eropa yang disesuaikan dengan diskrit dividen. Menggunakan saham teknologi anonim (XYZ Tech Corp.) sebagai studi kasus empiris, penelitian ini mencapai dua tujuan utama: memvalidasi konvergensi komputasi algoritma numerik terhadap tolok ukur analitik Black-Scholes yang tepat menggunakan Kesalahan Relatif, dan menganalisis penyimpangan harga empiris model terhadap pengamatan pasar nyata di berbagai zona uang. Pengujian komputasi menunjukkan bahwa metode Simpson 1/3, yang secara inheren dibatasi oleh kesalahan pemotongan orde keempat, mencapai konvergensi optimal dan cepat. Dengan mengatur partisi grid pada N=200, algoritma berhasil menekan kesalahan relatif secara ketat di bawah ambang batas 0,001% dibandingkan dengan solusi analitik, dan dieksekusi secara efisien dalam waktu kurang dari 0,005 detik. Secara empiris, meskipun model teoritis menunjukkan akurasi tinggi untuk opsi In-The-Money (ITM) dengan deviasi minimal, model ini secara konsisten mengungkapkan bias valuasi yang signifikan untuk kontrak Call Out-Of-The-Money (OTM), sedangkan valuasi Put OTM menunjukkan pola deviasi yang berbeda secara struktural. Valuasi asimetri ini menunjukkan potensi batasan volatilitas historis konstan, yang tampaknya tidak mampu untuk sepenuhnya menangkap kemiringan volatilitas tersirat dan pergeseran persepsi risiko yang lazim terjadi dalam mikrostruktur pasar aktual.
Dynamics of Predator-Prey Model with Holling Type II Involving Predator Stage-Structured and Cannibalism Sari, Sela Tri Indah; 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.v11i1.41044

Abstract

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
Latent Household Food Security in Raja Ampat Marine Protected Areas: A Binary CFA Approach Anggriyani, Indah Ratih; Sumertajaya, I Made; Notodiputro, Khairil Anwar; Angraini, Yenni
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.v11i1.40979

Abstract

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.
Comparison Of Methods For Handling Imbalanced Datasets In Improving Classification Algorithm Performance Rini, Dyah Setyo; Agwil, Winalia; Agustina, Dian; Famuji, Ahmad
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.v11i1.35780

Abstract

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.

Page 47 of 48 | Total Record : 476

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