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EIGEN MATHEMATICS JOURNAL
Published by Universitas Mataram
ISSN : 26153599     EISSN : 26153270     DOI : -
Core Subject : Education,
Mathematics
Eigen Mathematics Journal mempublikasikan artikel yang berkontribusi pada informasi baru atau pengetahuan baru terkait Matematika, Statistika, dan Aplikasinya. Selain itu, jurnal ini juga mempublikasikan artikel berbentuk survey dalam rangka memperkenalkan perkembangan terbaru dan memotivasi penelitian selanjutnya dalam bidang matematika, statistika, dan aplikasinya.
Arjuna Subject : -
Articles 130 Documents
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Analisis Optimasi Hiperparameter Bayesian untuk Model Prediksi Kinerja Inovasi Berkelanjutan Puspita, Tika
Eigen Mathematics Journal Vol 8 No 2 (2025): December
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v8i2.266

Abstract

This study examines how well the Gaussian Process Regression (GPR) model performs in interpreting the optimization outcomes achieved through Bayesian Optimization (BO) with Keras Tuner, specifically in the context of Sustainable Innovation Performance (SIP). The GPR surrogate model serves to examine the outcomes of optimization and offers valuable insights into the strategies of exploration and exploitation while seeking the most effective hyperparameters. The evaluation of the effectiveness of GPR involved calculating the Mean Absolute Error (MAE), which was bootstrapped 1000 times to establish a 95\%. Confidence Interval (CI). This study's findings demonstrate the dependability of GPR in forecasting the validation loss generated by BO, characterized by minimal prediction errors and consistent confidence intervals. The results indicate that GPR serves as a dependable statistical method for assessing uncertainty in Bayesian-based optimization. Additionally, they offer valuable perspectives on how exploration and exploitation strategies can be utilized to attain optimal hyperparameter configurations. By strategically balancing exploitation and exploration, Bayesian Optimization can enhance the process of identifying optimal hyperparameter configurations within continuous innovation prediction models.
Prediksi Curah Hujan di Provinsi Lampung Menggunakan Distribusi Tweedie Campuran dengan Reduksi PCA Utami, Sari; Hayati, Ma’rufah; Permatasari, Reni
Eigen Mathematics Journal Vol 8 No 2 (2025): December
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v8i2.280

Abstract

Accurate rainfall prediction is crucial for supporting the agricultural sector in Lampung Province. This research employs the Exponential Dispersion Model (EDM), a special case of the Generalized Linear Model (GLM), incorporating a Tweedie mixture distribution with Principal Component Analysis (PCA) to reduce correlated variables. Rainfall data were obtained from the Meteorology, Climatology, and Geophysics Agency (BMKG) through twelve rain observation posts (2013-2022), and supplemented with precipitation data from the General Circulation Model (GCM) obtained from the European Centre for Medium-Range Weather Forecasts (ECMWF). The Tweedie mixture distribution was selected for its ability to handle non-normally distributed rainfall data containing zero values. The results show that the Root Mean Square Error of Prediction (RMSEP) for the Tweedie mixture-PCA model at the Gisting Atas station is 163.90, while the Normal-PCA model achieved 169.11. Therefore, the Tweedie mixture-PCA approach is more effective and recommended for improving rainfall prediction in Lampung Province, offering potential benefits for agricultural planning and resource management.
Simulation of Spring Oscillations in Second-Order Differential Equations Using the Finite Difference Method Al Paqih, Muhammad Imam; Hardi, Rida Al Kausar; Robbaniyyah, Nuzla Af'idatur
Eigen Mathematics Journal Vol 8 No 2 (2025): December
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v8i2.321

Abstract

This study aims to simulate the motion of a damped spring oscillation, modeled by a second-order ordinary differential equation, using the Finite Difference Method (FDM). The main focus is on implementing the central finite difference scheme to discretize the equation, deriving an explicit iterative formula, and analyzing the oscillation dynamics and the accuracy of the numerical solution. The simulation was conducted with specific parameters (mass m = 1.0 kg, spring constant k = 10.0 N/m, damping coefficient c = 0.5 Ns/m) and various time steps (\Delta t = 0.5 s, 0.1 s, 0.01 s). The simulation results qualitatively show damped oscillatory behavior consistent with physical theory, where the amplitude decreases over time. The accuracy of the numerical solution, measured by the Symmetric Mean Absolute Percentage Error (SMAPE) against the analytical solution, was significantly influenced by \Delta t; the smallest time step (0.01 s) yielded the highest accuracy with a SMAPE of 0.4495%. The Finite Difference Method proved effective in analyzing the spring oscillation system, demonstrating that the proper selection of \Delta t is crucial for balancing accuracy and computational efficiency.
Penerapan Kendali Optimal pada Model Matematika SEITRS Penularan Tuberkulosis dengan Variabel Kendali Sosialisasi dan Terapi Rafiq, Muhammad; Wigantono, Sri; Raming, Indriasri
Eigen Mathematics Journal Vol 8 No 2 (2025): December
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v8i2.322

Abstract

Tuberculosis (TB) is an infectious disease caused by Mycobacterium tuberculosis, which remains a serious public health concern. The objective of this study is to develop, analyze, and propose an optimal control strategy for the transmission dynamics of TB using an SEITRS mathematical model. The model consists of five population compartments: Susceptible (S), Exposed (E), Infected (I), Treatment (T), and Recovered (R). The methodology involves constructing the SEITRS model, determining the equilibrium points, and analyzing their stability under different conditions of the basic reproduction number. The model has two equilibrium points, namely the non-endemic and endemic equilibrium. If the basic reproduction number is less than one and certain conditions are satisfied, the non-endemic equilibrium is locally asymptotically stable. Conversely, if the basic reproduction number is greater than one and specific conditions are met, the endemic equilibrium becomes locally asymptotically stable. Furthermore, this study provides optimal control strategies in the SEITRS model. We use two control variables in this model, namely socialization and therapy, to reduce the number of infected individuals. The sufficient conditions for the existence of optimal controls are derived using Pontryagin’s Maximum Principle. Numerical simulations are then conducted to examine the impact of applying these controls on the system. The simulation results indicate that the simultaneous implementation of socialization and therapy controls is effective in reducing the number of TB-infected individuals.
Comparison of Cluster Average Linkage and K-Means Analysis Methods for Poverty Grouping in The Nusa Tenggara Area Alimuddin, Muhammad; Harsyiah, Lisa; Baskara, Zulhan Widya
Eigen Mathematics Journal Vol 9 No 1 (2026): June
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v9i1.243

Abstract

Poverty is a problem that often occurs and is a fundamental problem in almost all developing countries, including Indonesia. The Nusa Tenggara region consists of two administrative regions, namely the Provinces of West Nusa Tenggara (NTB) and East Nusa Tenggara (NTT) which have high poverty rates. The increase in the number of poor people was caused by several indicators such as environmental conditions, education, income, health, access to goods and services, and others. The purpose of this research is to determine the best method in the process of classifying poverty with the cluster analysis method. The methods used in this study are the average linkage and K-Means cluster analysis methods, as well as the silhouette index method in terms of cluster validation to obtain the best cluster analysis method. The data used is poverty data for the Nusa Tenggara Region in 2021 which includes four poverty sectors, namely employment, education, health, and housing and the environment. Based on the research results, the best method for grouping is the K-Means cluster analysis method by forming three clusters where the first cluster consists of 3 districts/cities, the second cluster consists of 22 districts/cities, and the third cluster consists of 7 districts/cities. The K-Means cluster analysis method is the best method with the highest silhouette index value of 0.28, higher than the average linkage method which obtained a silhouette index value of 0.27.
On the Iterated Cevian Triangle in Finite Euclidean Space Arfah, Arfah
Eigen Mathematics Journal Vol 9 No 1 (2026): June
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v9i1.336

Abstract

This paper investigates the iterative process of constructing Cevian triangles in a finite Euclidean plane. First, we prove that starting from an initial triangle, the process of iteratively taking Cevian triangles converges to a unique fixed point. Second, we show this convergence process is surjective onto the interior of the triangle; that is, for any target point in the interior, one can find an initial point whose sequence of iterated Cevian triangles converges to that target. Finally, we examine the limiting configuration of an infinite iteration and characterize a novel property intrinsic to the discrete nature of the finite geometric space, setting it apart from the classical real Euclidean case.
Analysis of Topological Indices in Unit Graphs of Modular Integer Rings Umam, Ashadul; Syarifudin, Abdul Gazir; Suwastika, Erma; Wardhana, I Gede Adhitya Wisnu
Eigen Mathematics Journal Vol 9 No 1 (2026): June
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v9i1.306

Abstract

Topological indices are numerical graph invariants that reflect structural properties of graphs and have broad applications in chemistry, algebra, and network analysis. This paper focuses on the analysis of several topological indices in the context of unit graphs associated with modular integer rings. In a unit graph, vertices represent ring elements, and two vertices are adjacent if their sum is a unit. We investigate and derive general formulas for six indices: the Narumi-Katayama index, the Forgotten index, the Atom-Bond Connectivity (ABC) index, the first and second Gourava indices, and the first Revan index. Two cases are considered for the ring of integers modulo $n$, namely when $n$ is a power of $2$ and when $n$ is an odd prime. The results offer a deeper understanding of the algebraic and combinatorial properties of unit graphs and contribute to the development of algebraic graph theory.
Penentuan Cadangan Asuransi Jiwa Last Survivor berdasarkan Metode Gross Premium Valuation (GPV) dengan Hukum De’Moivre Jefri, Rhanny Kirana; Anugrawati, Sri Dewi; Nurwahidah, Nurwahidah
Eigen Mathematics Journal Vol 9 No 1 (2026): June
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v9i1.326

Abstract

Insurance is one of the measures that can be used to prepare for various risks that can occur at any time. In the context of life insurance products, multiple life insurance is an efficient option because it is more economical than purchasing separate policies for two people with equivalent benefits. Unlike previous studies that focused on single life models using the GPV (Gross Premium Valuation) approach, this study develops an analysis of more complex multiple life insurance products, thereby providing a more representative picture of premium reserves for cases involving two insured parties. This study aims to formulate a mathematical model and conclude the results of prospective premium reserve calculations for last survivor whole life insurance using the GPV (Gross Premium Valuation) approach and De'Moivre's law De’Moivre This study uses a quantitative method with a documentation data collection technique, namely the 2019 Mortality Table IV data published by the Indonesian Life Insurance Association (AAJI). The results of this study show that the mathematical model of premium reserves for last survivor whole life insurance using the GPV (Gross Premium Valuation) approach and De'Moivre's law is ${_t}V^{GPV} = BA_{\bar{xy}} + U + PAG_{\bar{xy}} + A{\ddot{a}}_{\bar{xy}} + CA_{\bar{xy}} - G_{\bar{xy}}{\ddot{a}}_{\bar{xy}}$. However, when the insured ($y$) dies first, the mathematical model is ${_t}V^{GPV} = BA_{\bar{x}} + U + PAG_{\bar{xy}} + A{\ddot{a}}_{\bar{x}} + CA_{\bar{x}} - G_{\bar{xy}}{\ddot{a}}_{\bar{x}}$ while if the insured ($x$) dies first, the mathematical model is ${_t}V^{GPV} = BA_{\bar{y}} + U + PAG_{\bar{xy}} + A{\ddot{a}}_{\bar{y}} + CA_{\bar{y}} - G_{\bar{xy}}{\ddot{a}}_{\bar{y}}$. In addition, the results of the study show that there is a difference in the last survivor life insurance premium reserve between the conditions when both insured persons are still alive and when one of them dies, and that the use of De'Moivre's law results in a decreasing reserve pattern but ends up exceeding the promised benefits due to linear mortality assumptions so that the present value of the benefits does not fully decrease at the end of the coverage period. These findings indicate that the use of a uniform death distribution needs to be considered in order to produce more realistic premium reserves.
Peramalan Jumlah Perjalanan Wisatawan di Kota Pangkal Pinang: ARIMA vs. LSTM vs. Prophet” Hidayat, Muhammad Irfan; Kumala, Mei Dita
Eigen Mathematics Journal Vol 9 No 1 (2026): June
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v9i1.345

Abstract

Accurate forecasting of tourism demand is crucial for regional economic planning, yet existing studies often rely on univariate time-series models or single forecasting techniques without considering spatial interdependence among regions. This study proposes a correlation-based comparative forecasting framework to evaluate the performance of ARIMA, Long Short-Term Memory (LSTM), and Prophet in predicting domestic tourist trips in Pangkal Pinang City, Indonesia. Monthly data from January 2019 to July 2025 were obtained from Statistics Indonesia, and highly correlated neighboring regions were systematically selected using a heatmap correlation analysis to enhance model input relevance. After applying Min–Max normalization and an 80:20 train–test split, all models were evaluated using Root Mean Squared Error (RMSE) under identical experimental settings. The results indicate that Prophet consistently achieves the lowest RMSE, demonstrating superior capability in capturing non-linear dynamics, seasonal variability, and abrupt structural changes in tourism demand compared to ARIMA and LSTM. These findings provide empirical evidence that decomposable time-series models with automatic trend and seasonality handling offer distinct advantages over both classical statistical and deep learning approaches in medium-term tourism forecasting. The proposed framework contributes a concise, data-efficient, and replicable methodology that supports evidence-based tourism planning and strategic decision-making.
Axiomatization of a Fundamental System for Generalized Ambiguous Four–Degree Membership Function Set Theory Aji, Ali; Mshelia, Bello Inuwa; Haruna, Yusuf
Eigen Mathematics Journal Vol 9 No 1 (2026): June
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v9i1.356

Abstract

This paper presents the construction of an axiomatic system of Generalized Ambiguous Set Theory (AGAST)founded upon a four-valued logic, where the membership relation accepts four discrete degrees: True $(\alpha_A (x))$, Partially True $(\beta_A (x))$, Partially False $(\gamma_A (x))$, and Falsity $(\eta_A (x))$ membership degree functions, The contribution of this work is the rigorous adaptation of foundational Zermelo-Frankel set theory (ZFC) and Axiomatic Fuzzy Set Theory principles, including the Axiom of Extensionality and the Axiom Schema of Ambiguous Separation, to cohere within the four-degree semantics. Furthermore, the theory introduces the Anti-Classicality Axiom, which postulates the existence of sets exhibiting non-classical membership degrees.

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