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Majalah Ilmiah Matematika dan Statistika (MIMS)
Published by Universitas Jember
ISSN : 14116669     EISSN : 27229866     DOI : https://doi.org/10.19184
Core Subject : Education,
Mathematics
The aim of this publication is to disseminate the conceptual thoughts or ideas and research results that have been achieved in the area of mathematics and statistics. MIMS, focuses on the development areas sciences of mathematics and statistics as follows: 1. Algebra and Geometry; 2. Analysis and Modelling; 3. Graph Theory and Combinatorics; 4. Computer Science and Big Data; 5. Application of Mathematics and Statistics.
Arjuna Subject : Matematika - Matematika (Lain-Lain)
Articles 120 Documents
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Diagonalisasi matriks atas ring dengan metode pemfaktoran secara lengkap Nikita, Nikita; Suparwanto, Ari; Sutopo, Sutopo
Majalah Ilmiah Matematika dan Statistika Vol. 24 No. 2 (2024): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v24i2.35918

Abstract

Generally, discussion about diagonalization of matrices in linear algebra is a matrix over the field. This research presents the diagonalization of matrices over commutative rings. Previous studies have explained the diagonalization of the matrix over a commutative ring, but there are some shortcomings in it. Therefore, this paper will present a matrix diagonalization process that could overcome these shortcomings. This research proposes a method for diagonalization matrices where the characteristic polynomial splits completely over the image of a ring homomorphism. Furthermore, the diagonalization is done over ring localization, so that there are more commutative ring matrices which can be diagonalized in this way. Meanwhile, the sufficient condition for a matrix which can be diagonalized in this thesis is when the determinant of the matrix whose columns are the eigenvectors is regular. Furthermore, to show this diagonalization method applies in general, given a special matrix n × n which satisfies the sufficient condition. Keywords: Matrices, diagonalization, eigenvector, determinant, localizationMSC2020: 15A09, 15A18, 15A20,13B05,13B20
Fuzzy time series dalam meramalkan jumlah produksi karet di Sumatra Utara Arika, Arika; Daratullaila, Daratullaila; Sirait, Khairunnas Fadjriah; Sari, Riezky Purnama
Majalah Ilmiah Matematika dan Statistika Vol. 24 No. 1 (2024): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v24i1.35257

Abstract

Rubber (Hevea brasiliensis) belongs to the genus Heveadari familia Euphorbiaceae which is a tropical woody tree native to the amazon jungle. Rubber is one of the plantation crops that is very important for the economy in Indonesia. Rubber production in North Sumatra has increased every year. To find out whether the amount of rubber production in North Sumatra increases or decreases next year by forecasting the amount of rubber production and getting better forecasting results in the future. This estimate can use the fuzzy time series forecasting method. The fuzzy time series uses the fuzzy set theory as the basis for calculations and a concept used to forecast actual data formed with linguistic variables. The method used in predicting the amount of rubber production in North Sumatra is the fuzzy time series method with data from 1997 to 2021. And the result of forecasting rubber production in 2022 is 261997 with MAPE of 0.54%. Keywords: Forecasting, rubber production, fuzzy time seriesMSC2020: 62M10, 62M20, 62M86, 03E72
Modeling factors affecting poverty in Nusa Tenggara using the multivariate adaptive regression spline (MARS) method Arizal, Mulyasrihuda; Fitriyani, Nurul; Syechah, Bulqis Nebula
Majalah Ilmiah Matematika dan Statistika Vol. 24 No. 2 (2024): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v24i2.43167

Abstract

Poverty is still a fundamental problem in the economy of various regions or developing countries, including Indonesia. The Nusa Tenggara Islands are one of the regions in Central Indonesia, where East Nusa Tenggara Province is in 3rd place with 20.44%, and West Nusa Tenggara Province is in 8th place with 13.83%, the highest percentage of poor people in Indonesia. A study was conducted to model the factors that influence poverty in Nusa Tenggara and determine the factors that significantly affect the percentage of poverty in Nusa Tenggara. Poverty data caused by many predictor variables that interact with each other can be said to be high-dimensional data where the relationship between the response variable and the predictor variable does not show a specific pattern, so one of the appropriate nonparametric regression methods to use for this approach is the Multivariate Adaptive Regression Spline (MARS) method. The data used in this study is secondary data with 12 predictor variables. The results of this study indicate that the best model was the model with the values of basis function (BF) of 24, maximum interaction (MI) of 2, and minimum observation (MO) of one where this model has the minimum GCV value of 0.3523701. Keywords: Generalized cross-validation, multivariate adaptive regression spline, Nusa Tenggara Region, povertyMSC2020: 62G08
Penggerombolan provinsi di Indonesia berdasarkan instrumen akreditasi satuan pendidikan jenjang SMK menggunakan K-means dan average linkage Fahriya, Andina; Sembiring, Febryna; Susetyo, Budi
Majalah Ilmiah Matematika dan Statistika Vol. 24 No. 2 (2024): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v24i2.40822

Abstract

Improvement and updates need to be done in order to maintain the existence of a school. Accreditation is one of the references to assess the excellence of a school. There are several components used in the accreditation assessment included in the IASP, namely Graduate Quality, Learning Process, Teacher Quality, and School Management. Additionally, to determine which provinces have low, medium, or high IASP scores, clustering is performed on the IASP scores of those provinces. Cluster analysis is a method used to group research objects based on similarities in their characteristics. In this study, clustering was performed using the K-means and average linkage methods on the average IASP scores of vocational high schools (SMK) in 34 provinces in Indonesia. With the Elbow Criterion approach, four clusters were formed for each method. The results of Dunn Index showed that the average linkage method performed better in clustering compared to the K-Means method. Keywords: IASP, Cluster Analysis, K-Means, Average LinkageMSC2020: 62H30
GAMLSS application for modeling the level of open unemployment in East Java Maulidani, Noor Dyah; Tirta, I Made; Fatekurohman, Mohamat
Majalah Ilmiah Matematika dan Statistika Vol. 25 No. 1 (2025): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v25i1.51548

Abstract

This research analyzes the application of Generalized Additive Model for Location, Scale, and Shape (GAMLSS) using penalized spline smoothing and Rigby-Stasinopoulos (RS) algorithm for modeling open unemployment rate in East Java Province in 2022. Predictor variables in this research are labor force participation rate, average years of schooling, average wages, economic growth, and registered job vacancies. GAMLSS allows the estimation of several distribution parameters (location, scale, and shape) thereby providing a broader and more flexible approximation model. The number of parameters that can be estimated depends on the type of distribution that is suitable for the data. This research uses a penalized spline as a smoothing predictor variable for the nonparametric part. The RS algorithm is an iterative procedure developed for GAMLSS models and used to estimate model parameters efficiently. Several distributions were evaluated and Normal distribution was obtained as the most suitable with two parameters (𝜇,𝜎). The Normal distribution is chosen based on model evaluation standards Generalized Akaike Information Criterion (GAIC). The effectiveness of this model was further verified through significance test and stepwise procedure. The estimation results of the location parameter (𝜇) are modeled by economic growth, average years of schooling, and registered job vacancies with the identity link function, while the scale parameter (𝜎) is modeled by economic growth and average wage with the log link function.
Chaotic outbreak in discrete epidemic model with vaccination and quarantine interventions and limited medical resources Fahreza, Faizal Rifky; Hasan, Moh; Santoso, Kiswara Agung
Majalah Ilmiah Matematika dan Statistika Vol. 25 No. 1 (2025): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v25i1.53689

Abstract

The spread of infectious diseases can be analyzed dynamically using a discrete dynamic system. The characteristics of the infectious disease phenomenon are interesting to study as parameters considered in a dynamic system. Some of these include vaccination interventions, quarantine, or even an open condition such as limited medical resources. Analysis of a discrete epidemic model system with those three factors can be conducted to understand each of their impacts on the dynamics of disease spread within a population or even to determine the potential for a chaotic outbreak. In this study, an epidemiological model was formulated considering these three factors. Numerical simulations were also conducted to directly observe the influence of these three factors on the dynamics of disease spread. Additionally, efforts to control chaos were also implemented in the system. The limitation of medical resources affects the spread of diseases. Because the coverage of medical resources is limited, it can cause a high surge in cases within the population. This phenomenon of case surges can subsequently be mitigated by vaccination parameters such as vaccine efficacy and the rate of vaccine distribution within the population. Furthermore, the formulated system has the potential to exhibit chaotic behavior when the infection rate increases, in other words, the disease becomes an uncontrollable and unpredictable epidemic. Next, the thing that can be done to suppress this chaotic phenomenon is to directly intervene in the rate of disease spread within the population.
Pemodelan banyaknya kematian berdasarkan kasus konfirmasi COVID-19 di Indonesia, Malaysia, Thailand, dan Filipina menggunakan model linear tergeneralisasi Ha, Marlyn; Permana, Ferry Jaya; Yong, Benny
Majalah Ilmiah Matematika dan Statistika Vol. 25 No. 2 (2025): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v25i2.53694

Abstract

In early 2020, the COVID-19 disease, caused by the SARS-CoV-2 virus infection, became a global pandemic impacting the entire world, including Indonesia. To monitor the spread of COVID-19 and determine appropriate strategies to mitigate its impact, the World Health Organization (WHO) routinely reported confirmed case data and death case data due to COVID-19. Mathematical modeling can help understanding the relationship between the number of deaths based on daily confirmed cases. One simple mathematical model is the linear regression model. The linear regression model requires the assumption of homoscedasticity, and when this assumption fails, linear regression cannot be used. In this research, a generalized linear model (GLM) is used to address the shortcomings of the linear regression model. This research will predict the number of daily deaths based on daily confirmed case data using GLM based on historical data from Indonesia, Malaysia, Thailand, and Philippines. The functions used to describe the relationship between predictor and response variables include normal or Gaussian, Poisson, gamma, and negative binomial distributions. To evaluate whether the model fits the data, we used Akaike’s Information Criterion (AIC) and Bayesian Information Criterion (BIC). Additionally, the goodness of fit of the model in predicting the number of deaths is measured by finding the mean squared error (MSE). The best model is determined by considering the smallest AIC, BIC, and MSE values. The simulation results show that the GLM using the normal distribution is the best model in Indonesia, Malaysia, and Philippines, while the GLM using the negative binomial distribution is the best model in Thailand. Using the GLM, it was found that deaths occurred 14 days after a patient was confirmed with COVID-19 in Indonesia, 11 days in Malaysia, 12 days in Thailand, and 13 days in Philippines. Keywords: COVID-19, GLM, AIC, BIC, MSEMSC2020: 92C60, 62P10, 62J02, 62F10
Spatial modeling of hotel prices in the Yogyakarta city area using ordinary kriging and cokriging approaches Hannura Adriana; FAUZAN, Achmad Fauzan
Majalah Ilmiah Matematika dan Statistika Vol. 25 No. 2 (2025): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v25i2.53696

Abstract

Yogyakarta, renowned as one of Indonesia's most prominent tourist destinations, owes its appeal to its natural beauty, well-preserved environment, and rich cultural and historical heritage. Its reputation as a safe and comfortable destination has led to a consistent annual increase in tourist arrivals. Consequently, there is a growing demand for hotel accommodations that offer competitive pricing to avoid financial losses while meeting tourist expectations. Tourists often rely on ratings and reviews of hotel services and facilities, making these factors significant determinants of pricing strategies. This study aims to provide spatially informed pricing recommendations for potential hotel developments in Yogyakarta using kriging spatial interpolation methods. Two kriging approaches were employed: Ordinary Kriging (OK) and Cokriging (CK), incorporating hotel price and rating data as primary variables. The analysis identified the Exponential semivariogram model as optimal for OK and the Spherical semivariogram model as optimal for CK. Both methods predicted hotel prices around Yogyakarta City to range from IDR 300,000 to IDR 400,000 for locations farther from the city center. Among the two methods, CK demonstrated superior predictive performance, yielding lower Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE) values compared to OK. These findings highlight the potential of CK for providing accurate and actionable insights into hotel pricing strategies, offering valuable guidance for stakeholders considering investments in Yogyakarta’s thriving hospitality industry. Keywords: Cokriging, hotel price, interpolation, ordinary krigingMSC2020: 62H11
Pemodelan kerugian finansial pada gempa bumi megathrust Sulawesi Utara berdasarkan ukuran risiko expected shortfall Lengkas, Riski Ananda Putra; Azizah
Majalah Ilmiah Matematika dan Statistika Vol. 25 No. 2 (2025): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v25i2.53763

Abstract

Indonesia is one of the largest countries and is also the largest archipelagic country. Indonesia is also surrounded by large plates that cause eartquakes to occur very often. Earthquakes that occur cause financial losses that impact an area. This study aims to model the risk of financial losses due to the megathrust earthquake in North Sulawesi using the Earthquake Catastrophe (CAT) Model which has 4 modules consisting of hazard, inventory, vulnerability, and loss modules. This CAT Model allows structured analysis to identify potentian losses with the help of the Expected Shortfall (ES) risk measure. The result of this study indicate that 95th and 99th percentiles have large values, namely IDR 1,07 trillion and IDR 3,21 trillion. This finding indicates that the potential for extreme losses due to earthquakes in North Sulawesi is quite high, so risk mitigation is needed. Therefore, insurance companies need to allocate adequate reserves based on the expected shortfall risk measure and implement effective risk mitigation strategies. Keywords: CAT model, mega thrust earthquake, risk mitigation, expected shortfallMSC2020: 91G05
Perbandingan penerapan optimasi SGDM dan Adam pada model CNN dengan arsitektur VGG19 dan ResNet-50 dalam memprediksi penyakit paru-paru pneumonia Oktarina, Sachnaz Desta; Alpharofi, Deswita Nur; Hasanah, Delita Nur; Kurniawan, Rizky; Muzakki, Faiz Aji; Najdmuddin, Muhammad Tsaqif; Anisa, Rahma
Majalah Ilmiah Matematika dan Statistika Vol. 25 No. 2 (2025): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v25i2.53746

Abstract

Pneumonia is a leading cause of death among children under five, accounting for 14% of fatalities. Chest X-ray analysis is a key method for diagnosis, but many developing countries have only one radiologist per million people, making timely detection difficult. To address this challenge, Convolutional Neural Networks (CNN) offer a viable solution due to their ability to analyze visual data efficiently. This study evaluates two CNN architectures, VGG19 and ResNet-50, considering their effectiveness in pneumonia detection. Both models were trained using two different optimizers, SGDM and Adam, to determine the best combination for accurate classification. Results using test data indicate that VGG19 with the Adam optimizer achieves the highest accuracy at 90%, surpassing other models which recorded 62%, 77%, and 84% without overfitting. This highlights the potential of artificial intelligence driven diagnostic tools in bridging healthcare gaps and improving pneumonia detection in resource-limited settings. Keywords: Classification, CNN, Optimizer, PneumoniaMSC2020: 62

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