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Epsilon: Jurnal Matematika Murni dan Terapan
Published by Universitas Lambung Mangkurat
ISSN : 19784422     EISSN : 26567660     DOI : http://dx.doi.org/10.20527
Core Subject : Science, Engineering,
Decision Sciences, Operations Research & Management Transportation
Jurnal Matematika Murni dan Terapan Epsilon is a mathematics journal which is devoted to research articles from all fields of pure and applied mathematics including 1. Mathematical Analysis 2. Applied Mathematics 3. Algebra 4. Statistics 5. Computational Mathematics
Arjuna Subject : Matematika - Matematika Terapan
Articles 210 Documents
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TITIK TETAP PERSEKUTUAN EMPAT PEMETAAN KONTRAKTIF PADA RUANG METRIK CONE Ainal Mawaddah; Muhammad Mahfuzh Shiddiq; Nurul Huda
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 13, No 2 (2019): JURNAL EPSILON VOLUME 13 NOMOR 2
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (309.627 KB) | DOI: 10.20527/epsilon.v13i2.2468

Abstract

called cone metrics. A non-empty set X with a metric cone d is called cone metric space. A mapping has a unique fixed point if the mapping is contractive mapping. The concept of a fixed point of fellowship in the cone metric space must also satisfy some coincidence point, point of coincidence, and weakly compatible mapping conditions. This study examines the fixed point of fellowship for four contractive mappings in the cone metric space. The result of this study indicate that four mapping S, T, I and J have a unique fixed point of association in the cone metric space.Keywords: cone metric space, common fixed point,contractive mapping, coincidence point, point of coincidence, weakly compatible.
PENYUSUNAN MENU MAKANAN UNTUK PENDERITA DIABETES MELLITUS TIPE 2 TANPA KOMPLIKASI MENGGUNAKAN ALGORITMA GENETIKA Nafata Basdya Bayu; Akhmad Yusuf; Muliadi Muliadi
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 13, No 1 (2019): JURNAL EPSILON VOLUME 13 NOMOR 1
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (668.739 KB) | DOI: 10.20527/epsilon.v13i1.3192

Abstract

Diabetes Mellitus (DM) adalah suatu penyakit atau gangguan metabolisme kronis dengan multi etiologi yang ditandai dengan tingginya kadar gula darah (hiperglikemik) disertai dengan gangguan metabolisme karbohidrat, lipid dan protein sebagai akibat insufisiensi fungsi insulin. Penderita diabetes melitus sebenarnya dapat di cegah agar tidak lebih parah atau dapat di jaga berat badan ideal penderita diabetes ditambah dengan olahraga teratur. Pola makan yang baik merupakan kunci keberhasilan untuk mengatasi kelebihan kadar gula darah bagi penyandang diabetes, mengontrol pola hidup yang sesuai dapat mencegah atau mempertahankan kondisi penderita diabetes agar tidak lebih parah dari kondisi sebelumnya, salah satu caranya yaitu dengan mengatur pola makan yang sesuai dengan hasil diagnosis dokter atau yang disarankan oleh ahli gizi. Penelitian ini dilakukan untuk mengetahui proses penyusunan menu makanan menggunakan algoritma genetika, dan mengetahui hasil menu makanan yang sesuai untuk penderita diabetes menggunakan algoritma genetika. Algoritma genetika merupakan salah satu algoritma yang dapat melakukan penyusunan makanan berbasis Artificial Intellegent. Algoritma ini menitik beratkan pada pembangkitan populasi awal, proses crossover, proses mutasi, dan proses seleksi. Sehingga pada proses akhir seleksi terdapat nilai fitness atau nilai terbaik dalam sebuah data. Evaluasi hasil dari algoritma genetika pada penelitian kali ini adalah untuk mendapatkan nilai fitness terbaik pada setiap menu makanan. Dari hasil diperoleh bahwa nilai fitness berbanding terbalik dengan total harga makanan yang dihasilkan. Apabila nilai fitness dari perhitungan tinggi, maka total harga makan akan diperoleh harga yang paling minimal dan sebaliknya sesuai dengan kandungan kebutuhan kalori penderita diabetes mellitus. Proses algoritma genetika dalam menyusun menu makanan dengan hasil komposisi makanan terbaik menggunakan parameter probabilitas crossover 0.9 dan probabilitas mutase 0.1 dengan jumlah iterasi maksimal sebanyak 30 kali. Menghasilkan nilai fitness 0.246928066 dengan komposisi nasi, tahu dan telur sebagai penyusun makanan yang dominan agar tercapai harga minimum tetapi mencukupi kebutuhan kalori harian penderita.
APLIKASI PERSAMAAN GELOMBANG UNTUK MENENTUKAN KARAKTERISTIK GELOMBANG SENAR GITAR YANG DIPETIK Yuni Yulida; Haidir Ahsana; Muhammad Mahfuzh Shiddiq; Muhammad Ahsar Karim
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol. 15(2), 2021
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (746.422 KB) | DOI: 10.20527/epsilon.v15i2.4735

Abstract

Partial differential equations are often used to explain physical phenomena, one of which is the wave equation. One application of the wave equation is in plucked strings. This study describes the formation of a wave equation from guitar strings, determines the solution to the wave equation by using the variable separation method and certain boundary conditions and initial conditions, determines the amplitude of the wave, and simulates the movement of the wave based on the initial position of the plucked string. The result obtained is the wave equation of the guitar strings. When the string is plucked, the string will vibrate and produce a wave that can be formulated as a wave equation in the form of a homogeneous second order partial differential equation. The solution to this equation is in the form of a series. If given the initial conditions of plucking in the form of a function, then the amplitude of the wave is obtained. Simulations are given to see the movement of the amplitude and wave on the strings through three cases of the initial position of plucking the strings, namely: less than half, half, and more than half the length of the strings. The behavior of these amplitudes and waves is a characteristic or characteristic of the waves produced from a plucked guitar string
PENERAPAN REGRESI NONPARAMETRIK KERNEL DAN SPLINE DALAM MEMODELKAN RETURN ON ASSET (ROA) BANK SYARIAH DI INDONESIA Putri Indi Rahayu; Pardomuan Robinson Sihombing
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 14, No 2 (2020): JURNAL EPSILON VOLUME 14 NOMOR 2
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (320.868 KB) | DOI: 10.20527/epsilon.v14i2.2968

Abstract

Sharia Bank Return On Assets (ROA) modeling in Indonesia in 2018 aims to analyze the relationship pattern of Retturn On Assets (ROA) with interest rates. The analysis that is often used for modeling is regression analysis. Regression analysis is divided into two, namely parametric and nonparametric. The most commonly used nonparametric regression methods are kernel and spline regression. In this study, the nonparametric regression used was kernel regression with the Nadaraya-Watson (NWE) estimator and Local Polynomial (LPE) estimator, while the spline regression was smoothing spline and B-splines. The fitting curve results show that the best model is the B-splines regression model with a degree of 3 and the number of knots 5. This is because the B-splines regression model has a smooth curve and more closely follows the distribution of data compared to other regression curves. The B-splines regression model has a determination coefficient of R ^ 2 of 74.92%,%, meaning that the amount of variation in the ROA variable described by the B-splines regression model is 74.92%, while the remaining 25.8% is explained by other variables not included in the model.
PENGGUNAAN JUMAN & HOQUE METHOD (JHM) PADA PENENTUAN SOLUSI AWAL MASALAH TRANSPORTASI Andry Nor Indrawan; Pardi Affandi; oni Soesanto
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol. 15(1), 2021
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (576.108 KB) | DOI: 10.20527/epsilon.v15i1.2876

Abstract

Transportation problems are related to the efficient process of distributing goods by a company or industry. The purpose of solving transportation problems is to minimize the costs incurred in the process of distributing goods from several sources (supply) to several destinations (demand). One way to solve transportation problems is to find an initial feasible solution, continued by finding the optimal solution. This research was done by finding an initial feasible solution using the JHM (Juman & Hoque Method) for both the case of solving balanced transportation problems and unbalanced transportation problems. The method has the characteristic in the initial allocation process starting at the cell with the smallest cost in each column as much as the quantity of each demand. In addition, identification of whether the row if occupied or not was done based on the allocation for each row to the quantity of each inventory. This research aimed to explain about solving transportation problems by determining the initial feasible solution using JHM and performing optimality test using potential method. The methods of this research was to identify categories of transportation problems, determine the initial solution using JHM, and test the optimality using potential method. Based on the results of this research, JHM model may be used to solve transportation problems. In the steps of JHM there are explanations of some theorem regarding the selection of the column and row which will be the first to be processed to determine the value of intial solution of transportation problems. The initial solution by using JHM tends to approach the value of optimal solution after test of optimality was done by using the potential method.
MODEL OLIGOPOLI DENGAN FUNGSI HARGA DAN BIAYA YANG LINIER Muhammad Afief Balya; Yuni Yulida; Aprida Siska Lestia
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 14, No 1 (2020): JURNAL EPSILON VOLUME 14 NOMOR 1
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (260.016 KB) | DOI: 10.20527/epsilon.v14i1.2516

Abstract

Pasar merupakan tulang punggung perekonomian masyarakat, baik masyarakat dikalangan kelas bawah maupun kelas atas. Salah satu jenis pasar yaitu pasar oligopoli. Oligopoli menggambarkan suatu pasar dimana penawaran satu jenis barang dikuasai oleh beberapa perusahaan. Pada teori oligopoli terdapat beberapa model, salah satunya model Cournot. Tujuan dari penelitian ini adalah untuk menjelaskan terbentuknya model Cournot oligopoli dengan fungsi harga dan biaya yang linier, menentukan best response dari model Cournot oligopoli, menjelaskan terbentuknya model proses penyesuaian dinamis dengan fungsi harga dan biaya yang linier, serta menganalisa kestabilan proses penyesuaian dinamis dengan fungsi harga dan biaya yang linier. Pada penelitian ini digunakan fungsi penerimaan dan fungsi biaya yang diselisihkan untuk membentuk model Cournot oligopoli berupa fungsi keuntungan dan diturunkan satu kali untuk mencari titik kritis yang merupakan best response. Selanjutnya, proses penyesuaian dinamis muncul dengan menggunakan skema penyesuaian Cournot serta analisis kestabilan dengan menggunakan determinan matriks khusus dan polinomial karakteristik. Hasil dari penelitian ini didapatkan model Cournot oligopoli berupa fungsi keuntungan, terdapat tiga best response yang salah satunya menjadi titik ekuilibrium, muncul proses penyesuaian dinamis, dan titik ekuilibrium stabil asimtotik lokal.
KAJIAN FIRST-ORDER CFA DAN SECOND-ORDER CFA PADA STRUCTURAL EQUATION MODELING (SEM) UNTUK MENGANALISIS KEPUASAN PASIEN DI PUSKESMAS HALMAHERA KOTA SEMARANG Sefri Imanuel Fallo
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol. 16(1), 2022
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (934.138 KB) | DOI: 10.20527/epsilon.v16i1.5518

Abstract

Indikator keberhasilan pelayanan kesehatan adalah kepuasan pasien(Depkes RI, 2008). Konsep mutu layanan sangat memiliki kaitan dengan kepuasan pasien. Mutu pelayanan kesehatan menunjukkan pada tingkat kesempurnaan pelayanan kesehatan dalam menimbulkan rasa puas pada diri setiap pasien. Makin sempurna kepuasaan tersebut, makin baik pula mutu pelayanan kesehatan (Depkes RI, 2008). Pada penelitian ini kepuasan pasien diukur dengan ke adanya mutu pelayanan terkait kualitas pelayanan dan kompetensi pegawai di Puskemas Halmahera kota Semarang. Indikator yang membentuk secara signifikan variabel kepuasan pasien adalah K1,K2,K4 dan K6 , Indikator yang membangun variabel kompetensi pegawai adalah KOP1,KOP2,KOP3,KOP4, dan KOP7 sedangkan indikator-indikator pada variabel yaitu reliability, assurance, tangible, empathy dan responsiveness signifikan dalam membentuk variabel kualitas pelayanan. variabel kepuasan pasien dan kompetensi pegawai memiliki nilai construct reliability (CR)  lebih dari 0,7 sehingga  memiliki konsistensi tinggi namun nilai Average Variance Extracted (AVE) untuk keseluruhan variabel baik first-order maupun second-order kurang valid.An indicator of the success of a service in the world of health is patient satisfaction. The thing that is no less important in serving patients to achieve patient satisfaction is the quality of service at the hospital. The quality of health services shows the level of perfection of health services in creating a sense of satisfaction in each patient. The more perfect the satisfaction, the better the quality of health services. In this study, patient satisfaction was measured by the quality of service related to service quality and employee competence at the Halmahera Health Center in Semarang. The indicators that make up significantly the patient satisfaction variable are KP1, KP2, KP4, and KP6, the indicators that build the employee competence variable are KOP1, KOP2, KOP3, KOP4, and KOP7 while the indicators on the variables are reliability, assurance, tangibles, empathy, and responsiveness significant in shaping the service quality variable. The variable of patient satisfaction and employee competence has a construct reliability (CR) value of more than 0.7 so that it has high consistency but the Average Variance Extracted (AVE) value for all variables, both first-order and second-order, is less valid.
MODEL MANGSA-PEMANGSA DENGAN FUNGSI RESPON HOLLING DAN PEMANENAN Mustika Khadijah; Yuni Yulida; Dewi Sri Susanti
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol. 15(2), 2021
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (235.698 KB) | DOI: 10.20527/epsilon.v15i2.4593

Abstract

The mathematical model of prey-predator interaction is one of the stages of solving mathematical problems by simplifying events that occur in mathematical form. In this research, we discuss a prey-predator model using a type II Holling response function without harvesting and a prey-predator model using a type II Holling response function with harvesting. The purpose of this research was to explain the formation of a prey-predator model with a type II Holling response and a preypredator model with a type II Holling response with harvesting, to determine the stability at the equilibrium point of the model, and to create a model simulation using several sample parameters. The results obtained were three equilibrium points for the prey-predator model with type II Holling response without harvesting and two equilibrium points for the prey-predator model with type II Holling response with harvesting. The stability at two equilibrium points of the prey-predator model using the type II Holling response function without harvesting was asymptotically stable and the stability at one equilibrium point in the prey-predator model using the type II Holling response function in the presence of harvesting in the prey population was asymptotically stable. The comparison of numerical simulations showed that the number of predator population without harvesting was greater than the number of predator population with harvesting.
KOLABORASI JARINGAN SYARAF TIRUAN DAN MOVING AVERAGE CONVERGENCE DIVERGENCE UNTUK MEMPREDIKSI PERGERAKAN VALUTA ASING Miftakhul Huda; Akhmad Yusuf; Dwi Kartini
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 12, No 1 (2018): JURNAL EPSILON VOLUME 12 NOMOR 1
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (314.116 KB) | DOI: 10.20527/epsilon.v12i1.202

Abstract

Pasar valas merupakan pasar yang potensial untuk memperoleh keutungan finansial apabila dapat memprediksi pergerakan harga secara akurat pada masa yang akan datang. Pada penelitian ini dilakukan prediksi valas dengan mengkolaborasikan 2 algoritma yaitu Jaringan Syaraf Tiruan (JST) Backpropagation dan Moving Average Convergence Divergence (MACD). Ouput prediksi yang dihasilkan ada 3 yaitu Bearish (tren turun), Bullish (tren naik) dan Hold (tren netral). Tren turun dan tren naik dihasilkan apabila hasil prediksi JST dan MACD mempunyai sinyal tren yang sama, sedangkan tren netral dihasilkan apabila JST dan MACD mempunyai sinyal tren yang berbeda. Pada penelitian ini dilakukan prediksi harga penutupan pair USD/JPY setiap pukul 06.00 GMT selama 20 hari, data yang digunakan untuk training dan testing JST sebanyak 1440 data terdiri dari harga penutupan time frame 5 menit pukul 00.00 GMT hingga 05.55 GMT selama 20 hari sedangkan MACD menggunakan 560 data harga penutupan time frame 1 jam pukul 00.00 GMT hingga 23.00 GMT selama 20 hari. Dari 20 percobaan hasil kolaborasi (J-MACD) menghasilkan 12 sinyal hold, 5 transaksi sukses dan 3 transaksi gagal. Dengan demikian J-MACD mempunyai tingkat akurasi sebesar 62,5%.
REGRESI POISSON TERGENERALISASI I DALAM MENGATASI OVERDISPERSI PADA REGRESI POISSON Zakiah Zakiah; Nur Salam; Dewi Anggraini
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 9, No 1 (2015): JURNAL EPSILON VOLUME 9 NOMOR 1
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (157.462 KB) | DOI: 10.20527/epsilon.v9i1.8

Abstract

Regression analysis is one method to determine and test the causality relationship (cause-effect) between the dependent variable (Y) with the independent variables (X). In general, regression analysis is used to analyze non-free variable data in the form of continuous data and normal distribution. However, in some applications, non-free variable data to be analyzed in the form of discrete data and not normally distributed. One of the regression models that can be used to analyze the relationship between the dependent variable (Y) in the form of discrete data is Poisson regression model whose dependent variable is Poisson distributed. Poisson regression has the assumption of equidispersion that is the condition in which the mean and variance values of the dependent variable are equal, but sometimes there is an assumption violation, where the value of variance is greater than the so-called overdispersion value, so to overcome it can be used one of the extensions of the regression model Poisson is Poisson regression model generalized, this is because the assumption does not require the same mean value with the value of variance. The purpose of this study is how to estimate the Poisson regression model and Poisson regression model generalized I and explain how the generalized Poisson regression model I in overcoming the overdispersion in Poisson regression.

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