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All Journal Epsilon: Jurnal Matematika Murni dan Terapan Desimal: Jurnal Matematika BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Bubungan Tinggi: Jurnal Pengabdian Masyarakat Jurnal Abdimas Prakasa Dakara
Muhammad Ahsar Karim
Program Studi Matematika FMIPA Universitas Lambung Mangkurat
Humanities Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Energy Engineering Mathematics Mechanical Engineering Physics Social Sciences Transportation Other

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KRITERIA KEKONVERGENAN CAUCHY PADA RUANG METRIK KABUR INTUITIONISTIC Muhammad Ahsar Karim; Faisal Faisal; Yuni Yulida
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 6, No 1 (2012): JURNAL EPSILON VOLUME 6 NOMOR 1
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (143.296 KB) | DOI: 10.20527/epsilon.v6i1.78

Abstract

In this paper, we construct the Cauchy-convergence criterion in intuitionistic fuzzy metricspace. We start our aim by given the definition of concepts convergence sequence, Cauchysequence, and complete on intuitionistic fuzzy metric space.
TEOREMA TITIK TETAP BANACH PADA RUANG METRIK-D Muhammad Ahsar Karim; Dewi Sri Susanti; Nurul Huda
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 4, No 2 (2010): JURNAL EPSILON VOLUME 4 NOMOR 2
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (264.373 KB) | DOI: 10.20527/epsilon.v4i2.58

Abstract

In the space of metrics known the fixed point theorem of Banach. In this paper, the theorem will be constructed in the D-metric space. This study begins with construction concepts: open ball, open set, convergent lines, and Cauchy rows respectively in the D-metric space. Then given the concept of continuous mapping and mapping continuous uniform in the D-metric space. Further constructed Banach's fixed point theorem at in the D-metric space.
PEMBENTUKAN PERSAMAAN VAN DER POL DAN SOLUSI MENGGUNAKAN METODE MULTIPLE SCALE Farohatin Na'imah; Yuni Yulida; Muhammad Ahsar Karim
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 14, No 2 (2020): JURNAL EPSILON VOLUME 14 NOMOR 2
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (598.033 KB) | DOI: 10.20527/epsilon.v14i2.958

Abstract

Mathematical modeling is one of applied mathematics that explains everyday life in mathematical equations, one example is Van der Pol equation. The Van der Pol equation is an ordinary differential equation derived from the Resistor, Inductor, and Capacitor (RLC) circuit problem. The Van der Pol equation is a nonlinear ordinary differential equations that has a perturbation term. Perturbation is a problem in the system, denoted by ε which has a small value 0<E<1. The presence of perturbation tribe result in difficulty in solving the equation using anlytical methode. One method that can solve the Van der Pol equation is a multiple  scale method. The purpose of this study is to explain the constructions process of  Van der Pol equation, analyze dynamic equations around equilibrium, and determine the solution of Van der Pol equation uses a multiple scale method. From this study it was found that the Van der Pol equation system has one equilibrium. Through stability analysis, the Van der Pol equation system will be stable if E= 0 and  -~<E<=-2. The solution of the Van der Pol equation with the multiple scale method is Keywords: Van der Pol equation, equilibrium, stability, multiple scale. 
PEMODELAN MATEMATIKA PENYEBARAN COVID-19 DENGAN MODEL SVEIR Gian Septiansyah; Muhammad Ahsar Karim; Yuni Yulida
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol. 16(2), 2022
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v16i2.6496

Abstract

Coronavirus disease 2019 or also known as Covid-19 is a disease caused by a type of coronavirus called Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) or better known as the corona virus. Covid-19 become a pandemic since 2020 and has been widely studied, one of which is in mathematical modeling. In this study, the spread of Covid-19 is modeled using the SVEIR (Susceptible, Vaccination, Exposed, Infected, and Recovered) model. The purpose of this study explains the formation of the Covid-19 SVEIR model, determines the equilibrium point, determines the basic reproduction number, and analyzes the stability of the Covid-19 SVEIR model. The purpose of this study explains the formation of the Covid-19 SVEIR model, determines the equilibrium point, the basic reproduction number, and analyzes the stability of the Covid-19 SVEIR model. The result of this study is to explain the formation of the Covid-19 SVEIR model and obtained two equilibrium points, the disease-free equilibrium point and the endemic equilibrium point. Furthermore, the basic reproduction number  is obtained through the Next Generation Matrix method. The results of the stability analysis at the disease-free equilibrium point were locally asymptotically stable with conditions  while at the endemic equilibrium point local asymptotically stable with conditions . The natural death rate is greater than the effective contact rate. A numerical simulation is presented to show a comparison spread of Covid-19 by providing different levels of vaccine effectiveness using the Runge-Kutta Order method.
Pelatihan Calon Pembina Olimpiade Sains Nasional Bidang Matematika bagi MGMP Matematika SMA Kabupaten Hulu Sungai Tengah Muhammad Ahsar Karim; Yuni Yulida; Azkia Khairal Jamil; Riska Fitria; Gabriel Henokh Gultom; Raihan Nooriman; Rizky Purnama Wulandari
Bubungan Tinggi: Jurnal Pengabdian Masyarakat Vol 4, No 4 (2022)
Publisher : Universitas Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/btjpm.v4i4.6245

Abstract

Olimpiade Sains Nasional bidang Matematika tingkat SMA merupakan kompetisi bergengsi bagi siswa SMA/MA di seluruh Indonesia yang memerlukan strategi dan teknik penyelesaian soal-soal yang cenderung tidak standar, pemahaman konsep yang mendalam, dan ide kreatif. Melalui kegiatan PDWM ULM Tahun 2022, tim dosen Program Studi Matematika FMIPA ULM sebagai pelaksana dan MGMP Matematika SMA HST sebagai mitra bekerja sama menyelenggarakan kegiatan pelatihan Olimpiade Sains Nasional bidang Matematika bagi anggota MGMP Matematika SMA Kabupaten Hulu Sungai Tengah. Kegiatan ini bertujuan untuk menambah pengetahuan dan meningkatkan kemampuan anggota MGMP Matematika SMA HST agar dapat melaksanakan pembinaan Olimpiade Sains Nasional bidang Matematika bagi siswa di sekolah masing-masing. Metode yang digunakan dalam kegiatan ini adalah ceramah, diskusi, dan latihan mandiri. Kegiatan dilaksanakan selama dua hari, yaitu hari pertama yang berlangsung secara offline di sekretariat MGMP Matematika SMA HST dan hari kedua yang berlangsung secara online. Hasil evaluasi kegiatan melalui pree-test dan post-test menunjukkan adanya peningkatan signifikan dari pengetahuan dan kemampuan peserta, dengan rata-rata nilai hasil test dari peserta meningkat sebesar 41 poin pada post-test dibandingkan pada pree-test. Maksimum perubahan nilai dari pree test ke post-test adalah 90 poin, sedangkan minimum perubahan nilai dari pree test ke post-test adalah 5 poin. Melalui survey di akhir kegiatan, peserta menyampaikan harapan agar kegiatan pengabdian ini dapat berlanjut, diadakan secara berkala, dan dilaksanakan full offline.The National Science Olympiad in Mathematics at the Senior High School level is a prestigious competition for high school students throughout Indonesia who require strategies and techniques for solving questions that tend to be non-standard, in-depth understanding of concepts and creative ideas. Through the PDWM ULM 2022 program, a team of lecturers from the Program Studi Matematika FMIPA ULM as implementers and the association of MGMP Matematika SMA in Hulu Sungai Tengah Regency as partners collaborated in organizing training for the National Science Olympiad in Mathematics for members of the association. This activity aims to increase knowledge and improve the members' ability so that they can coach the National Science Olympiad in Mathematics for students in their respective schools. The methods used in this activity are lectures, discussions, and independent exercises. The activity was carried out for two days, the first day, which took offline at the MGMP Matematika SMA secretariat, and the second day, which took online. The results of the evaluation of activities through the pre-test and post-test showed a significant increase in the knowledge and abilities of the participants, with the average test score of the participants increasing by 41 points in the post-test compared to the pre-test. The maximum change in value from the pre-test to the post-test is 90 points, while the minimum change in value from the pre-test to the post-test is 5 points. Through a survey at the end of the activity, participants expressed their hope that this training could continue, be held regularly, and be carried out fully offline.
Pelatihan Olimpiade Sains Nasional Bidang Matematika pada Siswa SMAN 1 Bati-Bati Kabupaten Tanah Laut Provinsi Kalimantan Selatan Karim, Muhammad Ahsar; Yulida, Yuni; Faisal, Faisal; Hidayati, Nor; Arif, Alya Hanifah; Firmansyah, Audinta Sakti; Rosyadi, Gusti Muhammad
Jurnal Abdimas Prakasa Dakara Vol. 3 No. 2 (2023): Pengembangan Pendidikan dan Keterampilan Masyarakat
Publisher : LPPM STKIP Kusuma Negara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37640/japd.v3i2.1849

Abstract

Salah satu bidang favorit di kompetisi Olimpiade Sains Nasional adalah bidang Matematika. Dalam kompetisi ini, siswa memerlukan pemahaman konsep yang mendalam dan ide kreatif terhadap soal-soal olimpiade yang dihadapi. Kegiatan ini bertujuan untuk meningkatkan kemampuan dan pemahaman siswa dalam menyelesaikan soal-soal olimpiade. Metode yang dilakukan berupa ceramah, diskusi, dan latihan mandiri. Penyampaian materi yang paling ditekankan adalah bagaimana memahami soal dan memberikan tips penyelesaian. Untuk mengukur kemampuan dan pemahaman siswa, diberikan soal-soal yang relevan dengan olimpiade. Soal tersebut berupa pretes dan postes merupakan soal yang sama dengan tujuan untuk melihat apakah ada pengaruh sesudah dilaksanakan pelatihan. Hasil evaluasi kegiatan ini dilakukan melalui hasil pretes dan postes yang diperoleh, dengan menggunakan uji Wilcoxon, yaitu ada berpengaruh pelatihan terhadap kemampuan dan pemahaman siswa dalam menyelesaikan soal-soal olimpiade. Dari 21 siswa, 17 siswa mengalami peningkatan dan 4 siswa memiliki nilai yang sama. Nilai minimum dan maksimum yang diperoleh pada saat pretes adalah 0 dan 40 poin, sedangkan saat postes adalah 20 dan 60. Rata-rata total peningkatan nilai sebesar 28.571. Selain itu, hasil evaluasi peserta terhadap seluruh rangkaian kegiatan pelatihan disimpulkan baik dan sangat baik.
ANALISIS SENSITIVITAS MODEL EPIDEMI SIR DAN SVIR PADA PENYAKIT MENULAR Munaira, Hanna; Yulida, Yuni; Karim, Muhammad Ahsar
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN (EPSILON: JOURNAL OF PURE AND APPLIED MATHEMATICS) Vol 18, No 1 (2024)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v18i1.12139

Abstract

Penyakit menular merupakan penyakit yang disebabkan oleh mikroorganisme patogen seperti bakteri, virus, parasit, atau jamur. Penyakit ini dapat menyebar, baik secara langsung maupun tidak, dari satu individu ke individu lainnya. Penyebaran penyakit menular dapat dimodelkan dengan pemodelan matematika epidemi Kermack-McKendrick. Penelitian ini bertujuan untuk menjelaskan pembentukan model matematika, menentukan titik ekuilibrium serta bilangan reproduksi dasar, dan menganalisis kestabilan lokal pada model matematika. Selain itu, dilakukan analisis sensitivitas terhadap bilangan reproduksi dasar dan simulasi numerik dengan metode Runge-Kutta orde 4. Dari penelitian ini, diperoleh bentuk model epidemi SIR (Susceptible, Infected, Recovered) dan modifikasi model tersebut menjadi model SVIR (Susceptible, Vaccinated, Infected, Recovered). Berdasarkan model yang terbentuk, diperoleh titik ekuilibrium bebas penyakit dan titik ekuilibrium endemik pada masing-masing model. Bilangan reproduksi dasar masing-masing model ditentukan dengan menggunakan metode Next Generation Matrix. Kemudian, dengan menggunakan nilai eigen dari matriks Jacobian, diketahui jenis kestabilan kedua model pada masing-masing titik ekuilibrium adalah stabil asimtotik lokal dengan syarat tertentu. Analisis sensitivitas menunjukkan parameter yang paling sensitif terhadap perubahan bilangan reproduksi dasar jika diurutkan dari yang terbesar untuk model SIR adalah laju penularan, laju kelahiran/kematian, dan laju kesembuhan. Sedangkan, untuk model SVIR adalah laju penularan, laju kelahiran/kematian, laju kesembuhan, dan proporsi populasi yang telah divaksinasi. Analisis-analisis ini juga diperkuat oleh hasil simulasi numerik.
Analysis of stability and bifurcation in logistics models with harvesting in the form of the holling type III functional response Yulida, Yuni; Nurrobi, Firman; Faisal, Faisal; Karim, Muhammad Ahsar
Desimal: Jurnal Matematika Vol. 5 No. 1 (2022): Desimal: Jurnal Matematika
Publisher : Universitas Islam Negeri Raden Intan Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/djm.v5i1.11828

Abstract

The logistic model can be applied in the field of biological studies to investigate population growth problems and some important aspects of the ecological situation. This model is a growth model with a limited population growth rate, and ecologists describe this rate as carrying capacity. Carrying capacity can be interpreted as the ideal population size, where individuals in the population can live properly in their environment. The growth rate of a population can be influenced by the harvesting factor, in this case, it is assumed that harvesting is not constant. The effect of the harvest on the growth rate can be analyzed mathematically by using the Holling type III functional response. In this paper, describe the formation of a logistic model taking into account the effects of harvesting, using the Holling type III functional response. Then,  perform a nondimensional process in the model, namely simplifying a model that has four parameters to a model that only has two parameters. Next, determine the equilibrium point of the model, perform a stability analysis at that equilibrium point, and investigate the possibility of bifurcation. As result, first obtained a logistic model which has two non-dimensional parameters, where one of the equilibrium points is zero and is unstable. Next, determine another equilibrium point through an implicit equation and investigate its stability through simulation. Finally, obtained two equilibrium points, which are fold bifurcation.
SACR EPIDEMIC MODEL FOR THE SPREAD OF HEPATITIS B DISEASE BY CONSIDERING VERTICAL TRANSMISSION Yulida, Yuni; Wiranto, Agung Setyo; Faisal, Faisal; Karim, Muhammad Ahsar; Soesanto, Oni
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 4 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss4pp2491-2504

Abstract

Hepatitis B is an infectious disease that causes inflammation of the liver due to infection with the Hepatitis B virus. Hepatitis B is divided into two phases: the acute phase and the chronic phase. Hepatitis B virus (HBV) can be prevented through vaccination and treatment of susceptible and infected individuals. The spread of the virus can be modeled using mathematical modeling of epidemics. In this study, the model used consists of four classes, namely vulnerable individuals (S), acute individuals (A), chronic individuals (C), and recovered individuals (R). The purpose of this study is to explain the formation of the Hepatitis B disease epidemic model, analyze the stability of the model, perform simulations, and conduct parameter sensitivity analysis on the basic reproductive number. The result of this study is the construction of an epidemic model of the spread of hepatitis B disease in the form of a SACR model. This model takes into account the transmission that occurs not only through interactions between susceptible individuals and chronic individuals but also through the birth process, which occurs in chronic subpopulations because babies born can be chronically infected (vertical transmission from mother to baby). The model produces two equilibrium points, the disease-free equilibrium and the endemic equilibrium. Both points were analyzed for stability using the linearization method and were found to be asymptotically stable. Furthermore, the model simulation was carried out using the fourth-order Runge-Kutta method and sensitivity analysis of the basic reproduction number. From the results obtained, it can be concluded that the spread of hepatitis B disease can be minimized by reducing contact between susceptible and chronic individuals, increasing treatment of chronic individuals, and increasing the number of vaccinated individuals in susceptible populations.
Co-Authors Arif, Alya Hanifah Azkia Khairal Jamil Dewi Sri Susanti Faisal Faisal Faisal Faisal Faisal Faisal Farohatin Na&#039;imah Firman Nurrobi Firmansyah, Audinta Sakti Fitri Nor Annisa Gabriel Henokh Gultom Gian Septiansyah Gian Septiansyah Gita Sari Adriani Haidir Ahsana mariyati mariyati Miftahul Jannah Muhammad Mahfuzh Shiddiq Muhammad Mahfuzh Shiddiq Muhammad Mefta Eryshady Munaira, Hanna Nurrobi, Firman Nurul huda Oni Soesanto Pardi Affandi Raihan Nooriman Riska Fitria Rizky Purnama Wulandari Rosyadi, Gusti Muhammad Soesanto, Oni Wiranto, Agung Setyo Yuni Yulida