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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 493 Documents
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Coronary Heart Disease Risk Prediction under Class Imbalance Using XGBoost with SHAP-Based Interpretation Amiroch, Siti; Laili, Fitri Nur; Rohmah, Awawin Mustana; Kardono, Dicka Yale
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.v11i1.37938

Abstract

Coronary heart disease (CHD) risk prediction is challenging because clinical data are heterogeneous and the response variable is imbalanced. This study develops an interpretable predictive framework for CHD risk using Extreme Gradient Boosting (XGBoost), median imputation, IQR-based winsorization, standardization, the Synthetic Minority Over-sampling Technique (SMOTE), bootstrap-based uncertainty assessment, and Shapley Additive Explanations (SHAP). The learning problem is formulated within a regularized empirical risk minimization framework, so the model is viewed as a statistical estimator rather than merely an algorithmic classifier. To avoid information leakage, train–test splitting is performed before any resampling, and SMOTE is applied only to the training data. The primary analysis is fixed a priori at an 80:20 stratified split, whereas 60:40 and 70:30 splits are treated as sensitivity analyses rather than model-selection devices. In the primary analysis, the model attains accuracy of 79.36%, precision of 27.88%, recall of 22.48%, F1-score of 24.89%, and ROC–AUC of 0.6502. The 95% bootstrap confidence interval for ROC–AUC is [0.6017, 0.6981]. SHAP analysis in probability space identifies age, cigsPerDay, male, heartRate, and sysBP as the most influential predictors. These results show that the proposed framework is mathematically well-structured and interpretable, but that its out-of-sample discrimination on this dataset is moderate rather than high.
Higher-Order Numerical Solution of the KdV-BBM Equation: A Comparative Analysis of Temporal Integration Schemes in the Method of Lines Framework Ardiana, Dita; Habibah, Ummu; Trisilowati, Trisilowati; Ranom, Rahifa Binti
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.v11i1.41525

Abstract

This study investigates the numerical simulation of solitary wave propagation governed by the KdV-BBM equation using a robust Method of Lines (MOL) framework. The governing nonlinear equation is transformed into a system of ordinary differential equations through spatial discretization, and the performance of three temporal integration schemes is evaluated: the first-order Euler method, the fourth-order Runge-Kutta (RK-4), and the fifth-order iRK-5 method. Quantitative analysis using Mean Absolute Error (MAE) for various time steps (t = 0.2, 0.1, 0.05, and 0.01) reveals that the iRK-5 scheme provides enhanced temporal precision, achieving error magnitudes as low as 106 and consistently aligning with the exact traveling-wave solution. Notably, the iRK-5 method demonstrates greater algorithmic efficiency, achieving an accuracy level of 4.55 106 at a coarser time step of t = 0.1, whereas the RK-4 scheme requires a finer time step of t = 0.05 to reach the same precision. Both high-order methods eventually reach a spatial error floor where further temporal refinement yields no significant reduction in MAE, emphasizing that high-order temporal integration, particularly the iRK-5 scheme, is essential for preserving the physical integrity of complex nonlinear wave phenomena while maintaining optimal computational effort.
Total Edge Irregularity Strength of Cycle Snake Graphs Pranata, Stenly; Krisnawati, Vira Hari; Darmajid, Darmajid
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.v11i1.41552

Abstract

Let G be a simple undirected graph with vertex and edge sets. A total labeling that assigns integers from 1 to k to the union of the vertex and edge sets is called a k-total labeling. The weight of an edge uv, denoted by w(uv), is defined as the sum of the labels of the two vertices u, v, and the label of edge uv itself. A k-total labeling is called an edge irregular total k-labeling of G if the weights of all distinct edges are different. The minimum k for which every edge of G has a distinct weight is called the total edge irregularity strength of G, denoted by tes(G). A cycle snake graph CSm,n is obtained from the path graph Pn with n + 1 vertices and n edges by replacing each edge with a cycle graph Cm, where m 3 and n 2. In this paper, we study the graphs CS3,n and CSm,n and determine their total edge irregularity strength. The case m = 3 is considered separately because the structure of CS3,n gives a different representation of the vertex and edge sets than for m 4, requiring a different labeling construction.
The Charactherization Criterion of g-quasi-Frobenius Lie Algebra Corresponding to Inner Derivation Budiman, Muhammad Arief; Kurniadi, Edi; Sukono, Sukono
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.v11i1.41601

Abstract

The structure of a g-quasi-Frobenius Lie Algebra can be realized as a quasi-Frobenius Lie Algebra modules over a Lie Algebra g. This research discusses a special condition of the g-quasi-Frobenius Lie Algebra, namely when g acts on its self. This condition supports the construction of an inner derivation on g. The criterion investigated is the characterization of the g-quasi-Frobenius Lie Algebra in relation to the inner derivation. The result obtained is a criterion: a g-quasi-Frobenius Lie Algebra can be constructed on g itself if and only if the inner derivation is zero. Furthermore, several concrete examples are provided to test this criterion.
Modeling Airplane Passenger Volatility during the COVID-19 Crisis: a SARIMA and Intervention Analysis Faizin, Nur; Fauzan, Achmad
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.v11i1.40880

Abstract

The COVID-19 pandemic in early 2020 had a severe impact on air traffic at Indonesia’s Soekarno-Hatta International Airport, which is among the busiest in the world. This caused a sharp decline in passenger numbers in April 2020, resulting in significant data fluctuations that required statistical intervention. Therefore, to forecast passenger numbers during these fluctuating trends, this study used the SARIMA and Step Function Intervention analysis. The results showed that the Step Function Intervention model was more accurate than SARIMA in predicting the number of passengers at the domestic departure terminal. Based on data for the period between January 2006 and June 2024, the step function intervention model produced MAD, MSE, RMSE, and MAPE values that are smaller than the SARIMA model. The best model, SARIMA Intervention (2,1,0)(1,1,1)12 b = 0, s = 3, r = 1, fulfilled the white noise and normality assumptions with a MAD accuracy value of 82381.85 and MAPE of 9.62%. In addition, the Step Function Intervention Method further reduced the MAPE value by up to 6.93%.
Sentiment Analysis of Indonesia’s Free Nutritious Meal Program on X Using SVM and Random Forest Hasyim, Ferdy Aliansyah; Mahenindra, Talenta Parfaibya; Sriwahyuni, Lilis; Shapira, Alika Azka; Wigawijayanti, Wigawijayanti; Ghaisani, Nadhifa Zahra; Sujana, Mirlan; Nurdiati, Sri; Najib, Mohamad Khoirun
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.v11i1.40717

Abstract

The Free Nutritious Meal (Makan Bergizi Gratis/MBG) Program was introduced to address stunting in Indonesia, yet its implementation has sparked diverse public debate. This study aims to map public perception on social media X and compare the performance of Support Vector Machine (SVM) and Random Forest algorithms in sentiment classification. Utilizing a large-scale dataset of 7,452 tweets collected via stratified random sampling from January to October 2025, this research applies TF-IDF feature extraction and SMOTE data balancing. The analysis reveals that positive sentiment dominates at 47.62%, while negative sentiment accounts for 39.8\%, and neutral for 12.57%. In model comparison, SVM without SMOTE achieved the best performance with 80.66% accuracy and an F1-Score of 79.79%, outperforming Random Forest, which only reached a maximum accuracy of 72.23% after SMOTE application. These findings provide an objective overview of MBG policy acceptance and methodological insights into the effectiveness of SVM in handling high-dimensional text data.
The Triple Total Graph of The Ring Zn Kurniawan, Vika Yugi; Zyuhri, Syaifudin; Wiyono, Santoso Budi
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.v11i1.41488

Abstract

Let R be a commutative ring and let Z(R) denotes the set of zero-divisors of R. The triple total graph of R, denoted by TT(R), is a simple graph whose vertex set is R∖{0}. Two distinct vertices v1 and v2 are adjacent in TT(R) if and only if v1+v2∉Z(R) and there exists v3∈R∖{0}, with v3≠v1 and v3≠v2, such that v1+v3∉Z(R),  v2+v3∉Z(R), and v1+v2+v3∈Z(R).In this paper, we investigate the structural properties of the graph TT(Zn). We show that if n is even with n 2, then TT(Zn) is an empty graph. When n is prime with 2 n 11, the graph TT(Zn) is disconnected. In contrast, for prime integers n≥ 11, the graph becomes connected with diam(TT(Zn))=2 and gr(TT(Zn))=3. Moreover, each vertex has degree n−5, implying that the graph is (n−5)-regular and consequently both Eulerian and Hamiltonian. These results illustrate how the arithmetic nature of n determines the global structure of the triple total graph.
Spectral Analysis of a Cyclic Tank Mixing System Zanu, Pebrudal; Wahyu, Sri; Burhan, Mohammad Januar Ismail
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.v11i1.41466

Abstract

In this paper, we study a cyclic mixing tank system consisting of n identical tanks arranged in a closed-loop configuration, each operating under constant volume with equal inflow and outflow rates. The model is further generalized to an m-layer structure, where each layer comprises n circularly interconnected tanks. Based on mass balance principles, the concentration dynamics are formulated as a linear system of first-order ordinary differential equations. By exploiting the structured form of the system matrix, we derive an explicit analytical solution and obtain a closed-form characterization of its spectrum. We show that the eigenvalues of the system are explicitly given by k,j = (-2 + e2i(k-1)/n), which inherently guarantees the decay of all modes. In particular, the solution exhibits a polynomial-exponential form associated with the multilayer cyclic tank. We also establish that the system is exponentially stable under conditions ensuring decay of all modes. Finally, we present numerical simulations to validate the analytical results and to illustrate the transient dynamics of the multilayer system.
Stability Analysis of a Predator-Prey Model with Disease in Prey, Predator Harvesting, and Internal Migration of Susceptible Prey in a Closed Ecosystem Firmansyah, Muhammad Thariq; 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.v11i1.41546

Abstract

This study develops and analyzes a mathematical model of a predator-prey system incorporating three simultaneous ecological factors: disease in the prey population, harvesting of the predator, and internal migration of healthy prey within a closed ecosystem. The prey population is divided into two compartments healthy prey and infected prey where disease transmission follows the law of mass action. The predator population is subject to a constant harvesting rate representing external pressure such as hunting or capture. Internal migration of healthy prey is modeled as a density-dependent flux governed by a migration parameter m, which drives the redistribution of healthy prey across spatial patches without allowing permanent emigration from the system. The model is formulated as a system of three autonomous ordinary differential equations. Six equilibrium points are identified, representing a range of ecological scenarios from total extinction to full coexistence of all populations. The local stability of each equilibrium point is analyzed by linearization via the Jacobian matrix, and stability conditions are derived in terms of the model parameters, including the application of the Routh–Hurwitz criterion for the coexistence equilibrium. A key finding is that the migration parameter m does not alter the location of equilibrium points but directly influences the eigenvalues of the Jacobian, thereby affecting the rate at which the system recovers from perturbations. Numerical simulations are conducted to verify and illustrate the analytical results. This work extends the model of Mansur et al. [1] by introducing an internal spatial dimension, offering a more ecologically realistic framework for understanding population dynamics in ecosystems where disease, harvesting, and migration co-occur
Local Stability and Bifurcation Analysis of a Mangrove Detritus Small-Fish Model with Dynamic Harvesting Effort under a Beddington-DeAngelis Functional Response Kurniasih, Donna; 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.v11i1.41486

Abstract

This study develops a three-dimensional mangrove detritus small fish model with a dynamics harvesting effort governed by a threshold rule and a Beddington DeAngelis functional response. The main objective is to understand how adaptive harvesting and consumer interference shape long-term dynamics and stability. Equilibrium points are derived and their local stability is examined using the Jacobian matrix and eigenvalue-based criteria, supported by numerical simulations. Bifurcation analysis with respect to the threshold parameter is performed using numerical continuation to detect qualitative transitions in system behavior. The results show the existence of biologically feasible coexistence equilibria with active harvesting, including a stable branch and an unstable branch. A Hopf bifurcation is detected at approximately a = 6.6159, confirming the emergence of sustained oscillations limit cycles in fish density and harvesting effort, while a fold limit point occurs near a = 22.001, indicating changes in equilibrium structure. Moreover, simulation scenarios demonstrate that reducing environmental capacity and increasing fish mortality can drive the system toward a no-effort equilibrium where harvesting collapses. These findings highlight the threshold parameter as a key control factor that can switch the system between stable harvesting, effort extinction, and oscillatory harvesting regimes.

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