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All Journal Jambura Journal of Mathematics Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi InSTEM
Dewi Ika Ainurrofiqoh
Universitas Jember
Agriculture, Biological Sciences & Forestry Chemistry Computer Science & IT Mathematics Physics Other

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Karakteristik Modul Endoprima Lemah Ainurrofiqoh, Dewi Ika
Jambura Journal of Mathematics Vol 6, No 2: August 2024
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v6i2.26450

Abstract

In this research, we studied weakly endoprime module, which is a development of weakly prime module by reviewing its fully invariant submodule. This is similar to the development of endoprime module from prime module. This primary objective of this research are to determine the relationship between weakly endoprime module and endoprime module and examine the fully invariant submodules of weakly endoprime module. The method employed in this research involves studying the relationship between weakly prime modules and prime modules, endoprime modules and prime modules, as well as weakly endoprime modules and weakly prime modules. The results obtained are that each endoprime module is a weakly endoprime module, but the converse is not necessarily true. Moreover, a fully invariant submodule of a weakly endoprime module is not necessarily a weakly endoprime module.
Optimal Control for a COVID-19 and Tuberculosis Co-Infection Model with Asymptomatic COVID-19 Carriers Rizka, Sailah Ar; Ayu, Regina Wahyudyah Sonata; Ainurrofiqoh, Dewi Ika; Sari, Merysa Puspita; Kholifia, Nadia
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Volume 13 Issue 1 April 2025
Publisher : Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/euler.v13i1.31076

Abstract

This study applies optimal control theory to a deterministic co-infection model of COVID-19 and tuberculosis (TB) with asymptomatic COVID-19 carriers, who are assumed to be less infectious. The optimal control strategy aims to minimize intervention costs and reduce infections by implementing five control measures, including prevention and vaccination of COVID-19, treatment of both symptomatic and asymptomatic COVID-19-infected individuals, treatment of COVID-19 and active TB co-infected individuals, and prevention of treatment failure in active TB cases. Pontryagin's minimum principle is used to characterize the necessary conditions for optimal control in reducing infections. Numerical results demonstrate the effectiveness of the optimal control strategy in suppressing diseases. The incremental cost-effectiveness ratio (ICER) for different combinations of control measures is evaluated, showing that the intervention strategy performs best when all control measures are used.
Batas Perturbasi Mutlak Nilai Eigen dari Matriks Normal Ainurrofiqoh, Dewi Ika; Sari, Merysa Puspita; Rizka, Sailah Ar; Kholifia, Nadia
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Volume 13 Issue 2 August 2025
Publisher : Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/euler.v13i2.31084

Abstract

The eigenvalue problem in matrices is an important topic in numerical computation, particularly in analyzing the sensitivity of eigenvalues to disturbances or perturbations. This study discusses the absolute perturbation bounds on the eigenvalues of a matrix, focusing on normal matrices and their relationship to the condition of normal matrices. Based on existing theorems, the absolute perturbation bounds are presented in various forms involving the Frobenius norm and the condition number of the matrix eigenvectors. This research provides a detailed discussion of results concerning the absolute perturbation bounds on eigenvalues and their applications to normal matrices. Ultimately, an important result on the error bounds of eigenvalues in the case of normal matrices affected by perturbations is fully explained, proving the connection between the absolute error bound and the Frobenius norm of the perturbations.
Training on Creating Functions using GeoGebra at SMAN 5 Jember Merysa Puspita Sari; Ainurrofiqoh, Dewi Ika; Zahro, Millatuz; Mulyaningsih, Woro; Helmi, Muhammad Lutfi
Jurnal Inovasi Sains dan Teknologi untuk Masyarakat Vol. 3 No. 1 (2025): Mei
Publisher : Faculty of Mathematics and Natural Sciences, University of Jember. Jl. Kalimantan No.37, Krajan Timur, Jemberlor, Kec. Sumbersari, Jember Regency, East Java 68121

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/instem.v3i1.5504

Abstract

Mathematics education at the Senior High School level plays an important role in forming the foundational understanding of more complex mathematical concepts, one of which is algebraic function graphs. Despite its importance, many students face difficulties in understanding and drawing algebraic function graphs due to the limitations of traditional teaching tools. GeoGebra, a computer-based mathematics application, can be a solution to address this issue. GeoGebra offers advanced visual aids, allowing students to draw and analyze graphs interactively. The use of GeoGebra makes it easier to visualize various elements of graphs, such as intersection points, slopes, and extrema, and allows students to conduct experiments by manipulating function parameters. The aim of this community service activity is to introduce the concept of algebraic function graphs, teach the use of GeoGebra as a visual aid, and enhance students' analytical skills and learning motivation at SMAN 5 Jember. The methods applied includes the socialization and introduvtion of GeoGebra, interactive workshops, independent practice, and student understanding evaluation. The results of this activity show that students are more motivated and have a better understanding of algebraic function graphs after using GeoGebra. Therefore, the use of GeoGebra can be an effective alternative for teaching complex mathematical concepts at the Senior High School level.
Co-Authors Helmi, Muhammad Lutfi Kholifia, Nadia Merysa Puspita Sari Mulyaningsih, Woro Regina Wahyudyah Sonata Ayu Rizka, Sailah Ar Sari, Merysa Puspita Zahro, Millatuz