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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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The Hamiltonian and Hypohamiltonian of Generalized Petersen Graph (GP_(n,9)) Susilawati, Susilawati; Nasfianti, Iis; Agustiarini, Efni; Nasution, Dinda Khairani
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.v7i1.30053

Abstract

The study of Hamiltonian and Hypohamiltonian properties in the generalized Petersen graph GP_{n,k} is interesting due to the unique structure and characteristics of these graphs. The method employed in this study involves searching for Hamiltonian cycles within the generalized Petersen graph GP_{n,9}. Not all of GP_{n,9} graphs are Hamiltonian. For certain values of n, if the graph does not contain a Hamiltonian cycle, then one vertex should be removed from the graph to become Hamiltonian or neither. This research specifically investigates the Hypohamiltonian property of GP_{n,9}. The results show that for n ≡ 3 (mod 19) and n ≡ 5 (mod 19), GP_{n,9} is Hamiltonian. Meanwhile, for n ≡ 0 (mod 19), GP_{n,9} is Hypohamiltonian. Furthermore, for n ≡ 1 (mod 19), n ≡ 2 (mod 19), and n ≡ 4 (mod 19), GP_{n,9} is neither Hamiltonian nor Hypohamiltonian.
Identify Solutions to Systems of Linear Latin for Square Equations over Maxmin-ω 'Azizah, Nilatul; Mufid, Muhammad Syifa'ul
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.v7i1.30278

Abstract

Maxmin-\omega algebra is a mathematical system that generalizes maxmin algebra by introducing the parameter \omega (0 \omega \leq 1), which regulates the algebraic operations to enhance its applicability in optimization and decision-making processes. When \omega=1, the system corresponds to the max operation, whereas for \omega approaching 0, it behaves like the min operation. This research investigates the solution characteristics of a linear equation system in maxmin-\omega algebra, specifically A \otimes_{\omega} \textbf{x} = \textbf{b}, where A is a Latin square matrix. Understanding these solutions is crucial for determining the conditions of existence and uniqueness, which will ultimately influence the development of more efficient solution methods for various applications. Furthermore, the study analyzes the impact of the value of \omega and the matrix permutation structure on the solutions of the system. This study employs an analytical approach utilizing maxmin-\omega algebra theory to determine solution existence and assess the impact of \omega variations in linear equations with Latin square matrices. The results reveal that the solution existence heavily depends on the composition of matrix A and the vector \textbf{b}. We show that in specific cases where the matrix \( A \) is a Latin square and the vector \( \mathbf{b} \) satisfies certain constraints, the system has a unique solution in both the max-plus (\(\omega = 1\)) and min-plus (\(\omega = \frac{1}{n}\)) approaches. Moreover, column permutations of A do not affect the existence of solutions. However, row and element permutations alter the system structure, meaning solutions are not always guaranteed.
Comparative Study of Multilayer Perceptron and Recurrent Neural Network in Predicting Population Growth Rate in Brebes Regency Yazidah, Izzatul; Siswanah, Emy
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.v7i1.30199

Abstract

Due to its ever-growing population, Brebes had the biggest population in Central Java from 2020 to 2022. The government of Brebes has to predict the growth rate of the population and prepare the resources and employment opportunities to anticipate this population growth rate. This research aims to analyze the result of growth rate prediction in Brebes using Multilayer Perceptron (MLP) and Recurrent Neural Network (RNN). These two methods are applied to determine the most suitable one to predict the population growth rate. This is determined by comparing the smallest MAPE value of these two methods. The analyzed data of the total population from 1991-2022 is taken from Badan Pusat Statistik (BPS) of Brebes. The percentage of division between training and testing data is 80%:20%. According to the research results, the recurrent neural network is the most suitable method, with the smallest MAPE being 1.9973%.
Observation of Calculated Lapse Rate for Sharia Life Insurance Data : A Study Case Andaria, Rini; Sumarti, Novriana; Puspita, Dila
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.v7i1.30587

Abstract

Modeling a lapse rate is an important subject for life insurance companies because a lapse rate can impact the premium pricing, the reserves, and profitability. In this paper, we calculate the lapse rate and implement a similar approach proposed by the Life Insurance Marketing and Research Association (LIMRA) and the Society of Actuaries (SOA). We analyze lapse rate data from one Sharia insurance company in Indonesia, covering an eight-year period with a total of more than one hundred thousand policyholders. Sharia insurance is aimed at managing contributions based on Sharia principles for mutual assistance and protection by providing compensation to participants/policyholders for losses due to an uncertain event or by providing payments based on the death or the survival of participants. We observe the lapse rates by the face amount group, by genders, and by premium payment frequencies. We found three conclusions, which are mostly that the lower the face amount group, the higher the lapse rate; the lapse rate is not significantly different by gender; and the lapse rate for quarterly payment frequency is higher than for other frequencies.
Forecasting of Rice Harvest Results Using SVR Modeling Techniques Anamisa, Devie Rosa; Khotimah, Bain Khusnul; Hariyawan, Mohammad Yanuar; Irhamni, Firli; Jauhari, Achmad; Mufarroha, Fifin Ayu; Violina, Dina; Nuraini, Dinah
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.v7i1.30592

Abstract

Forecasting is an activity that predicts future values {}{}by utilizing existing track record data. The object of this study is rice plants because they are the primary food source for the Indonesian people. Every year, the Government strives for rice farmers throughout Indonesia to produce abundant rice harvests to meet the community's food needs. Therefore, rice farmers need a system that can predict their rice harvests to obtain information about future harvests to find out whether their harvests have decreased or increased so that they can determine efforts that can be made in the future and can be used as a policy maker for the Government in maintaining the national food security chain. This study uses time series data on rice harvests in Pamekasan, Madura, for 2007-2023 using the Support Vector Regression (SVR) model. The results of several trials have shown that the application of the SVR model for forecasting rice harvests in 2024 has produced good accuracy with a relatively low MAPE error rate of 3.97\%, and the rice harvest has reached an average prediction of 15470.08 tons with an average actual data of 7937.884 tons. Therefore, applying this SVR model can be recommended for predicting future rice harvests. 
Control Analysis on Dynamic System Model of Tuberculosis Disease with Educational Campaign, Vaccination, and Treatment Ilmayasinta, Nur; Riyantoko, Prismahardi Aji; Soemarsono, Annisa Rahmita; Rochmatin, Ulifatur
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.v7i1.30663

Abstract

Tuberculosis (TB) is caused by bacteria (Mycobacterium tuberculosis) that most commonly attacks the lungs. TB is spread from person to person through the air. When people with pulmonary TB cough, sneeze, or spit, they propel TB germs into the air. By inhaling only a small number of these germs, a person can become infected. Tuberculosis is curable and preventable. Prevention that can be done is by providing education about TB and vaccines. While treatment can be done by treating infected individuals. This study examines the TB epidemic model with the application of control, by finding optimal control solutions using the Pontryagin Minimum Principle method. In this study, three control variables were applied, namely education, vaccination and treatment. Numerical calculations were carried out using the Forward Backward Sweep 4th order Runge Kutta method and and then simulated. The results of the numerical simulation of the TB epidemic model show that by implementing control in the form of education, vaccination, and treatment, the population of infected individuals can be reduced.
Konstruksi dan Analisis r-Ideal di BG-aljabar Beauty, Meivy Andhika; Gemawati, Sri; Deswita, Leli
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.v7i1.30097

Abstract

A non-empty set G with a binary operation ∗ and a constant 0 that satisfies the following axioms: , , and  for all  is called a BG-algebra. A non-empty subset I of G is said to be an ideal in G if it satisfies: (i)  and (ii)  and  implies  for all . This article introduces the new concept of r-ideal in BG-algebra, which is an extension of the ideal in BN-algebra. Unlike the definition of an ideal in BN-algebra, an r-ideal only requires a non-empty subset I of G without the need to satisfy the full ideal conditions. This study examines the properties of r-ideals and their relationships with subalgebras, normal, and ideals in BG-algebra. In the final part, it is concluded that every subalgebra is an r-ideal in BG-algebra, and every normal ideal is also an r-ideal.
Parameter Estimation and Hypothesis Testing of GTW Compound Correlated Bivariate Poisson Regression Model: A Theoretical Development Hargandi, Priyanka Ratulangi; Purhadi, Purhadi; Choiruddin, Achmad
Jambura Journal of Mathematics Vol 7, No 2: August 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i2.32712

Abstract

Each observation location and time possesses distinct characteristics, reflecting heterogeneity at every observation point, both spatially and temporally. This condition renders the Compound Correlated Bivariate Poisson Regression (CCBPR) model inadequate for representing data dynamics that exhibit spatial and temporal heterogeneity. To address this limitation, the Geographically and Temporally Weighted Compound Correlated Bivariate Poisson Regression (GTWCCBPR) model is employed, which allows parameter variation across locations and time periods. This model also incorporates the exposure variable as a weighting factor to adjust for differences in risk across observational units. This study aims to estimate the parameters of the GTWCCBPR model using the Maximum Likelihood Estimation (MLE) approach. Due to the complex structure of the model, the log-likelihood function does not yield a closed-form solution. Therefore, parameter estimation is performed using the iterative Berndt-Hall-Hall-Hausman (BHHH) algorithm. Subsequently, hypothesis testing is conducted to evaluate the parameter similarity between the global model (CCBPR) and the spatiotemporal model (GTWCCBPR), as well as to assess the significance of each predictor variable. Simultaneous testing is carried out using the Maximum Likelihood Ratio Test (MLRT), while partial testing is conducted using the Z-test. The scope of this study is limited to theoretical formulation and methodological development, without empirical or simulation-based validation. Future research may extend this work by applying the GTWCCBPR model to practical datasets exhibiting spatio-temporal heterogeneity, particularly in areas such as public health (e.g., maternal and postneonatal mortality), epidemiology, or regional planning.
Estimasi Premi Bruto Asuransi Kendaraan Bermotor Menggunakan Metode Panjer Recursion dan Fast Fourier Transform Nugrahainy, Sintya Putri; Azizah, Azizah
Jambura Journal of Mathematics Vol 7, No 2: August 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i2.32280

Abstract

Insurance is an agreement between two parties, namely the insurance company as the insurer and the customer as the insured. In practice, an insurance product can have hundreds or even thousands of policy contracts. This condition requires the insurer to model the compound distribution of total aggregate loss, which involves repeated convolutions. However, applying convolution to a large number of policies becomes increasingly difficult and inefficient. Therefore, alternative methods are needed to optimize the calculation process. This study uses the Panjer Recursion and Fast Fourier Transform methods to approximate the aggregate loss distribution. The model applies the Zero-Truncated Negative Binomial distribution for claim frequency and the Burr distribution for claim severity. The results show that Panjer Recursion and Fast Fourier Transform yield the same values, resulting in identical probability distributions for all values of aggregate loss. The aggregate loss distribution is then used to estimate gross premium based on the pure premium principle and the expected value principle. The loading factors increase as the confidence level rises, with θ = 3.51 at the 95% confidence level and θ = 5.47 at the 99% confidence level, resulting in total gross premiums of IDR 109,510,000 and IDR 520,835,000, respectively. The choice of confidence level plays a strategic role for insurance companies in balancing risk protection with premium affordability.
Evaluation of the SARIMA and Prophet Models in Forecasting Ship Passenger Numbers at Balikpapan Port Cintani, Meavi; Nizar, Yeky Abil; Angraini, Yenni; Notodiputro, Khairil Anwar; Mualifah, Laily Nissa Atul
Jambura Journal of Mathematics Vol 7, No 2: August 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i2.31606

Abstract

Balikpapan Port serves as a vital transportation hub in eastern Indonesia, particularly in supporting the development of the Nusantara Capital City (IKN). This study evaluates the performance of Seasonal Autoregressive Integrated Moving Average (SARIMA) and Prophet models in predicting short-term ship passenger volumes using monthly data from January 2006 to December 2024 obtained from the East Kalimantan Provincial Transportation Office. Our analysis identifies SARIMA (MAPE = 24%) as the more accurate model compared to Prophet (MAPE = 34%). The optimal SARIMA model was then used to generate a focused forecast for December 2025, providing targeted insights for peak-season port management. These results assist port authorities in resource allocation, infrastructure planning, and policy formulation to accommodate anticipated passenger surges during critical periods.

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