JURNAL ILMIAH MATEMATIKA DAN TERAPAN
Jurnal Ilmiah Matematika dan Terapan adalah Jurnal yang diterbitkan oleh Program Studi Matematika FMIPA Universitas Tadulako. Jurnal ini menerbitkan artikel hasil penelitian atau telaah pustaka bersifat original meliputi semua konsentrasi bidang ilmu matematika dan terapannya, seperti analisis, aljabar, kombinatorika, matematika diskrit, statistika, dan semua aspek terapannya.
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<![CDATA[Model Matematika Kendali Optimal Intensitas Cahaya Dan Nutrisi Pada Pertumbuhan Mikroalga Dengan Menggunakan Metode Pontryagin ]]>
<![CDATA[Azim]]>;
<![CDATA[Ratianingsih, R]]>;
<![CDATA[Nacong, N]]>
<![CDATA[ JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 17 No. 1 (2020) ]]>
Publisher : <![CDATA[Program Studi Matematika, Universitas Tadulako ]]>
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DOI: 10.22487/2540766X.2020.v17.i1.15173
<![CDATA[Microalgae are the most primitive plant-sized cellular organisms commonly known as phytoplankton. The habitat of its life is in waters or humid places. This organism is a primary producer of water that has any capability to photosynthesis like any other high-level plants. This study examines mathematically the optimal control of light intensity and liquid waste nutrition in microalgae growth. Growth liter is done by setting the intensity of light in the process of glucose formation and nutrition tofu liquid waste, tapioca, industry, and households as the additional nutrients of microalgae. The Pontryagin maximun principles is used to determine the optimal control solution. The solution is solved from the state and co-state equation that stationery evaluated using the indexed performance maks ð½[ð‘¢1 + ð‘¢2 ] = ∫ ðº(ð‘¡) − ð‘¡ð‘“ ð‘¡0 ð‘†(ð‘¡) − 1 2 ð‘¢1 (ð‘¡) 2 − 1 2 ð‘¢2 (ð‘¡) 2ð‘‘ð‘¡ with the stationer condition that gives the optimal control ð‘¢1 ∗ = ð›¾2ð›¼2ð‘„ðµ and ð‘¢2 ∗ = −ð›¾5ðœŒ1ð‘†. The results shows that before the optimal control of light intensity and nutrition of liquid waste is applied, the concentration of microalgae biomass becomes 5.915 g / liter on the 20th day stayed at the 105th day. The lipid quota with an initial value of 0.6 g/liter will decrease to 0.2 g / liter at 4th day which is the equilibrium point. Optimal control of the regulation of light intensity of 2-9 klux and liquid waste nutrition provided a significant increase in the amount of microalgae biomass and lipid quota, with the regulation of light intensity of 2- 9 klux and tofu liquid waste nutrition which gave the largest increase in the amount of microalgae biomass and lipid quota]]>
<![CDATA[Kestabilan Model Matematika Infeksi Primer Penyakit Varicella Dan Infeksi Rekuren Penyakit Herpes Zoster Oleh Virus Varicella Zoster ]]>
<![CDATA[Hardiyanti]]>;
<![CDATA[Ratianingsih, R]]>;
<![CDATA[Hajar]]>
<![CDATA[ JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 17 No. 1 (2020) ]]>
Publisher : <![CDATA[Program Studi Matematika, Universitas Tadulako ]]>
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DOI: 10.22487/2540766X.2020.v17.i1.15180
<![CDATA[Varicella and herpes zoster are two infectious skin diseases of human that caused by varicella zoster virus, where varicella disease is a primary infection that often infected younger people while herpes zoster disease is a recurrent disease that often infected older people because of reactivation of latent varicella-zoster virus. If the pain caused by herpes zoster after recurrent phase is a appeared then the condition is known as postherpetic neuralgia. This study builds a mathematical model of primary infection (varicella disease) and recurrent infection (herpes zoster disease) developed from the SIR model (Susceptible, Infected, Recovered). The human population is divided into seven subpopulations, namely susceptible, infection, recovered of varicella, herpes zoster and postherpetic neuralgia subpopulation. Stability analysis at the critical point by linearization method gives a critical point ð‘‡1 that guaranted to exist and unstable if 𛼠ðœ‡(ð›½1+ðœ‡) ð´ , while the critical point ð‘‡1 does not have any reqruitment. Stability analysis at the endemic disease-free critical point is represented ð‘‡1 that will be unstable if ð‘‡2 exist and stable ð‘‡1 if ð‘‡2 exist. Numerical simulations by simulated to describe such temporary disease-free conditions and an endemic stable conditions.]]>
<![CDATA[Implementasi Metode K-Nearest Neighbor Untuk Mengklasifikasi Jenis Penyakit Katarak ]]>
<![CDATA[Safaat, M]]>;
<![CDATA[Sahari, A]]>;
<![CDATA[Lusiyanti, D]]>
<![CDATA[ JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 17 No. 1 (2020) ]]>
Publisher : <![CDATA[Program Studi Matematika, Universitas Tadulako ]]>
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DOI: 10.22487/2540766X.2020.v17.i1.15184
<![CDATA[The eyes is one of the five senses that are very important for humans that are used to see the beauty of nature and interact with the environment properly. If the eyes has a problems or diseases, it will be very severe. One of the disorders in the eye is cataract. Cataract if allowed, it will get worse for the sufferer. Therefore, the accuracy of determining the type and layout of early cataract is very important to prevent the more severe effects of cataract. One way to find out early on the type of cataract is by using the mathematical approach to data mining, namely the K-Nearest Neighbor (KNN) method. The concept of the KNN method is to find the nearest neighbor and choose the majority of the classes in the cluster. In this study, the system classified cataract types based on the symptoms experienced by cataract patients at Anutapura Palu Hospital whose research data was obtained from January 2018-March 2018 which amounted to 170 data. The results of this study indicate the accuracy of the KNN method for 170 data at 91.76% Keywords : Cataract, Classification, K-Nearest Neighbor (KNN)]]>
<![CDATA[Representasi Unitar Tak Tereduksi Grup Lie Dari Aljabar Lie Filiform Real Berdimensi 5 ]]>
<![CDATA[Kurniadi, E]]>
<![CDATA[ JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 17 No. 1 (2020) ]]>
Publisher : <![CDATA[Program Studi Matematika, Universitas Tadulako ]]>
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DOI: 10.22487/2540766X.2020.v17.i1.15185
<![CDATA[In this paper, we study a harmonic analysis of a Lie group of a real filiform Lie algebra of dimension 5. Particularly, we study its irreducible unitary representation (IUR) and contruct this IUR corresponds to its coadjoint orbits through coadjoint actions of its group to its dual space. Using induced representation of a 1-dimensional representation of its subgroup we obtain its IUR of its Lie group]]>
<![CDATA[Peramalan Jumlah Penumpang Datang Melalui Transportasi Udara Di Sulawesi Tengah Menggunakan Support Vector Regression (SVR) ]]>
<![CDATA[Purnama, D I]]>
<![CDATA[ JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 17 No. 1 (2020) ]]>
Publisher : <![CDATA[Program Studi Matematika, Universitas Tadulako ]]>
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DOI: 10.22487/2540766X.2020.v17.i1.15186
<![CDATA[The number of air transportation passengers in Central Sulawesi shows an increase and decrease every month. For this reason, a forecasting method is needed to predict the number of air transportation passengers in the future. Because the pattern of data on the number of air transportation passengers in Central Sulawesi Province has a nonlinear data pattern, a forecasting method is needed that can overcome these problems where in this study using the SVR model. In this study, the SVR model uses the RBF kernel function to overcome nonlinear data patterns and uses the grid search method to obtain the optimal parameters of the model.]]>
<![CDATA[Implementasi Sistem Inferensi Fuzzy Pada Pengambilan Keputusan Penentuan Kualitas Air PDAM ]]>
<![CDATA[Oktavia, S]]>;
<![CDATA[Musdalifah, S]]>;
<![CDATA[Lusiyanti, D]]>
<![CDATA[ JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 17 No. 1 (2020) ]]>
Publisher : <![CDATA[Program Studi Matematika, Universitas Tadulako ]]>
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DOI: 10.22487/2540766X.2020.v17.i1.15187
<![CDATA[Water is one of the most important natural resources for all living things. For humans, water is used for bathing, washing and drinking so that the quality needs to be considered. Water quality is a major factor to determine the feasibility of water to be used. The purpose of this research is to implement Fuzzy inference system on decision making to determine water quality of PDAM. Mamdani method is used as a fuzzy inference systems and GUIDE MATLAB is used as a program that can facilitate the users. Input of the system in the form of values of water quality parameters test results the parameters are Color, Turbidity, Total Dissolved Solid (TDS), Nitrite, Nitrate, Coliform, e-coli, and pH. System works well in determining the quality of water, it can be evidenced by the level of accuracy of 94,44% of the 72 data used in Laboratory Uwe Lino Donggala District Laboratory and Palu District PDAM Laboratory]]>
<![CDATA[Analisis Model Matematika Penyebaran Penyakit Kolera Dengan Mempertimbangkan Masa Inkubasi ]]>
<![CDATA[Nuha, A R]]>;
<![CDATA[Resmawan]]>
<![CDATA[ JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 17 No. 2 (2020) ]]>
Publisher : <![CDATA[Program Studi Matematika, Universitas Tadulako ]]>
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DOI: 10.22487/2540766X.2020.v17.i2.15200
<![CDATA[Cholera is a type of diarrheal disease caused by the presence of Vibrio cholerae in the patient's intestine. Bacteria V. cholerae has the ability to survive in water so that it will easily transmit disease to humans. This study discusses the dynamics of the spread of cholera caused by V. cholerae bacteria. The incubation period in the disease transmission system is a factor that considered in a compiled mathematical model. Besides giving the vaccine is considered a powerful way to reduce the rate of transmission. This study aims to modify the mathematical model of the spread of cholera, carry out the analysis of the stability of the modified model, and carry out numerical simulations. The modified model will be determined by its equilibrium and then stability analysis will be carried out at the equilibrium by considering the basic reproduction number (R0). Modification of the model with consideration of the incubation period produces a mathematical model of the spread of cholera type SVEIR-B. The stability of a fixed point is influenced by R0. The condition value R0 < 1 resulting in a disease-free equilibrium that is asymptotically stable, whereas the condition R0 > 1 results in an endemic equilibrium being asymptotically stable. Numerical simulations show an increase in the rate of vaccine delivery can decrease the value while increasing the rate of vaccine shrinkage and the incubation rate of each can increase the value.]]>
<![CDATA[Analisis Kontrol Optimal Pada Model Matematika Penyebaran Pengguna Narkoba Dengan Faktor Edukasi ]]>
<![CDATA[Resmawan]]>;
<![CDATA[Eka, M]]>;
<![CDATA[Nurwan]]>;
<![CDATA[Achmad, N]]>
<![CDATA[ JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 17 No. 2 (2020) ]]>
Publisher : <![CDATA[Program Studi Matematika, Universitas Tadulako ]]>
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DOI: 10.22487/2540766X.2020.v17.i2.15201
<![CDATA[ABSTRACT This paper discusses the mathematical model of drug users with education. Optimal control theory was used on this model with education as a control to achieve the goal of minimizing the number of drug users. The optimal control problem was analyzed using Pontryagin’s minimum principle and performed numerical simulation by using a 4th-order Runge-Kutta method. Based on the numerical simulation, there was a change in the number in each population which caused the population with education to increase, and control with education resulted in the reduced number of drug users. Keywords: Optimal control; mathematical model; drug users; education ABSTRAK Artikel ini membahas tentang model matematika penyebaran pengguna narkoba dengan faktor edukasi. Teori kontrol optimal diterapkan pada model ini dengan pemberian kontrol berupa edukasi dengan tujuan untuk meminimumkan jumlah pengguna narkoba. Kontrol optimal dianalisis menggunakan Prinsip Minimum Pontryagin dan dilakukan simulasi numerik dengan menggunakan metode Runge-Kutta orde 4. Berdasarkan simulasi diperoleh bahwa terjadi perubahan jumlah di tiap populasi dan mengakibatkan jumlah populasi dengan edukasi bertambah, serta pemberian kontrol dengan edukasi mengakibatkan jumlah pengguna narkoba berkurang. Kata kunci : Kontrol optimal; model matematika; pengguna narkoba; edukasi]]>
<![CDATA[Penerapan Vector Autoregressive Integrated (VARI) Pada Data Jumlah Peserta KB Aktif ]]>
<![CDATA[Sihombing, P R]]>;
<![CDATA[Yulianti, I F]]>;
<![CDATA[Istinah, A N]]>
<![CDATA[ JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 17 No. 2 (2020) ]]>
Publisher : <![CDATA[Program Studi Matematika, Universitas Tadulako ]]>
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DOI: 10.22487/2540766X.2020.v17.i2.15205
<![CDATA[Program KKBPK merupakan salah satu upaya yang telah dilakukan oleh pemerintah melalui Badan Kependudukan dan Keluarga Berencana Nasional (BKKBN) dalam menangani masalah kependudukan terutama dalam aspek kuantitas, yaitu dengan mengendalikan jumlah penduduk melalui penurunan fertilitas. Kab. Garut dan Kab. Bandung menjadi prioritas dalam rangka pengendalian fertilitas dipantau melalui perkembangan peserta KB aktif karena dianggap dapat memberikan sumbangan yang besar dalam menurunkan TFR dan meningkatkan Contraceptive Prevelance Rate (CPR) di Provinsi Jawa Barat. Penelitian ini menerapkan VARI dalam pemodelan peserta KB aktif pada Kab. Bandung dan Kab. Garut. Dua persamaan diatas menunjukkan bahwa variabel yang diamati, yaitu jumlah peserta KB aktif di Kab. Garut dan Kab. Bandung, saling mempengaruhi satu sama lain. Jumlah peserta KB aktif di Kab. Garut dipengaruhi oleh jumlah peserta KB aktif di Kab. Garut pada satu periode sebelumnya dan oleh jumlah peserta KB aktif di Kab. Bandung satu periode sebelumnya. Dengan demikian, Jumlah peserta KB aktif di Kab. Bandung dipengaruhi oleh jumlah peserta KB aktif di Kab. Bandung pada satu periode sebelumnya dan oleh jumlah peserta KB aktif di Kab. Garut satu periode sebelumnya.]]>
<![CDATA[Optimasi Hasil Produksi Olahan Daging Sapi Dengan Menggunakan Linear Programming (Studi Kasus : UD. Angkasa Timor Kupang) ]]>
<![CDATA[Adoe, V S]]>
<![CDATA[ JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 17 No. 2 (2020) ]]>
Publisher : <![CDATA[Program Studi Matematika, Universitas Tadulako ]]>
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DOI: 10.22487/2540766X.2020.v17.i2.15247
<![CDATA[ABSTRACTUD. Angkasa Timor is one of the business units engaged in beef processing with 3 forms of products produced, se'i, beef jerky and shredded beef. The obstacle faced is that entrepreneurs have not used the available resources optimally so the benefits have not been maximized. Therefore, this study aims to combine existing production resources so that entrepreneurs can obtain optimal production results and can obtain maximum profits. By using linear programming methods in the POM-QM For Windows V4 application, the analysis results are obtained X1 = 0.8571 kg, X2 = 1.8033 kg, and X3 = 0.2459 kg, with an Z value or an optimal profit of Rp. 7,197,893, Keywords : Linear Programming, Optimization]]>
