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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 179 Documents
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Lattices Constructions for Euclidean Space Rn and its Subspaces Hayyah, Zahira Najmatul; Kurniadi, Edi; Triska, Anita
Jambura Journal of Mathematics Vol 8, No 1: February 2026
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v8i1.36272

Abstract

A lattice is a discrete subgroup of n-dimensional Euclidean space that serves as a fundamental object of study in Algebra and the Geometry of Numbers. This structure has significant applications in various fields, particularly in lattice-based cryptography and coding theory. This paper aims to present the formal construction of lattices for $n$-dimensional Euclidean space Rn and its linear subspaces by analyzing the formal definitions and essential properties of lattices. The main results of this research lie in two main results which are presented in several propositions. First, the set Zn of standard integer points is proven to be a lattice in n-dimensional space with respect to the standard basis of V \subseteq Rn. Second, the set of integer points whose last component is zero is proven to be a lattice within (n-1)-dimensional non-trivial subspaces. Indeed, in this case, the obtained lattice is not equal to Zn. Moreover, it also discussed the lattices of a non-standard basis for V. Explicitly, this work contributes a rigorous formal verification that integer structures within subspaces, such as Z{n-1}x0, retain fundamental lattice properties even under non-standard basis constructions.
Estimasi Cadangan Klaim Individu untuk Klaim Short-Tailed dan Long-Tailed Menggunakan Algoritma Backpropagation Rabdika, Anas Satriya; Azizah, Azizah
Jambura Journal of Mathematics Vol 8, No 1: February 2026
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v8i1.35114

Abstract

In insurance, risk can occur at any time, causing claims to sometimes have a large amount of value, so that insurance companies may not be able to satisfy claim payments. If these situations occur, insurance companies need claim reserves to prepare for such events. There are several methods to calculate claim reserves, such as aggregate claim reserving. However, certain claim characteristics involve dependencies among claims, which result in a lack of detailed information for individual claims. In addition, an increasing number of claims becomes more difficult to compute using traditional methods. Therefore, this research aims to calculate individual claim reserves using one branch of machine learning, namely the Backpropagation Algorithm. The Backpropagation Algorithm is believed to remain relevant compared to other algorithmic models because, in several studies, it produces relatively low values of Mean Absolute Percentage Error (MAPE), at approximately 2.70%. The data used in this research are simulated using R software, generating 10,000 claims over 20 years, consisting of 6,000 short-tailed claims and 4,000 long-tailed claims. The data model is evaluated using MAPE. The resulting MAPE value is 0.55%, indicating that the data are highly suitable for predictive modeling. The prediction results show that the total claims to be paid in the 21st development year reach Rp22,945,450,000,000, with an average claim amount of approximately Rp2,294,545,152. This research contributes to both informatics and actuarial science by developing an individual claim reserving approach to predict claim payments more efficiently.
Mev-polynomial and K Banhatti Indices of Some Hat-graphs Karim, Akar H.; Ramadan, Ayad M.
Jambura Journal of Mathematics Vol 8, No 1: February 2026
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v8i1.35382

Abstract

A graph polynomial that has taken several attentions is M-polynomial due to it's significant a considerable number of studies have been conducting on it, moreover some other versions of this polynomial have been defined. In this paper an new version of M-polynomial is presented that will be known as Mve-Polynomial which is an extension of the notation of M-polynomial for comparison between vertices and corresponding adjacent edges. Then we investigate the mathematical relationship between Mve-Polynomial and two resent defined topological indices: first and second K Banhatti indices. Next, we establish explicit formulas for the Mve-Polynomial of some graphs in the family of hat-graphs with it's plots for special number of vertices. From these results we further deduce the corresponding K Banhatti indices.
Implementasi Metode Extreme Value Theory untuk Menghitung Maksimal Kerugian Akibat Bencana Alam Yusuf, Feby Indriana; A’la, Kevina Alal; Thalita, Bella Cindy
Jambura Journal of Mathematics Vol 8, No 1: February 2026
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v8i1.35193

Abstract

This study employs Extreme Value Theory (EVT) using the Block Maxima (BM) approach and the Generalized Extreme Value (GEV) distribution to model and estimate the potential maximum financial losses caused by natural disasters in Central Java, Indonesia. Historical loss data from 2022 are utilized to calibrate GEV distribution parameters, followed by Monte Carlo simulations to project risks over a 12-year horizon. The results reveal that the data exhibit heavy-tailed characteristics (indicated by a positive shape parameter), signaling significant extreme risks. Goodness-of-fit tests, specifically Kolmogorov-Smirnov and Anderson-Darling, confirm the validity of the GEV model. Return level analysis indicates a sharp escalation in risk; for a 100-year return period, potential losses reach a substantial magnitude. These findings contribute methodologically to regional fiscal risk estimation and underscore the necessity of precise financial mitigation instruments.
A Four-Step High-Order Iterative Method for Nonlinear Equations with Scientific Applications Putra, Supriadi; Putri, Ayunda; Zulkarnain, Zulkarnain; Marjulisa, Rike; Novita, Devi
Jambura Journal of Mathematics Vol 8, No 1: February 2026
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v8i1.35161

Abstract

In this paper, we propose a new four-step iterative method for solving nonlinear equations based on a predictor–corrector framework that combines Newton’s, Ostrowski’s, and Householder’s methods. To avoid explicit evaluation of higher derivatives, particularly the second derivative, polynomial interpolation is employed to approximate derivative information in the higher-order step, while retaining first-derivative evaluations where required. The resulting scheme attains an optimal convergence order of fourteen using six function evaluations per iteration. Numerical experiments on several benchmark functions and two classical application problems, namely the computation of libration points and a Fibonacci-type root-finding problem, demonstrate improved accuracy and robust convergence behavior. In the reported tests, the method achieves the expected computational order of convergence and typically converges within a small number of iterations. The convergence properties are further examined through residual errors, step differences, and the observed computational order of convergence.
Comparative Analysis of Hierarchical Cluster Methods in Inflationary Cities in Indonesia Based on Sectoral Inflation Patterns Khoirunissa, Husna Afanyn; Safitriani, Nur Rezky; Widyaningrum, Erlyne Nadhilah; Putri, Rizka Amalia; Fathan, Morina A.; Nisa, Nabilla Rida Tri
Jambura Journal of Mathematics Vol 8, No 1: February 2026
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v8i1.35105

Abstract

This study aims to assess the performance of single linkage, complete linkage, and average linkage hierarchical clustering algorithms in grouping cities used as inflation benchmarks in Indonesia into clusters based on sectoral inflation patterns. The data utilized are 150 regencies/cities divided into 11 sectors that drive inflation, identified by BPS Indonesia. Prior to clustering, a distance analysis using Euclidean distances was conducted to measure similarity between regions. Evaluation of the optimal number of clusters was conducted by applying the stability measure approach (APN, AD, ADM, and FOM), which showed that creating five clusters produced the most stable results. The results of the analysis revealed that the single linkage approach had the lowest within-cluster to between-cluster standard deviation ratio compared to the other two approaches, which revealed a greater level of homogeneity between the clusters. From an economic perspective, this clustering pattern revealed impressive differences in sectoral inflation pressures between provinces, even between cities within a province. Consequently, the single linkage method is proposed as the optimal method for identifying spatial variations in sectoral inflation in Indonesia.
Mathematical Analysis of Typhoid Fever Dynamics with Age-Structured Control Measures Kolawole, Mutairu Kayode; Ayoola, Rasheed Gbemisola; Adebisi, Folasade Ajimot
Jambura Journal of Mathematics Vol 8, No 1: February 2026
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v8i1.35225

Abstract

This research develops a mathematical model to investigate the dynamics of typhoid fever by incorporating age structure, vaccination and treatment strategies. Recognizing that different age groups display varying susceptibility and contact rates, the model provides a detailed representation of transmission. The analysis is to emphasize how vaccination programs and treatment interventions, when tailored to age-specific characteristics, can significantly reduce transmission and control outbreaks. The system of nonlinear differential equations describing the disease dynamics is analyzed and solved using the homotopy perturbation method. This analytical approach allows for an approximation of solutions while capturing the nonlinear interactions within the system. Sensitivity analysis is carried out to determine the most influential parameters on disease spread, particularly those affecting the basic reproduction number. The simulations reveal that increasing vaccination coverage and treatment rates leads to a decline in typhoid fever cases across all age groups. Age-targeted interventions are shown to enhance the effectiveness of control strategies compared with uniform measures. Sensitivity analysis result further indicate that parameters such as vaccination rate, treatment efficacy and contact patterns play vital roles in disease progression and a potential for its eradication.
Deret Maclaurin Turunan Fraksional Fungsi Inverse Trigonometri dan Radius Kekonverganannya Khoirunisa, Siti Miftahurrohmah; Anshori, Hafiz Iqbal; Karim, Eka Mulyawati S.
Jambura Journal of Mathematics Vol 8, No 1: February 2026
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v8i1.37016

Abstract

Fractional derivatives are a generalization of ordinary derivatives to non-integer or fractional orders. This study presents the fractional derivatives of inverse trigonometric functions (arcsin, arccos, and arctan) with the order constraint 0 α ≤ 1 . These inverse trigonometric functions are expressed in the form of Maclaurin series. Furthermore, their fractional derivatives can be determined using the Riemann–Liouville definition of fractional derivatives. The main results show an explicit formula for the fractional Maclaurin series and prove that the radius of convergence of the original function is equal to the radius of convergence of its fractional derivative.
An Integrated K-Means++–Davies–Bouldin Index Approach for Educational Resource-Based District Clustering: A Case Study of Districts in Surabaya Subaekti, Hendrik; Hakim, Lutfi; Khaulasari, Hani; Yuliati, Dian
Jambura Journal of Mathematics Vol 8, No 1: February 2026
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v8i1.35412

Abstract

Equitable distribution of educational resources is an important prerequisite to ensure that all communities benefit from human resource development. Access to education through the availability of schools and teachers at every level, plays a role in reducing the gap between regions. This study aims to group educational resources at the elementary and junior high school levels in 31 sub-districts of Surabaya City and evaluate the quality of grouping using the Davies–Bouldin Index (DBI). The analysis was carried out using secondary data from the Surabaya City Education Office which included the number of schools, teachers, and students based on education level in each sub-district. The clustering method used is K-Means++, which improves the centroid initialization process to produce more stable clustering. The results of the analysis identified three clusters, namely Development Education Areas (17 sub-districts), Elementary Focused Areas with Limited Junior High Schools (7 sub-districts), and Priority Education Areas (7 sub-districts: Rungkut, Sukolilo, Wonokromo, Sukomanunggal, Genteng, Kenjeran, and Krembangan). The quality of the grouping was validated with a DBI value of 0.752, which indicates a good cluster separation These findings can directly inform the Surabaya City Government in formulating targeted policies for educational equity, especially in teacher placement, student quota adjustment, and infrastructure development.

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