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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 15 Documents
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Search results for , issue "Vol 8, No 1: February 2026" : 15 Documents clear
Application of the Laguerre Perturbed Galerkin Analysis Method for Solving Higher-Order Integro-Differential Equations Adebisi, Ajimot Folasade; Ojurongbe, Taiwo Adetola; Okunola, Kazeem Adekunle
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.v8i1.34001

Abstract

This study presents the development and implementation of a novel numerical method, the Laguerre Perturbed Galerkin (LPG) method, for solving higher-order integro-differential equations. The method leverages the advantages of Laguerre polynomials as basis functions while incorporating Chebyshev polynomials as perturbation terms to enhance both accuracy and efficiency. In the LPG method, the solution is approximated using Laguerre polynomials of degree N, with the residual error minimized via the Galerkin approach. Chebyshev polynomials are introduced as perturbation terms to further refine the solution. The residual is systematically reduced to a system of (N + 1) equations, which is then solved to determine the unknown coefficients of the approximating Laguerre polynomials. Comparative analyses demonstrate that the LPG method achieves superior accuracy and faster convergence rates compared to existing techniques, particularly for higher-order integro-differential equations. The findings contribute to the advancement of numerical methods in this domain, providing a powerful computational tool for scientists and engineers.
Analisis Kinerja dan Efisiensi Energi k-means dan Gaussian Mixture Model Terdistribusi pada Klaster Single Board Computer dan Personal Computer dengan Apache Spark Noer, Deffin Purnama; Liebenlito, Muhaza; Sutanto, Taufik Edy
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.v8i1.35198

Abstract

This study aims to evaluate the performance and energy efficiency of distributed unsupervised learning algorithms on two types of clusters, namely Single Board Computers (SBC) and Personal Computers (PC), using Apache Spark. Two algorithms were tested—k-means and Gaussian Mixture Model (GMM)—executed across varying dataset sizes and numbers of processor cores to observe scalability. The results show that PCs consistently achieved faster execution times, particularly with k-means on large datasets. On the other hand, SBCs demonstrated higher energy efficiency in all scenarios, with energy savings of up to 93% for k-means and 86% for GMM compared to the highest-consumption configuration on PC. These findings affirm the potential of SBCs as a low-power and cost-efficient solution for green or sustainable computing, particularly for learning, academic experimentation, and small-scale edge computing development, and are relevant to sustainability efforts through their contribution to the Sustainable Development Goals (SDGs).
Pelabelan Prima pada Kelas Graf Hasil Operasi Perkalian Tensor Triwahyuniti, Suci; Rahmadani, Desi
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.v8i1.34596

Abstract

A graph  with a vertex set   is said to be a prime graph if there exists a bijective mapping , where  denotes the number of vertices in , such that for any two adjacent vertices  and  in  have . Tensor Product graph is a way to combine (compose) two graphs into one larger and more complex graph. The result is a new graph that reflects the connection properties of the two original graphs, but in a very specific and more complex way than other graph operations. Therefore, this research aims to determine whether there is prime labeling in the class of graphs resulting from the Tensor Product of the path graph  and the cycle graph . The research employed analytical and exploratory methods with a trial-and-error strategy to determine the labeling that possesses a prime property. The results of this study prove that two classes of the Tensor Product graph  for , and graph , for  are prime graph. This finding expands the results on classes of graphs that admit prime labeling  and provides a basis for further research on graph labeling in other graph operations
A Hybrid Grey Wolf Optimizer–Zebra Optimization Algorithm for Solving Optimization Problems Ali, Ayad
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.v8i1.34499

Abstract

Metaheuristic algorithms are widely applied to complex optimization problems, yet many suffer from premature convergence or slow search efficiency. To report these limitations, this paper proposes a new hybrid algorithm, Grey Wolf Optimizer–Zebra Optimization Algorithm (GWO–ZOA). The algorithm integrates the exploitation ability of the Grey Wolf Optimizer with the exploration capability of the Zebra Optimization Algorithm in a sequential framework, thereby enhancing both convergence accuracy and global search ability. The performance of GWO–ZOA is first evaluated on 23 standard benchmark functions, where it demonstrates competitive results in both unimodal and multimodal landscapes. Further validation is carried out on the CEC2017 and CEC2020 benchmark suites, confirming the hybrid’s robustness across higher-dimensional and more challenging composite problems. In all three benchmark categories, the Friedman statistical test ranks GWO–ZOA first among the compared algorithms, highlighting its superior overall performance. Finally, the algorithm is applied to two real-world engineering design problems, where it consistently achieves high-quality feasible solutions and demonstrates practical effectiveness. These results confirm that the proposed GWO–ZOA algorithm is both robust and reliable for solving diverse and complex optimization tasks.
Pemodelan Faktor Risiko Stunting Berbasis Titik Menggunakan Geographically Weighted Logistic Regression di Kabupaten Bone Bolango Akolo, Ingka Rizkyani; Djafar, Fatimah; Paembonan, Maya
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.v8i1.35871

Abstract

Stunting remains a major public health issue in Indonesia, including in Kabupaten Bone Bolango, which recorded a high prevalence in 2023. Variations in social, economic, and environmental conditions across observation locations indicate the need for analyses that account for spatial differences between areas. This study aims to identify the spatial variation in the effects of significant stunting risk factors using the Geographically Weighted Logistic Regression (GWLR) method. The data were obtained from the Health Office of Kabupaten Bone Bolango in 2019. The independent variables included complete basic immunization (X1), the percentage of low-birth-weight infants (X2), and the percentage of exclusive breastfeeding (X3), with the response variable defined as high stunting prevalence (1) and low stunting prevalence (0). The analysis comprised multicollinearity testing, the Breusch-Pagan spatial heterogeneity test, bandwidth selection using cross-validation, construction of an adaptive Gaussian kernel weighting matrix, and parameter estimation via maximum likelihood with the Newton-Raphson method. The multicollinearity test indicated that all variables were free from collinearity (VIF 10). The Breusch-Pagan test revealed the presence of spatial heterogeneity (p 0.10), confirming the appropriateness of the GWLR model. The results showed that the percentage of exclusive breastfeeding was significantly higher in Bone Raya, Bulawa, Bone, Bone Pantai, and Kabila Bone, whereas complete basic immunization and the percentage of low-birth-weight infants were not significantly different. These findings indicate that exclusive breastfeeding is a risk factor for stunting, with significant spatial variation, suggesting that stunting intervention strategies should be designed on a point-by-point, location-specific basis, taking into account the local characteristics of each observation point.
Parameter Estimation of Generalized Modified Weibull Using the Maximum Likelihood on Simulation and Real-World Data Putera, Muhammad Luthfi Setiarno; Purhadi, Purhadi
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.v8i1.36518

Abstract

This study estimates parameters of the generalized modified Weibull (GM Weibull) distribution using the Maximum Likelihood Estimation (MLE) method with the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm. The GM Weibull distribution, which includes four parameters (lambda, theta, phi, tau), offers greater flexibility than Weibull distribution in modeling data with monotonic and bathtub-shaped hazard patterns. Parameter estimation was conducted on three datasets: simulated data with sample sizes of 50, 200, and 500 observations; survival data from 45 heart transplant patients; and health indicator data from 27 districts/cities in Central and South Kalimantan provinces. The results demonstrate that while the standard Weibull remains a parsimonious choice for simple monotonic data, the GM Weibull produces parameter estimates closer to theoretical values in small-to-medium samples and significantly lower deviance in complex datasets. Specifically, for the heart transplant data, the GM Weibull offered better modeling long-term survival tails (800--1,000 days), while for the health indicator data, it effectively accommodated central tendencies within asymmetric distributions. Although AIC and BIC favor standard Weibull, the GM Weibull accurately identifies underlying structural fluctuations and non-monotonic failure characteristics. This study confirms that the MLE-based GM Weibull distribution is one of the robust tools for researchers requiring a more representative model for complex survival and health data.
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.

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