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Jl. Prof. Dr. Ing. B. J. Habibie, Moutong, Tilongkabila, Kabupaten Bone Bolango, Gorontalo, Indonesia
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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 Model of Coastline Changes in the Ujung Pangkah Gresik Using the Polynomial Lagrange Approach Hendrata Wibisana; Primasari Cahya Wardhani; Novie Handajani
Jambura Journal of Mathematics Vol 5, No 1: February 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (6898.664 KB) | DOI: 10.34312/jjom.v5i1.17077

Abstract

Ujung Pangkah Gresik is an area where there is an estuary of a vast river, the Bengawan Solo river. This area annually sends sediment loads transported by the Bengawan Solo river to the Ujung Pangkah estuary so that gradually accumulation occurs, which results in changes in the morphology of the coast on the edge of the Ujung Pangkah coast, Gresik. This study seeks to see the side of shoreline changes on the Ujung Pangkah coast for five years. Then take the change model as a mathematical model that can describe the speed of shoreline change per year using the Lagrange polynomial interpolation method for degrees 1, degrees 2, and degrees 3. The results of shoreline changes that occur are obtained by the Lagrangge polynomial algorithm of degree 3 with R2 of 0.3747 which has a better correlation than degree 1 (0.0313) and degree 2 (0.3741). The results of this study obtained a mathematical model with a Lagrange polynomial approach where degree 3 has the best correlation among other models. This study concludes that by using a mathematical model, an overview of the process of change or natural phenomena can be obtained, where the existing model can predict future changes in the existing coastline.
Peramalan Return Saham Menggunakan Model Integrated Moving Average Rizki Apriva Hidayana; Budi Nurani Ruchjana
Jambura Journal of Mathematics Vol 5, No 1: February 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (3360.988 KB) | DOI: 10.34312/jjom.v5i1.17381

Abstract

A popular investment that is in great demand among investors is stocked. Stocks are another type of financial instrument offering returns but carrying a higher risk level. Price time series are more difficult to manage than return time series. To equip investors with the knowledge to forecast future stock prices, mathematical models can be used to simulate stock price fluctuations. The time series method, especially the Integrated Moving Average (IMA) model, is a model that can be used to observe changes in stock prices. The Integrated Moving Average (IMA) model will be used in this study to simulate stock returns. The Integrated Moving Average (IMA) model is a Moving Average model that is carried out with a differencing process or an Autoregressive Integrated Moving Average model with a value of Autoregressive being zero. This study uses secondary data simulations from secondary sources, such as data on daily business stock prices for one year, to conduct a literature review and test experiments. The Integrated Moving Average (IMA) model is used in data processing, especially to test the differencing data process. The results obtained are the IMA (1,1) model with the following equation Zˆt = Zt-1 + 0, 5782at-1, which can be used to anticipate future stock returns. Based on these results, it is expected that investors can predict the value of shares within a certain period of time.
Optimasi Portofolio Saham Syariah Menggunakan Model Indeks Tunggal dan VaR Berbasis GUI Matlab Lindrawati Abdjul; Resmawan Resmawan; Agusyarif Rezka Nuha; Nurwan Nurwan; Djihad Wungguli; La Ode Nashar
Jambura Journal of Mathematics Vol 5, No 1: February 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjom.v5i1.18570

Abstract

Sharia-based investment is an investment by the community to obtain profits in accordance with Islamic principles and law. This study aims to calculate the optimal portfolio return value using the Single Index Model, calculate risk with VaR (Value at Risk), and then implement it with Matlab’s GUI (Graphical User Interface). The data used is closing stock price data on the JII (Jakarta Islamic Index) using 30 stocks for two consecutive years. Furthermore, these stocks are selected which have a positive average return value. The study results show that 14 stocks are candidates for optimal portfolios with positive return values, namely: ACES, ADRO, ANTM, BRPT, BTPS, CTRA, EXCL, INCO, MDKA, MNCN, SCMA, TPIA, UNTR, and WIKA. Then the optimal portfolio of the 14 stocks is determined using the Single Index Model considering the ERB (Excess Return to Beta) value ≥ cut-off point value (C*). Based on the value, 4 shares were obtained that belong to the optimal portfolio, namely: MDKA, BRPT, BTPS, and ANTM. Furthermore, VaR calculations are performed on the 4 optimal portfolios to obtain optimum VaR consistency values with 500 repetitions. The VaR calculation results with a 95% confidence level show that the average VaR result is in the range of -0.14704 to -0.3420 so that when investors invest in 4 optimal stocks, the losses experienced by investors are no more than 34%.
Near-Modul Kuat Faktor Meryta Febrilian Fatimah; Darmawati Darmawati
Jambura Journal of Mathematics Vol 5, No 1: February 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjom.v5i1.17595

Abstract

Near-ring is a generalization of ring. In ring theory, let R be a ring over addition and multiplication operation with unity element and G be a commutative group under addition operation. Then G together with scalar multiplication of R and holds several axioms called module over ring. Let N be a near-ring, here we can construct the module over near-ring called near-module. We have three definitions of module over near-ring, such that, near-module, modified near-module, and strong near-module. Then we showed that strong near-module can be constructed into strong near-module factor as well as module factor in G. Furthermore, we generalized the fundamental theorem of homomorphism in module over ring to strong near-module over strong near-ring.
Analisis Autokorelasi Spasial Global dan Lokal Pada Data Kemiskinan Provinsi Bali Windy Lestari; Adika Setia Brata; Alfian Anhar; Suci Rahmawati
Jambura Journal of Mathematics Vol 5, No 1: February 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjom.v5i1.18681

Abstract

Poverty is a crucial problem that often occurs in Indonesia, including in the province of Bali. The poverty rate rate in Bali has increased significantly over the last 3 years, so further analysis is needed so that this poverty rate can be reduced. The pattern of poverty between regions is different because it depends on the geographical and socio-cultural conditions in each area. The effect of location on poverty cases can be identified by global and local spatial autocorrelation methods. This study aimed to analyze the spatial autocorrelation of poverty data in Bali Province using the global autocorrelation test with the Moran’s and Geary’s C indices as well as the local spatial autocorrelation test with the Local Indicator of Spatial Association (LISA) and Getis-Ord G to obtain an overview of the spatial distribution of poverty data. Based on the global autocorrelation test, it is concluded that using Moran’s index there is a negative spatial autocorrelation in the 2020-2022 data for a=10%. Similar results were also obtained when using the Geary’s C test. In the local autocorrelation test using LISA, it was found that districts had negative spatial autocorrelation, namely in 2020 Buleleng Regency (high-low) and Klungkung (low-low), for 2021 there is Buleleng Regency (high-low) and Jembrana (low-low), while for 2022 only Buleleng Regency (high-low) has negative spatial autocorrelation. For local autocorrelation testing with the Getis-Ord G test, it was found that there were no districts/cities that showed spatial grouping or that there was no spatial autocorrelation locally.
Peramalan Data Cuaca Ekstrim Indonesia Menggunakan Model ARIMA dan Recurrent Neural Network Hikmah Hikmah; Asrirawan Asrirawan; Apriyanto Apriyanto; Nilawati Nilawati
Jambura Journal of Mathematics Vol 5, No 1: February 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (5265.505 KB) | DOI: 10.34312/jjom.v5i1.17496

Abstract

Extreme weather modeling is a challenge for modeling experts in Indonesia and the world. Extreme weather prediction is a complex problem because the chances of it happening are very small, so the developed models often have a low level of accuracy. The purpose of this research is to combine the classic model, Autoregressive Integrated Moving Average (ARIMA), recurrent neural network (RNN) model using Adam and SGD estimation (RNN-Adam and RNN-SGD) with the reLU, tanh, sigmoid and gaussian activation functions. In addition, the ARIMA-RNN mix model was also demonstrated in this study. These models are applied to monthly period extreme weather data obtained from the Meteorology, Climatology and Geophysics Agency (BMKG) of West Sulawesi Province which are converted into training data and test data. The RMSE value is used to see the level of prediction accuracy in both training data and test data. Based on the research results, the best model obtained for modeling Indonesia’s extreme weather is the ARIMA-RNN-Adam mix model with the reLU activation function based on the RMSE value on the training and test data. At n = 50, the smallest RMSE and MSE values of the third model are the ARIMA-RNN-Adam model which is 0.23212 using the reLU activation function, then the ARIMA-RNN-SGD model which is 0.25432 with the same activation function, while the ARIMA value is 0.3270. At n=100 it can be seen that the smallest RMSE and MSE values of the three models are the ARIMA-RNN-Adam model which is equal to 0.25149 using the reLU activation function, then the ARIMA-RNN-SGD model which is equal to 0.25256 with the same activation function, while the ARIMA value is 0.2644.
Perluasan Masalah Isoperimetrik pada Bangun Ruang Andri Setiawan; Denny Ivanal Hakim; Oki Neswan
Jambura Journal of Mathematics Vol 5, No 2: August 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjom.v5i2.20534

Abstract

In this paper, several extensions of the isoperimetric problem in solid figures are explored, focusing on oblique and right prisms with rectangular, right-angled triangular, and regular hexagonal bases. The objective of this research is to find the prism with the largest volume while keeping the surface area constant. Through manipulations of algebra and simple trigonometry, evidence is obtained that a right prism provides a larger volume than an oblique prism if their surface areas are equal. By utilizing partial derivatives of a two-variable function and the Lagrange multiplier method, conditions for the side lengths are derived to obtain the prism with the maximum volume. The results show that a cube is the solution to the isoperimetric problem, meaning it has the largest volume among prisms with rectangular bases, while for the isoperimetric solution on prisms with right-angled triangular bases, the base of the prism must be an isosceles right-angled triangle. A regular hexagonal prism has a larger volume than prisms with rectangular and right-angled triangular bases if their surface areas are the same.
Dinamika dan Stabilitas Populasi pada Model Penyebaran COVID-19 dengan Vaksinasi dan Migrasi Penduduk Resmawan Resmawan; Lailany Yahya; Agusyarif Rezka Nuha; Sri Meylanti S. Ali
Jambura Journal of Mathematics Vol 5, No 2: August 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjom.v5i2.19992

Abstract

This article discusses the mathematical model of the spread of COVID-19 by considering vaccination and population migration. The former model is analyzed by determining the equilibrium point, basic reproduction number, analyzing the stability of the equilibrium point, sensitivity analysis, and accompanied by numerical simulation. Analysis of the stability of disease-free and endemic equilibrium points using the Routh-Hurwitz Criteria and the Castillo-Chaves and Song theorems. The results of the analysis show that there are two equilibrium points, namely a disease-free equilibrium point (T1), which is locally asymptotically stable when R0 1, and an endemic equilibrium point (T2), which is locally asymptotically stable when R0 1. Furthermore, the sensitivity analysis showed that the most sensitive parameters to changes in the basic reproduction number were the emigration rate parameter (m2) and the infection probability parameter after contact between infected and susceptible individuals without vaccination (h). In addition, the numerical simulation results show that the sensitive parameter values, namely m2, h, zse, g, and # have a significant effect on the basic reproduction numbers. Suppressing the chance of infection in susceptible individuals and the rate of contact between susceptible and exposed individuals, as well as increasing the number of individuals who emigrate and who are vaccinated, can reduce the transmission of COVID-19.
Perbandingan Metode KNN, Naive Bayes, dan Regresi Logistik Binomial dalam Pengklasifikasian Status Ekonomi Negara N. K. Kutha Ardana; Ruhiyat Ruhiyat; Nurfatimah Amany; Teofilus Kevin Irawan; Raymond Raymond; Rizalius Karunia; Syifa Fauzia
Jambura Journal of Mathematics Vol 5, No 2: August 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjom.v5i2.21103

Abstract

The classification of a country's economic status as developed or developing often involves factors such as life expectancy and its underlying variables. This research aims to compare the performance of three machine learning algorithms, namely KNN (K-Nearest Neighbors), naive Bayes, and binomial logistic regression, in classifying the economic status of countries as developed or developing. The data used in this study is "Life Expectancy (WHO) Fixed," obtained from the Kaggle website. The first statistical analysis conducted was Principal Component Analysis (PCA) using 16 predictor variables. PCA resulted in three principal components capable of explaining 71.41% of the variance, which were subsequently used in the KNN, naive Bayes, and binomial logistic regression methods. The analysis results from the KNN, naive Bayes, and binomial logistic regression methods produced F1-scores of 100\%, 98.19%, and 97.36%, respectively.
Information Retrieval Performance in Text Generation using Knowledge from Generative Pre-trained Transformer (GPT-3) Kaira Milani Fitria
Jambura Journal of Mathematics Vol 5, No 2: August 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjom.v5i2.20574

Abstract

The rise of advanced language models like GPT-3 and text generation has witnessed remarkable progress. However, leveraging the vast amount of knowledge within these models to enhance information retrieval performance remains an area that needs to be explored. This research used Artificial Intelligence, specifically the OpenAI GPT-3 language model, to create an application to help make written content. This research investigates the impact of incorporating GPT-3's knowledge into text generation processes and evaluates its influence on information retrieval tasks. Several features in text generation generate text that requires exact information, such as specifications for a product and accurate descriptions of a job or product, which are included in the concept of information retrieval in text creation by language models. The research used the few-shot learning method in the GPT-3 language model. The generated responses are then evaluated using established information retrieval metrics such as precision, recall, and F1-score. The findings of this research reveal the effectiveness of utilizing GPT-3's knowledge in enhancing information retrieval performance. The generated responses demonstrate improved relevance to user queries, resulting in the same performance precision and recall scores compared to other paid text generator websites. Application results are testing in capabilities of retrieving some information. Application capabilities tested on other commercial text generator engines. The test results obtained BERTscore 86\% (precision), 88\% (recall), and 87\% (F1-Score). 

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