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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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Mathematical Modeling of the Decoy Effect to Shift Consumer Preferences in House-Type Purchases Baskoro, Sentot Eko; Sutapa, I Nyoman; Suhartono, Suhartono
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.v10i2.36937

Abstract

This study discusses the design of a Mechanism Design-based Decoy Effect Mathematical Model to shift consumer preferences from small-type houses to large-type houses. The model uses area-per-price utility that combines the ratio of building area and land area to price, and formulates the optimization of decoy attributes so that large-type houses dominate but remain close as comparators. The model is explained with a case study, namely large houses are set at a price of  IDR, land area of  m², and building area of  m²; small houses are priced at  million IDR, building area of  m², and land area of  m²; then two types of decoy house prices are set, namely  million and  million IDR. With the ratio of building and land area to price, namely  and  as well as  and , large-type houses excel in terms of building-per-price and are equivalent in terms of land-per-price. Asymmetric decoy houses can be constructed by selecting  and . The results of the mathematical model calculations obtained the closed solutions 'adjacent' and 'strong' for the two types of prices. Sensitivity analysis shows that the target margin advantage increases linearly with  and the context scale , above the base margin . This model provides an operational and easily auditable mechanism in practice.
Modeling Fuzzy Geographically Weighted Clustering with Flower Pollination Algorithm for Spatial Optimization and Clustering Gani, Friansyah; Pramoedyo, Henny; Efendi, 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.v10i2.36800

Abstract

This study aims to analyze the clustering of districts/cities in East Nusa Tenggara Province (NTT) using the Fuzzy Geographically Weighted Clustering method optimized through the Flower Pollination Algorithm (FGWC-FPA). The data consist of eight health and sanitation indicators for 2024. The analysis produced two clusters with distinct characteristics. Cluster 1 is dominated by areas with relatively higher rates of complementary feeding and good BCG immunization coverage but still shows a higher proportion of low birth weight (LBW) infants and limited access to drinking water and sanitation. Meanwhile, Cluster 2 demonstrates significant advantages in access to proper drinking water (90.37%) and proper sanitation (83.19%), as well as more optimal Hepatitis B immunization coverage. Evaluation of cluster validity using Classification Entropy (CE) and the Separation Index (SI) shows that the best configuration is obtained at m = 1.5 with c = 2, yielding the lowest CE value (0.584872) and reasonably good cluster separation (SI = 1.069092). Thus, the FGWC-FPA method is capable of producing optimal cluster partitioning and can serve as a basis for formulating more targeted health intervention strategies in NTT.
b-coloring Analysis on Tree Graph Families Prihandini, Rafiantika Megahnia; Kristiana, Arika Indah; Dana, Lusita Risma; Wihardjo, Edy; Adawiyah, Robiatul; Zulnaidi, Hutkemri
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.v11i1.32328

Abstract

A tree graph is a connected graph and has no circuits. Tree graphs used in this study include: broom graph, centipede graph, and Banana Tree graph. Graph coloring is the process of giving color to graph elements with the rule that neighboring elements must not have the same color, and the number of colors used must be as minimal as possible. b-coloring of a graph G is a coloring of the vertices of G such that each color class has at least one vertex adjacent to all other color classes. The b-chromatic number of a graph G is denoted by φ(G), is the largest integer k such that G has a b-coloring with k colors. The limit of b-coloring of graph G with maximum degree ∆(G) is as follows, χ(G) ≤ φ(G) ≤ ∆(G) + 1.χ(G) is the chromatic number of a graph G where χ(G) is the minimum value of the color required for proper coloring of graph G. While ∆(G) is the maximum degree of the vertices in graph G. This study uses an exploratory research type with an axiomatic deductive method and a pattern detection method. Based on this study, the results of the b-coloring analysis on the tree graph family are known. The results of this study are expected to be used as study material and the development of scientific knowledge related to b-coloring analysis on other graphs.
Modelling Factors Affecting the Middle Income Trap in Indonesia Using Generalized Additive Models (GAM) Amelia, Dita; Suliyanto, Suliyanto; Zhafira, Azizah Atsariyyah; Ramadhanti, Aulia; Suyono, Billy Christandy; Hizbullah, Firqa Aqila
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.v11i1.35119

Abstract

Indonesia is currently facing a significant challenge known as the Middle Income Trap (MIT), a condition where economic growth stagnates after reaching middle-income status, hindering progress toward becoming a high-income country. This study aims to identify and model the socio-economic factors influencing MIT at the provincial level in Indonesia during the 2020–2023 period. The Generalized Additive Model (GAM) is employed to estimate nonlinear relationships between predictors and the response variable while capturing complex patterns in panel data. GRDP per capita is used as an indicator of MIT, with six predictor variables: life expectancy, poverty rate, informal employment share, secondary education completion rate, food insecurity prevalence, and population density. The results showed that the best model was obtained based on the minimum GCV and AIC values of the Gaussian family with an identity link function and 5 knot points with the highest correlation of 99,9%. Five variables show nonlinear effects, while food insecurity exhibits a significant negative linear impact. The findings provide a valuable reference for designing inclusive and adaptive eco nomic policies based on each region’s socio-economic characteristics to mitigate MIT risks and also supports the achievement of Sustainable Development Goal (SDG) 8, which promotes decent work and sustained economic growth.
University Scheduling Optimization Using Integer Programming: A Case Study Simarmata, Gayus; Saragih, Rajainal; Syofra, Anil Hakim
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.v11i1.37815

Abstract

This paper presents an Integer Linear Programming (ILP) model to construct a weekly lecture timetable for the Mathematics Study Program at HKBP Nommensen University, Pematangsiantar. The case study comprises 25 courses, three rooms (RK 11, RK 12, and LAB 1), five teaching days (Monday–Friday), and 13 time periods per day. The model enforces hard constraints on room, lecturer, and cohort non-overlap; consecutive periods according to credit load; room-type compatibility between theory and practicum sessions; and an institutional worship-time restriction on Tuesday. Lecturers’ availability is represented by a binary acceptance matrix collected at the course level, and rejected time periods are penalized in the objective. The ILP is implemented in Python using the PuLP (Python Linear Programming) library and solved with the CBC (Coin-or Branch and Cut) solver. For the real instance, the solver returns an optimal solution with objective value Z∗ = 0 (no scheduled period falls in a rejected slot) in approximately 94 seconds. The resulting timetable is conflict-free and operationally interpretable, with a weekly room-time utilization of about 31.3%. To support verification and communication to stakeholders, the paper also provides a heatmap of the acceptance matrix and a graphical timetable by room and day.
Enhancing Spatio-Temporal PCA with FASTMCD for Climate Comfort Assessment Yarcana, Agus; Pramoedyo, Henny; Astutik, Suci
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.v11i1.37866

Abstract

This study presents a robust formulation of the Spatio-Temporal Principal Component Analysis (STPCA) by integrating the Fast Minimum Covariance Determinant (FASTMCD) estimator into the spatio-temporal decomposition framework. Unlike classical STPCA—which constructs the spatio-temporal matrix from sample-based means and is therefore highly sensitive to extreme observations—the proposed STPCA–FASTMCD replaces the classical mean and scatter structure with robust estimates derived from FASTMCD. The method incorporates functional Fourier-based temporal smoothing and an inverse power–distance spatial weight matrix to better capture the underlying spatio-temporal patterns. Monthly climate data (thermal comfort, cloud cover, rainfall, and wind speed) from 24 monitoring locations in Bali during 2010–2019 are analyzed. Performance is evaluated using mean-shift analysis, eigenvalue-stability assessment, and eigenvector perturbation diagnostics. The classical STPCA produces inflated and unstable leading components, with the first eigenvalue reaching 63.36, whereas STPCA–FASTMCD reduces this value to 37.79 and yields smoother, more coherent spatial loading patterns. The robust STPC1 reveals a clear thermal–wind variability mode, enhancing the interpretability of spatial gradients relevant to climate comfort. Overall, the proposed formulation substantially improves the stability and climatic relevance of dominant spatio-temporal modes, providing a more reliable foundation for climate comfort assessment in Bali.
Transmission Dynamics of Dengue Disease Incorporating Treatment, Mass Awareness, and Wolbachia Intervention Agustina, Rafika Nanda; Prawoto, Budi Priyo
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.v11i1.39026

Abstract

Dengue Hemorrhagic Fever (DHF) remains a serious global health threat, with transmission dynamics significantly influenced by vector control strategies and human behavior. This study constructs and analyzes a differential equation-based mathematical model to investigate dengue transmission dynamics by integrating three control strategies: medical treatment, mass awareness, and the release of Wolbachia-infected mosquitoes. The basic reproduction number (R0) is derived using the Next Generation Matrix (NGM) method as a threshold quantity for disease transmission. Simulation results demonstrate that when parameter values satisfy the condition R0 1, the system trajectories converge to the disease-free equilibrium, implying that the disease will be eliminated over time. Conversely, modifying parameters δ and p such that R0 1 results in system stability at the endemic equilibrium, indicating disease persistence within the population. This study concludes the importance of controlling these key parameters through integrated interventions to reduce the value of R0 to less than unity
Nasdaq Inc. Stock Price (NDAQ) Prediction Due to Trump’s Tariff Policy Using Pulse Function Intervention Analysis Sediono, Sediono; Siagian, Kimberly Maserati; Aditya, Josephin Viona
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.v11i1.37168

Abstract

Nasdaq Inc. (NDAQ) is one of the leading stock exchanges in the United States, ranking second globally after the New York Stock Exchange (NYSE) based on market capitalization. As a highly dynamic and information-sensitive market, Nasdaq Inc. stock prices respond quickly to internal corporate conditions and external macroeconomic or policy changes. One notable event affecting market stability was President Donald Trump’s import tariff policy, aimed at protecting U.S. industries from foreign competition, particularly Chinese imports. The implementation of this policy triggered significant volatility, including a sharp decline in Nasdaq Inc. stock prices on March 2, 2025. This study examines the impact of this policy on Nasdaq Inc. stock movements using the ARIMA(0,2,1) model with an intervention of order b = 0, r = 1, and s = 0. The results show that all model parameters are statistically significant and produce accurate forecasts, with a MAPE of 2.19%, an RMSE of 5.98766, and an MAE of 2.05232. These findings indicate that intervention analysis effectively captures the impact of import tariff policies on stock market dynamics and provides valuable insights for investors and policymakers in anticipating market fluctuations driven by global economic policy changes.
Implementation of DenseNet121 Based on Convolutional Neural Network with Geometric Augmentation for Breast Cancer Histopathology Image Classification Ariani, Nabilah Evi; Surono, Sugiyarto; Thobirin, Aris
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.v11i1.37896

Abstract

This study evaluates the performance of the DenseNet121 architecture for binary classification of breast cancer histopathological images using the BreakHis dataset. The model employs ImageNet pre-trained weights, fine-tuning, and geometric data augmentation to improve feature learning and generalization. To obtain more reliable results, three optimization algorithms (Adam, AdamW, and RMSprop) were evaluated through repeated experiments, and performance was reported using mean and standard deviation of test metrics. The experimental results demonstrate that DenseNet121 achieves consistently high classification performance across different optimizers, with the Adam optimizer showing the most stable results. These findings indicate that DenseNet121 combined with data augmentation provides an effective and robust approach for histopathological image classification while emphasizing the importance of repeated evaluation for reliable performance assessment.
Modeling the Dynamics of Tuberculosis-Diabetes Mellitus Coinfection with an Optimal Control Approach Muniroh, Muna Afdi; Oktafianto, Kresna; Kurniawati, Eriska Fitri
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.v11i1.37539

Abstract

Tuberculosis–Diabetes Mellitus (TB-DM) coinfection poses a significant public health challenge, contributing to increased morbidity, treatment failure, and healthcare costs. This study develops a mathematical model that stratifies TB infection into latent and active classes to examine the dynamics of TB–DM coinfection. The model is analyzed to determine the disease-free and endemic equilibrium points, supported by numerical evaluation using established parameter values. Furthermore, prevention strategies are assessed through an optimal control framework, formulated using Pontryagin’s Minimum Principle and validated through numerical simulations. The findings are expected to provide effective strategies to reduce TB-DM transmission and minimize optimal control costs, thereby supporting the development of improved public health policies.

Page 43 of 48 | Total Record : 476

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