Jurnal Riset Mahasiswa Matematika
Jurnal Riset Mahasiswa Matematika (JRMM) publishes current research articles in any area of Mathematics Research such as graph labelings, modeling, statistics, actuaria, optimal network problems, metric dimension, graph coloring, rainbow connection and other related topics. JRMM is published six times a year, namely in February, April, June, August, October, December JRMM is published by the Association of Indonesian Islamic Religious University Mathematics Lecturers and Department of Mathematics Universitas Islam Negeri Maulana Malik Ibrahim Malang (UIN Malang). All papers will be refereed in the normal manner of mathematical journals to maintain the high standards. JRMM is an open access journal. Full-text access to all papers is available for free. Jurnal Riset Mahasiswa Matematika (JRMM) has been indexed by Google Scholar
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173 Documents
<![CDATA[Metode Enhanced Trinomial Pada Aproksimasi Numerik Pada Barrier Options Pricing ]]>
<![CDATA[Muhammmad Hasan Asnawi]]>;
<![CDATA[Abdul Aziz]]>
<![CDATA[ Jurnal Riset Mahasiswa Matematika Vol 1, No 1 (2021): Jurnal Riset Mahasiswa Matematika ]]>
Publisher : <![CDATA[Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang ]]>
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DOI: 10.18860/jrmm.v1i1.13412
<![CDATA[Barrier options pricing sering digunakan dalam jual beli saham karena memiliki harga yang lebih murah dari harga saham plain vanilla option. Dengan menggunakan metode trinomial, didapatkan tiga kemungkinan nilai pergerakan saham yaitu nilai saham naik, turun, dan tetap. Nilai parameter-parameter dari metode trinomial diperoleh dengan menentukan nilai peluang tetapnya . Selanjutnya dicari nilai peluang naik dan turunnya dengan menyamakan ekspektasi diskrit dengan kontinu dan menyamakan variansi diskrit dengan kontinu.Metode enhanced trinomial merupakan metode trinomial yang nilai sahamnya didekati menggunakan nilai upper dan lower barrier dengan rumus enhanced numerical. Sehingga didapatkan nilai opsi saham yang lebih kecil daripada metode trinomial standar. Oleh karena itu, dengan metode enhanced trinomial nilai opsi saham yang lebih cepat konvergen. hal ini dibuktikan dari simulasi yang telah dilakukan dalam penelitian ini]]>
<![CDATA[Bilangan Kromatik Titik dari Dual Graf Berlian ]]>
<![CDATA[Nurul Hafidhoh Anwar]]>;
<![CDATA[Mohammad Nafie Jauhari]]>;
<![CDATA[Dewi Ismiarti]]>
<![CDATA[ Jurnal Riset Mahasiswa Matematika Vol 1, No 6 (2022): Jurnal Riset Mahasiswa Matematika ]]>
Publisher : <![CDATA[Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang ]]>
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DOI: 10.18860/jrmm.v1i6.14517
<![CDATA[A vertex coloring of a graph , is an assigments of colors to the vertices of , such that no two adjacent vertices are assigned the same color. The least number of colors needed for an vertices coloring of a graph is the chromatic number, denoted by . A graph is said to be planar if it can be drawn in the plane so that no edges crossing except at endpoints. A dual graph is constructed from the planar graph. Each region in planar graph can be represented by a vertex of the dual graph. Two vertices are connected if the region represented by these vertices are neugbours and have a common border. A diamond graph denoted by , can be used to model structure networks. In this study, it is shown that the chromatic number of dual diamond graph is χ(〖Br_n〗^* )={█(3,n=2 and n≥4@4,n=3.)┤]]>
<![CDATA[Metode Backward Time Central Space dalam Penyelesaian Model Matematika Vibrasi Dawai pada Alat Musik Petik ]]>
<![CDATA[Atik Damayanti]]>;
<![CDATA[Ari Kusumastuti]]>;
<![CDATA[Nurul A. Hidayati]]>
<![CDATA[ Jurnal Riset Mahasiswa Matematika Vol 1, No 4 (2022): Jurnal Riset Mahasiswa Matematika ]]>
Publisher : <![CDATA[Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang ]]>
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DOI: 10.18860/jrmm.v1i4.14454
<![CDATA[This research was conducted to obtain a numerical solution of the mathematical model of string vibration on stringed instruments. This mathematical model is a representation of the phenomenon of string vibration on a stringed instrument subject to deviation. The model was constructed by Kusumastuti, et al (2017) and is in the form of a second-order partial differential equation. The method used in completing this research is the BTCS (Backward Time Central Space) method. The numerical solution is obtained by the following steps, 1). Discretize mathematical models, as well as discretize initial conditions and boundary conditions. 2). Performing stability analysis of numerical solutions to determine the terms of solution stability and conducting consistency analysis as a condition of the convergence of the obtained numerical solutions. 3). Simulate numerical solutions and perform graph interpretations. The results show that the numerical solution of the mathematical model of string vibration on stringed instruments is unconditionally stable and has an error order (〖∆x〗^2,〖∆t〗^3).]]>
<![CDATA[Indeks Eksentrisitas Zagreb Pertama dan Kedua Graf Koprima dari Grup Matriks Upper Unitriangular atas Ring Bilangan Bulat Modulo Prima ]]>
<![CDATA[Muhammad Aris Abdillah]]>;
<![CDATA[Dewi Ismiarti]]>
<![CDATA[ Jurnal Riset Mahasiswa Matematika Vol 2, No 2 (2022): Jurnal Riset Mahasiswa Matematika ]]>
Publisher : <![CDATA[Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang ]]>
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DOI: 10.18860/jrmm.v2i2.15668
<![CDATA[The coprime graph of a group G is a graph Γ_G with G is its set of vertices and any two distinct vertices are adjacent if and only if their order are relatively prime. Let p be a prime number, then G_p denotes the multiplicative group of 2×2 upper unitriangular matrices over ring of integers modulo p. The purposes of this research are to study the coprime graph Γ_(G_p ) and find the first and the second Zagreb eccentricity indices of Γ_(G_p ) for p≥3. The results of this research are as follows. First Zagreb eccentricity index of coprime graph Γ_(G_p )isE_1 (Γ_(G_p ))=4p-3. Second Zagreb eccentricity index of coprime graph Γ_(G_p )isE_2 (Γ_(G_p ))=2p-2.]]>
<![CDATA[Simulasi Model Diskrit Respon Sistem Imun pada Penyebaran Tumor Otak dengan Metode Beda Hingga Standar ]]>
<![CDATA[Icha Zakiyya Nafisah Roza]]>;
<![CDATA[Usman Pagalay]]>;
<![CDATA[Heni Widayani]]>
<![CDATA[ Jurnal Riset Mahasiswa Matematika Vol 1, No 2 (2021): Jurnal Riset Mahasiswa Matematika ]]>
Publisher : <![CDATA[Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang ]]>
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DOI: 10.18860/jrmm.v1i2.14045
<![CDATA[Tumor otak merupakan penyakit dimana jaringan dalam sistem saraf pusat tumbuh secara abnormal. Pertumbuhan tumor tersebut mengalami interaksi dengan sistem imun untuk menghambat pertumbuhan tumor, hal tersebut dapat dideskripsikan dalam model matematika yang berbentuk persamaan diferensial biasa. Model matematika penyebaran tumor otak dengan respon sistem imun pada penelitian ini terdapat lima variabel yaitu, glioma , makrofag , sel T CD TGF- , dan IFN- . Model tersebut akan didiskritisasi dengan menggunakan metode beda hingga standar. Metode beda hingga standar atau metode euler merupakan metode yang diturunkan dari deret Taylor. Berdasarkan hasil analisis diketahui bahwa model diskrit penyebaran tumor otak dengan respon sistem imun memiliki jenis kestabilan model diskrit sama dengan model kontinunya dan memiliki dua titik kesetimbangan, yaitu kesetimbangan bebas penyakit dan kesetimbangan endemik. Titik kesetimbangan bebas penyakit dan endemik bersifat stabil asimtotik apabila memenuhi kriteria kestabilan Schur-Cohn. Simulasi numerik dilakukan untuk mengilustrasikan dan menguji hasil analisis yang diperoleh. Hasil simulasi numerik diperoleh bahwa model diskrit akan sama dengan model kontinunya saat tertentu.]]>
<![CDATA[Analisis Model Stokastik Penularan Virus Hepatitis B ]]>
<![CDATA[Arina Nur Laila]]>;
<![CDATA[Usman Pagalay]]>;
<![CDATA[Heni Widayani]]>
<![CDATA[ Jurnal Riset Mahasiswa Matematika Vol 2, No 1 (2022): Jurnal Riset Mahasiswa Matematika ]]>
Publisher : <![CDATA[Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang ]]>
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DOI: 10.18860/jrmm.v2i1.14467
<![CDATA[The spread of hepatitis B virus (HBV) infection has been widely studied using the deterministic SIR model, in which individuals who recover from acute infection have temporary immunity to the virus. However, this deterministic model uses a constant rate of viral infection over time. This is not in accordance with the fact that the infection rate is a random parameter that depends on time. This study discusses the analysis of the stochastic model of hepatitis B virus transmission. The purpose of this study is to construct the SIR stochastic model by dividing the infection rate into two, namely the rate of acute and chronic infection following the Wiener process. The model is then searched for an analytical solution referring to the Ito formula. The analytical solution and the Wiener process are described by substituting parameter values in the form of acute and chronic infection rates (β+α), cure rate (γ), and initial values (S(0) and I(0)) to obtain the mean value (μ). and the standard deviation (σ) of dS(t) and dI(t). The results of the simulation show that the number of infected individuals (I(t)) will decrease rapidly if (γ) is greater but will increase rapidly if (β+α) and (I(0)) are greater.]]>
<![CDATA[Dinamika Model Matematika Reaksi T-Helper ]]>
<![CDATA[Chilvia Tribhuana]]>;
<![CDATA[Usman Pagalay]]>;
<![CDATA[Elly Susanti]]>
<![CDATA[ Jurnal Riset Mahasiswa Matematika Vol 1, No 5 (2022): Jurnal Riset Mahasiswa Matematika ]]>
Publisher : <![CDATA[Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang ]]>
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DOI: 10.18860/jrmm.v1i5.14477
<![CDATA[T cells are a major component of the human immune system. These T cells have a number that varies depending on the body's immune response when fighting bacteria or viruses. However, the condition of excess immune cells in the body can also be dangerous. Theoretical studies on the dynamics of T-Helper cells in the body are needed to get the right simulation in treating patients without conducting medical tests on every patient on a daily basis. This study discusses the dynamics of the mathematical model of the T-Helper reaction with the influence of antigen and IL-2. From this study, two equilibrium points were obtained, namely disease-free equilibrium and endemic equilibrium. The use of parameter values from the experimental results shows that the disease-free equilibrium point is locally unstable, while the endemic equilibrium point is locally stable. The numerical simulation showed that the antigen increased from 1st day to the highest value at 0.926 on the 11th day until on the 20th day it started to be constant towards at the value which is the antigen could be activate the resting T-Helper. The process of activating T-Helper, create IL-2 which can stimulating the proliferation and activity of T-Helper cells, so they can divide the activated cell of T-Helper into two memory cells.]]>
<![CDATA[Analisis Dinamik Model Penyebaran Tumor Otak dengan Respon Sel Imun ]]>
<![CDATA[Resti Dwi Anggraini]]>;
<![CDATA[Usman Pagalay]]>;
<![CDATA[Achmad Nashichuddin]]>
<![CDATA[ Jurnal Riset Mahasiswa Matematika Vol 1, No 3 (2022): Jurnal Riset Mahasiswa Matematika ]]>
Publisher : <![CDATA[Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang ]]>
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DOI: 10.18860/jrmm.v1i3.14339
<![CDATA[The brain tumor distribution model with immune cell response is in the form of a non-linear system of ordinary differential equations with five equations. Each equation describes how immune cells in the brain, namely macrophages ( ), CD8+ T cells ( ), TGF- cytokines ( ) and IFN- ( ) cytokines interact with tumor cells, namely glioma cells ( ). From the calculation of the equilibrium point, the tumor cell-free conditions (DFE) and the endemic conditions (END) were obtained, in which tumor cells in long-term conditions were always present in the patient's brain. By using certain parameter values, it can be illustrated that the END condition is locally asymptotically stable while the DFE condition is locally unstable. This indicates that brain tumor cells, namely glioma cells ( ) will increase to their maximum value of 882650 cells and remain at that number from day 1000 onwards.]]>
<![CDATA[Implementasi Data Mining Menggunakan Algoritma C4.5 pada Klasifikasi Penjualan Hijab ]]>
<![CDATA[Faridatul Husna]]>;
<![CDATA[Hairur Rahman]]>;
<![CDATA[Juhari Juhari]]>
<![CDATA[ Jurnal Riset Mahasiswa Matematika Vol 2, No 2 (2022): Jurnal Riset Mahasiswa Matematika ]]>
Publisher : <![CDATA[Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang ]]>
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DOI: 10.18860/jrmm.v2i2.14891
<![CDATA[Indonesia is known as a country with a majority Muslim population, this makes the need for clothing in Indonesia must also pay attention to the criteria for Muslim clothing, one of which is the hijab. Business developments in the fashion world, especially hijab, have become a trend setter at this time so that the large amount of data in the fashion business world creates conditions where there are businesspeople who have a lot of data but lack of information from that data. To deal with these conditions, it is necessary to classify the data. A classification is a process to find the same properties in a data set to be classified into different classes. One of the classification methods is the Decision tree using the C4.5 Algorithm. This research aims to determine the model and the accuracy of the C4.5 algorithm in classifying hijab sales from several hijab brands. The Decision tree model is obtained using the C4.5 algorithm with the first root being the price attribute, where the first root is the attribute that most affected the sale of the hijab. The result of calculating the accuracy value is 87% so that the Decision tree model and the classification process using the C4.5 Algorithm are classified as good. This research is expected to help businesspeople in the fashion sector, especially hijab, to find out the factors that influence consumer interest in a hijab product.]]>
<![CDATA[Estimasi Parameter Capital Assets Pricing Model Dengan Metode Generalized Method of Moments Dalam Perhitungan Value At Risk ]]>
<![CDATA[Diah Maghfiroh Wahyuni]]>;
<![CDATA[Abdul Aziz]]>;
<![CDATA[Juhari Juhari]]>
<![CDATA[ Jurnal Riset Mahasiswa Matematika Vol 1, No 1 (2021): Jurnal Riset Mahasiswa Matematika ]]>
Publisher : <![CDATA[Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang ]]>
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DOI: 10.18860/jrmm.v1i1.13413
<![CDATA[Capital Assets Pricing Model merupakan persamaan regresi antara premi risiko aset terhadap premi risiko pasar. Risiko ada jika pembuat keputusan tidak memiliki data untuk menyusun suatu dugaan. Pendugaan tersebut dapat dilakukan dengan generalized method of moments.Penelitian ini bertujuan untuk mengetahui hasil estimasi parameter pada Capital Assets Pricing Model menggunakan Generalized Method of Moments pada data saham PT. Indofood Tbk., serta mendapatkan nilai Value at Risk pada data saham PT. Indofood Tbk..Hasil yang diperoleh yaitu : , m=1,2,…. Dengan nilai maka model regresi pada saham PT. Indofood Tbk.. yaitu . Dengan tingkat signifikansi 5%, investasi awal Rp10.000.000,00 , kerugian yang akan ditanggung oleh investor adalah Rp1.265.800,00 .]]>
