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All Journal Jurnal KARISMATIKA JURNAL SAINS INDONESIA
Sitompul, Pardomuan
Universitas Negeri Medan
Computer Science & IT Education Mathematics Social Sciences

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Analisis Perilaku Solusi Sistem Dinamik Glukosa-Insulin dari Model Minimal Bergman Manalu, Martha Devi; Sitompul, Pardomuan
Jurnal Sains Indonesia Vol 42, No 1 (2018): Jurnal Sains Indonesia
Publisher : Universitas Negeri Medan

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Abstract

Diabetes Mellitus is broadly classified into two categories, namely type 1 and type 2 diabetes. In this study, the model used was a model that interpreted the glucose-insulin dynamics in everyone, except for people who have type 1 diabetes. Bergman Minimal Model which interprets the dynamics of glucose-insulin in the human body is a non-linear autonomous system consisting of three equations and eight parameters. From the results of the study, it was concluded that in this model there is only one equilibrium point, namely x^*=(G_b,0,I_b ). This equilibrium point means that the glucose concentration over time will be as large as the basal concentration (G_b). Active insulin that is already in the body of every human being will go to zero, meaning that over time it will disappear, and the insulin that has been secreted by the pancreas will remain at the threshold (I_b). All eigenvalues of polynomials formed from the linearization process and the Jacobian matrix in the Bergman Minimal Model are of negative real value. Based on the Stability Criteria Theorem, the glucose-insulin system of the Bergman Minimal Model is asymptotically stable around its equilibrium point.
Analisis Perilaku Solusi Sistem Dinamik Glukosa-Insulin dari Model Minimal Bergman Manalu, Martha Devi; Sitompul, Pardomuan
Jurnal Sains Indonesia Vol 42, No 1 (2018): Edisi Januari - Juni
Publisher : Universitas Negeri Medan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24114/jsi.v42i1.12240

Abstract

Abstract  Diabetes Mellitus is broadly classified into two categories, namely type 1 and type 2 diabetes. In this study, the model used was a model that interpreted the glucose-insulin dynamics in everyone, except for people who have type 1 diabetes. Bergman Minimal Model which interprets the dynamics of glucose-insulin in the human body is a non-linear autonomous system consisting of three equations and eight parameters. From the results of the study, it was concluded that in this model there is only one equilibrium point, namely x^*=(G_b,0,I_b ). This equilibrium point means that the glucose concentration over time will be as large as the basal concentration (G_b). Active insulin that is already in the body of every human being will go to zero, meaning that over time it will disappear, and the insulin that has been secreted by the pancreas will remain at the threshold (I_b). All eigenvalues of polynomials formed from the linearization process and the Jacobian matrix in the Bergman Minimal Model are of negative real value. Based on the Stability Criteria Theorem, the glucose-insulin system of the Bergman Minimal Model is asymptotically stable around its equilibrium point.  [ANALYSIS OF GLUCOSE-INSULIN DYNAMIC SYSTEM SOLUTIONS BEHAVIOR FROM THE BERGMAN MINIMAL MODEL] (J. Sains Indon., 42(1): 1-6, 2018)
ANALISIS PENGARUH KUALITAS LAYANAN PADA E-WALLET TERHADAP LOYALITAS PELANGGAN MELALUI KEPUASAN PELANGGAN MENGGUNAKAN METODE SEM Syahriza . Aini; Pardomuan . Sitompul
KARISMATIKA: Kumpulan Artikel Ilmiah, Informatika, Statistik, Matematika dan Aplikasi Vol 7, No 2 (2021): Karismatika
Publisher : Universitas Negeri Medan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24114/jmk.v7i2.32314

Abstract

Structural Equation Modelling atau SEM adalah salah satu metode statistika yang dapat mengukur unobserved variable. Dalam mengukur unobserved variable SEM membutuhkan observed variable atau yang disebut variabel indikator. Unobserved Variable yang dimaksudkan meliputi variabel Kualitas Layanan, variabel Kepuasan Pelanggan dan variabel Loyalitas Pelanggan. Tujuan dari penelitian ini adalah melihat variabel kepuasan pelanggan mengintervening variabel kualitas layanan terhadap loyalitas pelanggan pada e-wallet di kalangan mahasiswa/i Universitas Negeri Medan. Kualitas layanan e-wallet diharapkan dapat meningkatkan kepuasan pelanggan dan menumbuhkan rasa loyal pelanggan. Berdasarkan hasil analisis SEM dengan bantuan program aplikasi AMOS, didapati pengaruh langsung (direct effect) paling signifikan terhadap loyalitas pelanggan adalah variabel kepuasan pelanggan dengan hasil estimasinya adalah 1,809, pengaruh tidak langsung (indirect effect) antar variabel tidak ada karena variabel kepuasan pelanggan tidak mengintervening varibel kualitas layanan terhadap loyalitas pelanggan sehingga pengaruh total (total effect) yang terbentuk sama dengan pengaruh langsungnya.Structural Equation Modeling or SEM is a statistical method that can measure unobserved variables. In measuring unobserved variables, SEM requires observed variables or so-called indicator variables. The intended Unobserved Variables include Service Quality variables, Customer Satisfaction variables and Customer Loyalty variables. The purpose of this study was to look at the customer satisfaction variable intervening the service quality variable on customer loyalty on e-wallet among students at the State University of Medan. The quality of e-wallet services is expected to increase customer satisfaction and foster a sense of customer loyalty. Based on the results of SEM analysis with the help of the AMOS application program, it was found that the most significant direct effect on customer loyalty is the customer satisfaction variable with the estimated result being 1.809, the indirect effect between variables does not exist because the customer satisfaction variable does not intervene in the variable. service quality on customer loyalty so that the total effect formed is the same as the direct effect. 
APLIKASI PEWARNAAN GRAF PADA PENYUSUNAN JADWAL MATA KULIAH JURUSAN MATEMATIKA DI FMIPA UNIVERSITAS NEGERI MEDAN Ria Rahadi Nasution; Pardomuan . Sitompul
KARISMATIKA: Kumpulan Artikel Ilmiah, Informatika, Statistik, Matematika dan Aplikasi Vol 6, No 2 (2020): Karismatika
Publisher : Universitas Negeri Medan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24114/jmk.v6i2.23337

Abstract

 ABSTRAKPenyusunan Jadwal perkuliahan adalah kegiatan rutin yang yang dikerjakan Universitas Negeri Medan dalam tiap semester untuk menunjang proses kegiatan belajar mengajar di perguruan tinggi. Oleh karena itu diperlukan cara atau solusi penyusunan jadwal yang efisien. Tujuan penelitian ini adalah untuk membangun aplikasi penjadwalan mata kuliah di Jurusan Matematika Universitas Negeri Medan menggunakan AlgoritmaWelch Powell yang berfungsi untuk mengoptimasi penyusunan jadwal mata kuliah dengan metode pewarnaan graf, dimana simpul yang bertetangga diberi warna berbeda satu sama lain, sehingga menghasilkan bilangan kromatik (jumlah warna). Metode penelitian yang digunakan adalah studi literatur. Setelah data diperoleh dari literatur utama maupun literatur pendukung, selanjutnya dianalisis untuk mengetahui aplikasi pewarnaan graf pada penjadwalan perkuliahan di Jurusan Matematika Universitas Negeri Medan. Kata Kunci: Penjadwalan Perkuliahan, Pewarnaan graf, Algoritma Welch PowellABSTRACTPreparation Lecture schedule is a routine activity that the State University of Medan in each semester to support the process of teaching and learning activities in universities. Therefore, an efficient way of planning or solution is needed. The purpose of this research is to build the application of subject scheduling at Department of Mathematics of State University of Medan using AlgorithmaWelch Powell which function to optimize the preparation of the schedule of course with graph coloring method, where neighboring nodes are given different color from each other, thus producing chromatic number (number of colors). The research method used is literature study. After the data obtained from the main literature and supporting literature, then analyzed to determine the application of graph coloring on lecturing scheduling at the Department of Mathematics, State University of Medan.Keywords : Lecturing Scheduling, Graph coloring, Welch Powell Algorithm
PERILAKU SOLUSI PADA MODEL EPIDEMI SUSCEPTIBLE INFECTED RECOVERED (SIR) DENGAN WAKTU TUNDA Muhammad Aidil Pahlevi; Pardomuan . Sitompul
KARISMATIKA: Kumpulan Artikel Ilmiah, Informatika, Statistik, Matematika dan Aplikasi Vol 7, No 3 (2021): Karismatika
Publisher : Universitas Negeri Medan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24114/jmk.v7i3.32458

Abstract

Model epidemi SIR adalah model penyebaran penyakit yang berbentuk sistem persamaan diferensial nonlinier. Adanya waktu tunda mempengaruhi kestabilan titik kesetimbangan model epidemi SIR. Waktu tunda menyatakan waktu inkubasi penyakit. Pada penelitian ini, tahapan yang dilakukan untuk mengetahui perilaku solusi model epidemi SIR dengan waktu tunda menggunakan beberapa asumsi, kemudian menentukan titik kesetimbangan, menganalisis kestabilan di sekitar titik kesetimbangan serta melakukan simulasi numerik menggunakan Matlab. Berdasarkan hasil analisis, model epidemi SIR dengan waktu tunda adalah stabil asimtotik di titik kesetimbangan bebas  penyakit   apabila syarat parameter  terpenuhi dan stabil di titik kesetimbangan endemik  apabila syarat parameter  terpenuhi. Selanjutnya, dari simulasi menggunakan Matlab diperoleh grafik yang dapat mempermudah menjelaskan perilaku solusinya. Abstract— The SIR epidemic model is a disease spread model in the form of a system of nonlinear differential equations. The time delay affects the stability of the equilibrium point of the SIR epidemic model. The time delay represents the incubation time of the disease. In this study, the steps were carried out to determine the behavior of the SIR epidemic model solution with a time delay using several assumptions, then determining the equilibrium point, analyzing the stability around the equilibrium point and performing numerical simulations using Matlab. Based on the results of the analysis, the SIR epidemic model with a time delay is asymptotically stable at the disease-free equilibrium point  if the parameter conditions  have been met and stable at the endemic equilibrium point  if the parameter conditions  have been met. Furthermore, from the simulation using Matlab, a graph is obtained that can make it easier to explain the behavior of the solution.
Co-Authors Manalu, Martha Devi Muhammad Aidil Pahlevi Ria Rahadi Nasution Syahriza . Aini