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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 17 Documents
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Search results for , issue "Vol 6, No 1: February 2024" : 17 Documents clear
Efek Perlindungan Mangsa dan Daya Dukung Variabel pada Sistem Mangsa-Pemangsa dengan Fungsi Respon Beddington-DeAngelis Hanifah, Aisyiah Kholifatul; Abadi, Abadi
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.v6i1.24288

Abstract

Several species in the world have experienced extinction. To save species from extinction, a system needs to be formulated, one of which is protecting prey. Changes in physical and biological processes also have a role in the environment, namely resulting in dynamically changing carrying capacity. The rate of prey consumption by the average predator, i.e. the response function is also important in the system formulation. In this study, a prey-predator system was constructed with a Beddington-DeAngelis response function that considers prey protection and variable carrying capacity as well as a predation process that takes into account the predator population. In this research, the equilibrium point for prey-predator extinction, predator extinction, and coexistence was determined and then continued to analyze its stability. With a large prey protection value, the predator extinction equilibrium point is asymptotically stable and the coexistence equilibrium point is asymptotically stable, if and only if within a certain range of prey protection parameter values. In addition, simulations were carried out and it was concluded that at certain prey protection values, changes occurred in the stability of the system which depended on the limits of its carrying capacity.
Struktur Simplektik pada Aljabar Lie Affine aff(2,R) Queency, Aurillya; 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.v6i1.23254

Abstract

In this research, we studied the affine Lie algebra aff(2,R). The aim of this research is to determine the 1-form in affine Lie algebra aff(2,R) which is associated with its symplectic structure so that affine Lie algebra aff(2,R) is a Frobenius Lie algebra. Realized the elements of the affine Lie algebra aff(2,R) in matrix form, then calculated the Lie brackets and formed the structure matrix of the affine Lie algebra aff(2,R). 1-form of the affine Lie algebra aff(2,R) is obtained from the determinant of the structure matrix of the affine Lie algebra aff(2,R). Furthermore, proved that the 2-form is symplectic and related to the 1-form. The result obtained is that the affine Lie algebra aff(2,R) has 1-form α=ε_12^*+ε_23^* on aff(2,R)^* which is related to its symplectic structure, β=ε_11^*∧ε_12^*+ε_12^*∧ε_22^*+ε_21^*∧ε_13^*+ε_22^*∧ε_23^* such that the affine Lie algebra aff(2,R) is a Frobenius Lie algebra. For further research, it can be developed into an affine Lie algebra with dimensions n(n+1).
Implementasi Penggunaan Generalisasi Thinning Process pada Penduga Fungsi Ragam Proses Poisson Periodik Majemuk Abdullah, Syarif; Mangku, I Wayan; Mursyidah, Himmatul; Huda, Mifathul; Ikhsan, Fajri; Chasanah, Sri Istiyarti Uswatun
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.v6i1.22491

Abstract

This article implements the thinning process algorithm, which has been generalized for estimators of compound periodic Poisson processes. The use of generalizations in the algorithm has been prepared with a linear trend in the periodic elements. This research aims to discuss estimators of the variance function. The method used in this research is the simulation method. Simulation results using a generalized algorithm thinning process show that in the case of a limited observation time interval, some estimators are good enough to approach the actual value. As the value of n increases, the simulated value of the estimator moves towards the predicted value. This is following the lemmas, theorems, and consequences that have been discussed. It was also found that several estimators were quite slow. This results in the movement of the bias, variance, and MSE values of the estimators being slow, even though they are moving towards 0. So that further modifications can be made to the model being studied.
Prediksi Harga Saham Syariah menggunakan Bidirectional Long Short Term Memory (BiLSTM) dan Algoritma Grid Search Puteri, Dian Islamiaty; Darmawan, Gumgum; Ruchjana, Budi Nurani
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.v6i1.23297

Abstract

Sharia stocks are one of the investment instruments in the Islamic capital market. In the capital market, it is known that stock prices are very volatile. This makes investors need to carry out a strategy for making the right decision in investing, one of which can be done by predicting stock prices. In this study, predictions were made using historical data on the closing price of Islamic shares of PT. Telkom Indonesia Tbk with the Bidirectional Long Short Term Memory (BiLSTM) method. In building the best prediction model, it is necessary to choose the right parameters and one way to do this is to use the grid search algorithm. Based on the results of the test analysis, it was found that the smallest Mean Absolute Percentage Error (MAPE) value was found in the BiLSTM model in the distribution of data with a percentage of 90% training data and 10% testing data and parameter values obtained based on parameter tuning using grid search, including the number of neurons 25, 100 epochs, 4 batches, and 0.2 dropouts. The MAPE obtained in this study was 10.83% and based on the scale on the MAPE value criteria, this shows that the resulting prediction model is accurate. As for the test results from the comparisons made on the BiLSTM and LSTM models using grid search as a tuning parameter and models without using a grid search or it can be called a trial and error approach as a tuning parameter, it is found that the model with better predictive performance is found in BiLSTM using a grid search. compared to other models.
The k-Tribonacci Matrix and the Pascal Matrix Gemawati, Sri; Musraini, Musraini; Mirfaturiqa, Mirfaturiqa
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.v6i1.24131

Abstract

This article discusses the relationship between the k-Tribonacci matrix Tn(k) and the Pascal matrix Pn, by first constructing the k-Tribonacci matrix and then looking for its inverse. From the inverse k-Tribonacci matrix, unique characteristics can be constructed so that general shapes can be constructed, and then from the relationship of the k-Tribonacci matrix Tn(k) and the Pascal matrix Pn obtain a new matrix, i.e. Un(k). Furthermore, a factor is derived from the relationship of the k-Tribonacci matrix Tn(k) and the Pascal matrix Pn i.e. Pn = Tn(k)Un(k).
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.
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.
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%.
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.
Kombinasi Metode Bilqis Chastine Erma dan Sumathi Sathiya dengan Metode Stepping Stone untuk Optimasi Masalah Transportasi Mardiansah, Rifki; Tastrawati, Ni Ketut Tari; Sari, Kartika
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.v6i1.23857

Abstract

Transportation problems experienced by UD. Raja Wangi in distributing Maha Dewa fragrant incense. UD. Raja Wangi incurs high transportation costs due to irregular direct distribution patterns and has not paid attention to the route to be passed. One way to solve the problem is to use transportation methods to get the optimal distribution route so that the transportation costs incurred are minimal. This study aims to solve transportation problems using the Bilqis Chastine Erma (BCE) method and the Sumathi Sathiya method with the Stepping Stone method to obtain the optimal solution. The Bilqis Chastine Erma (BCE) and the Sumathi Sathiya methods are indirect methods of solving transportation problems by obtaining an initial solution. After obtaining the initial solution, the Stepping Stone method is used to obtain the optimal solution. The results showed that the optimal solution using the Stepping Stone method based on the initial solution of the Bilqis Chastine Erma (BCE) method obtained a total transportation cost of Rp42,937.00 while the optimal solution using the Stepping Stone method based on the initial solution of the Sumathi Sathiya method obtained a total transportation cost of Rp38,727.00. In addition, the Sumathi Sathiya method gets a difference in total transportation costs of Rp11,790.00 or 23% of the total transportation costs incurred by the UD. Raja Wangi. Therefore, the Sumathi Sathiya method is the best solution for minimizing transportation costs.

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