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JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI
Published by Universitas Hasanuddin
ISSN : 18581382     EISSN : 26148811     DOI : -
Core Subject : Education,
Jurnal ini mempublikasikan paper-paper original hasil-hasil penelitian dibidang Matematika, Statistika dan Komputasi Matematika.
Arjuna Subject : -
Articles 12 Documents
Search results for , issue " Vol 16, No 1 (2019): JMSK, July, 2019" : 12 Documents clear
ANALISIS KESTABILAN DAN KONTROL OPTIMAL MODEL LESLIE-GOWER FUNGSI RESPON HOLLING III DENGAN PEMANENAN PADA POPULASI PREDATOR DAN PREY Febriyanti, Himmatul Ulya; Toaha, Syamsuddin; Kasbawati, Kasbawati
Jurnal Matematika, Statistika dan Komputasi Vol 16, No 1 (2019): JMSK, July, 2019
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/jmsk.v16i1.6784

Abstract

This article modified the leslie-gower model on harvesting with predator and prey population. This study aims at construct a modification of leslie-gower model with holing III response function. In addition, there is an effort harvesting in predator and prey population, analyzing an equilibrium point, finding bionomic equilibrium and the condition where the present value is maximum from net income by controlling harvesting in both populations. In the modified leslie-gower model there is an equilibrium point  which is asymptotically stable and when there have harvesting, the equilibrium point  is also asymptotically stable. Bionomic equilibrium from harvesting on the modified leslie-gower model is maximizing the profit function π of harvesting on a model with the maximum pontryagin principle resulting an optimal equilibrium) affected by instantaneous rate of discount δ.
NILAI EIGEN MATRIKS QUATERNION Ekawati, Susi
Jurnal Matematika, Statistika dan Komputasi Vol 16, No 1 (2019): JMSK, July, 2019
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/jmsk.v16i1.5943

Abstract

AbstrakMenurut Zhang (2007), jika  adalah matriks quaternion dengan  dan  adalah nilai eigen kiri dari , maka . Dalam penelitian ini akan ditunjukkan tiga hal. Pertama, jika  adalah matriks quaternion dengan  dan  adalah nilai eigen kiri dari  maka .Kata Kunci : Quaternion, Determinan Cayley, Nilai Eigen Kiri AbstractAccording to Zhang (2007), if  is a quaternion matrix with  and  is the left eigenvalue of , then . In this paper will be shown, if  is a quaternion matrix with  and  is the left eigenvalue of , then .Keywords : Quaternion, Cayley Determinant, Left Eigenvalue
PEMODELAN PEMROGRAMAN LINIER DENGAN KOEFISIEN FUNGSI OBJEKTIF, FUNGSI KENDALA DAN VARIABEL KEPUTUSAN BERBENTUK BILANGAN KABUR BESERTA APLIKASINYA Amrullah, Muhammad
Jurnal Matematika, Statistika dan Komputasi Vol 16, No 1 (2019): JMSK, July, 2019
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/jmsk.v16i1.5802

Abstract

Abstrak Dalam penelitian ini penulis akan mengusulkan algoritma untuk memodelkan masalah pemrograman linear kabur dengan bilangan kabur trapesium menggunakan metode simpleks. Secara khusus dalam aplikasi teori ini adalah masalah pengambilan keputusan pemrograman linear kabur dengan menyajikan metode baru untuk menyelesaikan masalah pemrograman linier kabur dengan menggunakan fungsi ranking. Pada dasarnya, langkah-langkah dalam metode penelitian ini sama dengan dengan metode simpleks yang digunakan untuk memecahkan masalah pemrograman linier tegas.Kata kunci: Fuzzy linear programming, fungsi ranking, metode simpleks. AbstractIn this paper author shall propose an algorithm for solving fuzzy linear programming problems with trapezoidal numbers using a simplex method. In particular, an application of  this theory in decision making problems is fuzzy linear programming with a new method for solving fuzzy linear programming problems, by use of rank function. Basically, our method is similar to simplex method that was used for solving linear programming problems in crisp environment before.Keywords: Fuzzy linier programming, rank function, simplex method.
MONITORING VARIABILITAS PROSES BERDASARKAN STATISTIK WILKS Barlian Sari, Suci; Tri Herdiani, Erna; Sirajang, Nasrah
Jurnal Matematika, Statistika dan Komputasi Vol 16, No 1 (2019): JMSK, July, 2019
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/jmsk.v16i1.6485

Abstract

In a manufacturing industry quality problems often occur. One of the main cause is due to variability process. Variability process is a variation that occurs in the process, both in manufacturing and non-manufacturing processes. One method for monitoring variabiliti process is by using Wilks Statistics. Wilks statistics is a method that is used based on individual observations. This study aims to monitor the variability of the process and apply it to Electric Resistance Welded (ERW) pipes with the Wilks statistical method. In addition, a capability process analysis is also carried out when the Wilks control chart has been controlled. The result showed that all observations carried out individually were in control limit with a capability process of  2.5386, which means the process capability of ERW pipe production using a multivariate Wilks statistical control chart was capable and match  with the specifications limit specified by company.
Analisis Risiko Pada Return Saham Perusahaan Asuransi Menggunakan Metode VaR dengan Pendekatan ARMA-GARCH Kuswanto, Heri; Damayanti, Endy Norma Chyntia
Jurnal Matematika, Statistika dan Komputasi Vol 16, No 1 (2019): JMSK, July, 2019
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/jmsk.v16i1.6197

Abstract

Pasar modal Indonesia merupakan salah satu negara tujuan investasi bagi investor di negara-negara maju (developed markets) yang dikenal sebagai emerging market. Perkembangan kondisi perekonomian di Indonesia sendiri dianggap baik bagi para investor untuk menanamkan dana. Saham sektor keuangan menjadi salah satu sektor yang ikut berkembang di sepanjang tahun ini. Tiga dari tujuh saham yang menunjukkan bertumbuh dengan baik adalah PT Asuransi Multi Artha Guna Tbk (AMAG), PT Paninvest Tbk (PNIN), dan PT Lippo General Insurance Tbk (LPGI). Terdapat dua hal penting yaitu tingkat pengembalian atau imbal hasil (return) dan risiko. Komponen lain yang tidak kalah penting adalah volatilitas return saham. Berdasarkan penjelasan diatas, maka dilakukan penelitian untuk menganalisis return saham dan volatilitas ketiga saham. Salah satu metode yang digunakan dalam mengestimasi risiko saham adalah metode VaR (Value at Risk). Untuk mengatasi volatilitas dapat menggunakan ARMA dan GARCH. Dihasilkan bahwa tiga saham perusahaan memberikan nilai rata-rata return yang positif sehingga memberikan keuntungan bagi investor. Saham perusahaan LPGI memiliki potensi risiko yang paling tinggi karena nilai standar deviasi yang tinggi. Model terbaik untuk return saham AMAG adalah ARMA ([7],[7]) dan model GARCH (1,2). Pada return saham LPGI model terbaik adalah ARMA ([2],[2]) dan GARCH (1,1). Return saham PNIN diperoleh model terbaik ARMA (0,[3]) dan GARCH (1,2). Pada pemodelan Parsimony didapatkan model ARMA (1,0) GARCH (1,1) untuk return saham perusahaan AMAG, ARMA (0,1) GARCH (1,1) untuk return saham perusahaan LPGI dan ARMA (1,1) GARCH (1,1) untuk return saham perusahaan PNIN. Pada perhitungan VaR didapatkan investor akan mengalami kerugian maksimum sebesar Rp 47.089.529,- bila menanamkan modal sebesar Rp 1.000.000.000,- di perusahaan AMAG, berlaku pula pada perusahaan LPGI, investor akan mengalami kerugian sebesar Rp 60.018.734,- dan Rp 39.196.540,- di perusahaan PNIN dengan tingkat keyakinan 95%.
Analisis Kestabilan Model Mangsa Pemangsa dengan Pemanenan Ambang Batas pada Populasi Pemangsa Yusrianto, Yusrianto; Toaha, Syamsuddin; Kasbawati, Kasbawati
Jurnal Matematika, Statistika dan Komputasi Vol 16, No 1 (2019): JMSK, July, 2019
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/jmsk.v16i1.6575

Abstract

                                                                                        Abstrak Penelitian ini mengkaji model satu mangsa dan satu pemangsa yang saling berkompetisi. Fungsi predasi dari pemangsa diasumsikan menggunakan fungs1 respon Holling tipe II. Dengan asumsi bahwa adanya kompetisi intraspesifik pada popuasi pemangsa serta dilakukan pemanenan ambang batas pada popuasi pemangsa. Pada model tersebut dilakukan analisis tentang syarat kewujudan dan kestabilan titik keseimbangan interior. Analisis kestabilan titik keseimbangan interior dilakukan dengan metode linearisasi dan dengan memperhatikan nilai eigen dari matriks Jacobi yang diperoleh. Terdapat sepuluh titik kesetimbangan yang diperoleh pada model, satu diantaranya dapat dinterpretasikan. Titik tersebut dinyatakan stabil asimtotik. Berdasarkan hasil anasis menggunakan beberapa parameter, diketahui bahwa ada suatu waktu pemanenan ambang batas harus dihentikan karna sudah tidak memenuhi syarat kriteria ambang batas yang telah ditentukan.Kata kunci : Model mangsa pemangsa, Pemanenan ambang batas, Titik kesetimbanganAbstract This study examines the model of one prey and one predator who mutates each other. The predation function of predators is assumed to use the Holling type II response function. Assuming that the existence of intraspecific competition in predatory population and theshold harvesting for predatory population is carried out. In this model, an analysis of the actual conditions and stability of the interior balance point is carried out. Analysis of the interior stability balance points was carried out by linearization method and by taking into account the eigenvalues of the Jacobian matrix obtained. There are ten equilibrium points of engagement obtained on the model, one of which can be interpreted. This point is stated as asymptotically stable. Based on the results of analysis using several parameters, it is known that there is a time when harvesting the threshold must be stopped because it has not fulfill the specified criteria for threshold.Keyword : Prey-predator model threshold harvesting, equibrium point
Nilai Total Ketidakteraturan-H pada Graf Cn x P3 aritonang, winda; Hinding, Nurdin; Amir, Amir Kamal
Jurnal Matematika, Statistika dan Komputasi Vol 16, No 1 (2019): JMSK, July, 2019
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/jmsk.v16i1.5788

Abstract

AbstrakPenentuan nilai total ketidakteraturan dari semua graf belum dapat dilakukan secara lengkap. Penelitian ini bertujuan untuk menentukan nilai total ketidakteraturan-H pada graf Cn x P3 untuk n ≥ 3 yang isomorfik dengan . Penentuan nilai total ketidakteraturan-H pada graf Cn x P3 dengan menentukan batas bawah terbesar dan batas atas terkecil. Batas bawah dianalisis berdasarkan sifat-sifat graf dan teorema pendukung lainnya. Sedangkan batas atas dianalisa dengan pemberian label pada titik dan sisi pada graf Cn x P3.Berdasarkan hasil penelitian ini diperoleh nilai total ketidakteraturan-H pada graf ths(Cn x P3, C4)=.Kata kunci : Selimut-H, Nilai total ketidakteraturan-HAbstractThe determine of H-irregularity total strength in all graphs was not complete on graph classes. The research aims to determine alghorithm the H-irregularity total strength of graph Cn x P3 for n ≥ 3 with use H-covering, where H is isomorphic to C4. The determine of H-irregularity total strength of graph Cn x P3 was conducted by determining lower bound and smallest upper bound. The lower bound was analyzed based on graph characteristics and other supporting theorem, while the upper bound was analyzed by edge labeling and vertex labeling of graph Cn x P3.The result show that  the H-irregularity total strength of graph ths(Cn x P3, C4)=.Keyword : H-covering, H-irregularity total strength
Analisis Data Panel pada Tingkat Pengangguran Terbuka Kabupaten/Kota di Pulau Jawa Pratiwi, Hasih; Prawastyorini, Ardina Nilam; Sugiyanto, Sugiyanto
Jurnal Matematika, Statistika dan Komputasi Vol 16, No 1 (2019): JMSK, July, 2019
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/jmsk.v16i1.6713

Abstract

Unemployment rate is the percentage of the number of unemployed to the total labor force, it has become some problems in economic development. The aim of this study is to choose the best model between common, fixed, and random effects in modeling open unemployment rate of regency/city in Java. It based on open unemployment rate with several influence factors in Java Island 2010-2016 which are panel data types. The best model choosen based on the results of the Chow test and Hausman test. The fixed effect model was obtained as the best model with a value of  79,26 percent.
Analisis Kestabilan Model SEIR Penyebaran Penyakit Campak dengan Pengaruh Imunisasi dan Vaksin MR Sihotang, Willyam Daniel; Simbolon, Ceria Clara; Hartiny, July; Tindaon, Desrinawati; Sinaga, Lasker Pangarapan
Jurnal Matematika, Statistika dan Komputasi Vol 16, No 1 (2019): JMSK, July, 2019
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/jmsk.v16i1.6594

Abstract

Measles is a contagious infectious disease caused by a virus and has the potential to cause an outbreak. Immunization and vaccination are carried out as an effort to prevent the spread of measles. This study aims to analyze and determine the stability of the SEIR model on the spread of measles with the influence of immunization and MR vaccines. The results obtained from model analysis, namely there are two disease free and endemic equilibrium points. If the conditions are met, the measles-free equilibrium point will be asymptotically stable and the measles endemic equilibrium point will be stable. Numerical solutions show a decrease in the rate of spread of measles due to the effect of immunization and the addition of MR vaccines.
Transformasi Fourier Fraksional dari Fungsi Gaussian SUTRISNA, IIN; Nasrun, Asriadi; Bahri, Mawardi; Toaha, Syamsuddin
Jurnal Matematika, Statistika dan Komputasi Vol 16, No 1 (2019): JMSK, July, 2019
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/jmsk.v16i1.5939

Abstract

The fractional Fourier transform is one of the generalizations of ordinary Fourier transform that depend on a particular angle . In this paper we will derive the fractional Fourier transforms of a function that is well known in the field of analysis, namely Gaussian function.

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