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All Journal MATEMATIKA SAINS DAN MATEMATIKA Jurnal Matematika Communication in Biomathematical Sciences International Journal of Supply Chain Management ComTech: Computer, Mathematics and Engineering Applications Jurnal Matematika UNAND Indonesian Journal of Electrical Engineering and Computer Science InPrime: Indonesian Journal Of Pure And Applied Mathematics Majalah Ilmiah Matematika dan Statistika (MIMS) Journal of Fundamental Mathematics and Applications (JFMA) Research Horizon Integra: Journal of Integrated Mathematics and Computer Science International Journal of Computing Science and Applied Mathematics-IJCSAM
Redemtus Heru Tjahjana
Department Of Mathematics, Diponegoro University Semarang, Indonesia
Arts Humanities Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Engineering Environmental Science Industrial & Manufacturing Engineering Law, Crime, Criminology & Criminal Justice Mathematics Social Sciences Transportation

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The Cleanness Property of The Integers Modulo n (ℤn) 'Aliyah, Dheva Ufiz; Puspita, Nikken Prima; Tjahjana, Redemtus Heru
Integra: Journal of Integrated Mathematics and Computer Science Vol. 1 No. 2 (2024): July
Publisher : Magister Program of Mathematics, Universitas Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/integrajimcs.20241214

Abstract

Assume that R is a ring with identity. A ring R is said to be clean when each of its elements can be written as the sum of an idempotent and a unit element within the ring. A stronger condition, known as strongly clean, requires that these elements commute under multiplication. As a special case, a module M over ring R is called a clean module when the endomorphism ring of the M is a clean module over R. Moreover, when the ring endomorphism of R-module M is a strongly clean, then the module M is referred to as a strongly clean. We know that the integers modulo n, denoted by ℤn, is a ring by the set of congruence classes modulo n, with standard addition and multiplication operations. In this study, we explore the cleanness properties of the ring ℤn and establish that it is a strongly clean ring. Furthermore, we study about the cleanness of ℤn as a module over ℤ and investigate the strongly cleanness of it module.
Uncoupled Two Agents Modeling Via Bilinear Optimal Control Tjahjana, R. Heru
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol. 4 No. 1 (2022)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v4i1.24969

Abstract

In this paper, uncoupled two agents modeling is proposed using an optimal bilinear control approach. The model is proposed using assumptions: an absence of the multi agent leader, each agent cannot control the others, each agent never collides with the others, and each agent has the same properties. The special functional cost consisting of a repellent cost is considered. The Pontryagin Maximum Principle is used to determine the optimal path for each agent. After control and optimal path for each agent are obtained some of the simulation results are exposed in this paper.Keywords: uncoupled agent; modeling; bilinear system. AbstrakDalam penelitian ini, pemodelan dua agen yang tidak berpasangan disajikan dengan pendekatan kontrol optimal bilinear. Model yang diusulkan dalam paper ini ditulis dengan asumsi: tidak adanya pemimpin dalam sistem multi agen, setiap agen tidak dapat mengendalikan atau mempengaruhi agen yang lain, setiap agen tiak boleh bertabrakan satu sama lain, dan para agen mempunyai sifat-sifat yang identik. Fungsional biaya khusus yang membuat para agen tidak bertabrakan dipertimbangkan dalam penulisan paper ini. Prinsip maksimum Pontryagin digunakan dalam penentuan lintasan optimal dari para agen.  Beberapa hasil simulasi disajikan dalam paper ini.Kata Kunci: agen tak berpasangan; pemodelan; sistem bilinear.
Optimal Control Approach For HIV-1 Infection in CD4+T Cells with RTI and PI Treatments R. Heru Tjahjana; Sutimin Sutimin
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol. 6 No. 2 (2020)
Publisher : LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

The purpose of this paper is to expose the optimal approach of controlling HIV-1 infection in CD4+T cells with Reverse Transcriptease Inhibitors (RTI) and Protease Inhibitors (PI) treatments. The scope of the paper includes a proposed model of the dynamic system of HIV-1 infection in CD4 cells with RTI and PI as controls and a proposed objective function model that minimizes infected CD4+T Cells, the population of free virus and therapeutic costs. From the dynamics system model and objective function model, we designed an optimal control for HIV-1 infection control. In this paper, we obtained optimal control for RTI and PI therapies. The results of this paper are as follows: by using the optimal control approach, we obtained infectious control strategy that minimizes actively infected CD4+T Cells, the population of free virus and the cost of treatment. In other words, optimal control is a good approach in determining infection control strategies that minimizes the objective function.
Local Stability Analysis of Mathematic Model SEIHR-VW on Dengue Haemorrhagic Fever Transmission Nolaika Arsiani Norramandhany; Widowati Widowati; Redemtus Heru Tjahjana
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol. 11 No. 2 (2025)
Publisher : LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/j24775401.ijcsam.v11i2.6054

Abstract

Dengue fever is caused by the dengue virus (DENV) and is mainly transmitted by mosquitoes, particularly Aedes aegypti. In this study, we develop a mathematical model to describe and analyze how dengue spreads within a population. The mathematical model is expressed as a nonlinear system of differential equations and consists of seven compartments (SEIHRVW): susceptible, exposed, infected, hospitalized, and recovered humans, along with susceptible and infected mosquitoes. The model has two possible equilibrium points: a non-endemic and endemic equilibrium point. To better understand the dynamics of the model, we calculate the basic reproduction number (R0) using the Next Generation Matrix (NGM) method, and then the Routh-Hurwitz criterion method is applied to analyze the local stability of both equilibrium points. The results indicate that the nonendemic equilibrium point is asymptotically stable when R0 < 1, while the endemic equilibrium point becomes asymptotically stable when R0 > 1. In general, our analysis concludes that the proposed dengue transmission model is asymptotically stable at the endemic equilibrium point, with R0 = 3.85011.
Co-Authors 'Aliyah, Dheva Ufiz Agus Setyawan Agus Subagio Aulia, Lathifatul Bambang Irawanto Devi Larasati Djalal Er Riyanto Etna Vianita Harjum Muharam I Gusti Ngurah Antaryama Jatmiko Endro Suseno Kartono . L Niswah, L Lucia Ratnasari Lucia Ratnasari Madchan Anis Mahardika, Dhimas MINARSIH MINARSIH Moch. Abdul Mukid Muhammad Nur Mustafid Mustafid Nikken Prima Puspita Nolaika Arsiani Norramandhany Okky Widya Arditya Prameswari, Balqies Gabriella Priyo Sidik Sasongko Rahman, Aini Ririn Sulpiani Robertus Heri Sulistyo Utomo Satriyo Adhy SITI KHOLIFAH Solichin Zaki Solikhin Solikhin Sudarno Sudarno Sunarsih Sunarsih Sutimin Sutimin Sutimin Sutimin sutimin sutimin Sutrisno Sutrisno Sutrisno, Sutrisno Titi Udjiani SRRM Udi Harmoko Utomo, R. Heri Soelistyo Utomo, R. Heri Soelistyo Vianita, Etna Widowati, Widowati Yundari, Yundari