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Jambura Journal of Mathematics
Published by Universitas Negeri Gorontalo
ISSN : 26545616     EISSN : 26561344     DOI : https://doi.org/10.34312/jjom
Core Subject : Education,
Mathematics
Jambura Journal of Mathematics (JJoM) is a peer-reviewed journal published by Department of Mathematics, State University of Gorontalo. This journal is available in print and online and highly respects the publication ethic and avoids any type of plagiarism. JJoM is intended as a communication forum for mathematicians and other scientists from many practitioners who use mathematics in research. The scope of the articles published in this journal deal with a broad range of topics, including: Mathematics; Applied Mathematics; Statistics; Applied Statistics.
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Articles 165 Documents
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Mathematical Analysis of Tuberculosis Transmission Model with Multidrug and Extensively Drug-resistant Incorporating Chemoprophylaxis Treatment Kitaro, Damtew Bewket; Bole, Boka Kumsa; Rao, Koya Purnachandra
Jambura Journal of Mathematics Vol 6, No 1: February 2024
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v6i1.22127

Abstract

Tuberculosis has remained the principal cause of mortality worldwide, and one of the major sources of concern is drug-resistant TB. The increasing emergence of extensively drug-resistant and multidrug-resistant TB has further increased the TB epidemic. In this current work, we suggest a model to study the transmission of TB with extensively drug-resistant and multidrug-resistant compartments, incorporating chemoprophylaxis treatment. In the theoretical analysis, the concept of the next-generation matrix and the Jacobian method are applied to obtain a formula that states the reproductive number. The existence of endemic and disease-free equilibrium points was checked, and their stability has been analyzed using the Lyapunov method. The qualitative-based analysis indicated the local asymptotic stability of the disease-free-state for R0 1, whereas the endemic state is globally asymptotically stable if R0 1. Moreover, sensitivity analysis was carefully done using normalized forward sensitivity, and numerical simulation was carried out. Based on the results of numerical simulation and sensitivity analysis, chemoprophylaxis treatment was found to drastically minimize the progression of exposed individuals to infectious classes and also reduce the progression to extensively drug-resistant and multidrug-resistant classes, which decreases disease transmission.
Forecasting the Rupiah Exchange Rate Influenced by Several Factors Using the Improve Grey Model (1,3) Pratiwi, Dian Meilin; Firdaniza, Firdaniza; Kusuma, Dianne Amor
Jambura Journal of Mathematics Vol 7, No 1: February 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i1.27954

Abstract

The rupiah exchange rate is one of the important indicators of a country's economic stability, but the rupiah exchange rate often fluctuates following the factors that influence it. Forecasting the rupiah exchange rate is very important for economic planning, it helps the government make monetary policy decisions to maintain the stability of the rupiah exchange rate. Common methods used to forecast the rupiah exchange rate are ARIMA, FTS Markov Chain, and exponential smoothing. These methods are widely used to show the relationship between variables, but these methods have the disadvantage that they must meet the assumptions of data patterns. The contribution of this research is the use of the improve Grey model (1,3) predict the rupiah exchange rate in 2024, which is influenced by inflation and the balance of payments. The improve Grey model (1,3) was chosen because it does not require data distribution assumptions and can consider several external factors, thus providing more specific results for certain fields. The improve Grey model (1,3) uses the Grey model (1,1) to calculate the parameter values of the independent variables in the calculation of the improve Grey model (1,3) whitening equation. The calculation of the improve Grey model (1,3) whitening equation is calculated using a first-order ordinary differential equation. The use of the improve Grey (1,3) model for forecasting the rupiah exchange rate is considered accurate based on the Mean Absolute Percentage Error (MAPE) value. The rupiah exchange rate influenced by inflation and the balance of payments using the improve Grey model (1,3) for 2024 is predicted to increase from the previous year to Rp. 18.076, which indicates a weakening in value. This weakening has a positive impact on the balance of payments and a negative impact on inflation.
Klasifikasi Aljabar Lie Forbenius-Quasi Dari Aljabar Lie Filiform Berdimensi ≤ 5 Pratiwi, Putri Nisa; Kurniadi, Edi; Firdaniza, Firdaniza
Jambura Journal of Mathematics Vol 6, No 1: February 2024
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v6i1.22481

Abstract

In this research, we studied quasi-Frobenius Lie algebras and filiform Lie algebras of dimensions â‰¤ 5 over real field. The primary objective of this research is to classify the classification of filiform Lie algebras of dimensions â‰¤ 5 into quasi-Frobenius Lie algebras. The method employed in this research involves constructing a skew-symmetric 2-form in real Lie algebra, which also a nondegenerate 2-cocycle. The outcomes of this research reveal that there exists a class of filiform Lie algebras of dimensions $\le 5$ that can be classified as a quasi-Frobenius real Lie algebra. Furthermore, this research can be developed to classify higher dimensional filiform Lie algebras as quasi-Frobenius real Lie algebras.
Comparison of Seasonal ARIMA and Support Vector Machine Forecasting Method for International Arrival in Lombok MY, Hadyanti Utami; Setyowati, Silfiana Lis; Notodiputro, Khairil Anwar; Angraini, Yenni; Mualifah, Laily Nissa Atul
Jambura Journal of Mathematics Vol 6, No 2: August 2024
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v6i2.26478

Abstract

Seasonal Autoregressive Integrated Moving Average is a statistical model designed to analyze and forecast data with that shows seasonal patterns and trends. Support Vector Machine (SVM) is a machine learning-based technique that can be used to forecast time series data. SVM uses the kernel tricks to overcome non-linearity problems, whereas The SARIMA model is well-suited for data that exhibit seasonal fluctuations that repeat over time. Lombok International Airport is the main gateway to West Nusa Tenggara and has become a symbol of tourism growth in the region. Time series analysis is a very useful tool in determining patterns and forecasting the number of international arrivals at Lombok International Airport within a certain period. This study aims to compare the SARIMA model and SVM which can read non-linear patterns in the number of international arrivals at Lombok International Airport. After obtaining the SARIMA and SVM models, the two models are evaluated using test data based on the smallest RMSE value. The SVM model with a linear kernel trick provides the smallest RMSE when compared to SARIMA with SVM RMSE is 238,655. While the best model in Seasonal ARIMA is SARIMA (3,1,0)(1,0,0)12, the forecasting results show SARIMA is better in the forecasting process for the next 10 months.
Efektivitas Metode Hibrida ARIMA-MLP untuk Peramalan Nilai Tukar Petani Mulyawati, Saffanah Nur Elvina; Kartikasari, Mujiati Dwi
Jambura Journal of Mathematics Vol 6, No 1: February 2024
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v6i1.23944

Abstract

The agricultural sector remains a crucial pillar of Indonesia's economy, making the most significant contribution. Still, the situation of farmers, primarily the elderly, indicates physical limitations and low income leading to high poverty levels, coupled with fluctuations in the Farmer Exchange Rate (FER) annually tending to decline in D.I. Yogyakarta, indicating losses due to increased production costs. This research aims to assess the effectiveness of the Hybrid Autoregressive Integrated Moving Average (ARIMA) – Multilayer Perceptron (MLP) method in forecasting NTP in D.I. Yogyakarta. This is based on the analysis of comparing the accuracy values of forecasts using Mean Absolute Percentage Error (MAPE) evaluation or through visualizing the forecast graphs generated between the ARIMA and Hybrid ARIMA-MLP methods. The combination (hybrid) of ARIMA and MLP methods addresses the complexity of time series, where ARIMA anticipates NTP changes by handling linear patterns. At the same time, MLP improves forecast accuracy by managing more complex patterns (both linear and nonlinear). Thus, it can provide more accurate information about the welfare development of farmers. The results show that the Hybrid ARIMA-MLP method is significantly better than the individual ARIMA method, with the obtained model being Hybrid ARIMA-MLP (12-5-10-2) and an accuracy of 99.993%.
Perbandingan Value at Risk dan Expected Shortfall pada Portofolio Optimal menggunakan Metode Downside Deviation Nugrahaeni, Indah; Perdana, Hendra; Satyahadewi, Neva
Jambura Journal of Mathematics Vol 6, No 2: August 2024
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v6i2.24326

Abstract

Portfolio formation is one of the strategies that investors can do to get the best results Portfolio formation can use the Downside Deviation method. The optimal portfolio with this method uses downside deviation and sets the return below the benchmark as a measure of risk. Every optimal portfolio certainly cannot be separated from risk. To measure risk, you can use the Value at Risk (VaR) and Expected Shortfall values. This study aims to form an optimal portfolio using the Downside Deviation method and continued by comparing the possible losses that occur from the formed portfolio using the VaR and Expected Shortfall values. The data used in this study is the daily closing price data of LQ-45 Index stocks in the banking sector in the period February-June 2023. From the stock data, data selection is carried out by selecting stocks that have a positive expected return and are normally distributed. Then, the optimal portfolio formation stage is continued using the Downside Deviation method and comparing the possible risks formed with the VaR and Expected Shortfall values. The results of this study show that the optimal portfolio with the Downside Deviation method consists of four stocks, namely with the stock codes BRIS.JK, BBRI.JK, BBNI.JK, and BBCA.JK. This study uses a case example by investing capital of Rp100,000,000 with a one-day time period and three levels of confidence, namely 90%, 95%, and 99%. Based on the comparison of the risk value of the portfolio formed using VaR and Expected Shortfall, it is shown that the possible risk with the Expected Shortfall method is greater than the VaR value. Therefore, Expected Shortfall is better in estimating the maximum risk.
Comparative Study in Controlling Outliers and Multicollinearity Using Robust Performance Jackknife Ridge Regression Estimator Based on Generalized-M and Least Trimmed Square Estimator Saputri, Gustina; Herawati, Netti; Ruby, Tiryono; Nisa, Khoirin
Jambura Journal of Mathematics Vol 6, No 2: August 2024
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v6i2.24828

Abstract

Regression analysis is one of the statistical methods used to determine the causal relationship between one or more explanatory variables to the affected variable. The problem that often occurs in regression analysis is that there are multicollonity and outliers. To deal with such problems can be solved using ridge regression analysis and robust regression. Ridge regression can solve the problem of multicollinearas by assigning a constant k to the matrix Z′Z. But in this method the resulting bias value is still high, so to overcome this problem, the jackknife ridge regression method is used. Meanwhile, to overcome outliers in the data using robust regression methods which have several estimation methods, two of which are the Generalized-M (GM) estimator and the Least Trimmed Square (LTS) estimator. The aim of the study is to solve the problem of multicollinearity and outliers simultaneously using robust jackknife ridge regression method with GM estimators and LTS estimators. The results showed that the robust ridge jackknife regression method with LTS estimator can control multicollinearity and outliers simultaneously better based on MSE, AIC and BIC values compared to the robust ridge jackknife regression method with GM estimators. This is indicated by the value MSE = -6.60371, AIC = 75.823 and BIC = 81.642 on LTS estimators that are of lower value than GM estimators.
Optimizing Random Forest Parameters with Hyperparameter Tuning for Classifying School-Age KIP Eligibility in West Java Setyowati, Silfiana Lis; Qalbi, Asyifah; Aristawidya, Rafika; Sartono, Bagus; Firdawanti, Aulia Rizki
Jambura Journal of Mathematics Vol 7, No 1: February 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i1.28736

Abstract

Random Forest is an ensemble learning algorithm that combines multiple decision trees to generate a more stable and accurate classification model. This study aims to optimize Random Forest parameters for classifying school-age students' eligibility for the Kartu Indonesia Pintar (KIP) in West Java, based on economic factors. The research uses secondary data from the 2023 National Socio-Economic Survey (SUSENAS) of West Java, with a sample size of 13,044 individuals. To address class imbalance, Synthetic Minority Oversampling Technique (SMOTE) is applied. Hyperparameter tuning through grid search identifies the optimal combination of parameters, including the number of trees (ntree), random variables per split (mtry), and terminal node size (node_size). Model performance is evaluated using balanced accuracy, sensitivity, and specificity. Results indicate that the optimal parameters (mtry = 5, ntree = 674, node_size = 26) yield a balanced accuracy of 65.47%. Significant variables include PKH status, floor area of the house, source of drinking water, and building material type. The model accurately identifies students in need of educational assistance. In conclusion, optimizing Random Forest parameters improves the accuracy of KIP eligibility classification, supporting educational equity policies in West Java. These findings provide a foundation for developing more effective beneficiary selection systems for educational aid.
Group of All Taxicab Isometries: A Combinatorial Approach Neswan, Oki; Sumartono, Harry
Jambura Journal of Mathematics Vol 6, No 1: February 2024
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v6i1.23789

Abstract

In this work, we give a more thorough and exhaustive proof of the set of all isometries in taxicab geometry using a combinatorial approach. We show that isometries preserving taxicab distance while leaving the origin fixed are uniquely determined by how they permute the vertices of circles. Then, we use this principle to identify all isometries in taxicab geometry.
Implementasi CNN-BiLSTM untuk Prediksi Harga Saham Bank Syariah di Indonesia Mushliha, Mushliha
Jambura Journal of Mathematics Vol 6, No 2: August 2024
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v6i2.26509

Abstract

Stock price forecasting plays a crucial role in stock investment. Accuracy in predicting stock prices can provide significant financial benefits and help reduce investment risks. Stock price data are time series with high-frequency characteristics, non-linearity, and long memory, which makes stock price prediction a complex challenge. This research proposes a method for predicting the stock prices of Islamic banks in Indonesia using CNN-BiLSTM. This method aims to improve prediction accuracy by utilizing the feature extraction capabilities of CNN and the ability of BiLSTM to understand the temporal sequences of stock data. The data used in this research are the closing stock prices of Bank Syariah Indonesia (BSI), Bank Tabungan Pensiunan Negara Syariah (BTPN Syariah), and Bank Panin Dubai Syariah (PDSB) from January 2, 2020, to July 4, 2024. Testing these three stocks yielded MAPE values of 2.376%, 2.092%, and 0.629%, respectively. The study results show that the CNN-BiLSTM prediction model produced has very good accuracy in predicting stock prices.

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