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Jambura Journal of Mathematics

jjom
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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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A Fractional-Order Predator-Prey Model with Age Structure on Predator and Nonlinear Harvesting on Prey Hasan S. Panigoro; Resmawan Resmawan; Amelia Tri Rahma Sidik; Nurdia Walangadi; Apon Ismail; Cabelita Husuna
Jambura Journal of Mathematics Vol 4, No 2: July 2022
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

In this manuscript, the dynamics of a fractional-order predator-prey model with age structure on predator and nonlinear harvesting on prey are studied. The Caputo fractional-order derivative is used as the operator of the model by considering its capability to explain the present state as the impact of all of the previous conditions. Three biological equilibrium points are successfully identified including their existing properties. The local dynamical behaviors around each equilibrium point are investigated by utilizing the Matignon condition along with the linearization process. The numerical simulations are demonstrated not only to show the local stability which confirms all of the previous analytical results but also to show the existence of periodic signal as the impact of the occurrence of Hopf bifurcation.

Bifurkasi Pada Model Penyebaran Penyakit MERS-CoV di Dua Wilayah dengan Populasi Konstan Livia Owen
Jambura Journal of Mathematics Vol 4, No 2: July 2022
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Middle East Respiratory Syndrome Coronavirus (MERS-CoV) is caused by a novel coronavirus and it can be a human-to-human transmission disease. World Health Organization (WHO) reported the disease outbreak first happened in Saudi Arabia in 2012 and the last case is reported in 2019. In 2018, MERS-CoV outbreaks were reported in the Republic of Korea, United Kingdom of Great Britain, Northern Ireland, Saudi Arabia, Uni Arab Emirates, Oman, and Malaysia. Cases that are identified outside the Middle East are usually caused by traveling people who were infected in the Middle East and then traveled back to their country. The previous research had constructed a mathematical model for the transmission of MERS-CoV in two areas by separating the human population into susceptible and infectious groups. It focused on the basic reproductive number and sensitivity analysis. In this paper, we simplify the model with the assumption that the total population of each area is constant. Using Lagrange Multiplier Method, we find some co-dimension one and co-dimension two bifurcations i.e.fold bifurcation and cusp bifurcation, respectively. We get the domain of parameters where three, two and one non-trivial equilibrium point occurs. We also find a transcritical bifurcation point such that the disease-free equilibrium point is stable on some parameter domains.

Bilangan Invers Dominasi Total Pada Triangular Snake Graph, Line Triangular Snake Graph, dan Shadow Triangular Snake Graph Nurhamzah Nurhamzah; Nilamsari Kusumastuti; Fransiskus Fran
Jambura Journal of Mathematics Vol 4, No 2: July 2022
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Let G = (V(G), E(G)) be a connected graph, where V(G) is the set of vertices and E(G) is the set of edges. The set Dt(G) is called the total domination set in G if every vertex v 2 V(G) is adjacent to at least one vertex in Dt (G). Furthermore, Dt(G) must satisfy the property N(Dt ) = V(G), where N(Dt) is an open neighbourhood set of Dt(G). Suppose that Dt(G) is the total domination set with minimum cardinality. If V(G) - Dt(G) contains a total domination set Dt-1(G), then Dt-1(G) is the inverse set of total domination relative to the total domination set Dt (G). The inverse’s number of the total domination set denotes the minimum cardinality of the inverse set of total domination. This number is denoted by gt-1 (G). This article discusses the inverse’s number of total domination of the triangular snake graph (Tn), line triangular snake graph (L (Tn)), and shadow triangular snake graph (D2 (Tn)). Graph Tn is a graph obtained from the path graph (Pn) by replacing each side of the path with a cycle graph (C3). Graph L (Tn) is a graph where the vertex set in L(Tn) is the edge set on Tn, or V(L(Tn)) = E(Tn). Graph D2 (Tn) is a graph obtained by combining two copies of a graph Tn, namely Tn0 and T00n. This research shows that the graph Tn does not have an inverse of domination total, gt-1 (L (Tn)) = n for n = 4, 6, 8, gt-1 (L (Tn)) = n - 1 for n = 3, 5, 7, or n ≥ 9 with n 2 N, and gt-1 (D2 (Tn)) = b23nc for n ≥ 3 with n 2 N.

Formulation of Sudoku Puzzle Using Binary Integer Linear Programming and Its Implementation in Julia, Python, and Minizinc Fahren Bukhari; Sri Nurdiati; Mohamad Khoirun Najib; Nandika Safiqri
Jambura Journal of Mathematics Vol 4, No 2: July 2022
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Sudoku is a number puzzle game popular among people with various difficulty levels (easy, medium, hard, and extremely hard). Sudoku can be modeled as a linear programming problem in mathematics, particularly binary integer linear programming (BILP). Completing Sudoku using BILP is quite tricky because it requires many iterations. Therefore, this study aims to analyze the Sudoku problem using the BILP formulation and implement the problem using Julia, Python, and MiniZinc. Out of 15 cases for each difficulty level, Julia performs better than Python and MiniZinc based on computation time. Moreover, Sudoku with easy difficulty levels is solved with a longer computation time than the other three difficulty levels. The computation time for solving BILP is getting faster as the difficulty level of the Sudoku problem increases. This is because Sudoku problems with easy difficulty levels have more known values as clues and generate more constraints than other difficulty levels.

Implementasi Metode Perhitungan Aktuaria Program Dana Pensiun Menggunakan Flask Muthia Dishanur Izzati; Mujiati Dwi Kartikasari
Jambura Journal of Mathematics Vol 4, No 2: July 2022
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

The pension fund program is a program that seeks future planning by providing pension benefits to participants. The vital thing that becomes a concern in the pension fund program is the actuarial cost method. There are two categories for actuarial cost methods, which are Accrued Benefit-Cost Method and Projected Benefit-Cost Method. The normal contribution characteristic of the Projected Benefit-Cost Method is more stable than the Accrued Benefit-Cost Method, so it is better to use it from the participants’ perspective. This study discusses the use of the Projected Benefit-Cost Method by calculating normal contributions and actuarial liabilities from the methods included in it, which are Attained Age Normal, Entry Age Normal, and Individual Level Premium. Based on the calculation results, the Entry Age Normal and Individual Level Premium methods have a smaller final value of normal contribution payments and have a larger actuarial liability than the Attained Age Normal. Thus, of the three methods included in the Projected Benefit-Cost Method, the Entry Age Normal and Individual Level Premium methods are better used from the perspective of participants. For the calculation of pension funding using the Attained Age Normal, Entry Age Normal, and Individual Level Premium methods to be widely implemented by the public, this study created an application website using flask, which can be accessed at https://perhitunganaktuariadapen.herokuapp.com/.

Systematic Literature Review on Troubleshooting Delivery of Production Product Using n-Vehicle with Vogel Total Difference Approach Method Al Fataa Waliyyul Haq; Sudradjat Supian; Diah Chaerani
Jambura Journal of Mathematics Vol 4, No 2: July 2022
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

The product delivery strategy using n-vehicle is the application of optimization for transportation problems. The product delivery strategy using n-vehicle is useful for minimizing the shipping costs of a company’s production. This article presents a peer-reviewed bibliometric analysis based on the topic of production delivery strategies using n-vehicle. Overall, there are 91 articles from the Dimension, Science Direct, and Google Scholar databases in 2013-2021 that use the topic of production delivery strategies using n-vehicle based on the keywords ”Capacitated transportation problem” and ”cost” and ”vehicle” and” optimal solutions”. The researcher presents the relationship of each cited article so that it can show the collaboration of all the cited articles. This article aims to generate and review analysis results through Preferred Reporting Items for Systematic reviews and Meta-Analyses (PRISMA) and State of The Art. Bibliometric analysis, PRISMA, and State of The Art show how the development of research on production delivery strategies using n-vehicle. So, it can produce suggestions in conducting the latest research related to studies on the topic of production delivery strategies using n-vehicle. Based on PRISMA’s analysis, 91 articles were obtained, of those 91 articles, 11 articles discussed the strategy of delivering production products using n-vehicle in depth. The State of The Art also shows how the development of research on production delivery strategies using n-vehicle is developing. It can be seen that apart from the classical method, other methods are also emerging to solve transportation problems. One of them is Vogel Total Difference Approach Method (VTDM).

Invers Moore-Penrose pada Matriks Turiyam Simbolik Real Ani Ani; Mashadi Mashadi; Sri Gemawati
Jambura Journal of Mathematics Vol 5, No 1: February 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

The symbolic Turiyam matrix is a matrix whose entries contain symbolic Turiyam. Inverse matrices can generally be determined if the matrix is a non-singular square matrix. Currently the inverse of the symbolic Turiyam matrix of size m × n with m 6= n can be determined by the Moore-Penrose inverse. The purpose of this research is to determine the inverse Moore-Penrose algorithm on a real symbolic Turiyam matrix of size m × n with m 6= n. Algebraic operations on symbolic Turiyam is a method used to obtain the Moore-Penrose inverse on real symbolic Turiyam matrices by applying symbolic Turiyam algebraic operations on the concept of Moore-Penrose inverses. The main result obtained is the inverse Moore-Penrose algorithm on the real symbolic Turiyam matrix. The demonstration example given shows that the Moore-Penrose inverse on a real symbolic Turiyam matrix always exists even though the matrix is not a square matrix.

Model Regresi Kuantil Spline Orde Dua Dalam Menganalisis Perubahan Trombosit Pasien Demam Berdarah Anisa Anisa; Anna Islamiyati; Sitti Sahriman; Jusmawati Massalesse; Bunga Aprilia
Jambura Journal of Mathematics Vol 5, No 1: February 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Quantile regression can be used to analyze data containing outliers including DHF data. The spline is able to identify several patterns of change in the regression model, so this study uses a second-order quantile spline regression model in analyzing DHF data that occurred in Makassar City. In this article, the authors analyze the pattern of changes that occur in platelets based on changes in the hematocrit content of DHF patients. The selected quantiles are quartiles 0.25; 0.50; and 0.75 with 3-knot points. Based on the results of the analysis, the minimum GCV value obtained at the use of knot points is 30.30; 44.80; 47.10 for the 0.25 quartile; 0.50; and 0.75. This shows that in each quartile, there are four patterns of quadratic changes that occur in the platelet count of DHF patients. The parabolic curve formed in each pattern segmentation shows that there are times when platelets are increasing and there are times when platelets are decreasing. However, the average platelets decreased drastically, especially when the hematocrit reached 47.10%.

Modeling and Control of the Extreme Ideology Transmission Dynamics in a Society Nur Azizah; Toni Bakhtiar; Paian Sianturi
Jambura Journal of Mathematics Vol 5, No 1: February 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

In this work, we propose a mathematical model to analyze the spread of extreme ideology in society. The so-called SERTA model divides the entire population into five compartments, namely susceptible, extremist, recruiter, treatment, and aware, to describe the state of the willingness of community members toward extreme ideology. We first present a model with constant control, i.e., a model without a dynamical control instrument, and provide the stability analysis of its equilibrium points based on the basic reproduction number. We then reformulate the model into an optimal control framework by introducing three control variables, namely prevention, disengagement, and deradicalization, to enable intervention of the dynamical process. The optimality conditions are obtained by employing Pontryagin's maximum principle, showing the optimal interdependence of state, co-state, and control variables. Numerical simulations based on the well-known Runge-Kutta algorithm and forward-backward sweep method are carried out to evaluate the effectiveness of control strategies under different scenarios. From the simulation results, it is found that by applying the three controls, the optimum solution is obtained. Besides that, in this study, disengagement contributes the most effect in suppressing extremist and recruiter populations, both by using single control and multiple controls.

Akurasi Model Hybrid ARIMA-Artificial Neural Network dengan Model Non Hybrid pada Peramalan Peredaran Uang Elektronik di Indonesia Muktar Redy Susila; Mochamad Jamil; Bambang Hadi Santoso
Jambura Journal of Mathematics Vol 5, No 1: February 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

The purpose of this study is to model electronic money in Indonesia using a hybrid model and compare its accuracy with the non-hybrid model. The hybrid model used is Autoregressive Integrated Moving Average (ARIMA)-Artificial Neural Network. The data used is the amount of electronic money circulation for the monthly period January 2009 to October 2021. The ARIMA model formed from research data is ARIMA (1,1,0) with additive outliers and level shift outliers. For Artificial Neural Network modeling is limited by using one hidden layer with three neurons. In the modeling process, 20 repetitions were carried out. The smallest repetition value was obtained, namely the 13th repetition with an error value of 2.569. In this study, it was found that the ARIMA- Artificial Neural Network hybrid model had a smaller Root Mean Squared Error (RMSE) in sample and out sample than the non-hybrid model. Based on the results of the study, it can be concluded that by combining the ARIMA model with Artificial Neural Network, it can increase the accuracy of the data fit results and forecast results.

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Resmawan

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Jl. Prof. Dr. Ing. B. J. Habibie, Moutong, Tilongkabila, Kabupaten Bone Bolango, Gorontalo, Indonesia

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Kota gorontalo,

Gorontalo

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Home Page

OAI Link

Editorial Team

Contact

Reviewer

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Contact Name Resmawan

Contact Email resmawan@ung.ac.id

Phone +6285255230451

Journal Mail Official info.jjom@ung.ac.d

Editorial Address Jl. Prof. Dr. Ing. B. J. Habibie, Moutong, Tilongkabila, Kabupaten Bone Bolango, Gorontalo, Indonesia

Location Kota gorontalo, Gorontalo INDONESIA

Abstract

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Abstract

Contact Name
Resmawan

Contact Email
resmawan@ung.ac.id

Phone
+6285255230451

Journal Mail Official
info.jjom@ung.ac.d

Editorial Address
Jl. Prof. Dr. Ing. B. J. Habibie, Moutong, Tilongkabila, Kabupaten Bone Bolango, Gorontalo, Indonesia

Location
Kota gorontalo,

Gorontalo

INDONESIA