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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 20 Documents

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Search results for , issue "Vol 5, No 1: February 2023" : 20 Documents clear

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.

An Exact Solution for a Single Machine Scheduling Under Uncertainty Rebaz Abdulla Sharif; Ayad M. Ramadan
Jambura Journal of Mathematics Vol 5, No 1: February 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Here we have n jobs on one machine where the processing times are triangular fuzzy numbers. The jobs are available to process without interruption. The purpose is to find a best sequence of the jobs that minimizes total fuzzy completion times and maximum fuzzy tardiness. In this paper a new definition is presented called D-strongly positive fuzzy number, then an exact solution of the problem through this definition is found. This definition opens new ideas about converting scheduling problems into fuzzy cases.

Surjektifitas Pemetaan Eksponensial untuk Grup Lie Heisenberg yang Diperumum Edi Kurniadi; Putri Giza Maharani; Alit Kartiwa
Jambura Journal of Mathematics Vol 5, No 1: February 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

The Heisenberg Lie Group is the most frequently used model for studying the representation theory of Lie groups. This Lie group is modular-noncompact and its Lie algebra is nilpotent. The elements of Heisenberg Lie group and algebra can be expressed in the form of matrices of size 3×3. Another specialty is also inherited by its three-dimensional Lie algebra and is called the Lie Heisenberg algebra. The Heisenberg Lie Group whose Lie Algebra is extended to the dimension 2n+1 is called the generalized Heisenberg Lie group and it is denoted by H whose Lie algebra is h_n. In this study, the surjectiveness of exponential mapping for H was studied with respect to h_n=⟨x ̅,y ̅,z ̅⟩ whose Lie bracket is given by [X_i,Y_i ]=Z. The purpose of this research is to prove the characterization of the Lie subgroup with respect to h_n. In this study, the results were obtained that if ⟨x ̅,y ̅ ⟩=:V⊆h_n a subspace and a set {e^(x_i ) e^(x_j ) ┤| x_i,x_j∈V }=:L⊆H then L=H and consequently Lie(L)≠V.

Robust Coloring Optimization Model on Electricity Circuit Problems Viona Prisyella Balqis; Diah Chaerani; Herlina Napitupulu
Jambura Journal of Mathematics Vol 5, No 1: February 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

The Graph Coloring Problem (GCP) is assigning different colors to certain elements in a graph based on certain constraints and using a minimum number of colors. GCP can be drawn into optimization problems, namely the problem of minimizing the color used together with the uncertainty in using the color used, so it can be assumed that there is an uncertainty in the number of colored vertices. One of the mathematical optimization techniques in dealing with uncertainty is Robust Optimization (RO) combined with computational tools. This article describes a robust GCP using the Polyhedral Uncertainty Theorem and model validation for electrical circuit problems. The form of an electrical circuit color chart consists of corners (components) and edges (wires or conductors). The results obtained are up to 3 colors for the optimization model for graph coloring problems and up to 5 colors for robust optimization models for graph coloring problems. The results obtained with robust optimization show more colors because the results contain uncertainty. When RO GCP is applied to an electrical circuit, the model is used to place the electrical components in the correct path so that the electrical components do not collide with each other.

Value at Risk dan Tail Value at Risk dari Peubah Acak Besarnya Kerugian yang Menyebar Alpha Power Pareto Ruhiyat Ruhiyat; Berlian Setiawaty; Muwafiqo Zamzami Dhuha
Jambura Journal of Mathematics Vol 5, No 1: February 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Value at Risk (VaR) and Tail Value at Risk (TVaR) are two measures that are commonly used to quantify the risk associated with a loss severity distribution. In this paper, both values are calculated analytically and estimated using a Monte Carlo simulation when the loss severity random variable has an alpha power Pareto distribution. This distribution is the result of alpha power transformation on a Pareto distribution. The random numbers used in the Monte Carlo simulation are generated from the alpha power Pareto distribution using the inverse transformation technique. In the special case used, the estimated VaR and TVaR values obtained from the Monte Carlo simulation for some security levels used are close to the actual VaR and TVaR values as long as the number of random numbers generated in the Monte Carlo simulation is sufficiently large.

On the Effects of Saturation Terms on A SEIR Epidemic Model with Infected and Susceptible Compartments Mutairu Kayode Kolawole; Olakunle L. Moshood; Kehinde A. Bashiru; Adedapo I. Alaje; Amos O. Popoola; Hammed O. Adekunle
Jambura Journal of Mathematics Vol 5, No 1: February 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

The importance of the saturation term in an SEIR (Susceptible, Exposed, Infected, and Recovered) epidemic model was examined in this article. To estimate the basic reproduction number (R0), examine the stabilities and run numerical simulations on the model, the next generation matrix, the Lyapunov function and Runge-Kutta techniques were used. The numerical simulation results reveal that, the saturation term has a significant influence in the model’s susceptible and infected compartments. However, as demonstrated by the simulation results, saturation term has a greater influence on vulnerable people than on infected people. As a result, greater sensitization programs through seminars, media, and awareness will be more beneficial to the vulnerable class than the afflicted class during disease eradication.

Metode AdaBoost dan Random Forest untuk Prediksi Peserta JKN-KIS yang Menunggak Ikhlasul Amalia Rahmi; Farit Mochamad Afendi; Anang Kurnia
Jambura Journal of Mathematics Vol 5, No 1: February 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

The contribution of participants, employers, and/or the government is one of the most important things in the National Health Insurance Program-Healthy Indonesia Card (JKN-KIS) implementation. All Indonesian residents were required to participate in the JKN-KIS program which is divided into four types of participation, one of which is Non-Wage Recipient Participants (PBPU) whose contributions are paid independently. However, based on December 2021 data, 60% of PBPU participants were late in paying monthly until they were in arrears. Arrears in payment of contributions cause several problems, including payment of claims to deficits. This research utilized big data owned by the Healthcare and Social Security Agency (BPJS Kesehatan) and machine learning based on ensemble trees, namely AdaBoost and random forest to get the predictions of participants in arrears. The results showed that machine learning based on an ensemble tree was able to predict PBPU participants in arrears with high accuracy, as evidenced by the AUC values in both models above 80%. The random forest model has an F1-score and the AUC value is better than the AdaBoost, namely the F1-score of 85,43% and the AUC value of 87,20% in predicting JKN-KIS participants who are in arrears in payment of contributions.

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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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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

Abstract

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Abstract

Abstract

Abstract

Abstract

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