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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 438 Documents
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Mathematical Stability Analysis of Bullying’s Impact on Student's Mental Health Putri, Devi Marita; Zulaikha, Zulaikha
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.v10i2.33212

Abstract

Bullying is a problem that takes root from the previous generation to the next. The most common bullying cases occur in junior high school students or equivalent with an age range of 13-15 years. Bullying can have an impact on student's mental health. This study develops and analysis a SEIRS-type mathematical model to understand the dynamics of mental health disorders due to bullying among junior high school students. The model includes four subpopulations: subpopulations are vulnerable to mental health disorders due to bullying (S), subpopulations who experience bullying but have not shown any mental health disorders (E), subpopulations that experience mental health disorders due to bullying (I), and subpopulations who have recovered from mental health disorders due to bullying (R). Based on the results of the analysis, two equilibrium points were obtained, namely the mental disorder-free equilibrium point (P_1^*) and the endemic equilibrium point (P_2^*). Next, determine the basic reproduction number using the next matrix generation method. Based on the results of numerical simulation using Matlab R2013a software, it was obtained that if R_01 then the mental disorder-free equilibrium point is stable local asymptotic and mental health disorders due to bullying cannot spread in the student population. Meanwhile, if R_01 then the endemic equilibrium point is stable, local asymptotic and mental health disorders due to bullying can spread in the student population. The rate of interaction between subpopulations vulnerable to mental health disorders due to bullying and subpopulations that experience mental health disorders due to bullying (\alpha) has a significant influence on the number of individuals in each subpopulation.
Notes on 2-Normed Spaces Through Their Quotient Spaces Rumlawang, Francis Yunito; Hernita, Hernita; Lesnussa, Yopi Andry; Batkunde, Harmanus
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.v10i2.35824

Abstract

In this paper, we defined new norms in 2-normed spaces derived from the 2-norm with respect to its quotient spaces. Moreover, these norms were used to observe some aspects of 2-normed spaces namely, a Convergent sequence, a Cauchy sequence, completeness, a closed set, and a bounded set. Furthermore, we used these aspects to prove the Fixed-Point Theorem in a 2-Banach Space.
Model of Three Species Commensalism-Amensalism Symbiosis with Beddington-DeAngelis Functional Responses Shofiyya, Nada; Kusumawinahyu, Wuryansari Muharini; Habibah, Ummu
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.v10i2.36718

Abstract

This study investigates the dynamical behavior of a three species ecological system involving unilateral interactions of commensalism and amensalism with Beddington–DeAngelis functional responses. The positivity, boundedness, existence, and uniqueness of the model solutions are established, and four equilibrium points are identified. Stability analysis shows that the coexistence equilibrium point and the neutral species only equilibrium point are locally asymptotically stable, whereas the other equilibria are always unstable. Numerical simulations are conducted to confirm the analytical findings. Ecologically, the results indicate that stability can be achieved only when all neutral species coexist, even though without the commensal–amensal species. In contrast, the commensal-amensal species cannot persist without the presence of all neutral species.
Odd Harmonious Labeling of Lotus Flower Graphs Firmansah, Fery; Tasari, Tasari; Yuwono, Muhammad Ridlo
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.v10i2.35272

Abstract

The purpose of the research is to obtain the construction of a new graph class definition and the new graph class satisfies the properties of odd harmonious labeling. The research method consists of a preliminary stage, namely the stage of finding open problems, the stage of analyzing data for the formation of definitions and theorems, the stage of verifying the results of proving the theorems mathematically. The research results obtained three new graph class definitions, namely the definition of lotus flower graph, the definition of lotus flower graph with pendant, and the definition of lotus flower graph variation. Furthermore, it has been proven that lotus flower graph, lotus flower graph with pendant, and variation of lotus flower graph satisfy the properties of odd harmonious labeling so that they are odd harmonious.
Pricing Double Barrier Options with Time-Varying Interest using Standard, Antithetic, and Control Variate Monte Carlo Thalita, Bella Cindy; Darti, Isnani
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.v10i2.37010

Abstract

This study develops an integrated framework for pricing double barrier options under time-varying interest rates by combining ARIMA-based forecasting with Monte Carlo simulations. Monthly U.S. Treasury Bill rates from 2019–2025 are modeled using the ARIMA(2,2,0) process to generate dynamic risk-free rates, which are incorporated into three Monte Carlo approaches standard, antithetic variate, and control variate. Tesla Inc. stock prices are used as the underlying asset modeled through Geometric Brownian Motion. The integration of ARIMA-based dynamic rates within the Monte Carlo framework enables more realistic pathwise discounting and improves simulation convergence. The results show that the control variate method provides the most accurate and stable estimates for knock-in call options, whereas the antithetic variate technique yields superior accuracy for knock-in put, knock-out call, and knock-out put options. Overall, the combined use of ARIMA-forecasted interest rates and variance-reduction techniques enhances the precision and stability of double barrier option valuation under dynamic financial conditions.
Analysis of Geographically Weighted Logistic Regression Models with A Bisquare Weighting Matrix on Poverty Status in West Java Saifudin, Toha; Chamidah, Nur; Aldawiyah, Najwa Khoir; Marthabakti, Citrawani; Ramadhanti, Aulia; Nahar, Muhammad Hafidzuddin; Muzakki, Naufal
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.v10i2.36315

Abstract

This research addresses the first Sustainable Development Goal and aims to analyze poverty status in West Java Province, which has the second highest number of poor people in Indonesia. The study employs Geographically Weighted Logistic Regression (GWLR) and compares it with global logistic regression. Influential variables include GDP, unemployment, population density, access to safe water, and roof type (bamboo/wood). Results show that 55.6% of regions are classified as poor, with the GWLR model using a Fixed Bisquare kernel achieving 81.4% accuracy, outperforming global logistic regression at 66.7%. Significant variables vary by region: unemployment rate in Bogor, Depok, and Bekasi; population density in Bekasi, Karawang, and Purwakarta; water access in Sukabumi; and roof type in Indramayu and Bogor. These spatial variations suggest that poverty reduction requires a region-specific approach. Consequently, policies should be formulated considering the priorities and characteristics of each region in West Java Province.
Cluster Analysis Of Cities/Districts In West Kalimantan Based On Stunting Response Indicators Using The Calinski Harabasz Index Priyatna, Tegar Rama; yundari, yundari; Huda, Nur'ainul Miftahul
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.v11i1.34510

Abstract

The stunting rate in West Kalimantan has reached 27%, mainly due to the government's inability to prioritise regions for essential services and education, especially for adolescents and pregnant women. This study aims to explain the role of modified K-Means and CHI methods in forming optimal clusters and interpreting their conditions. Eight research variables, sourced from BPS and SIGA in 2023, were used: number of adolescents receiving counselling, informed consents, complication cases, aslokon expenditure, aslokon stock, population growth rate, population density, and life expectancy. These variables were validated using PCA with the Kaiser and PVE approaches. Clustering was done by analysing the data for each variable and the characteristics of the objects using the Euclidean distance, determining the centroid values, and iterating until the results stabilised. The clusters were evaluated from one to seven to find the optimal amount using CHI. The results identified five clusters: cluster 1 (relatively poor, three objects), cluster 2 (inferior, four objects), cluster 3 (good, three objects), cluster 4 (exquisite, three objects) and cluster 5 (good, one object).
Sensitivity of Bayesian Truncated Spline Regression to Prior and Knot Configuration in Stunting Models Zahra, Septi Nafisa Ulluya; Fernandes, Adji Ahmad Rinaldo; Efendi, Achmad; Solimun, Solimun; Nasywa, Alfiyah Hanun; Junianto, Fachira Haneinanda
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.v10i2.37381

Abstract

This study develops a Bayesian bi-response regression model using a truncated spline approach to examine nonlinear effects of economic, dietary, and environmental factors on nutritional and physical stunting. Sensitivity analysis was conducted to evaluate the influence of prior types and knot numbers on model performance using Deviance Information Criterion (DIC), Root Mean Square Error (RMSE), and bias. Results show that the informative Normal–Gamma prior combination yields the best performance, with the lowest DIC, smallest RMSE, and minimal bias. Models with three knots provide higher predictive accuracy, while noninformative Uniform priors cause instability and overfitting. Overall, the findings indicate that prior specification has a stronger effect on model robustness than the number of knots, emphasizing the importance of informative priors in Bayesian spline modeling for understanding complex, nonlinear determinants of child stunting.
Development of a Fuzzy Logic Model for Tsunami Early Detection Using Tunami F1 on the Southern Coast of Yogyakarta International Airport, Jogja Naqiya, Sadiyana Yaqutna; Khoirunnisa, Hanah; Pradananta, Galih
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.v10i2.35416

Abstract

Tsunami disaster mitigation requires a reliable early warning system to reduce traumatic impacts and material losses. This study develops a fuzzy logic model for early tsunami detection by integrating wave height (SSH) and estimated tsunami arrival time (ETATSU) parameters. The model is combined with the TUNAMI F1 simulation, which considers seabed topography and fluid dynamics. Simulations were conducted on 36 earthquake scenarios on the southern coast near Yogyakarta International Airport (YIA). The results show that the model successfully classifies tsunami risks into three categories: alert, standby, and emergency, with an overall accuracy of 83.3%. Some scenarios showed invalid results at high magnitudes (Mw ≥ 8.5). This research improves the accuracy of tsunami early warning systems, potentially saving more lives and minimizing the impact of disasters.
Generalized Poisson Spatial Autoregressive Modeling of Pneumonia Cases in Children Under Five in Tuban Sihombing, Joshua Capri Gunawan; Sutikno, Sutikno; Choiruddin, Achmad
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.v10i2.37288

Abstract

The number of pneumonia cases in children under five in Tuban Regency presents two significant data challenges, namely, overdispersion and spatial dependency. This study aims to develop and apply the Generalized Poisson Spatial Autoregressive (GPSAR) model to address both issues simultaneously. The model was estimated using a MLE-BHHH procedure and validated using 10-fold cross-validation (CV). The results confirm the model's validity and superiority. The GPSAR model outperformed the non-spatial GPR model in terms of goodness-of-fit (AIC: 1301.09 vs. 1312.67) and predictive accuracy (Out-of-Sample CV-RMSE: 8.451 vs. 8.716). Statistically, the structural parameters for spatial lag and overdispersion were highly significant. Two predictor variables, exclusive breastfeeding and complete basic immunization, were also found to be statistically significant factors. This research provides a robust regression framework for spatial count data exhibiting overdispersion and offers new insights into pneumonia case determinants in the region.

Page 41 of 44 | Total Record : 438

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