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INDONESIA
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 126 Documents
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Modeling of Economic Growth Rate in West Nusa Tenggara Province with Longitudinal Kernel Nonparametric Regression Zulhan Widya Baskara; Rizaldi, Muhammad; Fitriyani, Nurul; Baskara, Zulhan Widya
Eigen Mathematics Journal Vol 7 No 1 (2024): June
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v7i1.188

Abstract

Economic growth can indicate the success of economic development in people's lives, so it is essential to study the relationship between economic growth and factors that affect economic growth. Regression analysis is one of the most widely used statistical data analysis methods to determine the relationship pattern between the independent and dependent variables. Three methods can be used to estimate the regression curve, one of which is nonparametric regression. Economic growth data is one form of longitudinal data, with observations of independent subjects, with each subject being observed repeatedly over different periods. Kernel nonparametric regression model applications can be used for longitudinal data. This research aims to estimate the curve and get the best regression model. In this research, the smoothing technique chosen to estimate the nonparametric regression model for longitudinal data is the kernel triangle estimator, which can be obtained by minimizing the square of error using Weighted Least Squares (WLS) and selecting the optimum bandwidth using the Generalized Cross Validation (GCV) method. This study uses the economic growth rate in West Nusa Tenggara as the dependent variable and the human development index, population density, general allocation funds, local revenue, and labor force participation as independent variables. The result showed that the model is less accurate because of the low value of the coefficient for determination and the high value of the mean absolute percentage error (MAPE). This can be caused by the selection of bandwidth intervals that are too small.
Modeling of the Spread of Malaria in the Bangka Belitung Islands Province Using the SEIR Method Halim, Nikken; Putri, Marwah Hotimah Nada; Alviari, Irfaliani; Luthfiyah, Fadillah; Septiani, Hera; Prayanti, Baiq Desy Aniska
Eigen Mathematics Journal Vol 7 No 1 (2024): June
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v7i1.189

Abstract

Malaria is an infectious disease caused by plasmodium through the bite of the Anopheles sp. female mosquito. (Roach, 2012). Malaria disease which hit the Bangka Belitung Islands Province in 2005 experienced a spike, reaching 36,901 people out of 981,573 residents and claimed the lives of 12 local residents. In 2011, the Bangka Belitung Islands Province was declared an endemic area for malaria. This research aims to model and interpret the spread of malaria using the SEIR model and predict the spread of malaria using parameter estimates. The steps in analyzing the SEIR model on the spread of malaria are making assumptions, forming a SEIR model, determining the equilibrium point and analyzing the stability of the equilibrium point, determining the basic reproduction number, and carrying out a simulation of the SEIR model that has been obtained. The SEIR model is classified into 4 classes, namely Susceptible (susceptible individuals), Exposed (individuals who have symptoms), Infected (infected individuals), and Recovered (recovered individuals). The data used in this research is data on the number of Susceptible, Exposed, Infected, and Recovered malaria cases in 2022 obtained from the Bangka Belitung Islands Provincial Health Service. The SEIR mathematical model is used to calculate the equilibrium point and basic reproduction number. Based on the SEIR model simulation results, it was found that the susceptible population decreased from the 0th month to the 48th month. As for the exposed population, there were 9,623 people in month 0, but in this condition the population decreased drastically per month. Furthermore, for the infected population there were 129 people in month 0, but in this condition the number of infected decreased drastically per month along with the decrease in the exposed population. For individuals who recovered, there was a increase from the 0th month to the 48th month.
Solusi Numerik pada Persamaan Korteweg-De Vries Equation menggunakan Metode Beda Hingga Haizar, Maulana Rifky; Rizki, Miptahul; Robbaniyyah, Nuzla Af'idatur; Syechah, Bulqis Nebulla; Salwa, Salwa; Awalushaumi, Lailia
Eigen Mathematics Journal Vol 7 No 1 (2024): June
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v7i1.190

Abstract

The Korteweg-de Vries (KdV) equation is a nonlinear partial differential equation that has a key role in wave physics and many other disciplines. In this article, we develop numerical solutions of the KdV equation using the finite difference method with the Crank-Nicolson scheme. We explain the basic theory behind the KdV equation and the finite difference method, and outline the implementation of the Crank-Nicolson scheme in this context. We also give an overview of the space and time discretization and initial conditions used in the simulation. The results of these simulations are presented through graphical visualizations, which allow us to understand how the KdV solution evolves over time. Through analysis of the results, we explore the behavior of the solutions and perform comparisons with exact solutions in certain cases. Our conclusion summarizes our findings and discusses the advantages and limitations of the method used. We also provide suggestions for future research in this area.
Analisis Dinamik Model Predator-prey dengan Perilaku Anti Predator serta Efek Allee pada Prey Hady Rasikhun; Putra, M. Adib Jauhari Dwi; Robbi, Rizka Rizqi
Eigen Mathematics Journal Vol 6 No 2 (2023): December
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v6i2.191

Abstract

We explore a predator-prey model that incorporates both anti-predator behavior by the prey and the Allee effect, where population growth declines at low densities. Four equilibrium points emerge: extinction for both species (E0), two predator extinction points (E1 and E2), and one coexistence point for both populations (E3). While the stability of E0, E2, and E3 depends on the given parameters, E1 is always unstable. We then verified this analysis through numerical simulations using Runge-Kutta method in Python.
Solution of The Duffing Equation Using Exponential Time Differencing Method Illahi, Ramadian Ridho; Marzuki, Marzuki; Hudha, Lalu Sahrul
Eigen Mathematics Journal Vol 7 No 1 (2024): June
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v7i1.195

Abstract

To describe the spring stiffening effect that occurs in physics and engineering problems, Georg Duffing added the cubic stiffness term to the linear harmonic oscillator equation and is now known as the Duffing oscillator. Despite its simplicity, its dynamic behavior is very diverse. In this research, the Exponential Time Difference method is introduced to solve the Duffing oscillator numerically. To formulate the ETD method, we were using the integration factors. It is a function which, when multiplied by an ordinary differential equation, produces a differential equation that can be integrated. This method is an effective numerical method for solving complex differential equations, especially equations that have strong non-linearity The ETD method delivers highly accurate numerical solutions for the Duffing oscillator, with minimal discrepancy from the analytical results. Through parameter variation, the ETD method's applicability extends to diverse Duffing oscillator configurations.
Comparison of Several Univariate Time Series Methods for Inflation Rate Forecasting Salfina, Salfina; Hernanda, Yunissa; Silfiani, Mega
Eigen Mathematics Journal Vol 7 No 2 (2024): December
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v7i2.200

Abstract

Forecasting inflation is very crucial for a country because inflation is one of indicator to measure development of the country. This study aims to evaluate the effectiveness of three univariate time series methods i.e., ARIMA (Autoregressive Integrated Moving Average), Double Exponential Smoothing (DES), and Trend Projection (TP), in forecasting Indonesia’s monthly inflation rates using data from 2018 to 2022. The analysis identifies DES as the most accurate method, evidenced by its lowest Root Mean Square Error (RMSE) value of 2.9296, outperforming ARIMA and TP, which have RMSE values of 13.1479 and 3.47053, respectively. Consequently, DES was selected as the preferred model for forecasting inflation over the next 36 month, with the forecasts indicating a consistent downward trend in inflation throughout the year. While these findings highlight DES's effectiveness, the study also acknowledges limitations, including its reliance on univariate models that do not incorporate other economic variables, and the potential limitations of the dataset’s specific time frame. To address these limitations, future research should consider multivariate models, integrate machine learning techniques, and conduct scenario analyses to improve forecast accuracy and robustness. Despite these constraints, the study provides valuable insights into inflation forecasting in Indonesia, offering a practical tool for policymakers and contributing to more informed economic decision-making.
Forecasting Coffee Exports to the United States Using the Holt-Winters Exponential Method Achmadin, Wahyu Nur; Retnowardani, Dwi Agustin; Mashitasari, Dewi; Fatimah, Fita
Eigen Mathematics Journal Vol 7 No 1 (2024): June
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v7i1.202

Abstract

A study was conducted to estimate coffee exports to the United States using the Holt-Winters Exponential method. The aim of this research is to project coffee export activity over the next four periods. Data on coffee exports to the United States from 2000 to 2022 was obtained from the Indonesian Central Bureau of Statistics and used as a research object. The range of values used in this study is between 0.1 and 0.5 for α, between 0.1 and 0.5 for β, and between 0.1 and 0.9 for ϒ. The results of this research state that it is estimated that in 2023, Indonesia will export coffee to the United States amounting to 61,332.60 tons, in 2024 amounting to 60,661.50 tons, in 2025 amounting to 61,563.27 tons, and in 2026 amounting to 60,196.50 tons
Optimization of Classification Algorithms Performance with k-Fold Cross Validation Aprihartha, Moch. Anjas; Idham, Idham
Eigen Mathematics Journal Vol 7 No 2 (2024): December
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v7i2.212

Abstract

Supervised learning is a predictive method used to make predictions or classifications. Supervised learning algorithms work by building a model using training data that includes both independent and dependent variables. Several methods for building classification include Logistic Regression, Naive Bayes, K-Nearest Neighbor (KNN), decision tree, etc. The lack of capacity of a classification algorithm to generalize certain data can be associated with the problem of overfitting or underfitting. K-fold cross-validation is a method that can help avoid overfitting or underfitting and produce a algorithm with good performance on new data. This study will test the Naive Bayes, K-Nearest Neighbor (KNN), Classification and Regression Tree (CART), and Logistic Regression methods with k-fold cross-validation on two different datasets. The values of k set for cross-validation are 2, 3, 5, 7, and 10. The analysis results concluded that each classification algorithm performed best at 10-fold cross-validation. In DATA 1, the Naive Bayes algorithm has the highest average accuracy of 0.67 (67%) and the error rate is 0.33 (33%), followed by the CART algorithm, KNN, and finally logistic regression. While DATA 2, the KNN algorithm has the highest average accuracy of 0.66 (66%) and an error rate of 0.34 (34%), followed by the CART algorithm, Naive Bayes, and finally logistic regressionbut can be a reference if you want to predict the growth direction of the accommodation and food service activities sector.
Natural Cubic Spline Method as a Method in Constructing a Life Table in Gegelang Village West Lombok Fauzi, Andri Azmul; Ridwan, Lalu Muhammad; Agustini, Dwi; Putri, Desi Febriani; Tumilaar, Rinancy; Asmaidi, Asmaidi; Raming, Indriasri
Eigen Mathematics Journal Vol 7 No 1 (2024): June
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v7i1.215

Abstract

This research aims to reconstruct a life table based on real data obtained in Gegelang Village, West Lombok. The data used in this research is the population in 2016, the death rate in 2014-2018 and the birth rate in 2014-2018. The first step taken was to compile a rough life table using the partial data situation and full data situation methods. Both methods are included in the maximum likelihood method. After carrying out calculations, different life expectancy figures are obtained. The respective calculation results were 62.21 years for the partial data situation method and 73.07 years for the full data situation method. Next, a graduation is carried out using the natural cubic spline method on the life table obtained from a rough life table model calculation. The graphic model produced by the rough life table is fluctuating so it is necessary to graduate using the natural cubic spline method to obtain a monotonically decreasing graph. The life table model chosen for graduation is a life table whose life expectancy is close to the life expectancy of West Lombok Regency in 2015, namely 65.1 years. After graduation, the new life expectancy was found to be 66.92 years.
Algebraic Structures and Combinatorial Properties of Unit Graphs in Rings of Integer Modulo with Specific Orders Lestari, Sahin Two; Dewi, Putu Kartika; Wardhana, I Gede Adhitya Wisnu; Suparta, I Nengah
Eigen Mathematics Journal Vol 7 No 2 (2024): December
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v7i2.235

Abstract

Unit graph is the intersection of graph theory and algebraic structure, which can be seen from the unit graph representing the ring modulo n in graph form. Let R be a ring with nonzero identity. The unit graph of R, denoted by G(R), has its set of vertices equal to the set of all elements of R; distinct vertices x and y are adjacent if and only if x + y is a unit of R. In this study, the unit graph, which is in the ring of integers modulo n, denoted by G(Zn). It turns out when n is 2^k, G(Zn) forms a complete bipartite graph for k∈N, whereas when n is prime, G(Zn) forms a complete (n+1)/2-partites graph. Additionally, the numerical invariants of the graph G(Zn), such as degree, chromatic number, clique number, radius, diameter, domination number, and independence number complement the characteristics of G(Zn) for further research.

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