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INDONESIA
EIGEN MATHEMATICS JOURNAL
Published by Universitas Mataram
ISSN : 26153599     EISSN : 26153270     DOI : -
Core Subject : Education,
Mathematics
Eigen Mathematics Journal mempublikasikan artikel yang berkontribusi pada informasi baru atau pengetahuan baru terkait Matematika, Statistika, dan Aplikasinya. Selain itu, jurnal ini juga mempublikasikan artikel berbentuk survey dalam rangka memperkenalkan perkembangan terbaru dan memotivasi penelitian selanjutnya dalam bidang matematika, statistika, dan aplikasinya.
Arjuna Subject : -
Articles 118 Documents
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Optimasi Penyaluran Bahan Bakar Minyak di Wilayah Maluku Indonesia Rini Dian Sari; Farizal Farizal; Djoko Sihono Gabriel
Eigen Mathematics Journal VOL. 3 NO. 2 DESEMBER 2020
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v3i2.81

Abstract

Fossil fuel (BBM) is a vital commodity and has a strategic value for people's lives. On the demand side, the need for BBM tends to increase along with the increasing energy demand for people's lives. Therefore, the distribution system for BBM has to be optimized in order to fulfill the people’s demand. The aim of this paper is to optimize vehicle route for BBM distribution in Maluku so that it has minimum cost, distance, and time. The optimization method in this paper is Mix Integer Linear Programming (MILP). Decision variables in this paper are chosen from the most significant variables for BBM distribution in Maluku.
Comparison of Hierarchical and Non-Hierarchical Methods in Clustering Cities in Java Island using the Human Development Index Indicators year 2018 Alvia Rossa Damayanti; Arie Wahyu Wijayanto
Eigen Mathematics Journal Vol. 4 No. 1 Juni 2021
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v4i1.89

Abstract

The Human Development Index (HDI) is a composite index to assess the developmental level of life quality in a particular region. In 2018, Java Island, which geographically has the most regencies/ municipalities in Indonesia, achieved human development with “high” status and was followed by all its regencies which have also achieved human development with “high” status. Therefore, research was carried out on how the characteristics inherent in the high HDI have been achieved in regencies on Java Island and grouping them so that it is easy to interpret regencies/ municipalities with homogeneous characteristics. This study used the hierarchical cluster method (single linkage, average linkage, and ward) and non-hierarchical cluster methods (K-Means and FCM). The results show that the best hierarchical cluster method is the average linkage method which forms four clusters where the regencies/ municipalities with the best characteristics (dimensions of education, health, and high purchasing power) are Kepulauan Seribu, Bogor, and 78 other regencies/ municipalities. Then, the best non-hierarchical method is the FCM method which forms two clusters, with a prominent characteristic is those city areas have better characteristics than district areas.
Pengembangan Motif Batik Sasambo dengan Sistem Lindenmayer Subaiah Marlina; Qurratul Aini; I Wayan Sudiarta
Eigen Mathematics Journal VOL. 3 NO. 2 DESEMBER 2020
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v3i2.77

Abstract

Batik is an Indonesian intangible cultural heritage that needs to be preserved. Indonesia has a variety of batik patterns such as Sasambo (Sasak, Samawa, and Mbojo) batik patterns from West Nusa Tenggara. This study aims to develop Sasambo batik patterns by using the Lindenmayer System (L-System). The Sasambo batik patterns developed in this study are of two types: Lumbung (rice barn) and Kangkung (water spinach) patterns. By applying the L-System, there are three different ways that can be done, namely (1) making the Sasambo batik patterns as axioms, (2) making the batik patterns as generators, and (3) combining the Sasambo patterns with fractals. Based on the new patterns produced using the L-System, the selection of generators should have the initial and final segments which are both in a single line position, so that the original patterns unchanged.
Fuzzy Metric Space and Its Topological Properties Masriani Masriani; Qurratul Aini; Syamsul Bahri
Eigen Mathematics Journal Vol. 4 No. 2 Desember 2021
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v4i2.95

Abstract

The fuzzy set theory is mathematics that applies fuzziness characteristics, so that gives the truth value at interval [0,1]. It is different from the crisp set that gives a truth value of 0 if it is not a member and 1 if it is a member. The theory of fuzzy sets has been developed continuously by scientists. One of the developments of the fuzzy set is the fuzzy metric space which the definition was introduced by George and Veeramani. Based on the analysis results, it is found that every metric space X if and only if X is fuzzy metric space. As a result, the topological properties of the metric space still apply to the fuzzy metric space
Modifikasi Algoritma Kriptografi Hill Chiper dengan Matriks Generalisasi Bilanga Fibonacci dalam Penyandian Pesan Husni Fitroti; Mamika Ujianita Romdhini; Ni Wayan Switrayni
Eigen Mathematics Journal Vol. 4 No. 2 Desember 2021
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v4i2.107

Abstract

Hill Cipher algorithm is a technique of message encoding by implementing a matrix of order  as a key matrix. The key matrix is a matrix that has a multiplicative inverse. The security of message is measured by the number of processes in encoding. The more processes in encoding the longer time it takes. Consequently, the massage will be more secure. The purpose of this research is to modify the Hill Cipher algorithm by using generalized Fibonacci matrix  whose degree-p  and rank-n . This research showed that for any non-negative integer p and positive integer n, matrix  can be used as a key matrix in Hill Cipher algorithm. The modification of the Hill Cipher algorithm has been done by modifying the former key by making the degree and rank of  as the key used in the encryption and decryption process of data (message).
The Power Graph of a Dihedral Group Evi Yunartika Asmarani; Abdul Gazir Syarifudin; I Gede Adhitya Wisnu Wardhana; Ni Wayan Switrayni
Eigen Mathematics Journal Vol. 4 No. 2 Desember 2021
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v4i2.117

Abstract

Graph theory is one of the topics in mathematics that is quite interesting to study because it is applicable and can be combined with other mathematical topics such as group theory. The combination of graph theory and group theory is that graphs can be used to represent a group. An example of a graph is a power graph. A power graph of the group  is defined as a graph whose vertex set is all elements of  and two distinct vertices  and  are connected if and only if  or for a positive integer x and y. In this study, the author discusses the power graph of the dihedral group  The results obtained from this study are the power graph of the dihedral group  where  with  prime numbers and an  natural number is a graph consisting of two non-disjoint subgraphs, namely complete subgraphs and star subgraphs. And we find that its radius and diameter are 1 and 2.
Panel Data Regression Analysis of Human Development Index in West Nusa Tenggara Province with Fixed Effect Model Sapurah Sapurah; I Gde Ekaputra Gunartha; Nurul Fitriyani
Eigen Mathematics Journal Vol. 4 No. 2 Desember 2021
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v4i2.114

Abstract

Humans are the true wealth of the nation. It is appropriate if humans become the main goal in development. Then the United Nations Development Program (UNDP) initiated the Human Development Index (HDI) as an indicator in measuring the progress of human development. Indonesia took part in applying the HDI calculation. Increasing the value of HDI from various provinces in Indonesia continues to be carried out, including in the Province of West Nusa Tenggara. Improving human development is based on an increase in all dimensions of the HDI itself. West Nusa Tenggara Province consists of 10 regencies/ cities. With different geographical, social, and economic backgrounds, the achievement of HDI in each region will vary. The purpose of this study was to determine the model of the HDI in West Nusa Tenggara Province in 2010-2017 using a fixed-effect model, which was used to see the influence of dimensions on the HDI and explain the differences in intercepts in each district/ city in West Nusa Tenggara Province. Based on the research conducted, a fixed effect panel data model on HDI was obtained for each district/ city in NTB in 2010-2017. From the HDI model obtained, it is known that the slope coefficient is constant, but the intercept varies throughout the district/ city. The slope coefficient value shows the magnitude of the influence of life expectancy, school duration, the average length of schooling, and expenditure per capita adjusted to the HDI of each district/ city.
The Intersection Graph of a Dihedral Group Nurhabibah Nurhabibah; Abdul Gazir Syarifudin; I Gede Adhitya Wisnu Wardhana; Qurratul Aini
Eigen Mathematics Journal Vol. 4 No. 2 Desember 2021
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v4i2.119

Abstract

The intersection graph of a finite group G is a graph (V,E) where V is a set of all non-trivial subgroups of G and E is a set of edges where two distinct subgroups H_i , H_j  are said to be adjacent if and only if H_i \cap H_j \neq {e} . This study discusses the intersection graph of a dihedral group D_{2n} specifically the subgraph, degree of vertices, radius, diameter, girth, and domination number. From this study, we obtained that if n=p^2 then the intersection graph of D_{2n} is containing complete subgraph K_{p+2} and \gamma(\Gamma_{D_{2n}})=p. 
Pipeline Network Optimization using Hybrid Algorithm between Simulated Annealing and Genetic Algorithms Parizal Hidayatullah; Irwansyah Irwansyah; Qurratul Aini; Bulqis Nebula Syechah
Eigen Mathematics Journal Vol. 4 No. 2 Desember 2021
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v4i2.100

Abstract

The pipeline network is one of the most complex optimization problems consisting of several elements: reservoirs, pipes, valves, etc. The pipeline network is designed to deliver water to consumers by considering the demand and adequate pressure on the water pipe network. The main problem in designing reliable pipelines is the cost. The amount of cost that most influences the design of pipelines is the diameter of the pipe used. Therefore, this study aims to combine (hybrid) simulated annealing algorithm with genetic algorithm to optimize water pipe networks. The simulated annealing algorithm is the main algorithm in finding the optimal cost.Meanwhile, the genetic algorithm will assist in the pipeline update process using the roulette wheel selection. Simulation data is used to test the hybrid algorithm performance compared to the standard simulated annealing algorithm. The results show that the simulated annealing hybrid algorithm is able to get a more optimal cost in designing a water pipe network compared to the standard simulated annealing algorithm. Keywords: Optimization, Epanet 2.0, Simulated Annealing, and Genetic Algorithm
Comparison of Fuzzy Time Series Methods and Autoregressive Integrated Moving Average (ARIMA) for Inflation Data Asyifah Qalbi; Khalilah Nurfadilah; Wahidah Alwi
Eigen Mathematics Journal Vol. 4 No. 2 Desember 2021
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v4i2.122

Abstract

This study compares the Fuzzy Time Series (FTS) method with the Autoregressive Integrated Moving Average (ARIMA) method on time series data. These two methods are often used in predicting future data. Forecasting or time-series data analysis is used to analyze data in the form of time series. In this study, Indonesian inflation data was used to be analyzed in comparing the FTS and ARIMA methods. Inflation is one of the economic indicators used to measure the success of a country's economy. If the inflation rate is low and stable, it will stimulate economic growth. This inflation value is calculated every month where the value can decrease and increase from one period to another. Comparison of the FTS and ARIMA methods is seen in the error value generated by the two methods. A method can be better than other methods if the value of the resulting forecast error is smaller. In this study, Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE) were used to see the magnitude of the error value of the two methods on the fives data testing used. The results obtained in this study are the results of Indonesia's inflation forecast for the period January to May 2021 using the FTS method, respectively, at 0.57%, 0.375%, 0.2%, 0.2%, and 0.1125%, while the forecast results using the ARIMA method, respectively. Of 0.3715848%, 0.2362817%, 0.1508295%, 0.1731906%, and 0.2432851% and the results of calculating the size of error using MSE and MAPE indicate that the ARIMA method with the model ARIMA(3,0,0) is better at predicting inflation data in Indonesia with a value of MSE of 0.009 and MAPE of 64.987% compared to the FTS method resulted in MSE values of 0.047 and MAPE of 132.548%. 

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