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InPrime: Indonesian Journal Of Pure And Applied Mathematics

inprime
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Published by Universitas Islam Negeri Syarif Hidayatullah Jakarta

ISSN : 26865335 EISSN : 27162478 DOI : 10.15408/inprime

Core Subject : Science, Education,

Computer Science & IT Mathematics

InPrime: Indonesian Journal of Pure and Applied Mathematics is a peer-reviewed journal and published on-line two times a year in the areas of mathematics, computer science/informatics, and statistics. The journal stresses mathematics articles devoted to unsolved problems and open questions arising in chemistry, physics, biology, engineering, behavioral science, and all applied sciences. All articles will be reviewed by experts before accepted for publication. Each author is solely responsible for the content of published articles. This scope of the Journal covers, but not limited to the following fields: Applied probability and statistics, Stochastic process, Actuarial, Differential equations with applications, Numerical analysis and computation, Financial mathematics, Mathematical physics, Graph theory, Coding theory, Information theory, Operation research, Machine learning and artificial intelligence.

Arjuna Subject : Matematika - Matematika Terapan

Articles 197 Documents

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Non-linear Mixed Models in a Dose Response Modelling Madona Yunita Wijaya
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 1, No 1 (2019)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

AbstractStudy designs in which an outcome is measured more than once from time to time result in longitudinal data. Most of the methodological works have been done in the setting of linear and generalized linear models, where some amount of linearity is retained. However, this still be considered a limiting factor and non-linear models is another option offering its flexibility. Non-linear model involves complexity of non-linear dependence on parameters than that in the generalized linear class. It has been utilized in many situations such as modeling of growth curves and dose-response modeling. The latter modeling will be the main interest in this study to construct a dose-response relationship, as a function of time to IBD (inflammatory bowel disease) dataset. The dataset comes from a clinical trial with 291 subjects measured during a 7 week period. Both linear and non-linear models are considered. A dose time response model with generalized diffusion function is utilized for the non-linear models. The fit of non-linear models are found to be more flexible than linear models hence able to capture more variability present in the data.Keywords: IBD; longitudinal; linear mixed model; non-linear mixed model. AbstrakDesain studi dimana hasil diukur berulang kali dari waktu ke waktu menghasilkan data longitudinal. Sebagian besar metodologi yang digunakan untuk menganalisis data longitudinal adalah model linear dan model linear umum (generalized linear model) dimana sejumlah linearitas tertentu dipertahankan. Asumsi linearitas ini masih dipandang memiliki keterbatasan dan model non-linear adalah pilihan metode lainnya yang menawarkan fleksibilitas. Model non-linear telah digunakan di berbagai macam situasi seperti model kurva pertumbuhan , model farmakokinetika, dan farmakodinamika, dan model respon-dosis. Model respon-dosis akan menjadi fokus dalam penelitian ini untuk membangun hubungan dosis-respon sebagai fungsi waktu dari data IBD dengan menggunakan model linear dan non-linear. Hasil penelitian menunjukan bahwa model non-linear lebih fleksibel daripada model linear sehingga mampu menangkap lebih banyak variabilitas yang ada di dalam data.Keywords: IBD; longitudinal; model linear; model non-linear.

An Odd-Even Sum Labeling of Jellyfish and Mushroom Graphs Rusdan Nurhakim
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 2, No 2 (2020)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

AbstractA graph G(V,E) with p vertices and q edges called graph odd-even sum if there exists an injective function f from V to {+ 1, +2, +3, ..., +(2p-1)} such that induced a bijection f*(uv)=f(u)+f(v) as label of edge and u,v element of V forms the set {2,4,...,2q}, and f is called odd-even sum labeling. There are three criteria of graphs that can be labeled by this labeling, they are undirected, no loops, and finite for every edges and vertex. Jellyfish J(m,n) graph and Mushroom Mr(m) graph have the criteria. So in this paper will be showed that the Jellyfish and Mushroom graphs can be labeled by this labeling.Keywords: odd-even sum graph; odd-even sum labeling; Jellyfish and mushroom graphs. AbstrakGraf G(V,E) dengan banyak titik p dan sisi q dikatakan graf jumlah ganjil-genap jika terdapat suatu fungsi injetif f dari V ke {+ 1, +2, +3, ..., +(2p-1)} sehingga bijektif f*(uv)=f(u)+f(v) merupakan label sisi dengan u,v anggota dari V membentuk himpunan bilangan {2,4,...,2q}, dengan f merupakan pelabelan jumlah ganjil-genap. Kriteria graf yang dapat dilabeli oleh pelabelan jumlah ganjil-genap ada tiga, yaitu graf yang tidak berarah, tidak memiliki loop, dan terhingga, baik secara sisi maupun titik. Graf Jellyfish J(m,n) dan Mushroom Mr(m) memenuhi ketiga kriteria tersebut. Pada tulisan ini akan ditunjukkan bahwa kedua graf tersebut dapat dilabeli dengan pelabelan jumlah ganjil-genap.Keywords: graf jumlah ganjil-genap; pelabelan jumlah ganjil-genap; graf Jellyfish dan graf Mushroom.

Traffic Model Based Predictive Control: A Piecewise-Affine using METANET M. Wakhid Musthofa
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 2, No 1 (2020)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

AbstractTraffic congestion on the freeway is a serious problem for modern society. Dynamic traffic management is a good alternative solution to improve efficiency on congestion problems. This article aims to analyze parts of freeway traffic network by using METANET model which is part of macroscopic traffic flow model that describes a set of parameters such as mean speed, traffic flow, and density of a traffic system. The piecewise-affine (PWA) approximation on METANET model is used to design traffic predictive controls and test them on a traffic model structure. This approach guarantees more intensive calculation for METANET traffic flow model in nonlinear form in the context of model predictive control (MPC). Some equations in the METANET model will be approximated by PWA function. With PWA-MPC approximation as direct calculation, equation of PWA model can be transformed into mixed-integer linear programming (MILP). Furthermore, to see the control of the model with MPC control, numerical simulations will be carried out on mean speed, traffic density, traffic flow, queue length, and MPC control. We use time 0 – 2.5 hours. Simulation result shows that the density of traffic, traffic flow, and queue length decreased in this time period, while the mean speed increased.Keywords: traffic control; model predictive control; piecewise-affine model; METANET; mixed-integer linear programming (MILP). AbstrakKemacetan lalu lintas di jalan bebas hambatan merupakan masalah yang sangat serius bagi masyarakat modern. Pengelolaan lalu lintas yang dinamis merupakan solusi alternatif yang baik untuk meningkatkan efisiensi pada masalah kemacetan. Artikel ini bertujuan untuk menganalisis bagian jaringan pada jalan bebas hambatan dengan mengkaji model METANET yang termasuk bagian dari model arus lalu lintas secara makroskopik yang menggambarkan kumpulan parameter seperti kecepatan rata-rata, arus lalu lintas, dan kepadatan. Pendekatan piecewise-affine (PWA) pada model METANET digunakan untuk mendesain kendali prediktif lalu lintas dan mengujinya pada suatu struktur model lalu lintas. Pendekatan ini menjamin penghitungan yang lebih intensif untuk model arus lalu lintas METANET yang berbentuk nonlinear dalam konteks kendali model prediktif (model predictive control/MPC). Beberapa persamaan pada model METANET akan didekati oleh fungsi PWA. Dengan pendekatan PWA-MPC sebagai perhitungan secara langsung, persamaan model PWA dapat diubah menjadi program linear bilangan bulat campuran (mixed- integer linear programming/MILP). Selanjutnya untuk melihat keterkendalian model dengan kendali MPC, simulasi numerik akan dilakukan terhadap kecepatan rata-rata, kepadatan lalu lintas, arus lalu lintas, panjang antrian, serta kendali MPC. Waktu yang digunakan pada simulasi adalah 0 – 2.5 jam. Hasil simulasi menunjukkan bahwa kepadatan lalu lintas, arus lalu lintas, panjang antrian mengalami penurunan dalam kurun waktu tersebut, sedangkan kecepatan rata-rata mengalami peningkatan.Kata Kunci: endali lalu lintas; model lalu lintas berbasis kendali prediktif; pendekatan model piecewise-affine; METANET; program linear bilangan bulat campuran.

Rainbow Connection Number on Amalgamation of General Prism Graph Rizki Hafri Yandera; Yanne Irene; Wisnu Aribowo
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 1, No 1 (2019)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

AbstractLet be a nontrivial connected graph, the rainbow-k-coloring of graph G is the mapping of c: E(G)-> {1,2,3,…,k} such that any two vertices from the graph can be connected by a rainbow path (the path with all edges of different colors). The least natural number

Regency grouping in East Java based on Variable Type of Agriculture uses Hybrid Hierarchical Clustering Via Mutual Cluster Method Sulthan Fikri Mu'afa; Nurissaidah Ulinnuha
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 2, No 1 (2020)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

AbstractEast Java Province is one of the provinces that has the largest agricultural resources in Indonesia. The Government of East Java needs to produce superior commodities in each region. This study aims to group districts in East Java Province based on variable types of agriculture with the hybrid hierarchical clustering via mutual cluster method that combines the merging of bottom-up clustering advantages and top-down clustering advantages. Mutual cluster is a grouping with the largest distance between small groups of the shortest distance for each point outside the group. In this research, the calculation uses Euclidean distance. The data used in this study are from the East Java Central Statistics Agency (BPS) in 2017. The division calculation is obtained by finding the minimum (standard deviation of intra cluster) value and the maximum (standard deviation of inter clusters) value and using the analysis of variance calculation. The grouping results obtained were nine groups with value of 725.934, value of 1.475.978 and value of 7,908.Keywords: agriculture; Hybrid Hierarchical Clustering; mutual cluster; Euclidean distance; analysis of variance. AbstrakProvinsi Jawa Timur merupakan salah satu provinsi yang memiliki sumber daya pertanian terbesar di Indonesia. Pemerintah Jawa Timur perlu mengembangkan komoditi unggulan di tiap daerah di Jawa Timur. Penelitian ini bertujuan untuk mengelompokkan kabupaten di Provinsi Jawa Timur berdasarkan variabel jenis pertanian dengan metode hybrid hierarchical clustering via mutual cluster yaitu menggabungkan kelebihan bottom-up clustering dan kelebihan top-down clustering. Mutual cluster yakni pengelompokkan dengan jarak terbesar antara bagian dalam kelompok yang kecil dari jarak yang terpendek kepada tiap titik di luar kelompok. Dalam penelitian ini, perhitungan jarak menggunakan jarak Euclidean. Data yang digunakan dalam penelitian ini dari Badan Pusat Statistik Jawa Timur tahun 2017. Perhitungan pembagian didapat dengan mencari nilai (simpangan baku dalam klaster) yang minimal dan nilai (simpangan baku antar klaster) yang maksimal, serta digunakan perhitungan analyze of varians. Hasil pengelompokkan yang diperoleh didapatkan sebanyak sembilan kelompok dengan nilai sebesar 725.934, nilai sebesar 1.475.978 dan nilai sebesar 7,908.Kata Kunci: pertanian; Hybrid Hierarchical Clustering; mutual cluster; jarak Euclid; analisis variansi.

Mathematical Model for MERS-COV Disease Transmission with Medical Mask Usage and Vaccination Muhammad Manaqib; Irma Fauziah; Mujiyanti Mujiyanti
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 1, No 2 (2019)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

AbstractThis study developed a model of the spread of MERS-CoV disease using the SEIR model which was added by a health mask and vaccination factor as a preventive measure. The population is divided into six subpopulations namely susceptible subpopulations not using health masks and using health masks, exposed subpopulations, infected subpopulations not using health masks and using health masks, and recovering subpopulations. The results are obtained two equilibrium points, namely disease-free equilibrium points and endemic equilibrium points. Analysis of the stability of the disease-free equilibrium point using linearization around the equilibrium point. As a result, the asymptotic stable disease-free local equilibrium point if the base reproduction number is less than one. Numerical simulation models for MERS-CoV disease are carried out in line with the analysis of model behavior.Keywords: MERS-CoV, SEIR Model, Stability Equilibrium Point, Basic Reproduction Number. AbstrakPenelitian ini mengembangkan model penyebaran penyakit MERS-CoV menggunakan model SEIR yang ditambahkan faktor masker kesehatan dan vaksinasi sebagai upaya pencegahan. Populasi dibagi menjadi enam subpopulasi yaitu subpopulasi rentan tidak menggunakan masker kesehatan dan menggunakan masker kesehatan, subpopulasi laten, subpopulasi terinfeksi tidak menggunakan masker kesehatan dan menggunakan masker kesehatan, serta subpopulasi sembuh. Hasilnya diperoleh dua titik ekuilibrium yaitu titik ekulibrium bebas penyakit dan endemik. Analisis kestabilan titik ekuilibrium bebas penyakit menggunakan linearisasi disekitar titik ekuilibrium. Hasilnya, titik ekuilibrium bebas penyakit stabil asimtotik lokal jika bilangan reproduksi dasar kurang dari satu. Simulasi numerik model untuk penyakit MERS-CoV yang dilakukan sejalan dengan analisis perilaku model.Kata kunci: MERS-CoV, Model SEIR, Kestabilan Titik Ekuilibrium, Bilangan Reproduksi Dasar.

Application of Fuzzy K-Nearest Neighbor (FKNN) to Detect the Parkinson’s Disease L.N. Desinaini; Azizatul Mualimah; Dian C. R. Novitasari; Moh. Hafiyusholeh
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 1, No 1 (2019)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

AbstractParkinson’s disease is a neurological disorder in which there is a gradual loss of brain cells that make and store dopamine. Researchers estimate that four to six million people worldwide, are living with Parkinson’s. The average age of patients is 60 years old, but some are diagnosed at age 40 or even younger and the worst thing is some patients are late to find out that they have Parkinson's disease. In this paper, we present a diagnosis system based on Fuzzy K-Nearest Neighbor (FKNN) to detect Parkinson’s disease. We use Parkinson’s disease dataset taken from UCI Machine Learning Repository. The first step is normalize the Parkinson’s disease dataset and analyze using Principal Component Analysis (PCA). The result shows that there are four new factors that influence Parkinson’s disease with total variance is 85.719%. In classification step, we use several percentage of training data to classify (detect) the Parkinson's disease i.e. 50%, 60%, 70%, 75%, 80% and 90%. We also use k = 3, 5, 7, and 9. The classification result shows that the highest accuracy obtained for the percentage of training data is 90% and k = 5, where 19 are correctly classified i.e. 14 positive data and 5 negative data, while 1 positive data is classified incorrectly.Keywords: Parkinson's disease; Fuzzy K-Nearest Neighbor; Principal Component Analysis. AbstrakPenyakit Parkinson merupakan kelainan sel saraf pada otak yang menyebabkan hilangnya dopamin pada otak. Para peneliti mengestimasi bahwa, empat sampai enam juta orang di dunia, menderita Parkinson. Penyakit ini rata-rata diderita oleh pasien berusia 60 tahun, namun beberapa orang terdeteksi saat berusia 40 tahun atau lebih muda dan hal terburuk adalah seseorang terlambat untuk mendeteksinya. Di dalam artikel ini, kami menyajikan sistem diagnosa penyakit Parkinson menggunakan metode Fuzzy K-Nearest Neighbor (FKNN). Kami menggunakan Data uji yang diperoleh dari UCI Machine Learning Repository yang telah banyak diterapkan pada masalah klasifikasi. Tahapan pertama yang kami lakukan adalah menormalisasi data kemudian menganalisisnya menggunakan Analisis Komponen Utama (Principal Component Analysis). Hasil Analisis Komponen Utama menunjukkan bahwa terdapat empat factor baru yang mempengaruhi penyakit Parkinson dengan variansi total 87,719%. Pada tahap klasifikasi, kami menggunakan beberapa prosentase data latih untuk mendeteksi penyakit yaitu 50%, 60%, 70%, 75%, 80% and 90%. Selain itu, kami menggunakan beberapa nilai k yaitu 3, 5, 7, and 9. Hasil menunjukkan bahwa klasifikasi dengan akurasi tertinggi diperoleh untuk 90% data latih dengan k = 5, dimana 19 diklasifikasikan secara tepat yaitu 14 data positif dan 5 data negatif, sedangkan satu data positif tidak diklasifikasikan dengan tepat.Keywords: penyakit Parkinson; Fuzzy K-Nearest Neighbor; Analisis Komponen Utama.

Economic Ordering Policy for VAR Deterioration Model with Non-stationary Two-warehouse Inventory and Demand Abdullah Mohammed Alshami; Aniket Muley
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 2, No 2 (2020)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

AbstractThis paper adopts the two-warehouse inventory, determination on the first run-time and VAR (Vector Auto Regression) deterioration model. The optimal EOQ in the interval of the finite horizon is determined under critical considerations. The non-stationary two-warehouse inventory, i.e. the inventory and initial inventory are non-stationary at level, but stationary after lag difference similar to demand (demand and initial demand). The output of the proposed model represented the optimal order quantity and optimal first run-time, the optimal total cost as integration of first order with the significant trend and intercept. The optimal demand is decreased during more risk as a deterioration variable to reduce the quantity in the stock. The initial demand is stationary after a first lag and the demand is stationary.Keywords: initial inventory; optimal of first run-time; EOQ (Economic Ordering Quantity); total cost function (TC). AbstrakPenelitian ini mengadopsi inventori dengan dua gudang penyimpanan, penentuan pada waktu run (run-time) awal, dan model deteriorating VAR (Vector Auto Regression). Nilai optimal EOQ dalam interval horizon berhingga ditentukan dengan pertimbangan kritis. Inventori dengan dua gedung yang tidak stasioner, yaitu inventori dan inventori awal tidak stasioner pada level, tetapi stasioner setelah perbedaan lag seperti halnya pada permintaan (permintaan dan permintaan awal). Hasil dari model yang diajukan menunjukkan nilai orde yang optimal dan waktu run awal yang optimal, total biaya optimal sebagai integrasi dari orde pertama dengan tren dan intercept yang signifikan. Permintaan optimal mengalami penurunan ketika lebih banyak risiko sebagai variabel deteroriating untuk mengurangi jumlah dalam stok. Permintaan awal menunjukkan stasioner setelah perbedaan lag pertama dan permintaan juga stasioner.Kata kunci: inventori awal; optimal run-time awal; EOQ (Economic Ordering Quantity); fungsi biaya total.

Aggregate Risk Model and Risk Measure-Based Risk Allocation Khreshna Syuhada
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 2, No 1 (2020)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

AbstractIn actuarial modeling, aggregate risk is known as more attractive rather than individual risk. It has, however, usual difficulty in finding (the exact form of) joint probability distribution. This paper considers aggregate risk model and employ translated gamma approximation to handle such distribution function formulation. In addition, we deal with the problem of risk allocation in such model. We compute in particular risk allocation based on risk measure forecasts of Value-at-Risk (VaR) and its extensions: improved VaR and Tail VaR. Risk allocation shows the contribution of each individual risk to the aggregate. It has a constraint that the risk measure of aggregate risk is equal to the aggregate of risk measure of individual risk.Keywords: allocation methods; tail-value-at-risk; translated gamma approximation. AbstrakRisiko agregat merupakan kajian yang lebih menarik dalam pemodelan aktuaria, dibandingkan dengan risiko individu. Namun fungsi distribusi risiko agregat sulit ditentukan bentuk eksaknya. Artikel ini membahas mengenai model risiko agregat dan menggunakan metode aproksimasi Translasi Gamma untuk menentukan fungsi distribusi risiko agregat. Berdasarkan fungsi distribusi tersebut, dapat diprediksi alokasi risiko agregat. Metode alokasi risiko agregat diterapkan pada ukuran risiko Value-at-Risk (VaR) dan pengembangannya: improved VaR dan Tail-VaR. Alokasi risiko menyatakan nilai kontribusi setiap risiko individu terhadap ukuran risiko agregat. Jumlahan atau agregat dari setiap alokasi risiko individu sama dengan ukuran risiko agregat.Kata kunci: aproksimasi Translasi Gamma; alokasi risiko; Tail-Value-at-Risk.

Bounds of Adj-TVaR Prediction for Aggregate Risk Khreshna Syuhada
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 1, No 1 (2019)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

In ﬁnancial and insurance industries, risks may come from several sources. It is therefore important to predict future risk by using the concept of aggregate risk. Risk measure prediction plays important role in allocating capital as well as in controlling (and avoiding) worse risk. In this paper, we consider several risk measures such as Value-at-Risk (VaR), Tail VaR (TVaR) and its extension namely Adjusted TVaR (Adj-TVaR). Speciﬁcally, we perform an upper bound for such risk measure applied for aggregate risk models. The concept and property of comonotonicity and convex order are utilized to obtain such upper bound.Keywords: Coherent property, comonotonic rv, convex order, tail property, Value-at-Risk (VaR).

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Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah Jl. Ir H. Juanda No.95, Cemp. Putih, Kec. Ciputat, Kota Tangerang Selatan, Banten 15412

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