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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 511 Documents
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Minor-Eigenvalue Spectral Analysis in Intuitionistic Fuzzy Soft Sets for Multicriteria Decision Making Silfiatis Sabila Azra Shofa; Siti Amiroch; Awawin Mustana Rohmah
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.v11i1.41247

Abstract

Multi-criteria decision making (MCDM) under uncertain data requires a framework capable of capturing ambiguity and non-linear interactions among criteria. This study develops an Intuitionistic Fuzzy Soft Set (IFSS)-based MCDM model using spectral analysis of aggregation matrices constructed with the Einstein operator. Unlike approaches that rely mainly on global eigenvalues, the proposed method utilizes dominant eigenvalues of principal minors to capture local structural variations among alternatives. The method is validated using subdistrict-level economic facility data from Lamongan Regency. The results produce spectral scores ranging from 0.0683 to 2.0000, with Bluluk obtaining the lowest score and Lamongan obtaining the highest score. Several alternatives with comparable global structural characteristics also exhibit distinct minor-eigenvalue responses, indicating that the proposed approach can reveal local structural variations that may not be reflected in global spectral analysis. These findings suggest that minor-eigenvalue-based spectral analysis provides an alternative local perspective for distinguishing alternatives within the IFSS framework. The proposed framework contributes theoretically to IFSS-based spectral modeling and practically supports decision-makers in prioritizing subdistrict development based on local structural characteristics.
Spatial Regression Analysis using Queen Contiguity Weight Matrix and PCA Dimensionality Reduction Joko Purwadi; Iliana Dewinta
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.v11i1.40908

Abstract

Conventional linear regression often falls short in poverty analysis, as it fails to account for spatial interdependence between neighboring regions and frequently encounters multicollinearity among socioeconomic variables. This study investigates the presence and nature of spatial effects in poverty data across regencies and cities in Central Java Province, Indonesia, and assesses the performance of an enhanced spatial regression model. We employ a Spatial Autoregressive Model (SAR) integrated with a queen contiguity spatial weight matrix and apply Principal Component Analysis (PCA) to reduce dimensionality and mitigate multicollinearity. The results demonstrate a strong model fit, with a pseudo R2 of 0.94311, and reveal a statistically significant negative spatial lag coefficient ( = -0.2039, p-value = 0.04420), indicating that areas of lower poverty are often surrounded by higher poverty neighbors. This integrated approach provides a more accurate framework for spatial poverty mapping, offering actionable insights for designing regionally targeted development policies.
β-Duality of the Sequence Space ℓpL and a Geometric Realization via Wulff Shapes Adrian Taruna Barus; Meisya Shekina
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.v11i1.40008

Abstract

In the present paper, we investigate the structural and geometric properties of the non-absolute type sequence space ℓpλ. Our primary novel contribution lies in demonstrating that the natural norm on its β-dual coincides with the dual norm of ℓpλ. We then investigate geometric properties of the space and prove that ℓpλ inherits uniform convexity and uniform smoothness from the classical space ℓp for 1 p ∞, while these properties fail in the case p = 1. Finally, by considering finite-dimensional truncations, we interpret the dual norm geometrically through the Wulff construction. This yields a visualization of the norm unit sphere as a Wulff shape and shows that geometric features of the resulting shape reflect the convexity and smoothness properties of the underlying sequence space.
Qualitative and Numerical Analysis of an SVEIR Model for HIV-HBV Co-Infection Maria Lobo; Adelya Hanaya Mage; Ariyanto Ariyanto
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.v11i1.40185

Abstract

The dynamics of HIV-HBV co-infection present significant epidemiological challenges, particularly in resource-limited areas. This study employs the SVEIR mathematical model to explore the transmission and control of HIV-HBV co-infection in Kupang City, Indonesia. Using the Next Generation Matrix method, the basic reproduction number (R0) was estimated at 1.36, indicating persistent disease transmission without effective intervention. Sensitivity analyses identified HBV vaccination coverage and treatment accessibility as critical parameters significantly influencing infection dynamics. Numerical simulations validated the theoretical model, demonstrating that increased vaccination rates and enhanced antiviral therapy access substantially reduce co-infection prevalence. Furthermore, equilibrium analyses revealed that effective interventions capable of lowering R0 below unity could transition the system from persistent endemicity toward disease elimination. These results emphasize the necessity of integrated intervention strategies, including expanded HBV vaccination, improved antiviral therapy access, and comprehensive community education to mitigate HIV-HBV co-infection. Future research should address existing limitations, incorporating behavioral and socioeconomic determinants to enhance model accuracy and applicability.
A Two-Stage Kalman Filter and ARIMA Framework for High-Frequency Wind Speed Modeling in Equatorial Regions Nurfitri Imro'ah; Nur'ainul Miftahul Huda; Kartika Sari; Rahmi Hidayati
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.v11i1.41753

Abstract

High-frequency wind speed data collected via environmental monitoring systems often contain significant stochastic noise that can obscure underlying patterns and degrade the reliability of statistical models. A two-stage modeling framework (integrating a Kalman Filter (KF) for signal purification and Autoregressive Integrated Moving Average (ARIMA) for predictive modeling) was developed and applied to five-minute interval wind speed data in Pontianak, West Kalimantan. The dataset, comprising 3,742 observations recorded from December 11 to 24, 2024, was utilized to evaluate the effectiveness of the KF in enhancing model fitting. The model quality was further assessed using Individual Moving Range (IMR) control charts to monitor residual stability and detect localized anomalies. Results demonstrate that the KF-ARIMA approach significantly improves performance, reducing the Root Mean Square Error (RMSE) from 1.123 m/s to 0.145 m/s, representing an 87.1\% improvement in precision compared to the standalone ARIMA model. The I-MR charts confirmed that the KF-ARIMA residuals remained consistently within the $3\sigma$ control limits, effectively identifying transient variations that standard diagnostic tests might overlook. This integrated framework proves that combining state-space filtering with traditional time-series models provides a robust approach for characterizing high-frequency meteorological data in equatorial regions.
Comparison of Extreme Value Logistic and Copula Approaches for Bivariate Extreme Value in Pekanbaru Fadilla Afsari; A'yunin Sofro
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.v11i1.41081

Abstract

Global climate change has intensified extreme weather events in tropical regions, increasing heat-related risks in Pekanbaru City. This study aims to analyze the joint behavior of extreme maximum temperature and humidity using a multivariate extreme value framework. Daily data from 20142024 were processed using a seasonal block maxima approach, resulting in 24 seasonal extreme observations. The marginal distributions follow a Weibull-type Generalized Extreme Value (GEV) distribution, indicating bounded extreme values. Dependence analysis indicates a weak association, where the Joe copula converges to the independence case, while the Frank copula yields the lowest AIC value among the fitted copula models. However, the difference in AIC values is small and should be interpreted cautiously. Joint return period analysis indicates that joint exceedance of seasonal block maxima is relatively infrequent (approximately 100 years), whereas single-variable exceedances occur more frequently (approximately 5.2 years). These return period estimates are exploratory and subject to uncertainty due to the limited sample size. Overall, the results suggest a weak dependence structure between the variables, and the findings should be interpreted cautiously in the context of climate-related risk assessment.
Design of Fuzzy Logic Controller Based on Gustafson-Kessel Clustering for Quadcopter Altitude Control Belgis Ainatul Iza; Heri Purnawan; Moh. Khoridatul Huda; Nurul Laili
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.v11i1.41543

Abstract

Quadcopter altitude control is a critical issue in unmanned aerial vehicle systems due to its nonlinear dynamics and impact on operating conditions. Various fuzzy logic-based approaches have been used to address these nonlinear characteristics. However, in many previous studies, the rule structure and membership function were determined heuristically or based on expert knowledge, resulting in a less systematic design process that did not fully represent the distribution of system dynamics data.This study proposes a data-driven fuzzy control approach using the Gustafson–Kessel clustering algorithm to automatically generate fuzzy rules from system data. This algorithm is used to identify an ellipsoidal cluster structure in the input space formed by the error variable (e) and the error change (Delta e). The cluster center parameters are used to construct Gaussian membership functions and a rule base for the fuzzy inference system that generates control signals for the quadcopter's vertical dynamics.Evaluation is conducted through quadcopter altitude control simulations using several error metrics. The simulation results show Integral Squared Error value of 0.363789, Integral Absolute Error of 0.554409, Root Mean Square Error of 0.190637, and Mean Absolute Error of 0.055386, with a maximum error of 0.999600 in the beginning of the system response.
Risk Analysis of Shallot Farm Income Using D-vine Copula-Based Monte Carlo Simulation Fatimah Fuzzaroh; Berlian Setiawaty; I Gusti Putu Purnaba
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.v11i1.41556

Abstract

Shallot farm income is highly uncertain due to fluctuations in yields, prices, and production costs, which are interdependent and significantly correlated. This study evaluates income risk by modeling the dependence structure among the variables that constitute income, while addressing data limitations. Two approaches are employed. First, a parametric approach models income as a univariate variable under the assumption of a normal distribution, ignoring dependence among its components. Second, a multivariate simulation approach utilizes a D-vine copula, combined with Monte Carlo simulation, to capture the dependence among income components and generate synthetic observations that better represent tail behavior. Risk is measured using Value-at-Risk (VaR) and Expected Shortfall (ES) based on 32 observations of average shallot farm income per harvest season over the period 2014–2024, and the results are compared with empirical estimates. Due to limited data, the empirical approach produces relatively coarse estimates, particularly in the tail region. The normal distribution approach yields higher and smoother estimates, indicating a higher level of risk. In contrast, the D-vine copula approach provides lower estimates than the normal distribution. These differences indicate that each method offers a distinct perspective on income risk.
A Mathematical Model of Human-to-Human Transmission of Monkeypox with Reinfection Eka Widia Rahayu; Noorma Yulia Megawati
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.v11i1.40140

Abstract

Monkeypox is a zoonotic disease caused by the monkeypox virus and remains a public health concern due to its potential for sustained human-to-human transmission. This study analyzes the transmission dynamics of monkeypox by developing a deterministic compartmental model that explicitly incorporates reinfection arising from waning immunity. The model is analyzed by deriving the basic reproduction number and determining the disease-free and endemic equilibrium points, whose local and global stability properties are rigorously investigated. A sensitivity analysis is conducted to identify key parameters driving transmission dynamics. Motivated by these results, an optimal control problem is formulated in which vaccination is implemented as a time-dependent control, and the optimal strategy is characterized using Pontryagin’s Minimum Principle. Numerical simulations reveal that even low reinfection rates can sustain endemic transmission in the absence of control, while appropriately timed vaccination strategies significantly reduce infection levels and prevent long-term persistence.
Application of Reich-Perov -Contractive Mapping in Vector Valued Metric Space Sunarsini Sunarsini; Mahmud Yunus; Subiono Subiono
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.v11i1.41240

Abstract

This paper presents two new applications of a fixed point theorem for Reich–Perov α-contractive mappings in vector-valued metric spaces. As a new application, we first demon-strate the existence and uniqueness of a solution to the vector valued Volterra-Fredholm integral equation system. By constructing suitable integral operators, we show that they satisfy the α-contractive Reich-Perov condition. The second application concerns the determination of the fixed point for discrete recursive systems with coupled components, for which the existence of a unique solution is established.

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