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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 533 Documents
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Dynamical Analysis of a Trophic Model on Guano, Invertebrates, and Fish in Cave Ecosystems M Niko Axsella Ibrahim; Dian Savitri
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.41524

Abstract

This study investigates the dynamical interaction between guano biomass density (x), invertebrate biomass density (y), and fish biomass density (z) through a three-compartment trophic model representing a nutrient-based cave ecosystem. The analysis identifies three equilibrium points: the consumer-free equilibrium E0, the predator-free equilibrium E1, and the coexistence equilibrium E2. Local stability analysis shows that the coexistence equilibrium is asymptotically stable, characterized by eigenvalues with negative real parts (1 = -0.519706 and 2,3 = -0.085385 0.188169i). Numerical simulations using the fourth–fifth order Runge–Kutta method (RK45) support these analytical results, showing trajectories that exhibit damped oscillations before converging to the steady state. Furthermore, a bifurcation analysis reveals a critical Branching Point (BP) at the predation rate b2 0.043956. This threshold signifies a transcritical bifurcation where the system transitions from a predator-extinction regime to a stable coexistence regime, highlighting the sensitivity of the food web to energy transfer efficiency. These findings suggest that under the assumed parameter set, the interaction between guano nutrients, invertebrates, and fish can maintain a stable ecological balance through top-down control and nutrient-dependent dynamics.
Properties of Clear Graph of Ring ℤp Mohammad Ilham Maulana; Vira Hari Krisnawati; Ratno Bagus Edy Wibowo
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.41856

Abstract

Let ℤp be the ring of integers modulo a prime p 3. The clear graph of ℤp, denoted by Cr2(ℤp), is a graph whose vertices are ordered pairs (x,u), where x is a nonzero regular unit and u is a unit of ℤp, and two vertices (x,u) and (y,v) are adjacent if either xy = yx = 0 or uv = vu = 1. This work extends previous research on clear graphs, which established the basic structure of Cr2(R) for certain rings, including aspects of isomorphism, connectedness, and other structural properties. In this paper, we focus on the prime ring ℤp and analyze several fundamental graph-theoretic properties of Cr2(ℤp). Specifically, we show that this graph has order (p−1)2, size ½(p2−2p−1)(p−1), diameter ∞, radius at most 2, independence number ½(p2−4p+7), and clique, chromatic, and domination numbers each equal to p−1. The results provide a deeper understanding of how algebraic properties of ℤp influence the combinatorial structure of its associated clear graph.
Two-Parameter Exponential Estimation via EM Algorithm: Uterine Leiomyosarcoma Survival Risk Analysis Ardi Kurniawan; Deby Victoria; Christabel Lee Angie Sugianto
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.41855

Abstract

Accurate survival prognosis is critical for clinical decision-making, yet analyzing censored on cological data remains a statistical challenge. This study aims to implement the Expectation Maximization (EM) algorithm for the two-parameter exponential distribution to estimate parameters and forecast extreme survival risks in uterine leiomyosarcoma (uLMS). Using clinical data from 122 patients, the EM algorithm achieved rapid convergence after 19 it erations, yielding a scale parameter of 68.7037 months and a 2-month survival threshold. Statistical validity was confirmed by a Kolmogorov-Smirnov test (p = 0.2084) and a 94.5% coverage probability from Monte Carlo simulations. A key contribution of this research is the integration of Value-at-Risk (VaR) and Tail Value-at-Risk (TVaR) metrics, which identified a 95% survival threshold of 207.82 months. Sensitivity analysis further demonstrated the es timator’s structural stability across varying censoring proportions. These results signify that the proposed framework provides a robust and reliable tool for quantifying extreme survival probabilities, offering clinicians a sophisticated method for long-term risk management and personalized patient prognosis.
Toward Optimal Quantum Multipliers: Space–Time Efficiency and Asymptotic Bounds for Advanced Toom–Cook Methods Rini Wisnu Wardhani; Dedy Septono Catur Putranto
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.41908

Abstract

This paper studies the asymptotic bounds of quantum resources required for high-degree multiplication based on the Toom–Cook algorithm. This work extends prior investigations on high- and half-degree quantum multiplication and proposes an optimized Toom–Cook 25.5-way quantum multiplication architecture to establish optimal asymptotic bounds on quantum resource consumption for Toom–Cook-based multiplication schemes. We provide asymptotic expressions for qubit complexity, Toffoli gate count, and Toffoli depth. The proposed Toom–Cook 25.5-way architecture achieves improved asymptotic performance, requiring a qubit count of n1.176, approximately 648nlog2651 − 666n Toffoli count, and n1.03025 Toffoli depth. Compared with existing classical and quantum Toom–Cook-based methods, the proposed 25.5-way Toom–Cook algorithm achieves lower asymptotic complexity and reduced quantum resource costs, yielding tighter bounds for optimal quantum multiplication.
On Temperature-Dependent and Spatially Structured Dengue Transmission Models: A Mathematical Review Abdullahi Abdu; Admi Nazra; Arrival Rince Putri; Mahdhivan Syafwan
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.42040

Abstract

Dengue fever remains a major public health concern in tropical and subtropical regions, where transmission dynamics are strongly influenced by environmental variability and human mobil ity. Mathematical modelling provides a rigorous framework for capturing these interactions and informing effective control strategies.This review presents recent advances in deterministic and spatially structured dengue transmission models that incorporate temperature-dependent parameters and human mo bility. Emphasis is placed on compartmental formulations, including multi-patch and meta population models, where movement between regions plays a key role in disease spread. The influence of temperature on key epidemiological parameters, such as mosquito biting rates, development rates, and survival probabilities, is examined through nonlinear functional relationships.In addition, common analytical approaches are discussed, including the derivation of the basic reproduction number, stability analysis of equilibria, and sensitivity analysis. The integration of control strategies within these frameworks is also reviewed, demonstrating how intervention policies can be evaluated under varying environmental and mobility conditions.Overall, the review highlights the importance of combining environmental and spatial effects to better understand dengue transmission and support adaptive control strategies.
Geometry-Based Differentially Private Synthetic Tabular Data Generation via K-Means Clustering with Bounded and Discrete Feature Constraints Robby Robby; Agus Sukmana; Erwinna Chendra
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.41403

Abstract

Most clustering-based differentially private synthetic data generation methods assume unconstrained continuous feature spaces and offer no mechanism for hard feature bound enforcement or discrete-valued attribute handling, which limits their practical applicability to real-world tabular data where such constraints are common. This paper proposes a geometry-based mechanism that generates synthetic tabular data by application of Laplace noise jointly to K-means cluster centroids and within-cluster radial distances, calibrated via a data-dependent sensitivity approximation. Three components distinguish the approach from prior work: coordinate-wise centroid reflection to enforce hard feature bounds after perturbation, coordinate-wise clipping to enforce bounds on reconstructed synthetic points, and randomized rounding for discrete features as a post-processing step. A utility-driven calibration strategy selects the privacy budget to meet a user-specified target Adjusted Rand Index (ARI), which makes the privacyutility trade-off directly interpretable. Baseline comparisons on a two-dimensional illustrative example show that the proposed mechanism achieves ARI=0.666 at 1.60, which substantially outperforms direct coordinate-wise noise addition at the same budget (ARI=0.199), while it matches the non-private synthesis baseline (ARI=0.624). Across 30 independent runs the mechanism achieves mean ARI=0.6290.108, which confirms that the calibration target is reliably met under stochastic variation.
Binary Logistic Regression Modeling using Bayesian method: Analysis and Simulation on the Poverty Percentage of Districts in East Java Achmad Efendi; Restilia Anggita Sari; Samingun Handoyo; Nur Silviyah Rahmi; Friansyah Gani
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.41326

Abstract

In conducting logistic regression modeling, parameter estimation is considered an important stage. Determination of parameter estimates is often influenced by sample size and data characteristics. To cope with this issue, the Bayesian method is used as it is expected to be more robust, for instance to small sample size. In this method, MCMC is used to determine parameter values that are difficult to solve analytically. The study aims at determining the binary logistic regression model and its application to determine the factors that influence the percentage of city/district poverty rates in East Java in 2023. East Java was chosen because it has the highest percentage of poverty rates in Indonesia. This study uses informative and non-conjugate priors which is normal distribution in this case. Based on the results of the MCMC simulation with the Gibbs Sampling Algorithm, the random sample of study converged at the 266, 000th iteration with a burn-in of 60, 000 and a thin of 10. The results of this study indicate that the variables influencing the percentage of the poverty rate of cities/regencies in East Java are the Human Development Index (HDI), Life Expectancy (LE), and Gini Ratio (GR) which have significant effects. The residual deviance value shows a number that is smaller than the chi-square value. This means that the resulting model is appropriate. The model can predict data correctly by 84.2%. Simple simulations are carried out with different observed sample sizes. The simulation results show that the Bayesian method is somewhat better than likelihood estimation, particularly for data with small samples. Furthermore, we suggest the government of East Java would have more concern on HDI, LE, and GR as well as other factors related to them for poverty reduction policies.
Modeling the Dynamics of Cardiovascular Disease Using a SEICRD Framework Arista Fitri Diana; Mia Siti Khumaeroh; Tarita Intan Soraya
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.41645

Abstract

Cardiovascular disease remains a major public health challenge worldwide, often progressing silently toward chronic complications. Increasing awareness through media and individual behavioral responses plays an important role in preventing disease transmission and reducing long-term complications. Motivated by this, we formulate a deterministic compartmental model to investigate the dynamics of cardiovascular disease by incorporating media awareness and individual awareness as control-related parameters. The population is divided into susceptible, exposed, infected, chronic, recovered, and deceased compartments. A qualitative analysis of the linear dynamical system is carried out, including positivity of solutions, bound- edness, equilibrium points, and local stability analysis using eigenvalue criteria. Numerical simulations are performed to illustrate the effects of key epidemiological and awareness-related parameters on disease progression. The simulation results indicate that increased media and individual awareness significantly reduce the long-term burden of chronic cardiovascular complications. In contrast, higher incidence and disease progression rates lead to increased accumulation in the chronic compartment, even when the number of active infections declines more rapidly. Sensitivity analysis confirms that awareness parameters have a negative influ- ence on chronic disease prevalence, whereas core epidemiological parameters exert a strong positive effect. These findings highlight the critical role of awareness-based interventions in mitigating chronic cardiovascular disease and provide a quantitative framework to support effective prevention and control strategies.
Profit Optimization for MSMEs in the Patchwork Fabric Industry Using Linear Programming and Simulated Annealing Afnaria Afnaria; Rina Filia Sari; Isnaini Halimah Rambe
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.32585

Abstract

Maximizing profitability is a key objective for Micro, Small, and Medium Enterprises (MSMEs), particularly those in the patchwork fabric industry. This study develops a multi-constraint Linear Programming (LP) model integrated with Simulated Annealing (SA) to determine the optimal production plan that maximizes profits while considering resource constraints. The LP model provides an optimal solution by selecting the most profitable product mix, whereas the SA heuristic explores a broader solution space to find alternative production plans. The results indicate that the LP model achieves a maximum profit of 16,640,000, primarily by selecting Tote bag as the most profitable product, while the SA approach distributes production across multiple products, resulting in a lower total profit of 7,739,000. Sensitivity analysis of the LP model highlights high reduced costs for non-selected products, making their inclusion in the production plan economically unfeasible. The findings suggest that LP is superior for-profit maximization, while SA provides alternative solutions for production diversification. Future research should explore hybrid approaches that integrate LP’s precision with SA’s flexibility to optimize MSME production strategies under uncertain demand conditions.
Rolling-Origin Evaluation of Lag-Based Regularized Regression Models for Indonesian Inflation Forecasting Rehan Risqi Saputra; Atik Wintarti; Riska Wahyu Romadhonia
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.41964

Abstract

Inflation forecasting studies often rely on external macroeconomic predictors or complex machine learning models, while the predictive value and limitations of the internal lag structure of Indonesian inflation remain less explicitly examined. This study evaluates Indonesian inflation forecasting within a univariate lag-based framework using monthly inflation data from January 2010 to December 2025. Lagged inflation values are used to construct regression predictors, and OLS, Ridge, LASSO, and Elastic Net are evaluated through rolling-origin forecasting with an expanding window. To strengthen the time-series basis of the analysis, this study also conducts stationarity diagnostics, ACF and PACF analysis, seasonal diagnostics, lag-specification robustness checks, and comparisons with standard forecasting benchmarks, including Naive, Seasonal Naive, AR selected by AIC, and ARIMA selected by AIC. The ADF test produces a p-value of 0.608360, indicating weak evidence of stationarity in level form. Among the regularised regression models, Ridge produces the lowest descriptive forecast errors, with RMSE of 0.405018 and MAE of 0.308967. However, Diebold–Mariano tests indicate that the differences among OLS, Ridge, LASSO, and Elastic Net are not statistically significant. Benchmark comparisons show that the Naive forecast achieves the lowest RMSE of 0.373819, while ARIMA selected by AIC achieves the lowest MAE of 0.279641 and MAPE of 16.560958. Robustness checks also show that the twelve-lag specification is competitive for OLS and Ridge, but it is not uniformly optimal across all models. These findings suggest that the main value of lag-based regularised regression lies in clarifying the limited but useful short-run predictive information contained in the internal temporal structure of Indonesian inflation, rather than in providing a statistically dominant or complete inflation forecasting model.

Page 51 of 54 | Total Record : 533

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